संदेश

विद्यालयी विक्षा में िैवक्षक उत्कृष्टता प्राप्त करना केन्द्रीय विद्यालय संगठन की सिोच्च िरीयता है।

हमारे विद्यार्थी, विक्षक एिं िैवक्षक नेतृत्व कताा वनरं तर उन्नवत हे तु प्रयासरत रहते हैं । राष्टरीय विक्षा नीवत

2020 के संदर्ा में योग्यता आधाररत अवधगम एिं मूल्ांकन संबन्धित उद्दे श्ों को प्राप्त करना तर्था

सीबीएसई के वदिा वनदे िों का पालन, ितामान में इस प्रयास को और र्ी चुनौतीपूर्ा बनाता है।

केन्द्रीय विद्यालय संगठन के पांचों आं चलिक लशक्षा एवं प्रलशक्षण संस्थान द्वारा संकवलत यह ‘विद्यार्थी

सहायक सामाग्री’ इसी वदिा में एक आिश्क कदम है । यह सहायक सामग्री कक्षा 9 से 12 के

विद्यावर्थायों के वलए सर्ी महत्वपूर्ा विषयों पर तैयार की गयी है । केन्द्रीय विद्यालय संगठन की ‘विद्यार्थी

भौविकी सहायक सामग्री’ अपनी गुर्ित्ता एिं परीक्षा संबंधी सामाग्री-संकलन की वििेषज्ञता के वलए जानी जाती

है और अन्य विक्षर् संस्र्थान र्ी इसका उपयोग परीक्षा संबंधी पठन सामग्री की तरह करते रहे हैं । िुर्-

Physics आिा एिं विश्वास है वक यह सहायक सामग्री विद्यावर्थायों की सहयोगी बनकर सतत मागादिा न करते हुए

उन्हें सफलता के लक्ष्य तक पहुंचाएगी ।

कक्षा/Class: XII
िुर्ाकांक्षा सवहत ।
2024-25
लनलि पांडे
विद्यार्थी सहायक सामग्री भाग- 1
Student Support Material Part-1 आयुक्त, केन्द्रीय लवद्यािय संगठन

केन्द्रीय विद्यालय संगठन

Kendriya Vidyalaya Sangathan
 विषय सूची
अध्ययन सामग्री वनमााता टीम ---मंबई संभाग
INDEX
TEAM OF PREPARERES – MUMBAI REGION

क्र सं पाठ का नाम पृष्ठ सं

S. No. NAME OF CHAPTER PAGE NO.
Unit Name of the Unit Name of the Name of the Teacher 1. ELECTRIC CHARGES AND FIELDS 1-15
No. Chapter
1 Electrostatics Chapter 1 Mrs S Sugandhi
KV Mankhurd 2. ELECTRIC POTENTIAL AND CAPACITANCE 16-35

Chapter -2 Ms Neha Sharma CURRENT ELECTRICITY

3. 36-68
KV INS Mandovi

2 Current Electricity Mr Mandip 4. MOVING CHARGES AND MAGNETISM 69-89

Chapter -3 KV NAD Karanja
3 Magnetic Effects of Current and Mrs Minta Mehra 5. MAGNETISM AND MATTER 90-107
Magnetism Chapter -4 KV. Lonavala
Chapter -5 Mrs Minu Singh
6. ELECTROMAGNETIC INDUCTION 108-120
KV Ganeshkhind
4 Electromagnetic Induction and Mr. Sunil Jadhav
Alternating Currents Chapter -6 K.V Aurangabad 7. ALTERNATING CURRENT 121-141
Chapter -7 Mr Sachin Sonawane
KV Army Area, Pune 8. ELECTROMAGNETIC WAVES 142-152
5 Electromagnetic waves Chapter -8 Mr Santosh Sontakke
9. RAY OPTICS AND OPTICAL INSTRUMENTS 153-176
KVNo.1 Dehu Road
6 Optics Chapter -9 Mrs Neelam
K.V SC Pune 10. WAVE OPTICS 177-191
Chapter -10 Mrs Swati Chhabra
KV, THANE 11. DUAL NATURE OF RADIATION AND MATTER 192-213
7 Dual Nature of Radiation Chapter -11 Mr. Ganesh Ahirrao
and Matter KV Panvel
12. ATOMS 214-227
8 Atoms and Nuclei Chapter -12 Mrs Savita Ruhela
KV Panvel
Chapter -13 Mr Rahul Shirbhate 13. NUCLEI 228-237
KV.VSN Nagapur
9 Electronic Devices Chapter -14 Mr Sandip Kamat 14. SEMICONDUCTOR MATERIAL: ELECTRONIC DEVICES 238-262
KV DIAT Pune
15. SAMPLE QUESTION PAPERS 263-284
Unit III: Magnetic Effects of Current and Magnetism 25 Periods Chapter–7: Alternating Current

Chapter–4: Moving Charges and Magnetism Alternating currents, peak and RMS value of alternating current/voltage;
reactance and impedance; LCR series circuit (phasors only), resonance,
Concept of magnetic field, Oersted's experiment.
power in AC circuits, power factor, wattless current.
Biot - Savart law and its application to current carrying circular loop. AC generator, Transformer.
Ampere's law and its applications to infinitely long straight wire. Straight
Unit V: Electromagnetic waves 04 Periods
solenoid (only qualitative treatment), force on a moving charge in uniform
magnetic and electric fields. Chapter–8: Electromagnetic Waves

Force on a current-carrying conductor in a uniform magnetic field, force Basic idea of displacement current, Electromagnetic waves, their
between two parallel current-carrying conductors-definition of ampere, characteristics, their transverse nature (qualitative idea only).
torque experienced by a current loop in uniform magnetic field; Current loop
Electromagnetic spectrum (radio waves, microwaves, infrared, visible,
as a magnetic dipole and its magnetic dipole moment, moving coil
ultraviolet, X-rays, gamma rays) including elementary facts about their uses.
galvanometer- its current sensitivity and conversion to ammeter and
voltmeter. Unit VI: Optics 30 Periods

Chapter–9: Ray Optics and Optical Instruments

Chapter–5: Magnetism and Matter
Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction
Bar magnet, bar magnet as an equivalent solenoid (qualitative treatment
only), magnetic field intensity due to a magnetic dipole (bar magnet) along of light, total internal reflection and optical fibers, refraction at spherical

its axis and perpendicular to its axis (qualitative treatment only), torque on a surfaces, lenses, thin lens formula, lens maker’s formula, magnification,

magnetic dipole (bar magnet) in a uniform magnetic field (qualitative power of a lens, combination of thin lenses in contact, refraction of light

treatment only), magnetic field lines. through a prism.

Magnetic properties of materials- Para-, dia- and ferro -magnetic substances Optical instruments: Microscopes and astronomical telescopes (reflecting and

with examples, Magnetization of materials, effect of temperature on magnetic refracting) and their magnifying powers.

properties.
Chapter–10: Wave Optics

Wave optics: Wave front and Huygen’s principle, reflection and refraction of
Unit IV: Electromagnetic Induction and Alternating Currents 24 Periods plane wave at a plane surface using wave fronts. Proof of laws of reflection

Chapter–6: Electromagnetic Induction and refraction using Huygen’s principle. Interference, Young's double slit
experiment and expression for fringe width (No derivation final expression
Electromagnetic induction; Faraday's laws, induced EMF and current; only), coherent sources and sustained interference of light, diffraction due to
Lenz's Law, Self and mutual induction. a single slit, width of central maxima (qualitative treatment only).
 UNIT-I ELECTROSTATICS
CHAPTER 1 -ELECTRIC CHARGES AND FIELDS
Gist:
1 Charge :
Charge is an intrinsic property of elementary particles of matter which gives rise to
electric force between various objects.

2 Two types of charges: Positive and negative.

3 Transference of electrons is the cause of frictional electricity.

4 Basic properties of electric charge :

i) Additivity of charges: Total charge is the algebraic sum of individual charges.

ii) Conservation of charges: The total charge of an isolated system is always
conserved.
iii) Quantization of charges : Charge of an object is always in the form of integral
multiple of electronic charge and never its fraction

5 Coulomb’s Law
It states that the electrostatic force of interaction or repulsion acting between two
stationary point charges is given by

i) linear charge distribution( λ ): = Charge/Length =C/m

ii) Surface charge distribution(σ): σ= Charge/Area = C/m2
iii) Volume charge distribution(ρ) : ρ = Charge/ Volume = C/m3

Electric Field Lines Electric field lines are a way of pictorially mapping the electric
field around a configuration of charge(s). These lines start on positive charge and
end on negative charge. The tangent on these lines at any point gives the direction
of field at that point.

Properties:
1. Field lines from a positive charge to negative charge
2. Direction of filed lines shown by the tangent to the field lines.
3. Electric field lines emerge normal from positive charge and terminate at
negative charge.
4. They never intersect each other.
This can be explained by method of contradiction at two field lines E1 & E2
interest at P as shown in the figure. Then there may be two tangents at E1 and
6 Dielectric constant E2. Which is not possible. Since one and only one tangent can be drawn.
The ratio of force between two charges in vacuum to the force acting between when Therefore, our assumption is wrong.
they are shifted in a medium is called relative permittivity or dielectric constant of the 5. Electric field contract in length which shows that opposite charges attract.
medium. where is also called the relative permittivity and is the permittivity of medium. 6. Electric field lines exert lateral pressure which shows that like charges repel.
N is a point which shows field intensity is zero called neutral point.

7 Electrostatic force due to continuous charge distribution:

1 2
 MCQ-LEVEL1
1 A force of 4N is acting between two charges in air. If the space between them is
completely filled with glass (relative permittivity = 8), then the new force will be
(a) 2N ( b) 5N (c) 0.5N (d) 0.2N

2 A charge q is placed at the center of the line joining two equal charges Q. The system
of three charges will be in equilibrium if q is equal to
(a) –Q/2 ( b) –Q/4 (c )Q/2 (d) Q/4

3 Two point charges Q and -3Q are placed some distance apart. If the electric field at the
location of Q is E, the field at the location of -3Q is
(a) E (b) -E (c) E/3 (d) -E/3

4 An electric dipole when placed in a uniform electric field will have minimum potential
energy, if the angle between dipole moment and electric field is
(a) Zero (b) π/ 2 (c) π/3 (d) π

5 An electric dipole consists of two opposite charges of magnitude 1µC separated by a

distance of 2cm. The dipole is placed in an electric filed 10-5 V/m. The maximum torque
(a) 10-3 Nm ( b) 2 x10-13 Nm (c) 3 x10-3 N (d) 4x10-3 Nm

ASSERTION AND REASON QUESTIONS

DIRECTION: Read the two statements
Assertion (A) and Reason (R) carefully to mark the correct option out of the options
given below:
(a) Assertion and Reason both are correct statements and Reason is correct
explanation for Assertion.
(b) Assertion and Reason both are correct statements but Reason is not correct
explanation for Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement

6 Assertion: No two electric lines of force can intersect each other.

Reason: Tangent at any point of electric line of force gives the direction of electric
field
7 Assertion: Coulombs law of force is applicable for point charges at rest.
Reason: Coulombs law is a central force.
8 Assertion: Electric charge is quantized.
********** Reason: Charging is because of transfer of an integral number of protons or
electrons.
9 Assertion: If there exists coulomb attraction between two bodies, both of them may
not be charged.
Reason: In coulomb attraction two bodies are oppositely charged
10 Assertion: Surface charge density of an irregularly shaped conductor is non uniform
Reason: Surface density defined as charge per unit area

11 An electric dipole having a dipole moment of 4 × 10 -9 C m is placed in a uniform

electric field such that the dipole is in stable equilibrium. If the magnitude of the electric

5 6
7 A uniform electric field E= 2X103 N/C is acting along the positive x axis. The flux in 6 An electron falls from rest through a vertical distance h in a uniform and vertically
(NC-1m2) of this field through a square of 10cm on a side whose plane is parallel to upward directed electric field E. The direction of electric field is now reversed, keeping
the y-z plane is its magnitude the same. A proton is allowed to fall from rest in it through the same
(a) 20 (b) 30 (c) 10 (d) 40
vertical distance h. The time of fall of the electron, in comparison to the time of fall of
the proton is
8 An electric dipole is placed at an angle of 30◦ with an electric field of intensity 2x10 5N/C. (a) Smaller (b) 5 times greater (c) 10 times greater (d)equal
It experiences a torque equal to 4Nm.The charge on the diploe length is 2cm is
(a) 8 mC (b) 4 m C (c ) 6 mC (d) 2 mC 7 A spherical conductor of radius 10 cm has a charge of 3.2 × 10-7 C distributed uniformly.
That is the magnetude of electric field at a point 15 cm from the centre of the sphere?
9 A metal cube of side 5cm is charged with 6 µC. The surface charge density of the (a) 1.28x105 N/C (b) 1.28x107 N/C (c) 1.28x10-9 N/C (d)1.28x1011 N/C
cube is
(a) 0.125x10-3Cm-2 (b)0.25x10-3Cm-2 (c )4x10-3Cm-2 (d)0.4x10-3Cm-2
8 Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are
10 separated by a distance of 2 cm. If the spheres are connected by a conducting wire,
The electric field due to a short electric dipole at a large distance (r) from center of
then in equilibrium condition, the ratio of the magnitudes of the electric fields at the
dipole on the equatorial plane varies with distance as
surface of the sphere A and B will be :
(a) r (b) 1/r (c) 1/r3 (d) 1/r2 (A) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 4(JEE MAINS 2022)
MCQ LEVEL3
1 A vertical electric field of magnitude 4.9x105N/C just prevents a water droplet of mass 9 Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 µC
0.1 g from falling .The value of charge on the droplet will be are combined to form a bigger drop. The ratio of surface density of bigger drop to the
(a)1.6 x10-9 C (b) 2.0x10-9C (c) 3.2x10-9 C (d) 0.5x 10-9C smaller drop will be :
(JEE MAIN 2022) (A) 1 : 4 (b) 4 : 1 (c) 1 : 8 (d) 8 : 1 (JEE MAINS 2022)

2 For a uniformly charged ring of radius R, the electric field on its axis has the largest **************
magnitude at a distance h from the centre .Then the value of h is
CASE STUDY QUESTIONS
R/√5 (b) R/√2 (c ) R (d) R√2 (JEE MAIN 2019)
Photocopiers work on the principle that ‘opposites attract’. Toner is a powder that
3 According to Gauss law of electrostatics, electric flux through a closed surface depends is used to create the printed text and images on paper. The powder is negatively
on charged, and so it is attracted to something positive – the paper. The drum, which
(a) Area of the surface is located in the heart of a photocopier, is positively charged using static electricity.
(b) The quantity of charges enclosed by the surface An image of the master copy is transferred onto the drum using a laser. The light
(c) The shape of the surface parts of the image (the white areas on a piece of paper) lose their charge so
(d) The volume enclosed by the surface become more negative, and the black areas of the image (where the text is) remain
positively charged.
4 An electric dipole is placed at an angle of 30∘ with an electric field of intensity 2x105
N/C. It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the • Which of the following figures represent the electric field lines due to a single
dipole, if the dipole length is 2 cm. negative charge?
(a) 6 mC (b) 4 mC (c) 2 mC (d) 8 Mc

5 Two identical conducting spheres P and S with charge Q on each, repel each other with
a force 16 N. A third identical uncharged conducting sphere R is successively brought
in contact with the two spheres. The new force of repulsion between P and S is
( JEE MAINS 2024)

(a) 1 N (b) 6 N (c) 12 N (d) 4 N

9 10
 COMPETENCY BASED QUESTION SELF ASSESSSMENT TEST
M.M 40
1.Electric field lines are pictorial
representations of electric fields due to static ANSWER ALL THE QUESTIONS
1. What is the work done in moving a test charge q through a distance of 1 cm along the
charges on the plane of a paper
equatorial axis of an electric dipole? (1)

Study the given electric field representation 2. S1and S2are two parallel concentric spheres enclosing charges
and identify one INCORRECT qualitative Q and 2 Q respectively as shown in Fig.The ratio of the electric flux
impression given by this representation. through S1and S 2 (1)
A The electric field at point A is stronger than
at point B. 3. What is the dimensional formula for 0 ? (1)
B. The electric field distribution is two-dimensional.
4. Define electric flux(1)
C. The electric field at point C is zero.
D. The electric field always points away from a positive charge. 5. Name the physical quantity whose S.I unit is J/C.Is it a scalar or a vector quantity?(1)
2 For a Gaussian surface through which the net flux is zero, the following statements
COULD be true. 6. An oil drop of 12 excess electrons is held stationary under a constant electric field of
P) No charges are inside the Gaussian surface. 2.55 ‫ױ‬04 V m –1in Millikan's oil drop experiment. The density of the oil is 1.26 g cm –3.
Q) The net charge inside the surface is zero. Estimate the radius of the drop. Given that g = 9.81 m s–2and e = 1. 6 x10–19 C. (2)
R) The electric field is zero everywhere on the surface.
7. What is the force between two small charged spheres having charges of 2x10 -7c and
S) The number of field lines entering is equal to the number of lines exiting the surface. 3x10-7c placed 30 cm apart in air ? (2)
Which of the statements is/are DEFINITELY true?
A. Only statement 8. The sum of two point charges is 9 µc .They repel each other is force of 2 N. When
B. Q B. Both statements P and S kept 30 cm apart in free space. Calculate the value of each charge. (2)
C. Both statements Q and R
9.An electric dipole with dipole moment 4x10-9Cm is aligned at 30оwith the direction of
D. D. Both statements Q and S
a uniform electric field of magnitude 5x104N/C. Calculate the magnitude of the torque
CCT acting on the dipole (2)
Two positive charges q1 and q2 lie along a straight line separated by a distance of 2 m
as shown. 10.Two charges 5x10-8c and -3x10-8C are located 16cm apart. At what points on the
(a) Find a location along the straight line joining the two charges, where if a positive line joining the two charges is the electric potential zero? (2)
charge q3 is placed, it experiences a zero-resultant force.
(b) Will the resultant force on q3 placed at the location of part (a) still be zero, if it is 11.Derive the formula for electric field of an electric dipole for the following two cases(a)
axial line (b) equatorial line. (5)
negatively charged? Explain.
CASE STUDY -5marks
1. Lightning is an electric current. Within a thundercloud way up in the sky, many small
bits of ice (frozen raindrops) bump into each other as they move around in the air. All of
those collisions create an electric charge. After a while, the whole cloud fills up with
electrical charges. The positive charges or protons form at the top of the cloud and the
negative charges or electrons form at the bottom of the cloud. Since opposites attract,
that causes a positive charge to build up on the ground beneath the cloud. The grounds
electrical charge concentrates around anything that sticks up, such as mountains, people,
************ or single trees. The charge coming up from these points eventually connects with a
charge reaching down from the clouds and lightning strikes.

(i) Charge is the property associated with matter due to which it produces and
13 14
 ➢ Insertion of a dielectric reduces the electric field between the plates of a capacitor

➢ In a series combination of capacitor, the charges on each capacitor are same but
the potential difference across any capacitor is inversely proportional to its
capacitance.
➢ In a parallel combination of capacitors, the potential difference across each
capacitor is same but the charged stored in any capacitor is proportional to its
capacitance.

➢ When charges are shared between any two bodies, their potential become equal.
The charges acquired are in the ratio of their capacities. No charges is lost, but
some loss of energy does occur.

➢ The capacitance of a capacitor depends neither on Q nor on V. It depends upon

the shape and size of the conductor.

➢ The maximum electric field that a dielectric medium can withstand without break-
down (of its insulating property) is called its dielectric strength; for air it is about
3 × 106 Vm–1 . For a separation between conductors of the order of 1 cm or so, this
field corresponds to a potential difference of 3 × 10 4 V between the conductors.
Thus, for a capacitor to store a large amount of charge without leaking, its
capacitance should be high enough so that the potential difference and hence the
IMPORTANT POINTS electric field do not exceed the break-down limits. Put differently, there is a limit to
the amount of charge that can be stored on a given capacitor without significant
➢ Work done by an electrostatic force in moving a charge from one point to another leaking. In practice, a farad is a very big unit.
depends only on the initial & final position and not on the path followed by the charged
particle. GRAPHS

➢ Work done by the electrostatic force in moving a charge in closed path is zero

➢ The potential due to a dipole depends not just on r but also in the angle between
the position vector (𝑟 ) and dipole moment vector (𝑃⃗ ).

➢ The electric dipole potential falls off as 1/ 𝑟2 not as 1/𝑟 characteristic of the
potential due to a single charge .

➢ No work is done in moving a test charge over an equipotential surface. 3.Graph between E & C 4.Graph of E & V verses distance r

➢ electric field is always normal to the equipotential surface at every point . for a point charge

➢ No two equipotential surface can intersect each other.

➢ Electric field is in the direction in which the potential decreases steepest.

Its magnitude is given by the change in the magnitude of potential per unit
displacement normal to the equipotential surfaces at the point.

➢ On equatorial points of dipole , V=0 but E ≠ 0

➢ Inside a charged spherical shell , E=0 but V ≠ 0

. ➢ Net electric charge in the interior of a conductor is zero.

17 18
 QUESTION BANK Q9.Capacitors A and B are identical. Capacitor A is charged so it stores 4 J of energy
and capacitor B is uncharged. The capacitors are then connected in parallel. The total
MULTIPLE CHOICE QUESTIONS (LEVEL 1)
stored energy in the capacitors is now:
Q1. If voltage applied on a capacitor is increased from V to 2V, choose the correct a) 16 J b) 8 J c) 4 J d) 2 J
conclusion. Q10.If both the plate area and the plate separation of a parallel-plate capacitor are
(a) Q remains the same, C is doubled doubled, the capacitance is:
a) doubled b) halved c) unchanged d) tripled
(b) Q is doubled, C doubled
Q11.An electric dipole of dipole moment p is placed in a uniform electric field of
(c) C remains same, Q doubled
strength E in a direction perpendicular to the field. The work done in rotating the dipole
(d) Both Q and C remain same by an angle 900 without acceleration in a plane perpendicular to the field is:
Q2. A parallel plate capacitor is charged. If the plates are pulled apart a) pE b) –pE c). Zero d). -2pE
(a) The capacitance increases Q12.A small metallic ball having charge q is placed inside an insulated box. The
insulated box is then placed inside a metallic box. The net charge enclosed inside the
(b) The potential differences increase metallic box is:
(c) The total charge increases a)Zero b) q c)–q d) 2q
(d) The charge & potential difference remain the same Q13.In a parallel plate capacitor, the capacity increases if
Q3. Which of the following is an example of a molecule whose centre of mass of (a) area of the plate is decreased.
(b) distance between the plates increases.
positive and negative charges coincide each other?
(c) area of the plate is increased.
(a)CO2 (b) CO (c) CH3OH (d) NH3
(d) dielectric constantly decreases.
Q4.What is the angle between electric field and equipotential surface? Q14 An electron moves from point i to point f, in the direction of a uniform electric field.
(a) 90o always (b)0o always (c)0o to 90 (d)0o to 180o During this displacement:

Q5.If we carry a charge once around an equipotential path, then work done by the
charge is:
a) The work done by the field is positive and the potential energy of the electron-field
(a) Infinity (b) Positive (c) Negative (d) Zero system increases.
Q6. Capacitor of a spherical capacitor may depend upon b) The work done by the field is negative and the potential energy of the electron-field
system increases.
(a) radius of capacitor (b)dielectric medium (c)applied potential difference (d)both
c) The work done by the field is positive and the potential energy of the electron-field
(a) and (b) system decreases.
Q7. The decreasing order of the electrostatic potential energies for the given system d) The work done by the field is negative and the potential energy of the electron-field
of charges will be- system decreases.
ASSERTION – REASON QUESTIONS
Directions: These questions consist of two statements, each printed as Assertion and
Reason. While answering these questions, you are required to choose any one of the
following four responses.
(a) c > b > a > d (b) d > a > c = b (c) a > c > d = b (d) c > b > a = d
(a) Both Assertion and Reason are correct and the Reason is a correct explanation of
the Assertion.
Q8. An electron is accelerated from rest through a potential difference V. Its final speed
is proportional to: (b) Both Assertion and Reason are correct but Reason is not a correct explanation of
a) V b) V/2 c) √V d) 1/V the Assertion.
(c) Assertion is correct, Reason is incorrect
21 22
 Q8.In a certain region of 0.1 cubic metre of space ,electric potential is found to be 5V
throughout .What is the electric field in this region ?
(a) 10uf and 48uC (b) 05uf and 48uC (c) 10uf and 24uC (d) 2.5uf and 48uC (a)0.5 v/m (b)2 V/m (c)0v/m (d)0.02 V/m

Q3.Find the total energy stored in the capacitors Q9.A thin metal sheet is placed in the middle of a parallel plate capacitor. What will be
in the given network. the effect on its capacitance ?
(gets doubled (b)no effect (c)halved (d)becomes three times

(a) 3.6 × 10 -5 J (b) 3.6 ×10 -6 J Q10.Three capacitors of 3 ,3 and 6 micro farad are connected in series to a 10V
(c) 7.2 ×10 -6 J (d) 7.2 ×10 -5J source. The charge on the 3icro farad capacitor is
(a)5 µC (b)12 µC (c)15µC (d)10 µC
Q4.Two point charges 10 ˟10−8 µC and -2 ˟10−8
µC are separated by distance of 60 cm in air. Find at what distance from the 1st
charge, would the electric potential will be zero. ***********
(a) 5m (b) 5cm (c) 50cm (d) 1m
2 MARKS QUESTIONS (Level 1)
Q5.Two charges of same nature and magnitude +q are kept fixed at points X inside a Q1.Sketch equi potential surfaces for
uniform electric field. Now to shift the charges, Rahul used a path X → Y → Z (shown (a) A negative point charge (CBSE 2001)
as ‘R’ in the diagram) and Amol used a different path of direct X → Z (shown as ‘A’ in (b) Two equal and positive charges separated by a small distance. (CBSE
the diagram). Find the ratio of their work done to move the charge from X to Y. 2015)
Q2.Deduce the expression for the potential energy of an electric dipole placed with its
axis at an angle θ to the external field 𝐸⃗ .Hence discuss the conditions of its stable and
unstable equilibrium. (CBSE 2008,2019,2021 Compt.)
Q3.A metal plate is introduced between the plates of a charged parallel plate capacitor.
What is its effect on the capacitance of the capacitor.
Q4.Two capacitors have a capacitance of 5µF when connected in parallel and 1.2µF
(a) 2:1 (b) 1:2 (c) 1:3 (d) 1:1
when connected in series. Calculate their capacitances.
Q6.An uniform electric field exists in the negative-Y direction. Which of the following Q5.An isolated capacitor of unknown capacitance C is charged to a potential
statement(s) is/are correct: difference V. It is then connected in parallel to an uncharged capacitor of cap
i. The potential decreases as one moves along positive Y axis acitance Co such that the potential difference across the combination become
s V/3. Determine the unknown capacitance C.
ii. The potential remains constant as one moves along negative Y axis
Q6.A parallel plate capacitor C with a dielectric in between the plates is charged to a
iii. The potential remains constant as one moves along negative Z axis potential V by connecting it to a battery. The capacitor is then isolated. If the dielectri
iv. The potential remains constant as one moves along positive X axis c is withdrawn from the capacitor,
a. i, ii, iii and iv b. i and ii c. iii and iv d. i, iii and iv (a) Will the energy stored in the capacitor increase or decrease?
(b)Will the potential difference across the capacitor plates increase or decrease
? Give an explanation.
Q7.Samir founds that a conductor has a potential V ≠ 0 and there are no charges
Q7.A capacitor is connected across a battery .(i)Why does each plate receive a charge
anywhere else outside. Then he concludes-
of exactly the same magnitude ?(ii)Is this true even if the plates are of different sizes?
(1) There must be charges on the surface or inside itself.
Q8. Establish the equation for electric potential at any point in the electric field due
(2) There can’t be any charge in the body of the conductor. to a point change by using fundamental relation.
(3) There must be charges only on the surface.
(4) There must be charges inside the surface. The correct conclusions are-
(a) 1 and 4 (b) 1, 2 and 3 (c) 1 and 2 (d) all

25 26
 (i) before
5 MARKS QUESTIONS (LEVEL 1) (ii) after the dielectric has been put in between its plates.
Q1.A parallel plate capacitor of capacitance C is charged to a potential V by a Q2. Two identical capacitors of plate dimensions l × b and plate separation d have di-
battery. Q is the charge stored on the capacitor. Without disconnecting the battery,
electric slabs filled in between the space of the plates as shown in the figure.
the plates of the capacitor are pulled apart to a larger distance of separation.
What changes will occur in each of the following quantities? Will they increase, decreas
or remain the same? Give an explanation in each case.
(a) Capacitance (b) Charge (c) Potential difference (d) Electric field (e)
Energy stored in the capacitor

5 MARKS QUESTIONS (LEVEL 2)

Q1. a) Explain, using suitable diagrams, the difference in the behaivour of a Obtain the relation between the dielectric constants K, K1 and K2.

(i) conductor and Q3. A parallel plate capacitor of capacitance C is charged to a potential V by a battery.

(ii) dielectric in the presence of external electric field. Define the terms polarization of Without disconnecting the battery, the distance between the plates is tripled and a

a dielectric and write its relation with susceptibility. dielectric medium of k = 10 is introduced between the plates is tripled and a dielectric
medium of k = 10 is introduced between the plates of the capacitor. Explain giving
5 MARKS QUESTIONS (LEVEL 3)
reasons, how will the following be affected:
Q1..(a) Define potential energy of a system of two charges.
(b)Two-point charges q1 and q2, separated by a distance r12 are kept in an external (i) capacitance of the capacitor
electric field. Derive an expression for the potential energy of the system of two (ii) charge on the capacitor
charges in the field.
NUMERICALS (LEVEL 3)
NUMERICALS (LEVEL 1)
Q1. A network of four capacitors each of 12μF capacitance is connected to a 500 V
Q1.Two +ve charges of 0.2 μC and 0.01 μC are placed 10 cm apart. Calculate the supply as shown in the figure.
work done in reducing the distance to 5 cm.
Determine
Q2. A parallel plate capacitor has its plate of area 6.6 cm 2 separated by 0.7mm thick
mica slab. Calculate the capacitance of the capacitor if dielectric constant of mica is (a) equivalent capacitance of the network and
6. (b) charge on each capacitor.
Q3. A capacitor of unknown capacitance is connected across a battery of V volt. A
charge of 120 μC is stored in it. When the potential across the capacitor is reduced by
Q2. A capacitor of unknown capacitance is connected across a battery of V volt. A
40 V, the charge stored in the capacitor becomes 40 μC. Calculate V and the unknown
capacitance. What would have been the charge in the capacitor if the voltage were charge of 240 pC is stored in it. When the potential across the capacitor is reduced by
increased by 40 V? 80 V, the charge stored in the capacitor becomes 80 pC. Calculate V and the unknown
Q4. Two metal spheres, one of radius R and the other of radius 2R, both have same
capacitance. What would have been the charge in the capacitor if the voltage were
surface charge density σ. They are brought in contact and separated. What will be the
new surface charge densities on them? increased by 80 V?
NUMERICALS (LEVEL 2) Q3. Find equivalent capacitance between A
Q1. A parallel plate capacitor, of capacitance 20pF, is conneted to a 100 V supply. and B in the combination given below. Each
After sometime the battery is disconnected, and the space, between the plates of the capacitor is of 2 µF capacitance.
capacitor is filled with a dielectric, of dielectric constant 5. Calculate the energy stored
in the capacitor
29 30
 SELF ASSESSMENT carrying an α-particle across a potential difference of one volt.
MARKS 25 DURATION 40 MINUTES
3MARKS QUESTIONS
MULTIPLE CHOICE QUESTIONS
Q9. A charge of 24µC is given to a hollow metallic sphere of radius 0.2 m. find the
Q1. A parallel plate capacitor is connected with the terminals of a battery. The distance
potential
between the plates is 6mm. If a glass plate (dielectric constant K = 9) of 4.5 mm is
a. At the surface of the sphere
introduced between them, then the capacitance will become
b. At a distance 0.1cm from the centre of the sphere
(a) 2 times (b) the same (c) 3 times (d) 4 times. c. At the centre of the sphere.
Q2. A capacitor is charged by using a battery which is then disconnected. A dielectric Q10. Derive the expression for electrostatic potential due to dipole .Hence ,find the
slab is then introduced between the plates, which results in value of potential on axial and equatorial line of dipole.
(a) reduction of charge on the plates and increase of potential difference across the
plates. 5 MARKS QUESTION
(b) increase in the potential difference across the plate, reduction in stored energy, but
Q11. (a)Write any two properties of equipotential surfaces. What will be the
no change in the charge on the plates.
equipotential surface for a dipole.
(c) decrease in the potential difference across the plates, reduction in the stored
(b)Two charges –q and +q, are located at points (0, 0, –a) and (0, 0, a), respectively.
energy, but no change in the charge on the plates.
(i)What is the electrostatic potential at the points (0, 0, z) and (x, y, 0)?
(d) none of these
(ii)Obtain the dependence of potential on the distance r of a point from the origin when
Q3. Which of the following statement is true?
r/a >> 1.
(a) Electrostatic force is a conservative force.
(iii) How much work is done in moving a small test charge from the point (5,0,0) to
(b) Potential at a point is the work done per unit charge in bringing a charge from any
(–7,0,0) along the x-axis? Does the answer change if the path of the test charge
point to infinity.
between the same points is not along the x-axis?
(c) Electrostatic force is non-conservative
(d) Potential is the product of charge and work.
Q12.CASE STUDY BASED QUESTION
Q4.Which of the following statements is false for a perfect conductor?
(a) The surface of the conductor is an equipotential surface.
(b) The electric field just outside the surface of a conductor is perpendicular to the
surface.
(c) The charge carried by a conductor is always uniformly distributed over the surface
of the conductor.
(d) None of these
Q5. Assertion : Two equipotential surfaces cannot cut each other.
Reason : Two equipotential surfaces are parallel to each other.
Q6. Assertion : A dielectric is inserted between the plates of a battery connected
capacitor. The energy of the capacitor increases.
Reason : Energy of the capacitor, U=CV2 /2

2 MARKS QUESTIONS
Q7.Consider a uniform electric field 3 x 103 i N/C. calculate the flux of this field through
Q1.When a dipole is placed in uniform electric field ,then
a square surface of area 10 cm2 when
(a)It experiences torque but not force
(i) Its plane is parallel to the y-z plane
(b)It experiences force but not torque.
(ii) The normal to its plane makes a 60o angle with the x axis. (c) It experiences both force and torque.
Q8. Define potential difference .How is it related to work. Calculate the work done in (d) It experiences neither force not torque.
33 34
Relation between drift velocity and current: V-I characteristics

𝑣𝑑 =
𝐼
where I = current, A = Cross-section area of conductor, e = charge on • The variation of current (I) with voltage (V) at various temperatures for any
𝐴𝑛𝑒 device is called its V-I characteristics.
electron • For an ohmic device, V-I characteristic is linear.
Mobility(𝝁): the mobility of charge carrier is given by
𝑣𝑑
𝜇=
𝐸
𝑒𝐸⃗ 𝜏 𝑣𝑑 𝑒𝜏
As drift velocity, ⃗⃗⃗⃗
𝑣𝑑 = − 𝑚
∴𝜇= 𝐸
= 𝑚
SI unit of mobility = m2V-1s-1

Ohm’s law: the current flowing through a conductor is directly proportional to the • For a non-ohmic device, the V-I characteristic curve is non-linear.
V-I characteristic of some non-ohmic devices
potential difference applied across its ends, provided the temperature and other
physical conditions remain unchanged.

𝑉 𝛼 𝐼 𝑜𝑟 𝑉 = 𝑅 Where R = Resistance of the conductor.

Resistance: it is the property by virtue of which a conductor opposes the flow of

𝑉 V-I characteristic of Ohmic device – Metal conductor
charge through it.𝑅 = 𝐼
SI Unit: 1 ohm(Ω) = 1VA-1
Effect of temperature on resistance
Cause of resistance: Collisions are the basic cause of resistance
• The resistivity 𝜌 of a material depends on its temperature. For a small variation
Symbol of resistor: of temperature,
𝜌 = 𝜌0 (1 + 𝛼 (𝑇 − 𝑇0 ), where 𝛼 = temperature coefficient of resistance of the
Factor affecting the resistance: material.
𝑙
𝑅 = 𝜌 𝐴 where 𝜌 = specific resistance or resistivity of a conductor. • The resistance of a conductor at absolute temperature T is given by the
relation𝑅𝑇 = 𝑅0 (1 + 𝛼(𝑇 − 𝑇0 ),
−1
SI unit of 𝛼 = ℃
𝑚
resistivity of a conductor is given by 𝜌 = 𝑛𝑒 2𝜏 SI unit of resistivity: ohm meter(Ω𝑚) •
Distinctive values of 𝜶 for metal, alloys and semiconductor:
Resistivity of conductor depends only nature of material
1 1) For metals, 𝛼 is positive i.e., resistance of metals increases with the
Conductance: G = 𝑅 SI unit of conductance ohm-1or mho or siemens(S) increase in temperature.
1
Conductivity: σ = SI unit of conductivity is ohm-1 m-1 or Sm-1
ρ

Vector form of ohm’s law: 𝐽 = 𝜎𝐸⃗

Limitations of Ohm's Law

1. Ohm’s law is applicable only to metallic conductors at moderate temperatures
and moderate potential differences.
Variation of resistivity of copper variation of resistivity of nichrome with
2. Ohm’s law cannot be applied
temperature. with temperature
• to conductors maintained at very high temperatures or very low temperatures.
• to semiconductors and semi conducting devices.
• to conductors across which very high pd or very low pd is applied. 2) For alloy like constantan and manganin, the temperature coefficient of
resistance is very small. So, they are used for making standard resistor.

37 38
Kirchhoff’s second law or loop law: the Mind Map
algebraic sum of the emf’s in any loop of a circuit
is equal to the sum of the products of currents and
resistance in it.
ΣE = ΣIR
Wheatstone bridge: it is an arrangement of four
resistance used to determine one of these
resistance quickly and accurately in terms of the
remaining three resistance
When no current flows through the galvanometer.
The bridge is then said to be balanced . in the
balanced condition,
𝑃⃗ 𝑅
=
𝑄 𝑠

41 42
 14
a) If both Assertion and Reason are true and Reason is correct explanation of A. Ω C. 14Ω
3
Assertion. 20 D. 21Ω
B. Ω
b) If both Assertion and Reason are true but Reason is not the correct 3
4. Two solid conductors are made up by of same material, have same length and
explanation of assertion
same resistance. one of them has a circular cross section of area A 1 and the
c) If Assertion is true but Reason is false. 𝐴
other one has a square cross section area of A2. The ratio 1 is
d) If both Assertion and Reason are false 𝐴2

16. Assertion(A): A current flows in a conductor only when there ia an electric field A. 1.5 C. 0.8
B. 1 D. 2
within the conductor
5. The solids which have the negative temperature coefficient of resistance are
Reason(R): The drift velocity of electrons in presence of electric field A. Insulators and
decreases. semiconductors
17. Assertion(A): An electric bulb starts glowing instantly as it is switched on. B. Metals
Reason(R): Drift speed of electrons in a metallic wire is very large. C. Insulators only
18. Assertion(A): A wire carrying an electric current has no electric field around it. D. Semiconductor only
Reason(R): Rate of flow of electrons in one direction is equal to the rate of flow
of protons in opposite direction. For Questions 6 to 10, two statements are given –one labelled Assertion (A)
19. Assertion(A): Though large number of free electrons are present in the metal. and other labelled Reason (R). Select the correct answer to these questions
Yet there is no current in the absence of electric field. from the options as given below.
Reason(R): In the absence of electric field electrons move randomly in all
a) If both Assertion and Reason are true and Reason is correct explanation of
directions.
Assertion.
20. Assertion(A): The value of temperature coefficient of resistance is positive for
b) If both Assertion and Reason are true but Reason is not the correct
metals.
explanation of assertion
Reason(R): The temperature coefficient is resistance for insulator is also
c) If Assertion is true but Reason is false.
positive.
d) If both Assertion and Reason are false
LEVEL – 2 MCQ 6. Assertion(A): The conductivity of an electrolyte is very low as compared to a
metal at room temperature.
1. A current of 3 amp flows through the 2 ohm resistor Reason(R): The number density of free ions in electrolyte is much smaller as
shown in the circuit. The power dissipated in the 5 ohm compared to number density of free electrons in metals. Further, ions drift much
resistor is: more slowly, being heavier.
A. 4 watt C. 1 watt 7. Assertion(A): The dimensional formula for product of resistance and
B. 2 watt D. 5 watt conductance is same as for dielectric constant.
2. In the figure balanced condition of Wheatstone bridge Reason(R): Both have dimensions of time constant.
8. Assertion(A): The drift velocity of electrons in a metallic wire will decrease, if
A. B is at higher potential
the temperature of the wire is increased.
B. D is at higher potential
C. Any of the two B or D can be at higher potential Reason(R): On increasing temperature, conductivity of metallic wire decreases.
than other arbitrarily 9. Assertion(A): Bending a wire does not affect electrical resistance.
D. B and D are at same potential Reason(R): Resistance of wire is proportional to resistivity of material
3. Five resistances have been connected as shown in the 10. Assertion(A): A person touching a high power line gets stuck with the line.
figure. The effective resistance between A and B is Reason(R): The current carrying wires attract the man towards it.

45 46
 3. Under what condition is the heat produced in an electric circuit:
(i) Directly proportional
(2 MARKS QUESTIONS)
(ii) Inversely proportional to the resistance of the circuit.
LEVEL - 1 4. Use Kirchhoff’s rules to obtain the balance condition in Wheatstone bridge.
5. In the electric network shown in figure, use Kirchhoff’s rules to calculate the
1. Two cells of emfs and internal resistances 𝐸1 , 𝑟1 and 𝐸2 , 𝑟2 are connected in
power consumed by the resistance 𝑅 = 4Ω.
parallel. Derive the expressions for the emf and internal resistance of a cell
which replace this combination.
2. An arc lamp operates at 80 V, 10A. suggest a method to use it with a 240 V DC
source. Calculate the value of the electric component required for this purpose.
3. Prove that the current density of a metallic conductor is directly proportional to
the drift speed of electrons.
4. Define the electrical resistivity of a material. How it is related to the electrical
conductivity? of the factors, length, area of cross-section, nature of material and
temperature – which ones control the resistivity value of conductor?
5. Define the term ‘mobility’ of charge carries in a current carrying conductors. LEVEL - 3
Obtain the relation for mobility in terms of relaxation time. 1. A) Two wires of equal lengths, one of copper and the other of manganin have
6. State the conditions under which ohm’s law is not obeyed the same resistance. Which wire will be thicker
in a conductor. B) If a wire is stretched to double its original length without loss of mass, how
7. I – V graph for a metallic wire at two different will the resistivity of the wire be influenced?
temperatures,𝑇1 and 𝑇2 is as shown in figure. Which of the 2. The following graph shows the variation of terminal potential difference V,
across a combination of three cells in series
two temperature is lower and why?
to a resistor, versus the current, I :
a) Calculate the emf of each cell.
8. Two cells of emf’s 𝐸1 and 𝐸2 , and internal resistance 𝑟1and b) For what current I, will the power
𝑟2 respectively are connected in series. Obtain expression for the equivalent (i) dissipation of the circuit be maximum?
emf and (ii) resistance of the combination.
LEVEL - 2
1. Two metallic wires, P1 and P2 of the same
material and same length but different cross-
section areas, A1 and A2 are joined together 3. Using Kirchhoff’s rules, calculate the current through 40Ω and 20Ω in the circuit
and connected to a source of emf. Find the shown in below figure
ration of the drift velocities of free electrons in
two wires when they are connected (i) in series
and (ii) in parallel
2. A battery of emf 12 V and internal resistance 2
ohm is connected to 4 ohm resistor as shown
in figure show that a voltmeter when placed
across the cell and across the resistor in turn,
gives the same reading

49 50
 drift speed is so small, and the electron’s charge is small, how can we still obtain across the terminals of the cell and percentage error in the reading of the
large amounts of current in a conductor? voltmeter.
(c) When electrons drift in a metal from lower to higher potential, does it mean 3. Two aluminium wires have their lengths in the ratio 2 :3 and radii in the ration
that all the ‘free’ electrons of the metal are moving in the same direction? 1: 3. These are connected in parallel across a battery of emf E and of negligible
(d) Are the paths of electrons straight lines between successive collisions (with internal resistance. Find the ratio of drift velocities of the electrons in the two
the positive ions of the metal) in the (i) absence of electric field, (ii) presence of wires.
electric field? LEVEL – 3
LEVEL-2
1. A particle of the charge 2𝜇𝐶 and mass 1.6 g is moving with a velocity 4𝑖̂ 𝑚𝑠 −1 .
1. Deduce the condition for balance in a Wheatstone bridge. Write any two At t = 0 the particle enters in a region having an electric field 𝐸⃗ (𝑖𝑛 𝑁𝐶 −1 ) =
important precautions you would observe while performing the experiment. 80𝑖̂ + 60𝑗̂. Find the velocity of the particle at t = 5s
When is Wheatstone bridge most sensitive?
2. The circuit in figure shows two cells connected in opposition to each other. Cell
𝐸1 is of emf 6V and internal resistance
LEVEL-3
2.0 Ω; the cell 𝐸2 is of emf 4V and internal
1. Two cells of emf 3V and 4V and internal resistances 1 ohm and 2 ohms resistance 8.0 Ω. Find the potential
respectively are connected in parallel so as to send current in same direction difference between the points A and B.
through an external resistance of 5 ohm. Draw the circuit diagram using
Kirchhoff’s laws. Calculate the current through each branch of the circuit and
potential difference across 5-ohm resistance.
Numerical Problem 3. In the circuit shown in figure, with steady current,
calculate the potential difference across the
LEVEL - 1
capacitor and the charge stored in it.
1. The amount of charge passing through cross-section of wire is 𝑞𝑡 = 𝑡 2 + 𝑡 + 1
find the value of current at t = 1s
2. The resistance of a thin wire of silver is = 1.0 Ω at 20°𝐶. The wire is placed in a CASE STUDY QUESTION
liquid bath and its resistance rises to 1.2Ω. find the temperature of the bath Read the following text and answer the following
in°𝐶(𝛼𝑠𝑖𝑙𝑣𝑒𝑟 = 3.8 × 10−3 /°𝐶) questions on the basis of the same:
3. A cell of emf 2 V and internal resistance 0.1 Ω is connected to a 3.9 Ω external
resistance. What will be the potential difference across the terminals of the cell. Electric Toaster: Small Industries Service Institute takyelpat Industrial Estate Imphal
4. Two cells of emfs 1.5 V and 2.0 V having internal resistances 0.2 Ω and 0.3 Ω has designed an Electric toaster which is operated at 220 volts A.C., single phase
respectively are connected in parallel. Calculate the emf and internal resistance and available in four different rated capacity such as 600 W, 750 W, 1000 W and
of the equivalent cell. 1250 W. The heating element is made of nichrome 80/20 (80% nickel, 20%
LEVEL – 2 chromium), since Nichrome does not get oxidize readily at high temperature and
have higher resistivity, so it produces more heat.
1. A storage battery of emf 8 V, internal resistance 1.0 Ω, is being charged by a The element is wound separately on Mica sheets and fitted with body of toaster with
120 V dc source, using a 15.0 Ω resistor in series in the circuit. Calculate (i) the the help of ceramic terminals.
current in the circuit, (ii) terminal voltage across the battery during charging,
and (iii) the chemical energy stored in the battery in 5 minutes. i.) Heating element of the toaster is made of:
2. A voltmeter of resistance 998Ω is connected across a cell of emf 2 V and
internal resistance 2Ω. Find the potential difference across the voltmeter, that (A) copper (B) nichrome (C) chromium (D) nickel

53 54
 For Questions 5 to 6, two statements are given –one labelled Assertion (A) and other
Self-Assessment Test labelled Reason (R). Select the correct answer to these questions from the options as
Max. marks-25 Max. Time: 40 minute given below.

Section-A( 1 Mark each) a) If both Assertion and Reason are true and Reason is correct explanation
of Assertion.
1) Consider a current carrying wire (current I) in the shape of a circle. Note that as b) If both Assertion and Reason are true but Reason is not the correct
the current progresses along the wire, the direction of J changes in an exact
explanation of assertion
manner, while the current I remain unaffected the agent that is essentially
c) If Assertion is true but Reason is false.
responsible for is
d) If both Assertion and Reason are false
a) Source of emf 5) Assertion(A): Though large number of free electrons are present in the metal.
b) Electric field produced by charges accumulated on the surface of wire Yet there is no current in the absence of electric field.
c) The charge just behind a given segment of wire which push then just the
Reason(R): In the absence of electric field electrons move randomly in all
right way by repulsion.
directions.
d) The charge ahead
6) Assertion(A): The value of temperature coefficient of resistance is positive for
2) Kirchhoff’s junction rules is a reflection of
metals.
a) Conservation of current density vector.
Reason(R): The temperature coefficient is resistance for insulator is also
b) Conservation of charge positive.
c) The fact that the momentum with which a charged particle approaches a
Section-B (2 Mark each)
junction is unchanged (as a vector) as the charged particle leaves the
junction.
7) A heating element using nichrome connected to a 230 V supply draws an initial
d) None of these
current of 3.2 A which settles after a few seconds to a steady value of 2.8 A.
3) The resistance of a wire is 5Ω at 50℃ and 6Ω at 100℃. The resistance of the
What is the steady temperature of the heating element if the room temperature
wire at 0℃ will be
is 27.0 °C and the temperature coefficient of resistance of nichrome is 1.70 ×
a) 3Ω c) 1Ω
b) 2Ω d) 4Ω 10–4 °C–1 ?
8) Graph showing the variation of current versus voltage foe a GaAs is shown in
4) The potential difference (𝑉𝐴 − 𝑉𝐵 ) between the points A and B in the given

figure is
a) +6 V b) +9 V (c)-3V (d)3V
figure. Identify the region
i) Negative resistance
ii) Where ohm’s law is obeyed
Section-C (3-mark each)
9) Two cells of emfs 𝐸1 𝑎𝑛𝑑 𝐸2 , and internal resistance 𝑟1 𝑎𝑛𝑑𝑟2 respectively are
connected in series. Obtain expression for the equivalent (i) emf and (ii)
resistance of the combination.
10) The four arms of a Wheatstone bridge have the following resistance 𝐴𝐵 = 100Ω
, 𝐵𝐶 = 10Ω , 𝐶𝐷 = 5Ω and 𝐷𝐴 = 60Ω.

57 66
 UNIT III MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
CH 4– MOVING CHARGES AND MAGNETISM
The direction of the magnetic field at the center is perpendicular to the plane of the
GIST OF LESSON
coil.
1. Magnetic field- A magnetic field is associated with an electric current flowing
9. Ampere's circuital law- It states that the line integral of magnetic field B along
through a metallic wire. This is called the magnetic effect of current. On the
a closed boundary of an open surface is equal to µ0-times the current (I) passing
other hand, a stationary electron produces an electric field only.
through the open surface with closed boundary.
2. SI Unit of Magnetic field-
The SI unit of magnetic field is Wm-2 or T (tesla). The strength of magnetic field
is called one tesla, if a charge of one coulomb, when moving with a velocity of
1 ms-1 along a direction perpendicular to the direction of the magnetic field
experiences a force of one newton. 10. Magnetic field due to infinitely long straight wire using Ampere's law- According
3. 1 tesla (T) = 1 weber meter-2 (Wbm-2 ) = 1 newton ampere-1 meter-1 (NA-1 m -1) to Ampere’s circuital law.
4. CGS units of magnetic field is called gauss or oersted.
5. 1 gauss = 10-4 tesla.
6. Right hand thumb rule- Hold a conductor is Right Hand in such a way that 11. Straight solenoid- At the axis of a long solenoid, carrying current I
thumb indicates the direction of current and curled finger encircling the B=μ0 nI , where n = N/L = number of turns per unit length.
conductor will give the direction of magnetic field lines. Tip - When we look at any end of the coil carrying current, If the current is in
7. Biot- Savart law- It states that the magnetic field strength B produced due to a anticlockwise direction then that end of the coil behaves like north pole, and If
current element (of current I and length dl) at a point having position vector r the current is in clockwise direction then that end of the coil behaves like the
relative to current element is- south pole.
12. Force on a current-carrying conductor in a uniform magnetic field B
Magnitude of force is F = IlBsinө.
Direction of force is normal to and given by Fleming’s Left Hand Rule. If ө =
where µ0 is the permeability of free space, 0 (i.e. is parallel to B), then the magnetic force is zero.
θ is the angle between current element and position
vector r as shown in the figure. 13. Force on a moving charge in uniform magnetic field-The force on a charged
The direction of magnetic field B is perpendicular to particle moving with velocity in a uniform magnetic field is given by F =
the plane containing Idl and r qvBsinө.
14. . The direction of this force is perpendicular to both v and B ,
The value of µ0 = 4π ×10–7 Wb/A-m. When v is parallel to B ,ie ө=0, then F=0
8. Magnetic field due to a current carrying circular loop – When v is perpendicular to B , ie ө=90, then F is maximum, i.e., F=qvB
(a) The magnetic field due to current carrying circular coil of N-turns, radius a,
carrying current I at a distance x from the centre of coil is – Lorentz force -The total force on a charged particle moving in simultaneous
electric field and magnetic field is given by F= qvB + qE
This is called the Lorentz force equation.
15. The direction of this force is determined by using Fleming’s left hand rule
Fleming’s Left Hand Rule- Stretch the left hand such that the fore-finger, the
central finger and thumb are mutually perpendicular to each
other. When the fore-finger points in the direction of the
magnetic field and the central finger points in the direction of
(b) The magnetic field due to current carrying circular coil is along the axis. At current then thumb gives the direction of the force acting on
center, x=0 the conductor.
16. Force between two parallel current-carrying
conductors- Two parallel current carrying conductors

69 70
MIND MAP MULTIPLE CHOICE QUESTIONS
LEVEL 1

1 In a current-carrying loop, the magnetic field is strongest:

a) At the centre of the loop
b) Along the edges of the loop
c) Inside the loop
d) Outside the loop
2 The magnetic field inside a current-carrying conductor.
(a) increases with the increase in current
(b) decreases with the increase in current
(c) remains constant with the increase in current
(d) is zero
3 The direction of the magnetic field at the centre of a current-carrying circular
loop is:
(a) Along the axis of the loop
(b) Parallel to the plane of the loop
(c) Radially inward
(d) Tangential to the loop
4 Which of the following statements is correct regarding the magnetic field
around a straight current-carrying conductor?
a) The magnetic field lines form concentric circles centred on the
conductor.
b) The magnetic field lines form straight lines parallel to the conductor.
c) The magnetic field lines form radial lines away from the conductor.
d) The magnetic field lines form hyperbolic curves around the conductor.
5 A current carrying closed loop of an irregular shape lying in more than one
plane whe placed in uniform magnetic field, the force acting on it
(a) Will be more in the plane where its larger position is covered.
(b) Is zero.
(c) Is infinite.
(d) May or may not be zero.
6 A strong magnetic field is applied on a stationary electron. Then the electron
a) Moves in the direction of the field.
b) Remained stationary.
c) moves perpendicular to the direction of the field
d) moves opposite to the direction of the field
7 A charged particle is moving on circular path with velocity v in a uniform
magnetic field B, if the velocity of the charged particle is doubled and
strength of magnetic field is halved, then radius becomes
a) 8 times
b) 4 times
c) 2 times

73 74
 3 Two α-particles have the ratio of their velocities as 3: 2 on entering the
Select the most appropriate answer from the options field. If they move in different circular paths, then the ratio of the radii of
given below: their paths is
(a) Both A and R are true and R is the correct explanation of A
a) 2 : 3 b) 3 : 2 c) 9 : 4 d) 4 : 9
(b) Both A and R are true but R is not the correct explanation of A.
(c )A is true but R is false. 4 The time period of a charged particle undergoing a circular motion in a
(d) A is false and R is also false. uniform magnetic field is independent of:
(a) speed of the particle (b) mass of the particle
5 Assertion (A): If a proton and an α-particle enter a uniform magnetic (c) charge of the particle (d) magnetic field of the particle
field perpendicularly with the same speed, the time period of revolution 5 If an ammeter is to be used in place of a voltmeter, then we must connect
of α-particle is double than that of proton. with the ammeter a:
Reason (R): In a magnetic field, the period of revolution of a charged (a) low resistance in parallel (b) high resistance in parallel
particle is directly proportional to the mass of the particle and inversely (c) high resistance in series (d) low resistance in series
proportional to the charge of the particle. 6 A particle of charge q and mass m moves in a circular orbit of radius r with
6 Assertion (A): The magnetic field produced by a current carrying long angular speed ω. The ratio of the magnitude of its magnetic moment to
solenoid is independent of its length and cross- sectional area. that of its angular momentum depends on
Reason(R): The magnetic field inside the solenoid is uniform. (a) ω and q (b)ω, q and m (c) q and m (d) ω and m
7 Assertion (A): The voltage sensitivity may not necessarily increase on
increasing the current sensitivity Select the most appropriate answer from the options given below:
Reason (R): Current sensitivity decreases on increasing the number of (a) Both A and R are true and R is the correct explanation of A
turns of the coil (b) Both A and R are true but R is not the correct explanation of A.
8 Assertion (A): When radius of circular loop carrying current is doubled, (c ) A is true but R is false.
its magnetic moment becomes four times (d) A is false and R is also false.
Reason (R): Magnetic moment depends on area of the loop
9 Assertion (A): An electron projected parallel to the direction of magnetic 7 Assertion (A): If an electron and proton enter a magnetic field with equal
force will experience maximum force. momentum, then the paths of both of them will be equally curved.
Reason (R): Magnetic force on a charge particle is given by F = (IL x B). Reason (R): The magnitude of charge on an electron is same as that on
10 Along which axis the magnetic field due to a current element is a proton.
minimum? 8 Assertion (A): The torque acting on square and circular current carrying
(a) along its axis (b) perpendicular to its axis (c) at any angle to its axis coils having equal areas, placed in uniform magnetic field, will be same.
(d) at an angle of 450 with the axis. Reason (R): Torque acting on a current carrying coil placed in uniform
magnetic field does not depend on the shape of the coil, if the areas of the
LEVEL 3 coils are same.
9 Assertion (A): Electron enters into a magnetic field at an angle of 60
1 If a charged particle moves through a magnetic field perpendicular to it degree. Its path will be Parabola.
a) Both momentum and energy of particle change. Reason (R): Force on electron moving perpendicular to magnetic field is
b) Momentum as well as energy is constant. zero.
c) Energy is constant but momentum changes. 10 Assertion (A): Higher the range, lower is the resistance of ammeter.
d) momentum is constant but energy changes Reason (R): To increase the range of an ammeter, additional shunt is
2 The maximum current that can be measured by a galvanometer of added in series to it
resistance 40 Ω is 10 mA. It is converted into voltmeter that can read up to
50 V. The resistance to be connected in the series with the galvanometer ************
is
a) 2010 Ω b) 4050 Ω c) 5040 Ω d) 4960 Ω

77 78
2 A galvanometer of resistance ‘G’ can be converted into a voltmeter of range LEVEL 3
(0-V) volts by connecting a resistance ‘R’ in series with it. How much 1 (a) A uniform magnetic field B is set up along the positive x-axis. A particle of
resistance will be required to change its range from 0 to V/2 ? charge ‘q’ and mass ‘m’ moving with a velocity v enters the field at the origin
3 A voltmeter V of resistance 400 Ω is used to measure the potential difference in X-Y plane such that it has velocity components both along and
connected (in parallel) across a100 Ω resistance which is connected in perpendicular to the magnetic field B. Trace, giving reason, the trajectory
series with a 200Ω resistor to which a 84 V battery source is connected, followed by the particle. Find out the expression for the distance moved by
(i) What will be the reading on the voltmeter? (ii) Calculate the potential the particle along the magnetic field in one rotation.
difference across 100 Ω resistance before the voltmeter is connected (b) Two small identical
circular coils marked 1, 2
LEVEL 3 carry equal currents and
1 Two long parallel wires separated by 0.1 m carry currents of 1A and 2A are placed with their
respectively in opposite directions. A third current-carrying wire parallel to geometric axes
both of them is placed in the same plane such that it feels no net magnetic perpendicular to each other
force. Find the distance of the third wire. as shown in the figure.
2 A hollow cylindrical conductor of radii a and b carries a current I uniformly Derive an expression for
spread over its cross section. Find the magnetic field B for points inside the the resultant magnetic field
body of the conductor at a distance r from the axis. at O.
3 A long straight conductor PQ, carrying a current of 60 A, is fixed
horizontally. Another long conductor XY is kept parallel to PQ at a distance NUMERICALS
of 4 mm, in air. Conductor XY is free to move and carries a current ‘I’.
Calculate the magnitude and direction of current ‘I’ for which the magnetic
LEVEL 1
1 A circular coil of wire consisting of 100 turns, each of radius 8 cm carries 2
repulsion just balances the weight of the conductor XY.
a current of 0.4 A. What is the magnitude of magnetic field at its centre?
5 MARKS QUESTIONS 2 A long straight wire carries a current of 35 A. What is the magnitude of 2
LEVEL 1 magnetic field at a point 20 cm from the wire?
1 (a) State the principle of the working of a moving coil galvanometer, giving its 3 An electron of kinetic energy 25KeV moves perpendicular to the 2
labelled diagram. (b) “Increasing the current sensitivity of a galvanometer direction of a uniform magnetic field of 0.2 milli Tesla. Calculate the time
may not necessarily increase its voltage sensitivity.” Justify this statement (c) period of rotation of the electron in the magnetic field?
Outline the necessary steps to convert a galvanometer of resistance G into a 4 Two parallel straight wires X and Y separated by a distance 5 cm in air 2
voltmeter of a given range. carry current of 10 A and 5 A respectively in opposite direction as shown
in diagram. Calculate the magnitude and direction of the force on a 20
LEVEL 2 cm length of the wire Y.
1 (a) Derive an expression for the torque on a rectangular coil of area A carrying
current I and paced in a magnetic field B which is at an angle θ with the normal
to the plane of the coil.
(b) A rectangular loop of wire of size 2 cm × 5 cm
carries a steady current of 1 A. A straight long wire
carrying 4 A current is kept near the loop as shown
in the figure. If the loop and the wire are coplanar,
find (i) the torque acting on the loop and (ii) the
magnitude and direction of the force on the loop
LEVEL 2
1 A galvanometer gives deflection of 10 division per mA. The resistance 3
due to the current carrying wire.
of galvanometer is 60 Ω. If a shunt of 2.5 Ω is connected to the
galvanometer and there are 50 divisions on the galvanometer scale,
what maximum current can this galvanometer read?

81 82
 ii) There are 3 voltmeter A, B, C having the same range but their resistance 1. A circular loop of area 1cm2, carrying a current of 10 A is placed in a
are 15000 Ω, 10000 Ω and 5000 Ω respectively. The best voltmeter amongst magnetic field of 0.1 T perpendicular to the plane of the loop. The torque
them is the one whose resistance is on the loop due to the magnetic field is
a) 5000 Ω b) 10000 Ω c) 15000 Ω d) all are equally good
A) zero B) 10−4 Nm C)10−2 Nm D) 1 N m
iii) A milliammeter of range 0 to 25 mA and resistance of 10 Ω is to be
converted into a voltmeter with a range of 0 to 25 V. The resistance that 2. Relation between magnetic moment and angular velocity is
should be connected in series will be A) M ∝ ω B) M ∝ ω2 C) M ∝ √ω D) none of these
a) 930 Ω b) 960 Ω c) 990 Ω d) 1010 Ω
3. A current loop in a magnetic field
iv) To convert a moving coil galvanometer (MCG) into a voltmeter A) can be in equilibrium in two orientations, both the equilibrium states are
a) a high resistance R is connected in parallel with MCG
unstable
b) a low resistance R is connected in parallel with MCG
c) a low resistance R is connected in series with MCG B) can be in equilibrium in two orientations, one stable while the other is
d) a high resistance R is connected in series with MCG unstable
OR C) experiences a torque whether the field is uniform or non-uniform in all
v) The resistance of an ideal voltmeter is orientations
a) zero b) low c) high d) infinity D) can be in equilibrium in one orientation.

CREATIVE & CRITICAL THINKING 4. The magnetic moment of a current I carrying circular coil of radius r and
number of turns N varies as
1 1
1 TORQUE ON A RECTANGULAR LOOP PLACED IN UNIFORM 4 A) 𝑟2 B) 𝑟 C) r D) r2
MAGNETIC FIELD
When a rectangular loop PQRS of sides 'a' and 'b' carrying current I is
placed in uniform magnetic field →, such that area vector → makes an _________________________________________________________
𝐵 𝐴
angle θ with direction of magnetic field, then forces on the arms QR and
SP of loop are equal, opposite and collinear, there by perfectly cancel
each other, whereas forces on the arms PQ and RS of loop are equal and
opposite but not collinear, they give rise to torque on the loop.

Force on side PQ or RS of loop is F = Ib sin90=Ib B and perpendicular

distance between two non-collinear forces is a sinθ

So, torque on the loop, τ=I AB sinθ

In vector form torque, → = → × →
τ 𝑀 𝐵
where M= NIA is called magnetic dipole moment of current loop and is
directed in direction of area vector A i-e., normal to the plane of loop.

85 86
 (d) All of these UNIT III MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
CH–5: Magnetism and Matter
4. Proton, electron and deuteron enter a region of uniform magnetic field
with same electric potential-difference at right angles to the field. Which
one has a more curved trajectory? Gist of the chapter
(a) electron
(b) proton • A magnet is a substance or object that produces a magnetic field.
(c) deuteron • These days magnets have a lot of applications in areas such as electrical
(d) all will have same radius of circular path devices, motors, fans, power generation, etc.
• All magnets exhibit magnetic force around them which is represented
in magnetic field lines.
12 (i) State and explain Ampere’s circuital law? 5 • These lines start from the north pole of the magnet to the south pole.
(ii) Figure shows a long straight wire of a circular cross-section (radius a)
• The earth itself exhibits magnetic field lines around making it act like a magnet.
carrying steady current I. The current I is uniformly distributed across this
cross-section. Calculate the magnetic field in the region r < a and r > a
The properties of magnetic lines of force are as follows:
• Magnetic field lines emerge from the north pole and merge at the south pole.
• As the distance between the poles increases, the density of magnetic lines
decreases.
• The direction of field lines inside the magnet is from the South Pole to the North
Pole.
• Magnetic lines do not intersect with each other.
• The strength of the magnetic lines is the same throughout and is proportional
to how close are the lines.

Magnetic field pattern of a bar magnet

************
Coulomb's Law of Magnetic Force

According to Coulomb’s law of magnetic force,

the force between two magnetic poles of strengths qm1 and
qm2 lying at a distance r is directly proportional to the
product of the pole strengths and inversely proportional
to the square of the distance between their centers.
A magnetic dipole is a magnetic north pole and a
magnetic south pole separated by a small distance.
Magnetic dipole moments have dimensions of current
times area or energy divided by magnetic flux density.

m = 𝑞𝑚 × 2𝑙 direction south to north pole of magnet.

Magnetic field intensity due to bar magnet

Case 1: on a point on axial line

89 90
 CONCEPT MAP/MIND MAP

Effect of temperature on magnetic properties

https://www.britannica.com/video/185491/dependence-properties-temperature
According to Curie's Law, the magnetization in a paramagnetic material is directly
proportional to the applied magnetic field. If the object is heated, the magnetization is
viewed to be inversely proportional to the temperature

The Curie temperature (TC) of a ferroelectric material is the temperature at which the
material undergoes the phase transition from a low-temperature ferroelectric phase to
a high-temperature parmagnetic phase upon heating.

https://www.youtube.com/watch?v=haVX24hOwQI

93 94
18 ASSERTION : Ferro-magnetic substances become paramagnetic above Curie Which magnetic property distinguishes this behaviour of the field lines due to
temp. the two substances?
REASON : Domains are destroyed at high temperature. 11 Depict the behaviour of magnetic field lines when
(i) a diamagnetic material and
19 ASSERTION : The sensitivity of a moving coil galvanometer is increased by
(ii) a paramagnetic material is placed in an external magnetic field.
placing a suitable magnetic material as a core inside the coil. Mention briefly the properties of these materials which explain this
REASON : Soft iron has high magnetic permeability and cannot be easily distinguishing behaviour.
magnetized or demagnetized. 12 From a molecular viewpoint, discuss the temperature dependence of
20 ASSERTION : The poles of magnet can not be separated by breaking into two susceptibility for diamagnetism, paramagnetism and ferromagnetism.
pieces.
REASON : The magnetic moment will be reduced to half when a magnet is LEVEL 3 (2 M QUESTIONS)
broken into two equal pieces.
13 Three identical bar magnets are riveted
together at the centre in the same plane, as
LEVEL 1 (2 M QUESTIONS) shown in Fig. This system is placed at rest
1 Is the steady electric current the only source of magnetic field? Justify your in a slowly varying magnetic field. It is found
answer that the system of magnets does not show
2 What are permanent magnets? Give one example. any motion. The north-south poles of one
3 Which of the following substances are diamagnetic? magnet are shown in Fig. Determine the
Bi, Al, Na, Cu, Ca and Ni poles of the remaining two.
4 Which of the following substances are para-magnetic ?
Bi, Al, Cu, Ca, Pb, Ni
LEVEL 1 (3 M QUESTIONS)
5 Relative permeability of a material, µr = 0.5. Identify the nature of the magnetic 1 (i) The permeability of a magnetic material is 0.9983. Name the type of
material and write its relation to magnetic susceptibility. magnetic materials it represents.
6 In what way is the behaviour of a diamagnetic material different from that of a (ii) The susceptibility of a magnetic material is 1.9 × 10 -5. Name the type of
paramagnetic, when kept in an external magnetic field? magnetic materials it represents.
7 Define magnetic susceptibility of a material. Name two elements, one having (iii) The susceptibility of a magnetic material is – 4.2 × 10-6. Name the type of
positive susceptibility and the other having negative susceptibility. What does magnetic materials it represents.
2 Distinguish between dia, para and ferromagnetic materials.
negative susceptibility signify?
LEVEL 2 (2 M QUESTIONS) LEVEL 2 (3 M QUESTIONS)
8 A proton has spin and magnetic moment just like an electron. Why then its 3 Derive expression for magnetic field on an axial point of a magnetic dipole
effect is neglected in magnetism of materials?
9 The figure shows the variation of intensity of magnetisation ‘I’ versus the 4 Derive expression for magnetic field on an equatorial line of a magnetic dipole.
applied magnetic field intensity ‘H’ for two magnetic materials A and B :
LEVEL 3 (3 M QUESTIONS)
5 A circular coil of N turns and radius R carries a current I. It is unwound and
rewound to make another coil of radius R/2, current I remaining the same.
Calculate the ratio of the magnetic moments of the new coil and the original coil
6 A bar magnet of magnetic moment m and moment of inertia I (about the centre,
perpendicular to length) is cut into two equal pieces perpendicular to the length.
(a) Identify the materials A and B. Let T be the period of oscillations of the original magnet about an axis through
(b) Why does the material B, has a larger susceptibility than A, for a given field the midpoint, perpendicular to the length, in a magnetic field B. What would be
at constant temperature? the similar period ‘T’ for each piece?
10 Draw magnetic field lines when a 7 A small compass needle of magnetic moment ‘m’ is free to turn about an axis
(i) diamagnetic, perpendicular to the direction of uniform magnetic field ‘B’. The moment of
(ii) paramagnetic substance is placed in an external magnetic field.
inertia of the needle about the axis is ‘I’. The needle is slightly disturbed from

97 98
 4 What is the net magnetic moment of the (iv) In a coaxial, straight cable, the central conductor and the outer
system of magnetic poles shown in fig. below. conductor carry equal
currents in opposite
direction. The magnetic
field is zero

(a) Point P
CASE BASED/ SOURCE BASED QUESTIONS (b) for radius more than
1 Gauss's law for magnetism states that the magnetic flux B across any closed a and less than b
surface is zero; that is, div B = 0, where div is the divergence operator. This law (c) Inside the outer
is consistent with the observation that isolated magnetic poles (monopoles) do conductor
not exist. (d) Inbetween the two
(i) The net magnetic flux through any closed surface, kept in a conductors
magnetic field is
µ𝑜
(a) Zero (b) (c) 2 According to Neil Bohr’s atom model,
4𝜋
4µ𝑜 the negatively charged electron is
4𝜋µ𝑜 (d) 𝜋 revolving around a positively charged
(ii) Which of the following is not nucleus in a circular orbit of radius r.
the consequence of Gauss’s The revolving electron in a closed path
law? constitutes an electric current. The
(a) The magnetic poles motion of the electron in anticlockwise
always exist as unlike direction produces conventional
pairs of equal current in the clockwise direction.
strength. Current, I = e/T where T is the period of revolution of the electron. If v is
(b) If several magnetic the orbital velocity of the electron, then Due to the orbital motion of the
lines of force enter in a electron, there will be orbital magnetic moment μl
closed surface, then an equal number of lines of force must
leave that surface. 𝜇𝐿 = 𝐼𝐴, 𝑤ℎ𝑒𝑟𝑒𝐴𝑖𝑠𝑡ℎ𝑒𝑎𝑟𝑒𝑎𝑜𝑓𝑡ℎ𝑒𝑜𝑟𝑏𝑖𝑡
(c) Monopole do not exist in magnetism. 𝑒𝑣 𝑒𝑣𝑟 𝑒 𝑒
𝜇𝑙 = 2𝜋𝑟 𝜋𝑟 2 = 2
. If m is mass of electron then 𝜇𝑙 = 2𝑚 (𝑚𝑣𝑟) = 2𝑚 𝑙
(d) There are abundant sources or sinks of magnetic field inside
a closed surface. where mvr = lcalled angular momentum of the electron about the central
(iii) A closed surface S encloses a magnetic dipole of magnetic nucleus. Bohr hypothesized that the angular momentum of the orbiting
𝑛ℎ
moment 2ml. The magnetic flux emerging from the surface is electron has only discrete values given by the equation. 𝑙 = 2𝜋
2𝑚
(a) µ𝑜 𝑚 (b) zero (c) 2µ𝑜 𝑚 (d) µ𝑜
Substituting this in above equation magnetic moment of orbiting electron
is

𝑒 𝑛ℎ 𝑛𝑒ℎ
𝜇𝑙 = 2𝑚 2𝜋 = 4𝜋𝑚 The minimum value of magnetic moment is (𝜇𝑙 )𝑚𝑖𝑛 =
𝑒ℎ
4𝜋𝑚
. This value is called Bohr magneton. By substituting the values of e,
h and m the value of Bohr magneton is 9.27 x 10-24 Am2.
1. If an electron in an atom revolves around a nucleus in clockwise manner, the
direction of circulating current in the orbit is
a) Clockwise direction b) Perpendicular direction w.r.t orbit
c) Anti-clockwise direction d) none of the above

101 102
 SELF ASSESSMENT Three marks question
TOTAL MARKS: 25 Time: 40 min 9 A bar magnet of magnetic moment 1.5 𝐽𝑇 −1 lies aligned with the 3
S.No. QUESTIONS Marks direction of a uniform magnetic field of 0.22T.
One mark questions (a) What is the amount of work required by an external torque to
MCQ turn the magnet so as to align its magnetic moment
1 What is the property of a material that allows it to create a permanent 1 (i) Normal to the field direction? And (ii) opposite to the
magnet? field direction?
a)Diamagnetism c) Ferromagnetism (b) What is the torque on the magnet in case (i) and (ii)
b)Para magnetism d) Thermoelectricity 10 (a) Show that the time period (T) of oscillations of a freely 3
2. What is the significance of the Curie temperature in magnetism? 1 suspended magnetic dipole of magnetic moment (m) in a
a) The curie temperature is the temperature at which magnets
𝐼
stop working uniform magnetic field (B) is given by = 2𝜋√ , where 𝐼 is a
𝑚𝐵
b) The curie temperature is only relevant for non-magnetic moment of inertia of the magnetic dipole.
materials (b) Identify the following magnetic materials:
c) The curie temperature makes the transition from (i) A material having susceptibility -0.00015
ferromagnetism to paramagnetism in a material. (ii) A material having susceptibility 10−5
d) The curie temperature determines the colour of a magnet. Four marks case based question
3 Points A and B are located perpendicular to the axis of a 2cm long 1 11 According to Neil Bohr’s atom 4
bar magnet at large distances x and 3x from its centre on opposite model, the negatively charged
sides. The ratio of the magnetic fields at A and B will be electron is revolving around a
approximately equal to positively charged nucleus in a
1:9 (b) 2:9 (c) 27:1 (d) 9:1 circular orbit of radius r. The
revolving electron in a closed
4 The magnetic moment of a diamagnetic atom is 1
path constitutes an electric
a) Equal to one b) Between zero and one current. The motion of the
C) Equal to zero d) Much greater than one electron in anticlockwise
Assertion and reasoning direction produces
5 ASSERTION: The poles of a bar magnet cannot be separated 1 conventional current in the clockwise direction. Current, I = e/T
REASON: Magnetic monopoles do not exist. where T is the period of revolution of the electron. If v is the orbital
6 ASSERTION: When a magnetic dipole is placed in a non-uniform 1 velocity of the electron, then Due to the orbital motion of the
electron, there will be orbital magnetic moment μl
magnetic field, only a torque acts on the dipole.
REASON: Force would not act on magnetic dipole if magnetic field 𝜇𝐿 = 𝐼𝐴, 𝑤ℎ𝑒𝑟𝑒𝐴𝑖𝑠𝑡ℎ𝑒𝑎𝑟𝑒𝑎𝑜𝑓𝑡ℎ𝑒𝑜𝑟𝑏𝑖𝑡
were non uniform. 𝑒𝑣 𝑒𝑣𝑟
𝜇𝑙 = 𝜋𝑟 2 = .
2𝜋𝑟 2
𝑒 𝑒
Two mark questions If m is mass of electron then 𝜇𝑙 = 2𝑚 (𝑚𝑣𝑟) = 2𝑚 𝑙
7 A uniform magnetic field gets modified as shown below when two 2 where mvr = l called angular momentum of the electron about the
specimens X and Y are placed in it. Identify whether specimens X central nucleus. Bohr hypothesized that the angular momentum
and Y are diamagnetic, paramagnetic or ferromagnetic. of the orbiting electron has only discrete values given by the
𝑛ℎ
equation. 𝑙 =
2𝜋

Substituting this in above equation magnetic moment of orbiting

electron is
𝑒 𝑛ℎ 𝑛𝑒ℎ
𝜇𝑙 = 2𝑚 2𝜋 = 4𝜋𝑚 The minimum value of magnetic moment is
8 Write two point of difference between a diamagnetic and a 2 𝑒ℎ
(𝜇𝑙 )𝑚𝑖𝑛 = . This value is called Bohr magneton. By
paramagnetic substance. 4𝜋𝑚

105 106
 • Inductance (L): The property of a coil that quantifies self-induction. The MCQ
LEVEL – 1
induced EMF is given by: . 1. Faraday's law of electromagnetic induction states that the induced EMF in a
circuit is directly proportional to:
5. Mutual Induction: a) the resistance of the circuit
b) the magnetic flux through the circuit
Mutual induction occurs when a change in current in one coil induces an EMF in a
nearby coil. c) the rate of change of magnetic flux through the circuit
d) the current in the circuit
• Mutual Inductance (M): The property quantifying the induced EMF in one coil
due to the rate of change of current in another coil. The induced EMF in coil 2 2. The unit of magnetic flux is:
a) Tesla b) Weber c) Gauss d) Henry
due to the change in current in coil 1 is:
3. Lenz's law is a consequence of the law of:
a) conservation of energy b) conservation of charge
where M is the mutual inductance, I1 is the current in coil c) conservation of momentum d) conservation of mass
1, and E2 is the induced EMF in coil 2.
4. The direction of induced current in a conductor moving in a magnetic field is
given by:
Summary a) Fleming's right-hand rule b) Fleming's left-hand rule c) Lenz's law d)
Ampere's law
Electromagnetic induction is the process of generating an electric current by changing
the magnetic field. Faraday's laws quantify this induction, stating that a changing 5. Mutual induction between two coils depends on:
a) the resistance of the coils b) the rate of change of current in one coil
magnetic flux induces an EMF. Lenz's law provides the direction of the induced EMF
and current, ensuring it opposes the change in magnetic flux. Self-induction describes c) the physical dimensions of the coils d) the potential difference across the
the induction of EMF in the same coil due to changes in its own current, while mutual coils
induction describes the induction of EMF in one coil due to changes in current in 6. The SI unit of inductance is:
another coil. These principles are foundational for many electrical technologies, a) Farad b) Coulomb c) Weber d) Henry
including transformers and electric generators.
7. Which of the following can cause an induced EMF in a coil?
a) A steady magnetic field b) A changing magnetic field
CONCEPT MAP:
c) A constant current d) A steady electric field
8. The self-inductance of a solenoid depends on:
a) the length of the solenoid b) the number of turns in the solenoid
c) the area of cross-section of the solenoid d) all of the above
9. The induced EMF in a coil is zero when:
a) the coil is moved perpendicular to the magnetic field
b) the coil is stationary in a changing magnetic field
c) the magnetic flux through the coil remains constant
d) the magnetic field is zero
10. The phenomenon of electromagnetic induction was discovered by:
a) Newton b) Faraday c) Maxwell d) Ampere
11. In an AC generator, the frequency of the induced EMF depends on:
a) the speed of rotation of the coil b) the number of turns in the coil

109 110
9. Two coils have a mutual inductance of 0.2 H. If the current in the first coil 3. Describe how an EMF is induced in a coil when the magnetic field through it
changes at a rate of 3 A/s, what is the induced EMF in the second coil? changes.
a) 0.1 V b) 0.2 V c) 0.4 V d) 0.6 V 4. What factors affect the magnitude of the induced EMF in a conductor moving
10. A coil with a self-inductance of 6 H has a current of 2 A passing through it. If through a magnetic field?
the current changes uniformly to 0 A in 0.5 seconds, what is the induced EMF? 5. State Lenz’s Law and explain its significance in determining the direction of
a) 4 V b) 6 V c) 8 V d) 24 V induced current.
6. Provide an example to illustrate Lenz’s Law in a practical scenario.
LEVEL – 3
7. Define self-induction and explain what is meant by the self-inductance of a coil.
1. A straight line conductor of length 0.4 m is moved with a speed of 7 8. What is the physical significance of the self-inductance in an electrical circuit?
m/s perpendicular to a magnetic field of intensity 0.9 wb/m2. The induced e.m.f. 9. Define mutual induction and explain the concept of mutual inductance between
across the conductor is… two coils.
a) 5.04 V b) 1.26 V c) 2.52 V d) 25.2 V
2. A magnetic flux linked with a coil varies as 𝜙 = 2𝑡 2 − 6𝑡 + 5 wher LEVEL – 2
𝜙 is in weber and t is in second. The induced current is zero at 1. A circular coil of radius 0.1 m is placed in a uniform magnetic field of 0.5 T, with
a) t = 0 b) t = 1.5 c) t = 3 d) t = 5 its plane perpendicular to the magnetic field. If the magnetic field changes
3. A bar magnet is released along the vertical axis of the conducting uniformly to 1.5 T in 0.2 s, calculate the average induced EMF in the coil.
coil. The acceleration of the bar magnet is 2. A solenoid with 500 turns and a cross-sectional area of 0.01 m2 is placed in a
changing magnetic field. The magnetic flux through the solenoid increases from
a) greater than g b) less than g c) equal to g d) zero
4. A coil having an area A is placed in magnetic field which changes 0.02 Wb to 0.06 Wb in 0.1 s. What is the average induced EMF in the solenoid?
from B to 4B in time t. The average emf induced in the coil will be 3. A rectangular loop of wire is moved away from a long straight wire carrying a
3𝐴𝐵 4𝐴𝐵 3𝐵 4𝐵 steady current. Describe the direction of the induced current in the loop and
a) b) c) d)
𝑡 𝑡 𝐴𝑡 𝐴𝑡 explain how Lenz’s Law applies to this situation.

Predict the direction of induced current in following cases 4. A coil with an inductance of 2 H has a current that increases at a rate of 3 A/s.
Calculate the induced EMF in the coil.
5. wo coils are placed close to each other. A current change of 4 A/s in the first
coil induces an EMF of 0.8 V in the second coil. Calculate the mutual inductance
between the two coils.
LEVEL – 3
1. A coil of 50 turns is placed in a magnetic field that changes from 0.2 T to 0.6 T
in 0.4 seconds. The area of the coil is 0.1 m 2. Calculate the average induced
EMF in the coil.
2. Explain how Lenz’s Law applies when a metal ring is dropped into a region
where a magnetic field is increasing upwards. What will be the direction of the
induced current in the ring as it enters the magnetic field?
3. A solenoid with an inductance of 2 H carries a current that decreases uniformly
2 marks from 3 A to 0 A in 0.5 s. Determine the self-induced EMF in the solenoid during
LEVEL – 1 this time period.

1. State Faraday’s first law of electromagnetic induction.

2. How does the magnitude of induced EMF relate to the rate of change of
magnetic flux according to Faraday’s second law?

113 114
2. Two coils, Coil X and Coil Y, are arranged such that Coil X has 600 turns and
Coil Y has 1000 turns. Coil X has an inductance of 2 H and Coil Y has an 4. What is the magnitude of the induced current (III) in the loop?
inductance of 5 H. The mutual inductance between the coils is 1.2 H. A steady A. 0.25 A B. 0.5 A C. 0.75 A D. 1.0 A
current of 4 A is established in Coil X. If the current in Coil X is changed to zero
in 0.2 seconds, calculate the energy transferred to Coil Y and the induced EMF COMPETENCY BASED
in Coil Y. Two coils, Coil A and Coil B, are placed close to each other. Coil A has 300
3. A rectangular conducting loop with length l = 0.5 m and width w=0.3 m moves turns and an inductance of 2 H, while Coil B has 400 turns and an inductance
with a constant velocity v=2 m/s perpendicular to a uniform magnetic field of of 3 H. The mutual inductance between the two coils is 1 H. Coil A is connected
strength B = 0.4 T. The loop is moving in such a way that the entire loop remains to a variable power supply and a switch. Initially, there is no current in Coil A.
within the magnetic field. Calculate: At t=0, the switch is closed, and the current in Coil A increases uniformly from
a) The induced EMF in the loop. 0 A to 5 A in 1 second. Coil B is connected to a resistor of 2 Ω.
b) The induced current if the resistance of the loop is R=0.2 Ω. 1. Calculate the rate of change of current dIA/dt in Coil A.
c) The power dissipated in the loop due to the induced current. 2. Determine the induced EMF εB in Coil B.
LEVEL-3 (NUMERICALS) 3. Calculate the induced current IB in Coil B.
4. Find the total energy transferred to Coil B during the 1 second.
2. A solenoid with 1000 turns and a length of 0.5 meters has a cross-sectional
area of 0.01 m². It is connected to a circuit where the current increases from 2 CCT BASED
A to 8 A in 0.4 seconds. Calculate the induced EMF in the solenoid and the
A researcher is conducting an experiment to demonstrate Lenz’s Law using a
energy stored in the solenoid at the final current.
setup that includes a strong horseshoe magnet, a copper pipe, a solenoid, a
3. A coil with an inductance of 0.5 H is connected in a circuit. If the current through
sensitive ammeter, and a small aluminium ring. The following scenarios are
the coil changes sinusoidally according to the equation I(t) = 5sin(100t) where
being investigated:
I is in amperes and t is in seconds, calculate the maximum induced EMF in the
coil. 1. Dropping a strong magnet through a vertically oriented copper pipe.
4. Two coils, Coil A and Coil B, are placed close to each other. Coil A has 500 2. Moving a magnet rapidly towards and away from the solenoid connected to the
turns and a resistance of 1 Ω, while Coil B has 800 turns and a resistance of ammeter.
1.5 Ω. The mutual inductance between the coils is 3 H. If a current of 5 A in Coil 3. Placing the small aluminium ring on the top of the solenoid and turning the
A is changed to zero in 0.1 seconds, calculate the induced EMF in Coil B and current on and off in the solenoid.
the energy dissipated as heat in Coil B during this time. 1. In the first scenario, describe the motion of the magnet as it falls through the
CASE BASED copper pipe. Explain how Lenz’s Law applies to this scenario and predict
A conducting rectangular loop of wire with dimensions 10 cm×5 cm is placed in the experimental observations.
a uniform magnetic field of strength 0.5 T. The plane of the loop is perpendicular 2. In the second scenario, what will the ammeter show when the magnet is
to the magnetic field. The magnetic field is increased uniformly to 1.0 T over a moved towards and then away from the solenoid? Explain your answer
period of 2 s. The loop has a resistance of 0.1 Ω. using Lenz’s Law.
3. For the third scenario, predict and explain what happens to the aluminium
1. What is the rate of change of the magnetic field (dB/dt)? ring when the current in the solenoid is suddenly turned on and off.
A. 0.25 T/s B. 0.5 T/s C. 1.0 T/s D. 2.0 T/s 4. Consider a scenario where the copper pipe is replaced with a pipe made of
a different non-conducting material, such as plastic. Predict how the motion
2. What is the induced EMF ε in the loop during the change in magnetic field? of the magnet changes and explain why, based on Lenz’s Law.
A. 0.025 V B. 0.05 V C. 0.10 V D. 0.20 V
********
3. What is the direction of the induced current in the loop?
A. Clockwise, looking from above
B. Counterclockwise, looking from above
C. Alternating current
D. No current is induced
117 118
 UNIT IV ELECTROMAGNETIC INDUCTION AND ALTERNATING 𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡
𝑑𝑖
CURRENT 𝑉 − 𝐿 = 0 (using Kirchhoff’s
𝑑𝑡
rule)
CH 7 ALTERNATING CURRENTS 𝑑𝑖 𝑉 𝑉𝑚
= = 𝑠𝑖𝑛𝜔𝑡
GIST OF CHAPTER: 𝑑𝑡 𝐿 𝐿
𝑑𝑖 𝑉𝑚
Alternating currents, peak and RMS value of alternating current/voltage, ∫ 𝑑𝑡 = ∫ 𝑠𝑖𝑛𝜔𝑡𝑑𝑡
𝑑𝑡 𝐿
reactance and impedance, LCR series circuit (phasors only), resonance, power 𝑉𝑚
in AC circuits, power factor, wattless current, Transformer, AC generator. 𝑖=− 𝑐𝑜𝑠𝜔𝑡 + 𝐶
𝜔𝐿
𝜋 𝑉
Alternating currents: Alternating current 𝑖 = 𝑖𝑚 𝑠𝑖𝑛 (𝜔𝑡 − ) (𝑖𝑚 = 𝑚 )
2 𝜔𝐿
(AC) is an electric current that Inductive reactance, 𝑋𝐿 = 𝜔𝐿
periodically reverses direction and Current lags behind the voltage in
𝜋
changes its magnitude continuously with phase by 2 rad.
time. OR
𝐼 = 𝐼𝑚 𝑠𝑖𝑛𝜔𝑡 Voltage leads the current in phase
𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 𝜋
by rad.
Direct current: flows with a constant magnitude and in same fixed direction. 2

Advantages of AC over 1) Easily and efficiently converted from one voltage

DC: to the other by means of transformers.
2) Transmitted economically over long distances.
Average value of AC over a one complete 𝑞
𝐼𝑎𝑣 = = 0 AC voltage applied to a capacitor:
cycle 𝑡
Average value of AC over half of 2𝐼 𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡
𝐼𝑎𝑣 = 𝜋𝑚 = 0.637𝐼𝑚 (𝐼𝑚 = peak value) 𝑞
cycle 𝑉=
RMS value: To measure AC/AV heating effect of current is used which is 𝐶
𝑞
independent of the direction. 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 =
𝐶
RMS value also known as Effective or Virtual value. 𝑑𝑞 𝑑
Relation between RMS value and peak 𝐼𝑚 𝑉𝑚 𝑖= = (𝐶𝑉𝑚 𝑠𝑖𝑛𝜔𝑡)
𝐼𝑟𝑚𝑠 = 𝑎𝑛𝑑 𝑉𝑟𝑚𝑠 = 𝑑𝑡 𝑑𝑡
value √2 √2 = 𝜔𝐶𝑉𝑚 𝑐𝑜𝑠𝜔𝑡
𝑉𝑚 𝜋
AC voltage applied to a Resistor: = 𝑠𝑖𝑛 (𝜔𝑡 + )
1⁄ 2
𝜔𝐶
𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 𝜋
= 𝑖𝑚 𝑠𝑖𝑛 (𝜔𝑡 + )
𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 = 𝑖𝑅 (By Kirchhoff’s loop rule) 2
1
𝑉𝑚 Capacitive reactance, 𝑋𝐶 =
𝑖= 𝑠𝑖𝑛𝜔𝑡 𝜔𝐶
𝑅 Current leads the voltage in
𝑉
𝑖 = 𝑖𝑚 𝑠𝑖𝑛𝜔𝑡 (where 𝑖𝑚 = 𝑅𝑚 ) 𝜋
phase by 2 rad.
OR
Voltage lags behind the current
𝜋
in phase by 2 rad.

Voltage and current are in phase.

AC voltage applied to an Inductor:

121 122
 MIND MAP

AC Generator:
It is a device which converts mechanical energy into an electrical energy and
generates alternating current.
Principle: Works on principle of electro-magnetic induction.
Construction:
1. Armature coil
2. Filed magnet
3. Slip rings
4. Brushes

Theory:
When the armature coil rotates
between the pole pieces of field
magnet, the effective area of the coil
is A cos θ,
The flux at any time is,
∅=𝐵 ⃗ . 𝐴=NBA cos θ=NBA cosωt
The induced emf is,
𝑑∅ 𝑑(𝑁𝐵𝐴𝑐𝑜𝑠𝜔𝑡)
𝜀=− =−
𝑑𝑡 𝑑𝑡
𝑉 = 𝜀 = −𝑁𝐵𝐴𝜔𝑠𝑖𝑛𝜔𝑡

Formulae:
𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 = 𝑉𝑚 𝑠𝑖𝑛2𝜋𝜗𝑡 𝑃⃗ = 𝑉𝑟𝑚𝑠 𝑖𝑟𝑚𝑠 𝑐𝑜𝑠∅
𝑅 𝑅
𝑖 = 𝑖𝑚 𝑠𝑖𝑛𝜔𝑡 = 𝑖𝑚 𝑠𝑖𝑛2𝜋𝜗𝑡 Power factor = 𝑐𝑜𝑠∅ = 𝑍 =
√(𝑅)2 +(𝑋𝐶 −𝑋𝐿 )2
𝐼𝑚 𝑉𝑚 𝜀𝑆 𝑁𝑆 𝐼𝑃
𝐼𝑟𝑚𝑠 = 𝑎𝑛𝑑 𝑉𝑟𝑚𝑠 = = =
√2 √2 𝜀𝑃 𝑁𝑃 𝐼𝑆
𝑋𝐿 = 𝜔𝐿 𝑂𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
𝜂= × 100%
𝐼𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
1 𝑉 = 𝜔 = −𝑁𝐵𝐴𝜔𝑠𝑖𝑛𝜔𝑡
𝑋𝐶 =
𝜔𝐶
𝑉𝑚
𝑍= = √(𝑅)2 + (𝑋𝐶 − 𝑋𝐿 )2
𝑖𝑚
𝑋𝐶 − 𝑋𝐿
𝑡𝑎𝑛∅ =
𝑅

125 126
 Level – 2 (a) 100 Ω (b) 30 Ω (c) 3.2 Ω (d) 10 Ω
Q.1 In series LCR circuit, the capacitance is changed from C to 4C. For the same Q.2 An ac circuit consists of an inductor of inductance 0.5 H and a capacitor of
resonant frequency, the inductance should be changed from L to capacitance 8 μF in series. The current in the circuit is maximum when the
(a) 2L (b) L / 2 (c) L / 4 (d) 4 L angular frequency of ac source is
Q.2 A bulb and a capacitor are connected in series to a source of alternating (a) 500 rad/sec (b) 2X105 rad/sec (c) 4000 rad/sec (d) 5000 rad/sec
current. If its frequency is increased, while keeping the voltage of the source Q.3 An inductive circuit contains a resistance of 10 Ω and an inductance of 2.0 H.
constant, then If an ac voltage of 120 V and frequency of 60 Hz is applied to this circuit, the
(a) Bulb will give more intense light current in the circuit would be nearly
(b) Bulb will give less intense light (a) 0.32 A (b) 0.16 A (c) 0.48 A (d) 0.80 A
(c) Bulb will give light of same intensity as before Q.4 The power factor of an ac circuit having resistance (R) and inductance (L)
(d) Bulb will stop radiating light connected in series and an angular velocity ω is
𝑅 𝑅 𝜔𝐿 𝑅
(a) 𝜔𝐿 (b) 2 2 2
(c) 𝑅 (d) 2 2 2
√(𝑅 +𝜔 𝐿 ) √(𝑅 −𝜔 𝐿 )
Q.3 The i-V curve for anti-resonant circuit is
Q.5 A telephone wire of length 200 km has a capacitance of 0.014 μF per km. If
it carries an ac of frequency 5 kHz, what should be the value of an inductor
required to be connected in series so that the impedance of the circuit is
minimum
(a) 0.35 mH (b) 35 mH (c) 3.5 mH (d) Zero
Q.6 An LCR series circuit with a resistance of 100 Ω is connected to an ac source
of 200 V (r.m.s.) and angular frequency 300 rad/s. When only the capacitor
is removed, the current lags behind the voltage by 60 0. When only the
inductor is removed the current leads the voltage by 600. The average power
Q.4 If rotational velocity of an a.c. generator armature is doubled, then induced
dissipated is
e.m.f will become
(a) 50 W (b) 100 W (c) 200 W (d) 400W
(a) Half (b) Two times (c) Four times (d) Unchanged Q.7 A power transformer is used to step up an alternating e.m.f. of 220 V to 11
Q.5 In a step-up transformer, the turn ratio is 1: 2. A Leclanche cell (e.m.f. 1.5V)
kV to transmit 4.4 kW of power. If the primary coil has 1000 turns, what is the
is connected across the primary. The voltage developed in the secondary current rating of the secondary? Assume 100% efficiency for the transformer
would be (a) 4 A (b) 0.4 A (c) 0.04 A (d) 0.2 A
(a) 3.0 V (b) 0.75 V (c) 1.5 V (d) Zero
Q.8 A loss free transformer has 500 turns on its primary winding and 2500 in
Q.6 In a step-up transformer the turn’s ratio is 1:10. A resistance of 200 ohm
secondary. The meters of the secondary indicate 200 volts at 8 amperes
connected across the secondary is drawing a current of 0.5 A. What is the under these conditions. The voltage and current in the primary is
primary voltage and current?
(a) 100 V, 16 A (b) 40 V, 40 A (c) 160 V, 10 A (d) 80 V, 20 A
(a) 50 V, 1 A (b) 10 V, 5 A (c) 25 V, 4 A (d) 20 V, 2 A
Q.9 The figure shows variation of R, XL and XC
Q.7 The turns ratio of a transformer is given as 2:3.If the current through the with frequency f in a series L, C, R circuit.
primary coil is 3A, then the current in secondary coil is
Then for what frequency point, the circuit is
(a) 1A (b) 4.5A (c) 2A (d) 1.5A
inductive
Q.8 The peak value of AC voltage on a 220 V mains is
(a) 110 √2 (𝑏)200 √2 (𝑐)240 √2 (𝑑)220 √2 (a) A (b) B (c)
Q.9 In a series LCR circuit, resistance R = 10 and the impedance Z = 20. The C (d) All points
phase difference between the current and the voltage is
(a) 300 (b) 450 (c) 600 (d) 900 Q.10 Which of the following plots may represent the reactance of a series LC
Q.10 The frequency for which a 5 μF capacitor has a reactance of 1 Ω is given combination
1000
by
(a) a (b) b (c) c (d) d
1 1000 100
(a) 1000 Hz (b) 1000 𝐻𝑧 (𝑐) ℎ𝑧 (𝑑) 𝑀𝐻𝑧
𝜋 𝜋

Assertion – Reason Questions:

Level – 3
Q.1 An inductance of 1 mH a condenser of 10 μF and a resistance of 50 Ω are (a) If both assertion and reason are true and the reason is the correct explanation of
connected in series. The reactance of inductor and condensers are same. the assertion.
The reactance of either of them will be

129 130
Q.7 At an airport, a person is made to walk through the doorway of a metal Level – 2
detector, for security reasons. If she/he is carrying anything made of metal, Q.1 An alternating voltage 𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 applied to a series LCR circuit derives a
the detector emits a sound. On what principal does this detector work? current given by 𝑖 = 𝑖𝑚 𝑠𝑖𝑛(𝜔𝑡 + ∅). Deduce an expression for the average
Q.8 (i) Define power factor of an ac circuit. power dissipated over a cycle.
(ii) What are the maximum and minimum values of power factor of an ac Q.2 When a capacitor is connected in series with a series LR circuit, the
circuit? alternating current flowing in the circuit increases. Explain why.
Q.3 State the principal of an AC generator. Obtain the expression for the emf
Level – 2
induced in a coil with labelled diagram.
Q.1 Prove that an ideal capacitor in an ac circuit does not dissipate power.
Q.2 In a series LCR circuit, obtain the condition under which
Level – 3
(i) the impedance of circuit is minimum and
(ii) wattles current flows in the circuit. Q.1 An inductor L of inductance XL is connected in series with a bulb B and an
Q.3 State the principal of working of a transformer. Can a transformer be used to AC source. How would brightness of the bulb change when (i) number of
step up or step down a DC voltage? Justify your answer. turns in the inductor is reduced. (ii) an iron rod is inserted in the inductor and
Q.4 Differentiate between the term inductive reactance and capacitive reactance (iii) a capacitor of reactance XC=XL is inserted in series in the circuit. Justify
of an AC circuit. your answer in each case.
Q.5 Write the expression for the impedance offered by the series combination of Q.2 Does the current in an ac circuit lag, lead, or remain in phase with the voltage
resistor, inductor and capacitor connected to an AC source of voltage, frequency applied to the circuit, when (i) f=fr, (ii) f<fr and (iii) f>fr, where fr is
𝑉 = 𝑉0 𝑠𝑖𝑛𝜔𝑡. Show on a graph the variation of the voltage and the current with the resonant frequency?
𝜔𝑡 in the circuit.
LA (5 Marks each)
Level – 1
Level – 3 Q.1 (i) Differentiate between the term inductive reactance and capacitive
Q.1 “An alternating current doesn’t show any magnetic effect”. True/false. Justify
reactance of an ac circuit.
your answer.
(ii) If an inductor and a resistor are connected in series in an ac circuit, what
Q.2 A power transmission line feeds input power at 2200 V to a step down
will be the mathematical expression for the impedance of this circuit. How will
transformer with its primary windings having 3000 turns. Find the number of
the impedance get affected when the frequency of applied signal is decreased
turns in the secondary winding to get the power output at 220 V.
and why?
Q.3 A bulb B and a capacitor C are connected in series to the ac mains. The bulb
glows with some brightness. How will the glow of the bulb change when a
Level –2
dielectric slab is introduced between the plates of the capacitor? Give reasons Q.1 A device X is connected across as AC source of voltage 𝑉 = 𝑉𝑚 sin 𝜔𝑡. The
in support of your answer. 𝜋
current through X is given as 𝑖 = 𝑖𝑚 𝑠𝑖𝑛 (𝜔𝑡 + 2 ).
SA – II (3 Marks each) (i) Identify the device X and write the expression for its reactance.
Level – 1 (ii) Draw graphs showing variation of voltage and current with time over one
Q.1 What is inductive reactance? If an AC voltage is applied across an inductance cycle of AC, for X
L, find an expression for the current I flowing in the circuit. Also show the (iii) How does the reactance of the device X vary with frequency of the AC?
phase relationship between current and voltage in a phasor diagram. Show this variation graphically.
Q.2 What is capacitive reactance? If an ac voltage is applied across a capacitance (iv) Draw the phasor diagram for the device X.
C, find an expression for the current I flowing in the circuit. Also show the
phase relationship between current and voltage in a phasor diagram. Level – 3
Q.1 A device ‘X’ is connected to an ac source. The variation of voltage, current
Q.3 If the frequency of alternating current is tripled, how will it affect resistance R,
and power in one complete cycle is shown in the figure
inductive reactance XL and capacitive reactance XC?
Q.4 For a given ac circuit, differentiate between resistance, reactance and
impedance.

133 134
 used as the core material because it is a soft ferromagnetic substance and (iv) What is the impedance of a capacitor with capacitance C in an ac circuit
hence reduces hysteresis losses. Typical transformers have power having source of frequency 50 Hz
efficiencies from 90% to 99%. In the discussion that follows, we assume an (a) 1/C (b) 1/50 C (c)1/100 C (d) 1/314 C
ideal transformer, one in which the energy losses in the windings and core CCT Based Question:
are zero.
Q.1 An airport metal is essentially a resonant circuit. The portal you step through
1. Name the different types of losses involve in transformer. is an inductor (a large loop of conducting wire) that is part of the circuit. The
2. How to minimise eddy current losses in transformer? frequency of the circuit is tuned to the resonant frequency of the circuit when
3. What cause the Hysteresis loss? there is no metal in the inductor. Any metal on your body increases the
4. Which type of transformer used at the receiving end? effective inductance of the loop and changes the current in it. When you pass
through a metal detector, you become part of a resonant circuit. As you step
through the detector, the inductance of the circuit changes, and thus the
Competency based questions: current in the circuit changes.
Q.1 An alternating current is that whose magnitude changes continuously with
time and direction reverses periodically and the current that flows with same
magnitude in same direction is direct current.
(i) If an ammeter is used to measure alternating current in circuit, which value
of current will it read
(a) Peak (b) rms (c) Instantaneous (d) Average
(ii) If T is the time period of given alternating current, then how much time it
requires to reach its peak value starting from zero
(a) T (b) T/2 (c) T/4 (d) T/8
(iii) What is the average value of alternating current over one complete cycle
(a) 0 (b) Im (c) Im/2 (d) Im/4
(iv)For a 220 V mains of alternating voltage peak value will be
(a) 220 V (b) 220/√2 V (c) 220√2 V (d) 110 V 1. What is resonance?
2. On what factors does resonance frequency depends?
Q.2 Quantity that measures the opposition 3. For the metal detector to detect a small metal object the sharpness of the
offered by a circuit to the flow of current is current versus frequency graph be more or less? Justify your answer.
called impedance. For an ac circuit, 4. What is impedance of the circuit at resonance?
reactance corresponding to inductor and
capacitor is also considered, along with **********
resistance. So, impedance for the ac circuit
can be given mathematically as Z2 = R2 + X2,
where X is the reactance.
Impedance triangle is a right-angled triangle given as in the diagram and
satisfy the above mathematical equation. Also phase angle ∅ between
current and voltage can be given by using this impedance triangle.
(i) Impedance for a purely capacitive circuit depends on
(a) f (b) 2f (c) 1/f (d) 1/2f
(ii) Impedance for a purely inductive circuit depends on
(a) f (b) 2f (c) 1/f (d) 1/2f
(iii) For ac circuit containing resistor only, value of Φ will be
(a)0 (b) π/2 (c) - π/2 (d) π

137 138
 (i) If an ammeter is used to measure alternating current in circuit, UNIT V ELECTROMAGNETIC WAVES
which value of current will it read
(a) Peak (b) rms (c) Instantaneous (d) Average CH–8: Electromagnetic Waves
(ii) If T is the time period of given alternating current, then how
much time it requires to reach its peak value starting from zero GIST OF CHAPTER
(b) T (b) T/2 (c) T/4 (d) T/8
(iii) What is the average value of alternating current over one Basic idea of displacement current, Electromagnetic waves, their characteristics,
complete cycle their transverse nature (qualitative idea only). Electromagnetic spectrum (radio
(b) 0 (b) Im (c) Im/2 (d) Im/4 waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including
(iv)For a 220 V mains of alternating voltage peak value will be elementary facts about their uses.
(b) 220 V (b) 220/√2 V (c) 220√2 V (d) 110 V
Section – E
CONTENT/ CONCEPTS-
12 Explain with the help of a labelled diagram, the principle and 5
working of an ac generator. Write the expression for the emf Basic idea of displacement current
generated in the coil in terms of speed of rotation. Can the current Conduction Current (ic)- Conduction current is the current, which arises due to flow
produced by an ac generator be measured with a moving coil of electrons through the connecting wires in an electric circuit. Displacement current
galvanometer? (id)-Displacement current is the current, which arises due to time rate of change of
OR electric flux ( E).
12 (i) A device ‘X’ is connected to an ac source. The variation of 5 Flaw in Ampere’s circuital law
voltage, current and power in one complete cycle is shown in the
Modified Ampere’s circuital law states that the line integral of magnetic field B over
figure.
a closed boundary of an open surface is equal to, times the sum of the conduction
current (Ic) and the displacement current (Id) threading the surface.
Maxwell’s Equations: - Following four equations, which describe the laws of
electromagnetism, are called Maxwell‟s equations
(i) ∮EdS . = q/∈ 0 (Gauss‟s law in electrostatics)
(ii) ∮EdS . =0 (Gauss‟s law in magnetism)
(iii) ∮EdS . = d∅/𝑑𝑡 (Faraday‟s law of electromagnetic induction)
(a) Which curve shows power consumption over a full cycle? (iv) ∮EdS . =𝜇0 (Ic+Id)( (Ampere-Maxwell‟s circuital law)
(b) What is the average power consumption over a cycle? ELECTROMAGNETIC SPECTRUM:
(c) Identify the device ‘X’. Type of Radiation Frequency Range (Hz) Wavelength Range
(ii) A light bulb is rated as 150 W for 220 V AC supply of 60 Hz.
Calculate Gamma-rays 1020 – 1024 < 10-12 m
(a) resistance of the bulb
(b) the rms current through the bulb. X-rays 1017 – 1020 1 nm – 1 pm

Ultraviolet 1015 – 1017 400 nm – 1 nm

**********
Visible 4 x 1014 – 7.5 x 1014 750 nm – 400 nm

Near-infrared 1 x 1014 – 4 x1014 2.5 μm – 750 nm

Infrared 1013 – 1014 25 μm – 2.5 μm

Microwaves 3 x 1011 – 1013 1 mm – 25 μm

Radio waves < 3 x 1011 > 1 mm

141 142
 LEVEL 3- MCQ
ASSERTION AND REASON QUESTION
Q1. The relative magnetic permeability of the medium is 2.5 and the relative
electrical permittivity of the medium is 2.25. Compute the refractive index of the Directions: These questions consist of two statements, each printed as Assertion
medium. and Reason. While answering these questions, you are required to choose any one
of the following four responses.
(a) 2.37 (b) 4.75 (c) 0.25 (d) 1.05
Q2. Compute the speed of the electromagnetic wave in a medium if the amplitude (a) If both Assertion and Reason: are correct and the Reason: is a correct
of electric and magnetic fields are 3 × 104 and 2 × 10-4 tesla, respectively explanation of the Assertion.
(a)3 ×108m/s (b) 1.5 × 108m/s (c) 6 × 108 m/s (d) 5 ×108 m/s (b) If both Assertion and Reason: are correct but Reason: is not a correct
Q.3 As the speed decreases if we change the medium of electromagnetic waves explanation of the Assertion.
from air to water, the frequency (c) If the Assertion is correct but Reason: is incorrect.
(a) also decreases (b) also increases (c) remains same (d) may increase or (d) If both the Assertion and Reason: are incorrect.
decrease
Q1. Assertion: Electromagnetic waves are transverse in nature.
Q 4 When the medium of electromagnetic waves changes from air to water, their Reason: The electric and magnetic fields are perpendicular to each other and
speed perpendicular to the direction of propagation.
(a) increases (b) remains same (c)decreases (d)may increase or decrease
Q2. Assertion: The electromagnetic wave is transverse in nature.
L-3 HIGHER ORDER QUESTION(NEET/JEE)
Reason: Electromagnetic waves propagate parallel to the direction of electric and
magnetic fields.
Q.1 Which of the following are not electromagnetic waves? (cbse pmt ) 1
a) gamma rays b) beta rays c) x rays d)heat rays Q3. Assertion: The velocity of electromagnetic waves depends on electric and
Q.2 The structure of the solid is investigated by using (cbse pmt) 1 magnetic properties of the medium.
a) cosmic rays b) x rays c) Gamma rays d) Infrared radiations Reason: Velocity of electromagnetic waves in free space is constant.
Q.3 The energy of the electromagnetic wave is of the order of 15kev.to which part 1
of the spectrum does it belong. Q.4 Assertion: The frequencies of incident, reflected and refracted beams of
monochromatic light incident from one medium to another are the same.
a) gamma rays b) X- rays c)Infra res rays d) ultraviolet rays (AIPMT2015)
Reason: The incident, reflected and refracted rays are coplanar.
Q.4 The ratio of contributions made by the electric and magnetic components to 1
the intensity of electromagnetic wave is ( c= is speed of em wave) Q.5.Assertion: The earth without its atmosphere will be inhospitably cold.
a) 1:1 b) 1: c c) 1: c2 d) c : 1 NEET 2020
Q.5. A radiation energy E falls normally on a perfect reflecting surface. The Reason: All heat would escape in the absence of atmosphere.
momentum transferred to the surface ( c – velocity of light) is 1
a) 2E/c b) 2E/c2 c) E /c2 d) E/c (AIPMT2015) Q.6 Assertion: Microwaves are better carriers of signal than optical waves.
Q6. Out of the following options which one can be used to produced a propagating 1 Reason: Microwaves move faster than optical waves.
electromagnetic wave. (NEET 2016)
a) A charge moving at constant velocity Q.7 Assertion: Gamma rays are more energetic than x rays.
b) A stationary charge Reason: Gamma rays are of nuclear origin but x rays are produced due to sudden
c) A charge less particle deceleration of high energy electrons while falling in the metal of high atomic
d) An accelerating charge number.
Q.7.A 100 ohm resistance and a capacitor of 100ohm reactance are connected in 1
series across 220V source. When the capacitor is 50% charged ,the peak value of
L1-SHORT ANSWER QUESTIONS (2 MARKS)
the displacement is
Q.1 Why are infrared waves called heat waves. Explain. What do you understand 2
a) 4.4A b) 11√2 A c) 2.2A d) 11A (NEET 2016) by the statement “Electromagnetic waves transport momentum”?
Q.8. The dimension of(𝜇0𝜀0)-1/2 are 1 Q.2 Why are infrared radiations also referred as heat waves? Write the name of 2
a) L1/2 T-1/2 b) L-1T c) LT-1 d) L-1/2T1/2 (CBSE PMT 11,12) radiations which lie next to infrared radiations in the electromagnetic spectrum.

145 146
 CCT BASED
4 Q.1 Which wavelength of the Sun is used finally as electric energy? 1
The electromagnetic spectrum consists of visible light, x- rays, gamma rays, M (a) radio waves (b) infrared waves (c) visible light (d) microwaves
microwaves, ultraviolet rays, radio waves and infrared waves. The waves used in
radio and television communication are the radio waves having frequency range Q.2 Which of the following electromagnetic radiations have the longest 1
500 kHz to 1000MHz. In the ultrahigh frequency bands cellular phones use the wavelength?
radio waves to transmit the voice. Microwaves are the waves having short (a) X-rays (b) UV-rays (c) microwaves (d) radio waves
wavelengths. In aircraft navigation, for the radar system microwaves are used due Q.3 Which one of the following is not electromagnetic in nature? 1
to their short wavelength. Infrared waves are also called heat waves. Infrared (a) X-rays (b) gamma rays (c) cathode rays (d) infrared rays
radiation has the most importance in maintaining earth’s surface temperature
through the greenhouse effect. The infrared waves have vast applications in real Q.4 (v) The decreasing order of wavelength of infrared, microwave, ultraviolet and 1
life such as infrared detectors that are used for military purposes and also to see gamma rays is
the growth of crops. The waves which are visible to the human eye are the visible
(a) microwave, infrared, ultraviolet, gamma rays
rays. Visible rays are having frequency range as 4x1014Hz to 7x1014 Hz. The huge
(b) gamma rays, ultraviolet, infrared, microwave
source of ultraviolet light is the sun. Ultraviolet rays have wavelength range from (c) microwave, gamma rays, infrared, ultraviolet
4x10-7m to 6x10-10m. X-rays are the rays having most importance in medical (d) infrared, microwave, ultraviolet, gamma rays
applications which have a wavelength range 10nm to10 -4 nm. X-rays are used to
destroy the living tissue and organisms in the medical field. Then gamma rays are
the rays having wavelength range as 10-10m to 10-14m which are the high frequency
radiations mostly produced in nuclear reactions. Gamma rays are also used to **************
destroy cancer cells in the medical field.

Q.1The TV waves range from _____ which are the radio waves. 1
M
(a) 54Hz to 890Hz (b) 54 MHz to 890 MHz (c) 500 kHz to 1000 MHz (d) 1000
Hz to 1000 KHz

Q.2 The domestic application of microwaves used is____ 1

M
(a) electric induction (b) water heater (c) TV (d) microwave oven

Q.3 The part of the electromagnetic spectrum which is detected by human eye is 1
having wavelength range as M

a) 900 – 400 nm b) 200 – 400 mm c) 700 – 400 mm d) 700 – 400 nm

Q.4 Why infrared waves are also called heat waves? 1

OR M
How does the ozone layer in the atmosphere play a protective role?

COMPETENCY BASED QUESTION

All the known radiations from a big family of electromagnetic waves which stretch
over a large range of wavelengths. Electromagnetic wave include radio waves,
microwaves, visible light waves, infrared rays, UV rays, X-rays and gamma rays.
The orderly distribution of the electromagnetic waves in accordance with their
wavelength or frequency into distinct groups having widely differing properties is
electromagnetic spectrum.

149 150
 UNIT- VI OPTICS According to new cartesian sign conventions, when the image formed is real
(inverted), the magnification produced by the mirror is negative and when the image
CH-9 RAY OPTICS & OPTICAL INSTRUMENTS formed is virtual (erect), the magnification produced by the mirror is positive.

GIST Spherical aberration. The inability of a spherical mirror of large aperture to bring all
the rays in a wide beam of light falling on it to focus at a single point is called spherical
Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction of light, aberration.
total internal reflection and optical fibers, refraction at spherical surfaces, lenses, thin
lens formula, lens maker‟s formula, magnification, power of a lens, combination of thin 2. Refraction of Light
lenses in contact, refraction of light through a prism. Refraction. The phenomenon of change in the path of light as it goes from one
Optical instruments: Microscopes and astronomical telescopes (reflecting and medium to another is called refraction.
refracting) and their magnifying powers. Laws of refraction.
Reflection of Light 1. The incident ray, the normal to the refracting surface at the point of incidence and
Reflection. When light travelling in a medium strikes a reflecting surface, it goes back the refracted ray all lie in the same plane.
into the same medium obeying certain 2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction
laws. This phenomenon is known as reflection of light. is constant for any two- given media. It is called Snell's law.
𝑠𝑖𝑛𝑠𝑖𝑛 𝑖
Laws of reflection. 1. The incident ray, the normal to the reflecting surface at the Mathematically- = 𝜇𝑏𝑎
𝑠𝑖𝑛𝑠𝑖𝑛 𝑟
point of incidence and the reflected ray all lie in the same plane.
Absolute refractive index (𝜇). The absolute refractive index of a medium is defined
2. The angle of incidence (i) is always equal to the angle of reflection (r). as ratio of the velocity of light in vacuum (c) to the velocity of light in that medium(v).
Spherical mirror. The portion of a reflecting surface, which forms part of a sphere, is Real and apparent depth. When an object is placed in an optically denser medium,
called a spherical mirror. the apparent depth of the object is always less than its real depth.
Concave spherical mirror. A spherical mirror, whose reflecting surface is towards Mathematically-: 1.
𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ
= 𝜇𝑏𝑎
the centre of the sphere, of which the mirror forms a part is called concave spherical 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ
mirror. 1
2. Normal shift d= t (1 − )
𝜇𝑏𝑎
Convex spherical mirror. A spherical mirror, whose reflecting surface is away from
the centre of the sphere of which the mirror forms a part is called convex spherical Total internal reflection. The phenomenon of reflection of light that takes place when
mirror. a ray of light travelling in a denser medium gets incident at the interface of the two
Relation between f and R: f =R/2 media at an angle greater than the critical angle for that pair of media.
1
According to new cartesian sign conventions, both f and R, are taken as negative for Mathematically 𝜇𝑏𝑎 = 𝑠𝑖𝑛 𝐶
a concave mirror and positive for a convex mirror.
𝜇𝑏𝑎 is refractive index of the denser medium £ w.r.t. the rarer medium a and C is the
1 1 1
Mirror formula + = critical angle.
𝑣 𝑢 𝑓
Spherical refracting surface. The portion of a refracting medium, whose curved
where u and v denote the object and image distances from the pole of the mirror.
surface forms the part of a sphere, is called spherical refracting surface.
According to new cartesian sign conventions, the distances of the real objects and real
images (both lie in front of the mirror) are taken as negative, while those of virtual When object is situated in the rarer medium, the relation is as follows
objects and virtual images (both lie behind the mirror) are taken as positive. 𝜇1 𝜋2 𝜇2 −𝜇1
- 𝑢
+ 𝑣
= 𝑅
Linear magnification. The ratio of the size of the image (formed by the mirror) to the
When the object is situated in denser medium, the relation is as follows
size of the object is called linear magnification produced by the mirror.
𝜇2 𝜇1 𝜇1 −𝜇2
𝐼 𝑣 𝑓 𝑓−𝑣 - + =
Mathematically- m = = −𝑢 = = 𝑢 𝑣 𝑅
𝑂 𝑓−𝑢 𝑓

𝜇2 −𝜇1
Power of spherical refracting surface: P= 𝑅
Here, R is measured in metre.

153 154
 LEVEL-1 (MCQ QUESTIONS)
CONCEPT MAP
1 A convex lens of power 4D and a concave lens of power 3D are placed in contact.
What is the equivalent power of the combination?
4 3
a) 7D b) D c)1D d) D
3 4

2 An object approaches a convergent lens from the left of the lens with a uniform
speed
5 m/s and stops at the focus. The image
(a) moves away from the lens with a uniform speed 5 m/s.
(b) moves away from the lens with a uniform acceleration.
(c) moves away from the lens with a non-uniform acceleration.
(d) moves towards the lens with a non-uniform acceleration.
3 The refractive index of the material of an equilateral prism is √3 .What is the angle
of Minimum deviation?
(a) 45° (b) 60° (c) 37° (d) 30°
4 An object is placed at the focus of the convex mirror. If its focal length is 20cm,
the distance of image from the mirror is
(a)10cm (b)20cm (c)40cm (d)None
5 In an experiment to find focal length of a concave mirror, a graph is drawn between
the magnitude of u and v. The graph looks like:

6. Air bubble in water behaves as

(a) sometimes concave, sometimes convex lens
(b) concave lens
(c) convex lens
(d) always refracting surface
7 A ray of light passes from glass (μ = 1.5) to water (μ = 1.33). The value of the
critical angle of glass is _____ .
(a) sin-1 8/9 (b) sin-1√ 8/9 (c) sin-1 ½ (d) sin-1 2/1

158
157
 a)Zero b)f/2 c)f d)2f 3 Which of the following actions will lead to an increase in the magnifying power

5 When a thin convex lens of glass 5D is immersed in a liquid, it behaves as a of an astronomical telescope?
divergent lens of focal length 100 cm. What is the refractive index of the liquid?
A. Increase in the length of the telescope tube.
a)1/3 b)2/3 c)3/5 d)5/3 B. Interchange the objective and the eyepiece of the telescope.

6 incident on a glass plate at an incident angle of 60°. If reflected and refracted rays C. A small piece of paper on the objective of the telescope pointed towards
are mutually perpendicular, then refractrive index of the glass plate is _____ .
the moon.
(a)√2 (b) √3 (c)1/√2 (d)1/√3
D. Increase in the focal length of the objective and decrease in the focal length
7 Light of certain colour has 2000 waves in a millimeter in air. What will be the
wavelength of this light in medium of refractive index 1.25 ? of the eye piece.
(a) 1000 (b) 2000 (c) 3000 (d) 4000 4 A real image of size p times the size of an object is formed by a concave mirror
8 A convex lens of glass (n = 1.5) has focal length of 20 cm. The lens is immersed of focal length f.
in water of refractive index 1.33. The change in the focal length of convex lens is
(a) 1.86 cm (b) 58.2 cm (c) 4.62 cm (d) 6.44 cm What is the object distance from the mirror?
A. (p+1)*f/p B. (p‐1)*f/p C. p*f/(p+1) D. p*f/(p‐1)
9 For a thin lens when the heights of the object and the image are equal, object
distance and image distance are equal to _____ . 5 Read the following statements carefully:
(a)f (b) 4f (c) 3f (d) 2f
I. A drop of an oil in water or in a glass, both behave as convergent lens.
10 the refractive index of an equilateral prism when light is incident at grazing II. A water drop in air and a glass sphere in water, both behave as convergent
incidence and emerges at grazing emergence:
lens.
a)1.5 b) 1.8 c) 1.33 d) 2
III. An air bubble in water and a water bubble in glass, both behave as a
LEVEL 3 (MCQ QUESTIONS)
divergent lens.
1 A biconcave lens of power P vertically splits into two identical plano-concave parts.
IV. A frozen ice crystal inside a glass sphere and a bromine liquid drop inside a
The power of each part will be
(a) 2P (b) P/2 (c) P (d) P/√2 glass sphere, behave as divergent lens.

2 An incident light ray falls on a glass prism at an angle of 60o and emerges with [Reference values of refractive indices of common substances: Air = 1.001;

an angle of 30 with its initial incident direction. Water = 1.33; ice = 1.31; Glass = 1.51; Oil = 1.4; Bromine = 1.66]

If the angle of the prism is 30o, then which of the following is an INCORRECT Select the correct option.
A. Statements I and II are correct.
statement?
B. Statements I and III are correct.
A. Refractive index of the prism is √3.
C. Statements II and III are correct.
B. The light undergoes minimum deviation through the prism (i.e., r1 = r2).
D. Statements II and IV are correct
C. The emergent ray is perpendicular to the face from which it emerges.
6 An object is moved towards a concave mirror at a constant speed, from infinity
D. Angle of refraction r1 at the incident face is same as angle of the prism.
to its focus. Which of the following statements correctly describe the
corresponding motion in the image formed by the concave mirror?

161 162
 3 a)How does the angle of minimum deviation produced by a prism change with
increase in (i) the wavelength of incident light, and (ii) the refracting angle of
prism?
b) A glass prism is held in water. How is the angle of minimum deviation affected?
LEVEL-3 (2 M QUESTIONS)
c) When does a ray passing through a prism deviate away from its base?
1 (a) The bluish colour predominates in the clear sky. Why?
LEVEL - 3 (3 M QUESTIONS)
(b) Violet colour is seen at the bottom of the spectrum when white light is dispersed
by a prism. State reasons to explain these observations. 1 i)Redraw the diagram below and mark the position of the centre of curvature of
the spherical mirror used in the given set up
2 Write 4 advantages of reflecting type telescope over refracting type?
3 A concave lens made of material of refractive index ‘n2’is held in a reference
medium of refractive index ‘n1’. Trace the path of parallel beam of light passing
through the lens when: i)n1 = n2 (ii) n1 < n2 (iii) n1 > n2 . In which case the lens
will behave as plain glass? ii) State the principle of reversibility of light.
LEVEL-1 (3 M QUESTIONS) 2 Which two of the following lenses L1, L2 and L3 will you select as objective and
eyepiece for constructing the best possible (i) telescope (ii) microscope? Give
1 An equi-convex lens of radius of curvature R is cut into two equal parts by a vertical reason to support your answer. iii)the aperture of the objective of ……….. is
plane, so it becomes a Plano convex lens. If f is the focal length of the equi-convex preferred to be large?
lens, then what will be focal length of Plano convex lens?
2 Derive mirror equation for a convex mirror for real image.

3 a)A biconvex lens made of a transparent material of refractive index 1.25 is

immersed in water of refractive index 1.33. Will the lens behave as a converging
or a diverging lens? Give a reason.
3 a) Write the two important factors considered to increase the magnifying power of
b) A convex lens is placed in contact with a plane mirror. A point object at a a refracting type telescope.
distance of 20 cm on the axis of this combination has its image coinciding with
itself. What is the focal length of the lens? Draw related Ray Diagram. b)Two convex lenses A and B of an astronomical telescope having focal lengths
5cm and 20 cm respectively, are arranged as shown in the
4 Using the ray diagram for a system of two lenses of focal lengths f1 and f2 in
contact with each other, show that two lens system can be regarded as equivalent i)Which one of two lenses you will select to use
to a single lens of focal length f, where as objective lens and why?
(ii) What should be the change in the distance
between the lenses to have the telescope in its
normal adjustment position?
Also write the relation for the equivalent power of the lens combination.
(iii) Calculate magnifying power of telescope in the normal adjustment position
5 Derive thin prism formula
LEVEL-1 (5 M QUESTIONS)
LEVEL-2 (3 M QUESTIONS)
1. a) Derive expression for the lens maker's formula, i.e.,
1 Produce a relation between real depth and apparent depth.
1 1 1
𝐹
= (𝜇 − 1) [𝑅1 − 𝑅2
] where the symbols have their usual meanings. Why is it
2 Using MIRROR FORMULA , show that a convex mirror always produces a virtual
known as Lens Maker’s formula.
image, independent of the location of the object & draw the related ray diagram.

165 166
The reflecting telescope, which uses mirrors to collect and focus light, was COMPETENCY BASED QUESTIONS
invented within a few decades of the first refracting telescope.
A ray of light travels from a denser to a rarer medium. After refraction, it bends
In the 20th century, many new types of telescopes were invented, including radio
away from the normal. When we keep increasing the angle of incidence, the angle
telescopes in the 1930s and infrared telescopes in the 1960s..
of refraction also increases till the refracted ray grazes along the interface of two
media. The angle of incidence for which it happens is called critical angle. If the
1. angle of incidence is increased further the ray will not emerge and it will be
reflected back in the denser medium. This phenomenon is called total internal
reflection of light.

i) The magnifying power of an astronomical telescope in normal adjustment is 100.

What is the focal length of the objectives and eyepiece of the distance between
i)A ray of light travels from a medium into the water
them is 101 cm?
at an angle of incidence of 18°. The refractive
a. 1 cm and 10 cm respectively
index of the medium is more than that of water and
b. 1 cm and 100 cm respectively the critical angle for the interface between the two
c. 10 cm and 1 cm respectively media is 20°. Which one of the following figures
d. 100 cm and 1 cm respectively best represents the correct path of the ray of light?

ii) If the focal length of the objective lens is increased then ii) A point source of light is placed at the bottom of
a)Magnifying power of microscope will increase but that of telescope will decrease a tank filled with water, of refractive index µ, to a depth h. The area of the surface
b)Magnifying power of microscope and telescope both will increase of water through which light from the source can emerge is:
c)Magnifying power of microscope and telescope both will decrease a)πh²/2(μ²-1) b) πh²/(μ²-1)
d)The magnifying power of microscope will decrease but that of the telescope will
increase c) πh²/(√2√(μ²-1)) d) 2πh²/(μ²-1)
iii) Is the formula "Real depth/Apparent depth =µ" valid if viewed from a position
.iii) The magnifying power of a telescope is 9. When it is adjusted for parallel rays, quite away from the normal?
the distance between the objective and the eye-piece is found to be 20 cm. The
focal lengths of the lenses are iv) A diver in a swimming pool wants to signal his distress to a person lying on the
a) 18 cm, 2 cm b) 11 cm, 9 cm c)10 cm, 10 cm d) 15 cm, 5 cm edge of the pool by flashing his water proof flash light
a) He must direct the beam vertically upwards
iv) ) In a compound microscope, magnifying power is 95 and the distance of the
object from the objective lens is 1/38 cm. The focal length of the objective lens ¼ b) He has to direct the beam horizontally
cm. What is the magnification of eyepiece? c) He has to direct the beam at an angle to the vertical which is slightly less than
a) 5 b) 10 c) 100 d) 200 the critical angle of incidence for total internal reflection

169 170
 SELF ASSESMENT TEST A biconcave lens of power P vertically splits into two identical plano-concave parts. 1
5. The power of each part will be
Note: Q. No. 1-4 is of 01 mark each, Q. No. 5-6 is of 02 marks each, Q.No.7 is of
03 marks, Q. No. 8 is a case study based and is of 04 marks, Q. No. 11 is of 5
(a) 2P (b) P/2 (c) P (d) P/√2
marks.
A prism has refractive angle 60°. When a light ray is incident at 50°, then minimum 1
SN Question M 6. deviation is obtained. What is the value of minimum deviation?
ar (a) 40° (b) 45° (c) 50° (d) 60°
ks An object is placed in front of a concave mirror of focal length 20 cm. The image
Half of the lens is wrapped in black paper. How will it change the image? 7. formed is three times the size of the object. Calculate two possible distances of the 2
1. a)Size of image is halved 1 object from the mirror?
b)Intensity of image is halved A ray of light passing from air through an equilateral glass prism undergoes
8. minimum deviation when the angle of incidence is 3/4 of the angle of prism. 2
c)There is no change in the size of image or intensity Calculate the speed of light in the prism.
Three rays 1,2, 3 of different colours fall normally on one of the sides of an isosceles
d) intensity of the image is reduced
right angled prism as shown in fig. The refractive indices of prism for these rays are
A student measures the focal length of a convex lens by putting an object pin at a 9. 1.39, 1.47 and 1.52 respectively. Find which of these rays get normally reflected
2. distance 'u' from the lens and measuring the distance 'v' of the image pin. The graph 1 and which get only refracted from AC. Trace the path of rays. Justify your answer
between 'u' and 'v' plotted by the student should look like with the necessary calculations ? 3

10 Two parallel light rays pass through an isosceles prism of refractive index √3/2 as 3
shown in the figure. The angle between the two emergent rays is :

Assertion (A): Refractive index of glass with respect to air is different for red light
and violet light.
Reason (R): Refractive index of a pair of media does not depends on the
3. wavelength of light used. 1 CASE BASED QUESTION
a- Both assertion and reason are correct and the reason is the correct
explanation of assertion. Lens maker’s formula relates to the focal length (f) of a lens to the refractive index
b- Both assertion and reason are correct and the reason is not a correct of the lens and the radii of the curvature of its two surfaces. The focal length of the
explanation of assertion. lens depends upon the refractive index of the material used for making the lens and
c- Assertion is correct but the reason is incorrect 11 the radius of curvature. This formula is used by the manufacturers for making the 4
d- Assertion is incorrect but the reason is correct. desired lens; that’s it is called the lens maker’s formula.
Assertion: The focal length of the convex mirror will increase, if the mirror is placed Limitations of the lens maker’s formula. The lens should not be thick so that the
4. inwater. space between the 2 refracting surfaces can be small.
Reason: The focal length of a convex mirror of radius R is equal to , f = R/2 1 The medium used on both sides of the lens should always be the same. An array
of simple lenses with a common axis can be used to multiply the magnification of
an image. The real image formed by one lens can be used as the object for another
lens, combining magnifications. Two lenses at this separation form the simplest
173 174
 UNIT VI-OPTICS (i) By division of wavefront: In this method the wavefront (which is the locus of points
CH10: WAVE OPTICS of same phase) is divided into two parts. The examples are Young’s double slit and
Fresnel’s biprism.
GIST OF THE CHAPTER: (ii) By division of amplitude: In this method the amplitude of a wave is divided into
two parts by successive reflections, e.g., Lloyd’s single mirror method.
1. Wave Nature of Light: Huygen’s Theory 4. Interference of Light
There are some phenomena like interference, diffraction and polarisation which could
Interference is the phenomenon of superposition of two light waves of same frequency
not be explained by Newton’s corpuscular theory. These were explained by wave
and constantphase different travelling in same direction. The positions of maximum
theory first proposed by Huygen.
intensity are called maxima, while those of minimum intensity are called minima.
The assumptions of Huygen’s wave theory are: (i) A source sends waves in all 𝒏𝑫𝝀 𝟏 𝑫𝝀
possible directions.The locus of particles of a medium vibrating in the same phase is 𝒙𝒎𝒂𝒙𝒊𝒎𝒂 = 𝒙𝒎𝒊𝒏𝒊𝒎𝒂 = (𝒏 − )
𝒅 𝟐 𝒅
called a wavefront. For a point source, the wavefront is spherical; while for a line
𝜆𝐷 𝛽 𝜆
source the wavefront is cylindrical. A distant wavefront is plane. (ii) Each point of a Linear Fringe width= β = 𝑑
angular fringe width=𝐷 = 𝑑
wavefront acts as a source of secondary wavelets. The envelope of all wavelets at a
given instant gives the position of a new wavefront. Condition for sustained interference
(i) The two sources of light must be coherent which means the two light waves emitted
2. Wavefront by them must have a constant phase difference or in the same phase.
A wavefront is defined as the locus of all the particles which are vibrating in the same (ii) The two sources must emit light of the same wavelength but the amplitudes
phase. The perpendicular line drawn at any point on the wavefront represents the between them should differ as little as possible. The emitted waves should be
direction of propagation of the wave at that point and is called the ‘ray’. preferably of the same amplitude to get completely dark fringes.
Types of Wavefronts: The wavefronts can be of different shapes. In general, we (iii) The two sources should be very narrow. Otherwise with the increase of slit width,
experience three types of wavefronts. the coherence property will be lost. Hence, no interference pattern will be obtained.
(i) Spherical Wavefront: If the waves in a medium are originating from a point source, (iv) The two sources must lie very close to each other. Otherwise overlapping of bright
then they propagate in all directions. If we draw a spherical surface centred at point- and dark points will hinder interference.
source, then all the particles of the medium lying on that spherical surface will be in
5. Diffraction of Light
the same phase, because the disturbance starting from the source will reach all these The bending of light from the corner of small obstacles or apertures is called diffraction
points simultaneously. Hence in this case, the wavefront will be spherical and the rays of light.
will be the radial lines. 2𝜆𝐷 2𝜆
Linear central maxima= 2y= angular central maxima=
(ii) Cylindrical Wavefront: If the waves in a medium are originating from a line source, 𝑎 𝑎
then they too propagate in all directions. In this case the locus of particles vibrating in Difference between Diffraction and Interference
the same phase will be a cylindrical surface. Hence in this case the wavefront will be Interference Diffraction
cylindrical. Interference may be defined as waves Diffraction, on the other hand, can be
emerging from two different sources, termed as secondary waves that
(iii) Plane Wavefront: At large distance from the source, the radii of spherical or
producing different wavefronts. emerge from the different parts of the
cylindrical wavefront will be too large and a small part of the wavefront will appear to same wave.
be plane. At infinite distance from the source, the wavefronts are always plane and The contrast between maxima and The contrast between maxima and
the rays are parallel straight lines. minima is very good. minima is poor.
3. Coherent and Incoherent Sources of Light The sources of light emitting waves The width of the fringes in interference The width of the fringes is not equal in
of same frequency having zero or constant initial phase difference are called coherent is equal. diffraction.
sources.The sources of light emitting waves with a random phase difference are called
incoherent sources.For interference phenomenon, the sources must be coherent.
Methods of Producing Coherent Sources: Two independent sources can never be
coherent sources. There are two broad ways of producing coherent sources for the
same source.

177 178
 LEVEL 3 MCQ Reason : There will be an effect on clarity if the waves are of unequal intensity.
11 How can the fringe width increase in Young’s double-slit experiment? 19 Assertion : In YDSE, if a thin film is introduced in front of the upper slit, then
a. By decreasing the width of the slit the fringe pattern shifts in the downward direction.
b. By reducing the separation of slits Reason : In YDSE if the slit widths are unequal, the minima will be completely
c. By reducing the wavelength of the slits dark.
d. By decreasing the distance between slits and the screen
20 Assertion : Diffraction takes place for all types of waves mechanical or non-
12 What is the locus of all particles in a medium vibrating in the same phase mechanical, transverse or longitudinal.
called? Reason : Diffraction’s effect are perceptible only if wavelength of wave is
a. Fringe b.Wavelet c.Wavefront d.None of the above comparable to dimensions of diffracting device.
LEVEL 1 (2M QUESTIONS)
13 Which of the following factors does the intensity of light depend on?
a. Frequency b.Wavelength c.Amplitude d.Velocity 1 Write the important characteristic features by which the Interference can be
distinguished from the observed diffraction pattern.
14 Two light sources are said to be coherent when both the sources of light emit 2 One of the slits of Young’s double-slit experiment is covered with a semi-
light of transparent paper so that it transmits lesser light. What will be the effect on the
a. The same amplitude and phase
interference pattern?
b. The same intensity and wavelength
c. The same speed 3 A parallel beam of light of wavelength 600 nm is incident normally on a slit of
d. The same wavelength and constant phase difference width ‘a’. If the distance between the slits and the screen is 0.8 m and the distance
of 2nd order maximum from the centre of the screen is. 15 mm, calculate the
15 Which of the following is conserved when light waves interfere? width of the slit.
a. Intensity b. Amplitude c. Phase d. None of the above
LEVEL 2 (2M QUESTIONS)
ASSERTION AND REASON TYPE 4 (i) State the principle on which the working of an optical fibre is based.
Directions: These questions consist of two statements, each printed as Assertion (ii) What are the necessary conditions for this phenomenon to occur?
and Reason. While answering these questions, you are required to choose any one 5 Why are coherent sources necessary to produce a sustained interference
of the following four responses. pattern?
(a) If both Assertion and Reason are correct and the Reason is a correct explanation 6 Write the distinguishing features between a diffraction pattern due to a single slit
of the Assertion. and the interference fringes produced in Young’s double-slit experiment?
(b) If both Assertion and Reason are correct but Reason is not a correct explanation 7 In what way is diffraction from each slit related to the interference pattern in a
of the Assertion. double-slit experiment?
(c) If the Assertion is correct but Reason is incorrect.
(d) If both the Assertion and Reason are incorrect. LEVEL 3 (2M QUESTIONS)
8 When a tiny circular obstacle is placed in the path of light from a distance source,
16 Assertion : According to Huygen’s principle, no backward wave-front is a bright spot is seen at the centre of the shadow of the obstacle. Explain, why?
possible. 9 Write the conditions under which light sources can be said to be coherent.
Reason : Amplitude of secondary wavelet is proportional to (1 + cos θ) where 10 Why is it necessary to have coherent sources in order to produce an interference
θ is the angle between the ray at the point of consideration and the direction pattern?
of secondary wavelet.
17 Assertion : No interference pattern is detected when two coherent sources LEVEL-1 (3M QUESTIONS)
are infinitely close to each other.
1 A plane wavefront propagating in a medium of
Reason : The fringe width is inversely proportional to the distance between
refractive index µ1 is incident on a plane surface
the two sources.
making the angle of incidence i as shown in the figure.
18 Assertion : It is necessary to have two waves of equal intensity to study
It enters into a medium of refractive index µ2 (µ2>
interference pattern.
µ1). Use Huygens’ construction of secondary
181 182
 LEVEL 2 (5M QUESTIONS) (e) If the phase difference between the two waves reaching two slits from the
source slit is (i) 5π and (ii) 2π, then what will be the colour of central fringe?
4 (a) In Young’s double slit experiment, deduce the conditions for obtaining 9 A slit of width ‘a’ is illuminated by white light.
constructive and destructive interference fringes. Hence deduce the expression (a) For what value of a will the first minimum for red light of λ = 650 nm be at θ =
for the fringe width. 15°?
(b) Show that the fringe pattern on the screen is actually a superposition of single (b) What is the wavelength λ' of the light whose first side diffraction maximum is
slit diffraction from each slit. at 15°, thus coinciding with the first minimum for the red light?
(c) What should be the width of each slit to obtain 10 maxima of the double slit
pattern within the central maximum of the single slit pattern, for green light of LEVEL -1 (NUMERICALS)
wavelength 500 nm, if the separation between two slits is 1 mm? 1 Two plane monochromatic waves propagating in the same direction with
5 (a) Using Huygen’s construction of secondary wavelets explain how a diffraction amplitudes A and 2A and differing in phase by 𝜋/3 superimpose. Calculate the
pattern is obtained on a screen due to a narrow slit on which a monochromatic amplitude of resulting wave.
beam of light is incident normally. 2 Two slits are made 1mm apart and the screen is placed 1m away. What is the
(b) Show that the angular width of the first diffraction fringe is half that of the fringe separation when blue green light of wavelength 500nm is used?
central fringe.
LEVEL -2 (NUMERICALS)
(c) Explain why the maxima at become weaker and weaker with 1 A slit of width ‘d’ is illuminated by light of wavelength 5000Å. For what value of ‘d’
increasing n. will the first maximum fall at an angle of diffraction of 30o.
6 (a) Write three characteristic features to distinguish between the interference 2 Two spectral lines of sodium D1 and D2 have wavelengths approximately 5890Å
fringes in Young’s double slit experiment and the diffraction pattern obtained due and 5896Å. A sodium lamp sends incident plane wave on to a slit of width 2
to a narrow single slit. micrometer. A screen is located 2m from the slit. Find the spacing between the
(b) A parallel beam of light of wavelength 500 nm falls on a narrow slit and the first maxima of two sodium lines as measured on the screen.
resulting diffraction pattern is observed on a screen 1 m away. It is observed that LEVEL -3 (NUMERICALS)
the first minimum is a distance of 2.5 mm away from the centre. Find the width of 1 If one of the two identical slits producing interference in Young’s experiment is
the slit. covered with glass, so that light intensity passing through it is reduced to 50%,
LEVEL 3 (5M QUESTIONS) find the ratio of the maximum intensity of the fringes in the interference pattern.

7 State the essential condition for diffraction of light to take place. CASE BASED QUESTIONS
Use Huygen’s principle to explain diffraction of light due to a narrow single slit 1 Wavefront is a locus of points which vibrate in same phase. A ray of light is
and the formation of a pattern of fringes obtained on the screen. Sketch the perpendicular to the wavefront. According to Huygens principle, each point of the
pattern of fringes formed due to diffraction at a single slit showing variation of wavefront is the source of a secondary disturbance and the wavelets connecting
intensity with angle θ. from these points spread out in all directions with the speed of wave. The figure
8 Red colour of light of wavelength λ is passed from two narrow slits which are shows a surface XY separating two transparent media, medium-1 and medium-
distance d apart and interference pattern is obtained on the screen distance 2. The lines ab and cd represent
Dapart from the plane of two slits. Then find the answer to following parts wavefronts of a light wave
assuming that slit widths are equal to produce intensity I0 from each slit. travelling in medium- 1 and
(a) Intensity at a point on the screen, situated at a distance 1/4 th of fringe incident on XY. The lines ef and
separation from centre. gh represent wavefronts of the
(b) Intensity in the screen, if the sources become incoherent by using two light wave in medium -2 after
different lamps behind lamps S1 and S2. refraction.
(c) Angular position of 10th maxima, and the angular width of that fringe. (i) Light travels as a
(d) Find the distance between 5th maxima and 3rd minima, at same side of a) parallel beam in each medium
central maxima. b) convergent beam in each medium
c) divergent beam in each medium
185 186
 SELF ASSESSMENT 7 Name the phenomenon which is responsible for bending of light 2
Time allowed: 1 hour Max. marks: 25 around sharp corners of an obstacle. Under what conditions does
Q.No. QUESTIONS MARKS this phenomenon take place? Give one application of this
MCQ phenomenon in everyday life
1 Two waves are said to be coherent if they have. 1 8 A parallel beam of light of 600 nm falls on a narrow slit and the 2
(a) same phase and different amplitude resulting diffraction pattern is observed on a screen 1.2 m away. It
(b) different frequency phase and amplitude is observed that the first minimum is at a distance of 3 mm from
(c) same frequency but different amplitude the centre of the screen. Calculate the width of the slit.
(d) same frequency, phase and amplitude 9 .(a) If one of two identical slits producing interference in Young’s 3
2 A linear aperture whose width is 0.02 cm is placed immediately in 1 experiment is covered with glass, so that the light intensity passing
front of a lens of focallength 60 cm. The aperture is illuminated through it is reduced to 50%, find the ratio of the maximum and
normally by a parallel beam of wavelength5 × 10 –5 cm. The minimum intensity of the fringe in the interference pattern.
distance of the first dark band of the diffraction pattern from the (b) What kind of fringes do you expect to observe if white light is
centre of the screen is used instead of monochromatic light?
(a) 0.10 cm (b) 0.25 cm 10 Two wavelengths of sodium light 590 nm and 596 nm are used, in 3
(c) 0.20 cm (d) 0.15 cm turn, to study the diffraction taking place at a single slit of aperture
2 × 10–4 m. The distance between the slit and the screen is 1.5 m.
3 For light diverging from a point source 1 Calculate the separation between the positions of the first maxima
a) the wavefront is spherical of the diffraction pattern obtained in the two cases.
b) the intensity decreases in proportion to the distance 11 CASE BASED QUESTION 4
squared. For constructive interference, the path difference is equal to
c) the wavefront is parabolic. integral multiple of wavelengths and resultant intensity will be
(d) the intensity at the wavefront does not depend on the maximum at that points. While for destructive interference, the
distance. path difference is (n + 1/2) multiple of wavelengths and where
4 In Young’s double-slit experiment, the distance between the slit 1 resultant intensity is zero. When light is passed around the sharp
sources and the screen is 1 m. fringe width is edges of an obstacle it get bended and may enters into the
(a) 3 mm (b) 0.3 mm (c) 6 mm (d) 0.6 nm geometrical shadow of that obstacle such a phenomenon of light
is called as diffraction of light. In interference, there are equally
• Question no. 5 and 6 are assertion and reason type questions.
spaced alternate bright and dark bands are possible. While in
• Directions: These questions consist of two statements, each printed as
diffraction, the there is a only one bright central Maxima and
Assertion and Reason. While answering these questions, you are required to
around both sides of the central Maxima the intensity of the light
choose any one of the following four responses.
decreases as we go away from that central Maxima.
(a) If both Assertion and Reason are correct and the Reason is a correct
Q I.) For coherent sources of light the phase
explanation of the Assertion.
difference must be___
(b) If both Assertion and Reason are correct but Reason is not a correct
a) one
explanation of the Assertion.
b) zero
(c) If the Assertion is correct but Reason is incorrect.
c) either zero or constant
(d) If both the Assertion and Reason are incorrect.
d) 90°
5 Assertion : In Young’s double slit experiment if wavelength of 1 Q II.) If the phase difference is 0, +2π, -4π then the
incident monochromatic light is just doubled, number of bright interference should be
fringe on the screen will increase. a)constructive interference
b) destructive interference
Reason : Maximum number of bright fringe on the screen is c) both a and b
inversely proportional to the wavelength of light used d) diffraction of light
6 Assertion : Thin film such as soap bubble or a thin layer of oil on 1 Q III.) For destructive interference
water show beautiful colours when illuminated by white light. a) path difference is (n +1/2) times wavelength
Reason : It happens due to the interference of light reflected b) phase difference is π, -3π, +5π
from upper and lower face of the thin film c) path difference is integral multiple of wavelengths

189 190
Hertz’s observation: -While demonstrating the existence of electromagnetic waves, Hertz The Effect of the Potential:-
found that high voltage sparks passed across the metal electrodes of the detector loop more
easily when the cathode was illuminated by ultraviolet light from an arc lamp. The uv light falling
The photoelectric current increases with increase in
on metal surface caused the emission of negatively charged particles (electrons) into
accelerating (positive) potential of collector plate.
surrounding space and enhance the high voltage sparks.
For a certain positive potential of plate A, the
photoelectric current becomes maximum and
Hallwachs and Lenard Observation: - It was observed that if the frequency of incident
constant or saturates. This maximum value of the
light is less than certain minimum value (Threshold frequency) emission of photo electrons
photoelectric current is called saturation current.
do not takes place.
Saturation current corresponds to the case when all
Threshold frequency. The minimum frequency (𝑣𝑶), which the incident light must possess the photoelectrons emitted by the emitter plate C
so as to eject photoelectrons from a metal surface, is called threshold frequency of the reach the collector plate A.
metal. Saturation current increases with increase in intensity of incident radiation. The
Mathematically- Work function W = h𝑣𝑶 photoelectric current decreases with negative potential of collector plate.
Laws of photoelectric effect.
STOPPING POTENTIAL (𝑉0):-
1. Photoelectric emission takes place from a metal surface, when the frequency of incident
At certain negative potential of the collector plate the photocurrent becomes zero. This negative
light is above its threshold frequency.
potential is called STOPPING POTENTIAL (𝑉0).
2. The photoelectric emission starts as soon as the light is incident on the metal surface. The stopping potential is measure of maximum kinetic energy of photoelectron.

3. The maximum kinetic energy with which an electron is emitted from a metal surface is 1/2 mv2max = eVo
independent of the intensity of light and depends upon its frequency. Where 𝑣𝑚𝑎𝗑 is the maximum velocity with which the photoelectrons are emitted

4. The number of photoelectrons emitted is independent of the frequency of the incident

light and depends only upon its intensity. Effect of intensity of incident radiation on stopping potential
❖ Stopping potential does not change on changing the intensity of incident radiation.
The Effect of Intensity:- ❖ The maximum kinetic energy of photoelectron thus does not depend on intensity
of incident radiation.
The number of electrons emitted per second is observed to be directly proportional to the intensity
of light.
This happens above the threshold frequency.
Below this threshold frequency there is no
photocurrent at all, howsoever high the
intensityof light is.

The graph between the photoelectric current

straight line when the frequency of light used
is value.

193 194
 MIND MAP

197

198
 a. Magnetic field only b. Electric field only c. Electromagnetic field d. None of potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the
the above stopping potential is V/4. The threshold wavelength for the metallic surface is
14. The photoelectric effect is based on the law of conservation of a. 4λ b. 5λ c. 5/2λ d. 3λ.
7. In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the
a. Energy b. Momentum c. Mass d. Angular momentum voltage is changed to 224 kV, then the de Broglie wavelength associated with the
15. Photon does not possess electrons would
a. increase by 2 times b. decrease by 2 times c. decrease by 4 times
a. Energy b. Momentum c. Rest Mass d. Frequency
d. increase by 4 times.
16. The momentum of a photon of wavelength λ is
a. hλ b. h/λ c. λ/h d. h/c λ 8. A particle of mass 3 × 10–6 g has the same wavelength as an electron moving with a
17. Maximum KE of photo electrons is 4 e V Then the stopping potential is velocity 6×106 m s−1. The velocity of the particle is
a. 4 V b. 1.6 V c. 4 J d. 4 e V a. 1.82×10−18 m s−1 b. 9×10−2 m s−1 c. 3×10−31m s−1 d. 1.82×10−15 m s−1
18. The slope of stopping potential vs frequency of the incident light graph is 9. If a light of wavelength 330 nm is incident on a metal with work function 3.55 eV, the
a. e/h b. h/e c. h/c d. c/h. electrons are emitted. Then the wavelength of the emitted electron is (Take h = 6.6 ×
19. Photoelectric effect shows 10–34 Js)
a. wave like behavior of light a. < 2.75×10−9 m b. ≥ 2.75×10−9 m c. ≤ 2.75×10−12 m d. < 2.5×10−10 m
b. particle like behavior of light 10. A photoelectric surface is illuminated successively by monochromatic light of
c. both wavelike and particle like behavior wavelength λ and λ/2. If the maximum kinetic energy of the emitted photoelectrons in
d. neither wave like nor particle like behavior of light. the second case is 3 times that in the first case, the work function at the surface of
20. An electron and a proton have the same de Broglie wave length. Which of them material is
have greater velocity? a) hc/λ b) 2hc/ λ c) hc/3λ d) hc/2λ
a. Electron b. proton. c. both a and b d. none of the above. LEVEL 3
1. In photoelectric emission, a radiation whose frequency is 4 times threshold frequency
LEVEL 2 of a certain metal is incident on the metal. Then the maximum possible velocity of the
1. Photoelectric emission from a given surface of metal can take place when the value emitted electron will be
of a physical quantity is less than the energy of incident photon. The physical quantity
is
a. threshold frequency b. work function of surface c. threshold wavelength
d. stopping potential
2. The photoelectric work function for a metal surface is 4.14eV. The cut-off wavelength
for this is
a. 4125 A˚ b. 2062.5A˚ c. 3000A˚ d. 6000A˚
3. 1eV is energy acquired by an electron when it is accelerated through potential
difference of –
a. 1 V b. 2 V c. 3 V d. 4 V.
4. An electron, an alpha particle, a deutron and a proton have the same KE. which 2. Two radiations with photon energies 0.9 eV and 3.3 eV respectively are falling on a
one has shortest de Broglie wavelength? metallic surface successively. If the work function of the metal is 0.6 eV, then the ratio
a. α particle b. electron c. proton d. deutron. of maximum speeds of emitted electrons will be
a) 1:4 b) 1:3 c) 1:1 d) 1:9
5. Photons of energies 1eV and 2eV are successively incident on a metallic surface of
work function 0.5eV. The ratio of kinetic energy of most energetic photoelectrons in 3. A light source of wavelength 520 nm emits 1.04 × 1015 photons per second while the
the two cases will be second source of 460 nm produces 1.38 × 1015 photons per second. Then the ratio
a. 1:2 b.1:1 c. 1:3 d.1:4. of power of second source to that of first source is
a) 1.00 b) 1.02 c) 1.5 d) 0.98
6. When a metallic surface is illuminated with radiation of wavelength λ, the stopping

201 202
 4. Work function of sodium is 2.3eV. Does sodium show photo electric emission for
LEVEL 3 light of wavelength 6800A˚
11. Assertion: Photosensitivity of a metal is high if its work function is small. 5. Do all the electrons that absorb a photon come out as photoelectrons?
Reason: Work function = hf0 where f0 is the threshold frequency.
12. Assertion: In an experiment on photoelectric effect, a photon is incident on an LEVEL 3
electron from one direction and the photoelectron is emitted almost in the opposite direction. 1.The graph shows variation of stopping potential Vo verses frequency of incident
It violates the principle of conservation of linear momentum. radiation ϑ for two photosensitive metals A
Reason: It does not violate the principle of conservation of linear momentum. and B. (i) Which of the two metals has
13. Assertion: Two sources of equal intensity always emit equal number of photons higher threshold frequency and why? (ii)
in any time interval. What does intercept on –ve y axis
Reason: Two sources of equal intensity may emit equal number of photons in any time represent?
interval.
14. Assertion: Two photons of equal wavelength must have equal linear momentum.
Reason: Two photons of equal linear momentum will have equal wavelength.
2.The variation of the stopping potential (v0) with the
15. Assertion: The kinetic energy of photoelectrons emitted from metal surface does
frequency (v) of the light incident on two different
not depend on the intensity of incident photon.
photosensitive surfaces M1 and M2 is shown in the figure.
Reason: The ejection of electrons from metallic surface is not possible with
Identify the surface which has greater value of the work
frequency of incident photons below the threshold frequency.
function.

2 MARKS QUESTIONS 3.Show that the wavelength of electromagnetic radiation is

equal to the de-Broglie wavelength of its quantum.
LEVEL 1
1. If the wavelength of an electromagnetic radiation is doubled what will happen to the
3 MARKS QUESTIONS
energy of photons?
2. Two metals A and B have work functions 4 eV and 10 eV, respectively. Which metal
LEVEL 1
has higher threshold wavelength? 1. In photoelectric effect, why should the photoelectric current increase as the intensity
3. A proton and an electron have same kinetic energy. Which one has greater de-Broglie of monochromatic radiation incident on a photosensitive surface is increased?
wavelength and why? Explain.
4. Two lines, A and B, in the plot given below show the variation of de-Broglie 2. Light of wavelength 3500 Å is incident on two metals A and B. Which metal will yield
wavelength, λ versus 1√V, Where V is the accelerating potential difference, for two more photoelectrons if their work functions are 5 eV and 2 eV respectively?
particles carrying the same charge. Which one of two represents a particle of smaller 3. Plot a graph showing the variation of photo current vs collector potential for
mass? three different intensities I1 > I2 > I3, two of which (I1 and I2) have the same
5. An alpha particle and a proton are accelerated through same potential difference. frequency ν and the third has frequency ν1 > ν.
Find the ratio (vᾳ/vp) of velocities acquired by two particles. 4. Show the variation of photocurrent with collector plate potential for different
6. What is the effect of wavelength of incident photons on velocity of photoelectrons? A frequencies but same intensity of incident radiation.
beam of monochromatic radiation is incident on a photosensitive surface. Do the 5. Define the terms (i) cut-off voltage and (ii) threshold frequency in relation to the
emitted photoelectrons have the same kinetic energy? Explain. Phenomenon of photoelectric effect. Using Einstein’s photoelectric equation show
LEVEL 2 how the cut -off voltage and threshold frequency for a given photosensitive material
1. Electrons are emitted from a photosensitive surface when it is illuminated by green can be determined with the help of a suitable plot.
light but electron emission does not take place by yellow light. Will the electrons be .
emitted when the surface is illuminated by (i) red light, (ii) blue light?
2. A proton, a neutron, an electron and α particle have same energy. Then their de-
Broglie wavelengths compare as?
3. Why do we not observe the phenomenon of photoelectric effect with non-metal?

205 206
 LEVEL 2 COMPETENCY BASED QUESTIONS

5. Monochromatic light of frequency 6x1014 Hz is produced by a laser. The power 1. According to wave theory of light, the light of any frequency can emit electrons from
emitted is 2x103 W i) what is the energy of photon in the light? ii) How many photons metallic surface provided the intensity of light be sufficient to provide necessary
per second on the average are emitted by the source? energy for emission of electrons, but according to experimental observations, the light
6. In an experiment on photoelectric emission, following observations were made 1) of frequency less than threshold frequency cannot emit electrons; whatever be the
Wavelength of the incident light = 2 × 10–7m 2) Stopping potential = 3V Find (i) kinetic intensity of incident light. Einstein also proposed that electromagnetic radiation is
energy of photoelectrons with maximum speed (ii) work function. quantized. If photoelectrons are ejected from a surface when light of wavelength λ1
7. The work function of Cesium metal is 2.14eV. When light of frequency 6 x 10 14Hz is = 550 nm is incident on it. The stopping potential for such electrons is Vs =0.19. If
incident on the metal surface photoemission of electrons occurs. a. What is the photoelectrons are ejected from a surface when light of wavelength λ1 = 550 nm is
maximum kinetic energy of the emitted photoelectrons b. stopping potential c. incident on it. The stopping potential for such electrons is Vs =0.19. Suppose the
maximum speed of the emitted photoelectrons? radiation of wavelength λ2 = 190 nm is incident on the surface.

LEVEL 3 i) Photoelectric effect supports quantum nature of light because

8. Light of wavelength 2000 A0 falls on an aluminum surface. In aluminum 4.2 eV are a. there is a minimum frequency of light below which no photoelectrons are emitted.
required to remove an electron. What is the kinetic energy of (a) fastest (b) the b. the maximum K.E. of photoelectric depends only on the frequency of light and not
on its intensity
slowest photoelectron?
c. even when the metal surface is faintly illuminated, the photo electrons leave the
9. Using the graph shown in the figure for stopping potential surface immediately.
v/s the incident frequency of photons, calculate Planck’s d. electric charge of the photoelectrons is quantized.
constant.
10. The Kinetic Energy (K.E.), of a beam of electrons, ii) Calculate the stopping potential Vs2 of surface.
accelerated through a potential V, equals the energy of a. 4.47 b. 3.16 c. 2.76 d. 5.28
a photon of wavelength 5460 nm. Find the de Broglie
wavelength associated with this beam of electrons iii) Calculate the work function of the surface
a. 3.75 b. 2.07 c. 4.20 d. 3.60
CASE BASED QUESTIONS
iv) Calculate the threshold frequency for the surface
a. 500 x 1012 Hz b. 480 x 1013 Hz c. 520 x 1011 Hz d. 460 x 1013 Hz
1) According to de-Broglie a moving material particle sometimes acts as a wave and
sometimes as a particle or a wave is associated with moving material particle 2. Observations in Photoelectric Effect
which controls the particle in every respect. The wave associated with moving
1. For each metal there is a characteristic minimum frequency below which
material particle is called matter wave or de-Broglie wave whose wavelength
called de-Broglie wavelength, is given by λ = h/mv photoelectric effect is not observed. This is called threshold frequency. If frequency
of light is less than the threshold frequency, there is no ejection of electrons no matter
i) If the momentum of a particle is doubled, then its de-Broglie wavelength will how long it falls on surface or how high is its intensity.
a. remains unchanged b. become four times c. become two times 2. The kinetic Energy of electrons emitted is directly proportional to frequency of
d. become half striking photons & independent of their intensity.
3. The no. of electrons that are ejected per second from metal surface depends upon
ii) If an electron and proton are propagating in the form of waves having the same λ
, it implies that they have the same intensity of striking radiations and doesn’t depend upon their frequency.
a. Energy b. Momentum c. Velocity d. angular momentum 4. If frequency of incident light is more than threshold frequency, then the excess
energy is imparted to electrons in the form of kinetic energy.
iii) Velocity of a body of mass m, having de-Broglie wavelength λ , is given by relation
a. v = λ h/m b. v = λm/h c. v = λ/hm d. v = h/ λm i) Electrons are emitted with zero velocities from metal surface when exposed to
radiation of wavelength 6800Ao. Calculate (ν0 = photon’s frequency & W0 = work
iv) Moving with the same velocity, which of the following has the longest de Broglie function)?
wavelength? a. 3.21x 10 12 /sec & 9.7 x 10 -19 J
a. ᵦ -particle b. α -particle c. proton d. neutron. b. 4,14x 10 14 /sec & 2.92 x 10 -19 J

209 210
 (a) A (b) B (c) C (d) D UNIT VIII ATOMS AND NUCLEI
7. The energy required to remove electron from sodium is 2.3 eV. Does sodium show
photoelectric effect for orange light of wavelength 6800A o? CHAPTER 12-ATOMS
8. The given graphs show the variation of the
Gist
stopping potential V0 with the frequency ν of the
incident radiations for two different - Early atomic models and their limitations. Thomson’s model of atom
photosensitive materials A and B. Which one of
-Rutherford’s alpha ray scattering experiment
the two has higher value of work function?
Justify your answer. -Rutherford’s model of atom .
9. A proton and a deuteron are accelerated
- Bohr’s model of the atom and its postulates.
through the same accelerating potential.
Which one of the two has (a) greater value of de-Broglie wavelength associated - Hydrogen atom spectrum and energy level transitions.
with it (b) less momentum? Give reasons to justify your answer.
1. Introduction to Atomic Models
10. The work function for certain metal is 1.8 eV. (a) What is the stopping potential for
electrons ejected from metal, when light of 4000Ao shines on the metal? (b) What is - Dalton’s Atomic Theory: Early concept
the maximum speed of the ejected electrons? of the atom as an indivisible particle.
11. According to de-Broglie a moving material particle sometimes acts as a wave and
sometimes as a particle or a wave is associated with moving material particle which - Discovery of Electrons and Nucleus :
controls the particle in every respect. The wave associated with moving material Introduction to the electron discovered by
particle is called matter wave or de-Broglie wave whose wavelength called de-Broglie J.J. Thomson and the nucleus
wavelength, is given by λ = h/mv discovered by Rutherford through the
i) The dual nature of light is exhibited by gold foil experiment.
a. diffraction and photo electric effect b. photoelectric effect c. refraction and
interference d. diffraction and reflection
ii) If the momentum of a particle is doubled, then its de-Broglie wavelength will 2. Rutherford’s Model of the Atom
a. remains unchanged b. become four times c. become two times d. become half
iii) If an electron and proton are propagating in the form of waves having the same λ, - Description of the gold foil experiment.
it implies that they have the same
a. Energy b. Momentum c. Velocity d. angular momentum Setup of the Gold Foil Experiment
iv) Velocity of a body of mass m, having de-Broglie wavelength λ, is given by relation
a. v = λ h/m b. v = λm/h c. v = λ/hm d. v = h/ λm
12. a) What is photo electric effect? State the characteristics of photoelectric effect.
b) Explain effect of following terms on the photo electric current.
i) Intensity of light
ii) Frequency of light
iii) Potential difference between anode and cathode. OR
a) Derive the expression for the de Broglie wavelength of an electron moving under
a potential difference of V volts.
b) A deuteron and an alpha particle are accelerated through the same accelerating
potential. Which one of the two has-
(I) greater value of de Broglie wavelength (II)Less kinetic energy? Explain. Apparatus - A source of alpha particles (helium nuclei), a thin sheet of gold foil, a
fluorescent screen, and a detector.

********* Alpha Particles : High-energy particles emitted from a radioactive source, typically
radium or polonium.

213 214
 MIND MAP /CONCEPT MAP

5. Success and Limitations of Bohr’s Model

- Success in explaining the hydrogen atom spectrum and its limitations.

- Failure to explain spectra of multi-electron atoms and finer spectral details (Zeeman
effect and Stark effect).
Formulae :

1.Magnitude of force of α particle:

2.Total energy of the electron

3.Angular Momentum

4.Frequency of emitted photon

5.Radius of nth possible orbit

6.Energy of an electron
7.Difference in energy levels

8.The energy of an electron in Bohr’s orbit of hydrogen atom is given by the expression

Since Z = 1 for hydrogen En = -13.6/n2 eV

217 218
 - C) The speed of electrons in the atom 6.For an electron orbit to be non-radiating, it should be
- D) The mass of the nucleus A) such that the angular momentum should be integral multiple of h.
B) circular in nature
6.The ionisation potential of hydrogen is 13.6 V. The energy of the atom in n = 2 state C) elliptical in nature
will be D) none of these
A) -10.2 eV B) -6.4eV C) – 3.4 eV D)– 4.4 eV
7.The ratio of the angular momentum of an electron in first orbit to that in the second
7.In Bohr’s model of the hydrogen atom, the ratio between the period of revolution of an orbit is
electron in the orbit n = 1 to the period of revolution of electron in the orbit n = 2 is A) ½ B)1/4 C) 4/1 D) 2
A) ½ B) ¼ C)1/8 D) 2
8.The ionisation energy of hydrogen atom is E. When the electron in a hydrogen atom
8.To explain fine structure of spectrum of hydrogen atom, we must consider. jumps from the state n = 1 to the state n = 2, the energy absorbed by it is …………………
A) a finite size of nucleus. A) 3E/4 B) 4E/3 C) E/4 D) E/3
B) the presence of neutrons in the nucleus.
C) spin angular momentum. 9.In the Bohr model of the atom, which of the following quantities takes quantized
D) orbital angular momentum. values?**

9.When an electron jumps from some outer orb it to the innermost orbit in the hydrogen A) Linear momentum of electron B) Radius of electron orbit
atom, the spectral line belongs to
A) Lyman series C) Angular momentum of electron D) None of the above
B) Balmer series
C) Paschen series 10.The ionization energy of hydrogen is 13.6 eV. The energy required to remove an
D) Pfund series electron from the second orbit of Li2+ is:

A) 13.6 Ev B) 30.6 eV C) 40.8 eV D) 122.4 eV

10.How does the energy difference between two consecutive energy levels vary on the
quantum number n increases?
A) does not change 2 marks Questions
B) decreases
C) increases Level 1
D) may increase or decrease. Q1.Define ionisation energy. What is its value for a hydrogen atom?
Q2.Write the expression for Bohr’s radius in hydrogen atom.
Level 3 Q3.What is the ratio of radii of the orbits corresponding to first excited state and ground
state in a hydrogen atom?
1.If the electron in hydrogen atoms is excited to n = 5 state, the number of different Q4.Why is the classical (Rutherford) model for an atom—of electron orbiting around the
frequencies of radiation which may be emitted is: nucleus—not able to explain the atomic structure?
A) 4 B) 10 C) 8 D) 5 Q5.What is the maximum number of spectral lines emitted by a hydrogen atom when it
is in the third excited state?
2.The ionisation potential of hydrogen is 13.6 V. The energy of the atom in n = 2 state
will be Level 2
A) -10.2 ev B) -6.4eV C) – 3.4 eV D) – 4.4 eV Q1. What are the values of first and second excitation potential of hydrogen atom?
Q.2 The wavelength of some of the spectral lines of obtained in hydrogen spectrum are
3.The ratio of the energies of the hydrogen atom in its first to second excited state is : 1216 A0 , 6463 A0 and and 9546 A0 Which one of these wavelength belongs to the
A) ¼ B) 4/9 C) 9/4 D) 1/9 paschen series.
Q3.Name the series of Hydrogen spectrums lying in ultraviolet and visible regions.
4.When an electron jumps from some outer orb it to the innermost orbit in the hydrogen Q4. what are results What is 4 Do you expect if alpha particle, scattering experiment is
atom, the spectral line belongs to repeatedly using a thin sheet of hydrogen in place of a gold foil?
A) Lyman series B) Balmer series C) Paschen series D) Pfund series Q5.Define ionisation energy. What is its value for a hydrogen atom?

5.According to classical theory, Rutherford atom is

A) stable B) unstable C) metastable D) semistable

221 222
Case based study question / Source based question SELF ASSESSMENT TEST
Each element is having specific properties as it emits or shows the specific emission Total marks =25 Time = 40 Mins.
spectrum of radiation. The emission line spectrum has bright lines on the dark surface.
The hydrogen spectrum consist of series namely Balmer, Lyman, Paschen, Brackett and Question 1 to 6 each of 1 mark
Pfund series. The Lyman series is formed in the ultraviolet region while Paschen, Question 7to8 each of 2 mark
Brackett and Pfund series are in the infrared region. According to Bohr’s first postulate, Question 9to 10:each of 3 mark
electrons are revolving in particular stable orbits without radiating any form of energy. Question 11 of 4 mark
Question 12 is of 5 marks
And in his second postulate he told that, these electrons are revolving around the nucleus
in stable orbits which are having angular momentum equal to integral multiple of h/2π.
Q1.What is the main limitation of Rutherford’s model?
And third postulate tells us that, when electron jumps from higher energy state to lower
- A) Could not explain atomic spectra
energy state it will emits some amount of energy and which is equal to the energy - B) Could not explain the charge of the nucleus
difference between those energy levels. - C) Could not explain the mass of the atom
- D) Could not explain the behaviour of neutrons
And he gave the energy of an electron in an hydrogen atom as En = -13.6/ n2 eV

The negative sign shows that electron is tightly bound with the nucleus. And when n = 1, Q2 The spectral lines of hydrogen were explained using:
then corresponding energy of electron is called as ground state energy. Bohr’s model is - A) Thomson’s model B) Rutherford’s model C) Bohr’s model D) Dalton’s model
only applicable to single electron system like hydrogen and it cannot be applicable to
helium atom also which is having two electrons. Q3.Two H atoms in the ground state collide inelastically. The maximum amount by which
their combined kinetic energy is reduced is
Read the above passage and answer the rolling questions . -A) 10.20 eV - B) 20.40 eV - C) 13.6 eV - D) 27.2 eV
Q4.The Bohr model for the spectra of a H - atom.
1.) In hydrogen atom, the ground state energy is given by___
a) +13.6 Ev b) -13.6 J c) -13.6 KJ d) -13.6 eV
- A) will not be applicable to hydrogen in the molecular form
- B) will not be applicable as it is for a He -atom.
2.) According to Bohr’s second postulate, the angular momentum L is given by
a) L= h/2π b) L = nh/2π c) L = 2π/h d) L = 2π/ nh - C) is valid only at room temperature
- D) predicts continuous as well as discreeter spectral lines .
3.) What is the shortest wavelength in the Balmer series
a) 656.3 nm b) 364.6 nm c) 656.3 mm d) 364.6 mm Directions for Assertion-Reason Type Questions

4.) For ground state of hydrogen atom the value of principal quantum number is___ In each of the following questions, a statement of assertion (A) is followed by a statement
a) n = 2 b) n = 0 c) n = 1 d) n = infinity of reason (R). Mark the correct choice as: - (a) Both Assertion (A) and Reason (R) are
Competency Based Question true and Reason (R) is the correct explanation of Assertion (A). - (b) Both Assertion (A)
and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
Q1.Explain how the observation of spectral lines can be used to identify elements in
distant stars. - (c) Assertion (A) is true but Reason (R) is false.
Q2.Discuss the significance of the Balmer series in the context of hydrogen's atomic
spectrum and its application in astronomy. - (d) Assertion (A) is false but Reason (R) is true.
Q5.Assertion (A): in alpha rays, scattering experiment, most of the alpha particle goes
CCT BASED QUESTION on deflected.
Reason (R): most of the space in the atom is empty
A hydrogen atom is excited from its ground state (n = 1) to the n = 3 energy level. The Q6.Assertion (A): In Bohr’s model of the atom, the angular momentum of the electron is
atom then returns to the ground state by emitting photons.
quantized.
1. Describe how the wavelengths relate to the hydrogen emission spectrum. Reason (R): The electron in an atom revolves in circular orbits around the nucleus under
the influence of electrostatic forces.
2. Discuss the implications of these transitions in the context of Bohr's model of the Q7.State the limitations of Bohr’s atomic model
atom.

225 226
 • Mass defect (m) : It is found that the mass of a nucleus is always less than
Fission
the sum of masses of it's constituent nucleons in free state. This difference in fragm
masses is called mass defect. Hence mass defect
m = Sum of masses of nucleons – Mass of nucleus 235U
Fissio Neutr
   
= Zm p + ( A − Z)m n − M = Zm p + Zm e + ( A − Z)m z − M '
Neutr
n

where mp = Mass of proton, mn = Mass of each neutron, me = Mass of each Fission reaction of U235
electron 92 U
235
+ 0 n1 → 92 U
236
→ 56 Ba
141
+ 36 Kr
92
+ 3 0 n1 + Q
(unstable nucleus)
M = Mass of nucleus,Z = Atomic number, A = Mass number, M = Mass of atom
https://upload.wikimedia.org/wikipedia/commons/a/a0/PressurizedWaterReactor.gif
as a whole.
• Nuclear Fusion
• Binding energy (B.E.) P n P
(1) In nuclear fusion two or more than P 3He 4He P
The binding energy of a nucleus may be defined as the energy equivalent to the mass two lighter nuclei combine to form a P 2
H
P P
P n P n
P
defect of the nucleus. n n n n
single heavy nucleus. The mass of P
P P P
If m is mass defect then according to Einstein's mass energy relation single nucleus so formed is less than  e  +

P
Binding energy = m c2= [{mpZ + mn(A – Z)} – M]c2 the sum of the masses of parent nuclei. This
If m is measured in amu then B.E = mamu = [{mpZ + mn(A – Z)} – M] amu = m difference in mass results in the release of tremendous amount of energy
931 MeV Fission
fragment
• Binding energy per nucleon : The average energy required to release a
nucleon from the nucleus is called binding energy per nucleon.
Binding energy per nucleon Mind map
Total bind ing energy m  931 MeV 235U
= = Neutrons
Mass number (i.e. total number A Nucleon Fission
Neutrons
fragment
of nucleons)

• Binding Energy Curve

Fig. 26.18

It is the graph between binding energy per nucleon and total number of nucleons
(i.e. mass number A)
56
26Fe
Binding energy per

8.0 He
nucleon (MeV)

6.0
4.0 Li

2.0
H2
0
5056 10 15 20
0 number
Mass 0 0
A
Fig. 26.17

(1) Some nuclei with mass number A< 20 have large binding energy per nucleon than
their neighbour nuclei. For example 2 He 4 , 4 Be 8 , 6 C 12 , 8 O 16 and 10 Ne 20 . These nuclei are more
stable than their neighbours.
(2) The binding energy per nucleon is maximum for nuclei of mass number A = 56
( 26 Fe 56 ) . It's value
is 8.8 MeV per nucleon.
(2) For nuclei having A> 56, binding energy per nucleon gradually decreases for
uranium (A = 238), the value of binding energy per nucleon drops to 7.5 MeV.
• Nuclear Fission
(1) The process of splitting of a heavy nucleus into two lighter nuclei of comparable
masses (after bombardment with a energetic particle) with liberation of energy is called
nuclear fission.

229 230
10. The masses of neutron and proton are 1.0087 a.m.u. and 1.0073 a.m.u. 5)Two nuclei have mass number in the ratio 1 : 3. What is the ratio of their
respectively. If the neutrons and protons combine to form a helium nucleus (alpha nuclear densities?
particles) of mass 4.0015 a.m.u. The binding energy of the helium nucleus will be
(1 a.m.u.= 931 MeV) LEVEL 2
(a) 28.4 MeV (b) 20.8 MeV (c)27.3 MeV (d) 14.2 MeV short answer type ( 2 MARKS )
1) Calculate the energy equivalent of 1amu in MeV.
LEVEL 3 2) Distinguish between nuclear fission and nuclear fusion.
1. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the 3) State the necessary condition for nuclear fission.
ratio 8 : 1. The ratio of radii of the fragments is 4)Define atomic mass unit.
5) Write the number of proton and neutron in 56Ba144.
(a)1 : 2 (b)1 : 4 (c) 4 : 1 (d) 2 : 1 6)Two nuclei have mass number 3:9 what is their nuclear density ratio.
2. 1 g of hydrogen is converted into 0.993 g of helium in a thermonuclear reaction. The
LEVEL 3
energy released is short answer type ( 2 MARKS )
1) When 92 U 235 undergoes fission. 0.1% of its original mass is changed into
(a) 63  107 J (b) 63  1010 J (c)63  1014 J (d) 63  1020 J energy. How much energy is released if 1 kg of 92 U 235 undergoes fission?
3. The binding energy per nucleon of O16 is 7.97 MeV and that of O17 is 7.75 MeV. The
energy (in MeV) required to remove a neutron from O17 is
Level -1
(a) 3.52 (b) 3.64 (c)4.23 (d)7.86 Short answer type (3 MARKS)
4. The average binding energy per nucleon in the nucleus of an atom is approximately 1) Write any three characteristic properties of nuclear force.
2) Show that the nuclear density is independent of mass number.
(a) 8 eV (b) 8 KeV (c) 8 MeV (d) 8 J 3) Plot a graph showing the variation of potential energy of a pair of nucleons as
5. Binding energy per nucleon plot against the mass number for stable nuclei is a function of their separation. Write its two characteristic properties.
shown LEVEL 2
in the figure. Which curve is correct D Short answer type (3 MARKS)
Binding energy
per nucleon
B
(a) A(b) B 1) The sun radiates energy in all directions. The average radiations received on the
(c) C(d) D earth surface from the sun is 1.4 kilowatt / m 2 .The average earth- sun distance is
C
6. In the following reaction 12 Mg 24 + 2 He 4 → 14 Si x + 0 n 1 x is A 1.5  10 11 metres
. Find the mass lost by the sun per day.
Mass number (1 day = 86400 seconds)
(a) 28 (b) 27 (c)26 (d) 22
7. In the carbon cycle of fusion Level 3
1) Calculate the energy released in MeV in the following nuclear reaction:
(a) Four 1 H 1 fuse to form 2 He
4
and two positrons b) Four 1H
1
fuse to form 2 He
4
and
two electrons
(c) Two 1 H 2 fuse to form 2 He
4
(d) Four 1H
2
fuse to form 2 He
4
and two positrons
8. In atom bomb the reaction which occurs is
(a)Fusion (b)Controlled fission (c)Uncontrolled fission (d)Thermonuclear
9. Two Cu64 nuclei touch each other. The electrostatics repulsive energy of the
system
will be
(a) 0.788 MeV (b) 7.88 MeV (c) 126.15 MeV (d) 788 MeV Level -1
Long answer type ( 5 MARKS)
LEVEL 1 1) Using the curve for the binding energy per nucleon as a function of mass
number A, state clearly how the release of energy in the processes of nuclear fission
short answer type (2 MARKS)
and nuclear fusion can be explained.
1) Define Atomic Number and Mass Number.
2) Calculate binding energy per nucleon of 209Bi83 nucleus. Given that mass of
2) What is nuclear fission, and provide an example of a fission reaction? 209Bi83 = 55.934939u, mass of proton = 1.007825u, mass of neutron = 1.0086 MeV665
3) Explain the concept of binding energy per nucleon and its significance. u and 1 u = 931 MeV.
4) What are isotopes? Give two examples.

233 234
 Self Assessment Unit IX: Electronic Devices
MCQ Chapter–14: Semiconductor Electronics: Materials,
1) If in a nuclear fusion process the masses of the fusing nuclei be m1 and m2 and the Devices and Simple Circuits
mass of the resultant nucleus be m 3 , then
(a) m3 = m1 + m 2 (b) m 3 = | m1 + m 2 | (c) m3  (m1 + m 2 ) (d) m 3  (m1 + m 2 ) GIST OF THE CHAPTER:
Energy bands in conductors, semiconductors and insulators (qualitative ideas only)
2) The curve of binding energy per nucleon as a function of atomic mass number has
a sharp peak for helium nucleus. This implies that helium Intrinsic and extrinsic semiconductors- p and n type, p-n junction Semiconductor
(a) Can easily be broken up (b) Is very stable diode - I-V characteristics in forward and reverse bias, application of junction diode
(c) Can be used as fissionable material (d) Is radioactive -diode as a rectifier.
3) Which of the following is most unstable [AFMC 2005] Energy bands in solids:
(a) Electrons (b) Protons (c) Neutrons (d)  -particle ⮚ Due to influence of high electric field between the core of the atoms and the
4) The mass number of He is 4 and that for sulphur is 32. The radius of sulphur nucleus shared electrons, energy levels are split-up or spread-out forming energy
is larger than that of helium, by times bands.
(a) 8 (b) 4 (c) 2 (d) 8 ⮚ The energy band formed by a series of levels containing valance electrons
5) Assertion :Density of all the nuclei is same. is called valance band and the lowest unfilled energy level just above the
Reason : Radius of nucleus is directly proportional to the cube root of mass valance band is called conduction band.
number.
⮚ Filled energy levels are separated from the band of unfilled energy levels by
6) Assertion :Isobars are the element having same mass number but different
an energy gap called forbidden gap or energy gap or band gap.
atomic number.
Reason :Neutrons and protons are present inside nucleus.
Short answer type (2 marks)
7) Explain the concept of mass defect.
8) What is binding energy? How is it related to stability of nucleus?
Long answer type (3marks)
9) What are the differences between nuclear fission and nuclear fusion? Which one is
used in nuclear power plants and why?
10) Skech the curve for binding energy per nucleon vs mass no . write the significance
of it.
Long ans type ( 5marks) Energy band diagram for, Conductors Semiconductors and Insulators
11) a)Show that nuclear density is independent of mass .
b) Explain molecular interaction using potential energy curve .
c) Write the properties of nuclear force Conductors (Metals):The conduction band and valance band partly overlap each
12) Case base study ( 4marks) other and there is no forbidden energy gap in between.Large number of electrons
In nuclear physics, the mass defect refers to the difference between the mass of a are available for electrical conduction , hence the resistance is low of such
nucleus and the sum of the masses of its constituent protons and neutrons. This materials.Even if a small electric field is applied across the metal, these free
discrepancy arises because some mass is converted into binding energy, which holds electrons start moving.Hence metals behave as a conductor.
the nucleus together. Understanding mass defect is crucial for studying nuclear stability Semiconductors: The conduction and valance bands are separated by the small
and reactions.Imagine a laboratory experiment where scientists are investigating the energy gap ( 1 eV) called forbidden energy gap. The valence band is completely
mass defect in different isotopes. They have a sample of Helium-4 (4He) and are trying filled, while the conduction band is empty at zero kelvin. The electrons cross from
to calculate its mass defect and binding energy. valence band to conduction band even when a small amount of energy is supplied.
Q1) Calculate the theoretical mass of the Helium-4 nucleus based on the sum of the The semiconductor acquires a small conductivity at room temperature.
masses of Its constituent protons and neutrons. Insulators: Electrons, however heated, cannot practically jump to conduction band
Q2) Determine the mass defect of the Helium-4 nucleus. from valence band due to a large energy gap (>3 eV). Therefore, conduction is not
Q3) Calculate the binding energy of the Helium-4 nucleus in MeV. possible in insulators.
Q4) Explain the significance of the mass defect and binding energy in terms of nuclear INTRINSIC SEMICONDUCTORS:
stability. Intrinsic Semiconductor is a pure semiconductor.

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 Potential Barrier: The difference in potential between p and n regions across the
junction makes it difficult for the holes and electrons to move across the junction. 2. Full wave rectifier: A rectifier which rectifies both halves of each a.c. input cycle is
This acts as a barrier and hence called „potential barrier‟.Potential barrier for Si is called a full wave rectifier. The output of a full wave rectifier is continuous but
pulsating in nature. However, it can be made smooth by using a filter circuit.
nearly 0.7 V and for Ge is 0.3 V.The potential barrier opposes the motion of the
majority carriers.
Forward biasing:
The p-n junction is said to be forward biased, when the positive terminal of the external
battery is connected to p-section and the negative terminal to n-section of the
junction diode.

TABLES
1) DIFFERENCE BETWEEN INTRINSIC AND EXTRINSIC SEMICONDUCTORS
Reverse biasing: The p-n junction is said to be reverse biased, when the positive
terminal of the battery is connected to n-section and the negative terminal to p- S.NO INRINSIC SEMICONDUCTOR EXTRINSIC SEMICONDUCTOR
section of the junction diode.
1 Pure form of semiconductor. Impure form of semiconductor.

2 Conductivity is low Conductivity is higher than

intrinsic semiconductor.
3 The no of holes is equal to In n-type, the no. of electrons is
no of free electrons greater than that of the holes and
in p-type, the no. holes is greater
than that of the electrons.
Junction diode as rectifier: 4 The conduction The conduction depends on the
Because of its unidirectional conduction property, the p-n junction is said to convert an depends on concentration of doped impurity
a,c. voltage into d. c, voltage, It is, then, said to be acting as a rectifier. temperature. and temperature.
1. Half wave rectifier: A rectifier, which rectifies only one half of each a.c. input supply
cycle, is called a half wave rectifier. A half wave rectifier gives discontinuous and
DIFFERENCE BETWEEN HALF WAVE AND FULL WAVE RECTIFIER
pulsating d.c. output. As alternative half cycles of the a.c. input supply go waste, its
efficiency is very low.
S.NO HALF WAVE RECTIFIER FULL WAVE RECTIFIER

1 Only half cycle of AC is Both cycles of AC are rectified.

rectified.
2 Requires only one diode Requires two diodes.
3 The output frequency is equal The output frequency is double of
to input supply frequency. (F) the input supply frequency. (2F)
4 The electric current A continuous electric current
through the load is not flow through the load.
continuous

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10 Assertion: The energy gap between the valence band and conduction band is 2 Free electrons have more mobility than free holes due to the following
greater in silicon than in germanium. reasons:
(a) they are light (b) they carry negative charge
Reason: Thermal energy produces fewer minority carriers in silicon than in (c) They mutually collide less d) they require low energy to continue their
germanium motion
11 Assertion: The total current I in a semiconductor is the sum of electron current 3 The energy needed for an electron to move from the valance band to the
and hole current. conduction band in Germanium is
(a) 0.12 eV (b)0.72 eV (c)7.2 eV (d)None of these
Reason: In a semiconductor, motion of holes towards positive potential and 4. For semiconductors, which of the ones that follow is the most suitable?
free electrons towards negative potential. (a) large evacuated space (b)external heating arrangement
12 Assertion: A hole on p-side of a p n- junction moves to n-side just an instant (c) low operating voltages (d)high power
5 When a forward bias is applied to a p-n junction, it
after drifting of charge carriers occurs across junction.
(a) raises the potential barrier. (b) reduces the majority carrier current to
Reason: Drifting of charge carriers reduces the concentration gradient across zero. (c) lowers the potential barrier (d)None of the above.
junction.
6. In a full wave rectifier, input AC has a frequency ‘ν’. The output frequency of
13 Assertion (A): When a p-n junction diode is reverse biased, a feeble reverse-
current is
current flows known as reverse saturation current.
(a) ν /2 (b) ν (c) 2 ν (d) None of these
Reason (R): In reverse bias condition, the minority carries can cross the
7 When an electric field is applied across a semiconductor,
junction.
(a) Electrons move from lower energy level to higher energy level in the
14 Assertion : The resistivity of a semi-conductor increases with temperature. conduction band
Reason : The atoms of semi-conductor vibrate with larger amplitude as higher (b) Electrons move from higher energy level to lower energy level in the
temperatures thereby increasing its resistivity. conduction band
15 Assertion: If the temperature of a semiconductor is increased then it’s (c) Holes in the valence band move from lower energy level to higher
energy level
resistance decreases.
(d) None of the above
Reason: The energy gap between conduction band and valence band is very
small.
Directions: In the following questions, A statement of Assertion (A) is followed by a
16 Assertion: The number of electrons in a p-type silicon semiconductor is less statement of Reason (R). Mark the correct choice as.
than the number of electrons in a pure silicon semiconductor at room A: If both Assertion and Reason are correct and the Reason is a correct explanation of
temperature. the Assertion.
B: If both Assertion and Reason are correct but Reason is not a correct explanation of
Reason: It is due to law of mass action. the Assertion. C:If the Assertion is correct but Reason is incorrect.
D: If both the Assertion and Reason are incorrect
MCQ LEVEL 2 8 Assertion (A): For the same doping concentrations, n-type Si material has a
higher conductivity than p-type Si material.
1 Which diagram below best illustrates a reverse biased diode? Reason (R): In a semiconductor the electrons are less tightly bounded than
holes.
9 Assertion (A): n-type semiconductors of silicon are electrically charged.
Reason(R): In n-type semiconductors, the doped atom has no more valence
Electron than silicon.

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 2 MARK QUESTIONS 3. An a.c. signal is fed into two circuits X and Y
LEVEL-3 and the corresponding output in the two cases
1 What do energy bands mean? Based on energy band diagrams, list any two have the wavefront shown in figure. Name the
characteristics that separate conductors, semiconductors, and insulators. circuit X and Y. Also draw their detailed circuit
2 What happens when germanium metal is slightly doped with indium? diagram.
3 Who are the major charge carriers in n-type and p-type semiconductors? CASE STUDY/SOURCE BASED QUESTIONS
4 Describe the formation of the depletion area and potential barrier in a junction LEVEL-1
diode using a diagram. 1.
5 Is using a full wave rectifier preferable to a half wave rectifier? Why? On the basis of energy bands materials are also defined as metals, semiconductors
and insulators. These semiconductors are classified as intrinsic semiconductors and
3 MARK QUESTIONS extrinsic semiconductors also. Intrinsic semiconductors are those semiconductors
LEVEL-1 which exist in pure form. And intrinsic semiconductors have number of free electrons is
1 Draw a diode's voltage-current characteristic curve and highlight its key features. equal to number of holes. The semiconductors doped with some impurity in order to
2 Using a diagram, explain how the barrier potential and depletion region develop increase its conductivity are called as extrinsic semiconductors. Two types of dopants
at a p-n junction. are used they are trivalent impurity and pentavalent impurity also. The extrinsic
semiconductors doped with pentavalent impurity like Arsenic, Antimony, Phosphorus
3 MARK QUESTIONS
etc are called as n – type semiconductors. In n type semiconductors electrons are the
LEVEL-2
majority charge carriers and holes are the minority charge carriers. When trivalent
1 In the following diagram, which bulb impurity is like Indium, Boron, Aluminium etc are added to extrinsic semiconductors
out of B1 and B2 will glow and why?
then p type semiconductors will be formed. In p type semiconductors holes are majority
charge carriers and electrons are the minority charge carriers.
I) What is extrinsic semiconductor?
II) What is ratio of number of holes and number of electrons in an intrinsic
semiconductor?
2. Write any two distinguishing features between conductors, semiconductors and III) Why doping is necessary?
insulators on the basis of energy band diagrams.
IV) Majority charge carriers in p-type semiconductor are
3. Name two important processes that occur during the formation of a p-n junction.
4 The maximum wavelength at which solid begin to absorb energy is 10000 Å. 2.
Calculate the energy gap of a solid (in eV).
From Bohr's atomic model, we know that the electrons have well defined energy levels
3 MARK QUESTIONS in an isolated atom. But due to interatomic interactions in a crystal, the electrons of the
LEVEL-3 outer shells are forced to have
1 (a) Distinguish between n-type and p-type semiconductors on the basis of energy energies different from those in
band diagrams. isolated atoms. Each energy level
(b) Compare their conductivities at absolute zero temperature and at room splits into a number of energy levels
temperature forming a continuous band. The gap
2. Draw the input and output waveforms of half-wave rectifier and full wave rectifier. between top of valence band and
bottom of the conduction band in
which no allowed energy levels for
electrons can exist is called energy

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iii) Which of the following is not true about a rectifier circuit? ii) Based on the V-I characteristics of the diode, we can classify diode as
(a) It can convert DC to AC. (b) It can convert AC to DC. (a) bi-directional device (b) ohmic device
(c)It can shift voltage level .(d)None of these (c) non-ohmic device (d) passive element
iv) In the given circuit, iii) In the case of forwarding biasing of a p-n junction diode, which one of the
following statement is correct?
(a) effective barrier potential decreases
(b) majority charge carriers begins to flow away from junction
(c) width of depletion layer increases
(d) effective resistance across the junction increases
Capacitor c is used iv) If an ideal junction diode is connected as shown, then the value of the current I is.
(a) for storing potential energy
(b) as a bypass to DC component to get AC in RL
(c) to remove sparking
(d) as a bypass to AC component to get DC in RL
(a) 0.005 (b) 0.02 A (c) 0.01 A (d) 0.1A
v) The ratio of output frequencies of half-wave rectifier and a full wave rectifier,
when an input of frequency 200 Hz is fed at input, is
2.
(a) 1:2 (b)2: 1 (c) 4 :1 (d) 1 : 4
When the diode is forward biased, it is found that beyond forward voltage V = Vk,
called knee voltage, the conductivity is very high. At this value of battery biasing
CASE STUDY/SOURCE BASED QUESTIONS for p-n junction, the potential barrier is overcome and the current increases rapidly
LEVEL-3 with increase in forward voltage. When the diode is reverse biased, the reverse
bias voltage produces a very small current about a few microamperes which almost
1.When the diode is forward biased, it is found that beyond forward voltage V = Vk,
remains constant with bias. This small current is reverse saturation current. 36. In
called knee voltage, the conductivity is very high. At this value of battery biasing for
which of the following figures, the p-n diode is forward biased.
p-n junction, the potential barrier is overcome and the current increases rapidly with
i) In which of the following figures, the p-n diode is forward biased
an increase in forwarding voltage. When the diode is reverse biased, the reverse
bias voltage produces a very small current about a few microamperes which almost
remains constant with bias. This small current is reverse saturation current

i) i) In which of the following figures, the p-n diode is forward biased

ii) Based on the V-I characteristics of the diode, we can classify diode as
(a) bi-directional device (b) ohmic device
(c) non-ohmic device (d) passive element
iii) The V-I characteristic of a diode is shown in the figure. The ratio of forward to
(a) a,b and d (b) c only (c) c and a (d) b and d
reverse bias resistance is

253 254
 potential barrier of Vo. The holes approach the pn junction with a non-zero
4 A p-n junction diode has a depletion layer of thickness 500 nm and an electric 02 initial kinetic energy from either p or the n- side depending upon the nature
field 16 x 105 V/m. of biasing applied.
a. Find the barrier potential created. a. If the holes approach the pn junction from p-side,
b. Determine the minimum kinetic energy (in eV) that the conduction i. What type of biasing must have been applied across the pn junction?
electrons must have so that they can diffuse from n-side onto p-side, in case ii. Will the kinetic energy of the holes increase or decrease while crossing the
of: junction? Give reason for your answer.
i. the junction is unbiased b. If the holes approach the pn junction from n-side,
ii. the junction is forward biased at 0.5 V i. What type of biasing must have been applied across the pn junction?
iii. the junction is reverse biased at 0.5 V ii. Will the kinetic energy of the holes increase or decrease while crossing the
5 Almost a constant electric current of 20 μA flows through a given pn junction 02 junction? Give reason for your answer.
diode in reverse bias. The current becomes 4 times in case the pn junction 3 A diode is connected in series with a 3 V battery and a 30 Ω resistor. A drift 03
diode is forward biased. Determine the diffusion current that flows through current of 10 μA flows through the diode.
the given diode in case it is: (a) What is the potential drop across the diode?
a. unbiased b. reverse biased c. forward biased (b) Is the diode forward-biased or reverse-biased? Draw a circuit diagram to
represent the above connections.
COMPETENCY BASED QUESTIONS
COMPETENCY BASED QUESTIONS
3 MARK QUESTIONS 5 MARK QUESTIONS
1 The graph below shows the variation in the mobility of electrons and holes 03
1 The image below shows a circuit with three diodes and three resistors 05
for a Si semiconductor with doping concentration at 300 K.
connected to an AC source with an rms voltage V.
What is the average power delivered over one full cycle of AC in the above
circuit? Show your calculations and arrive at the final answer in terms of V
and R. (Assume the diode is ideal.)

The pentavalent doping concentration is 1015 cm-3 and the concentration of

intrinsic charge carriers at 300 K is about 1010 cm-3
(a) Find the concentration of majority and minority charge carriers.
(b) What is the conductivity of silicon at 300 K? (Calculate conductivity
assuming majority charge carriers only.)
The magnitude charge on an electron/hole is 1.6 x 10-19 C. Assume complete
dopant ionization.
2 A certain biasing voltage is applied across the pn junction with an initial 03

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 Reason (R) : In half-wave rectifier only one diode is used. charge carriers and holes are the minority charge carriers. When trivalent impurity
06 Assertion (A) : In a semiconductor diode, the reverse biased current is 01 is like Indium, Boron, Aluminium etc are added to extrinsic semiconductors then p
due to drift of free electrons and holes. type semiconductors will be formed. In p type semiconductors holes are majority
Reason (R) : The drift of electrons and holes is due to thermal charge carriers and electrons are the minority charge carriers.
excitations i) In case of p-type semiconductors__
a) nh<< ne b) nh = ne c) nh>> ne d) nh= ne = 0
SECTION B ii) An intrinsic semiconductor behaves like _____ at T = 0K.
07 Explain with the help of a diagram the formation of depletion region and 02 a) conductors b) semiconductors c) insulators d) superconductors
barrier potential in a p-n junction.
iii) If the energy band gap Eg> 3 eV then such materials are called as
08 Why are elemental dopants for silicon or germanium usually chosen 02
from group XIII or group XV ? a) conductors b) semiconductors c) insulators d) superconductors
iv) P- type semiconductor is obtained by adding ……… in pure semiconductor
SECTION C a) zinc b) Magnesium c) Phosphorous d) Aluminum
08 In half-wave rectification, what is the output frequency? If the input 03
frequency is 50 Hz, what is the output frequency of a full wave rectifier SECTION E
for the same input frequency? 11 (i) Can a slab of p-type semiconductor be physically joined to another 05
09 i) Differentiate between P-type and N-type semiconductors 03 n-type semiconductor slab to form p-n junction? Justify your answer.
ii) Draw their energy level diagrams. (ii) In a p-n junction diode, the forward bias resistance is low as
compared to the reverse bias resistance. Give reason.
SECTION D
CASE BASED STUDY
10
Semiconductors consist of Valence band and conduction band. On the basis of energy
bands materials are also defined as metals, semiconductors and insulators. In case
of metals, conduction band and Valence band overlaps with each other due to ************
which electrons are easily available for conduction. In case of insulators, there is
some energy gap between conduction band and Valence band due to which no
free electrons are easily available for conduction. And in semiconductors, there is
a small energy gap between conduction band and Valence band and if we give
some external energy then electron from Valence band goes to conduction band
due to which conduction will be possible. These semiconductors are classified as
intrinsic semiconductors and extrinsic semiconductors also. Intrinsic
semiconductors are those semiconductors which exist in pure form. And intrinsic
semiconductors has number of free electron is equal to number of holes. The
semiconductors doped with some impurity in order to increase its conductivity are
called as extrinsic semiconductors. Two types of dopants are used they are
trivalent impurity and pentavalent impurity also. The extrinsic semiconductors
doped with pentavalent impurity like Arsenic, Antimony, Phosphorus etc are called
as n – type semiconductors. In n type semiconductors electrons are the majority

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8 A plane wave front of light is incident on a plane mirror as shown in the figure. [1] SECTION-A
Intensity is maximum at P, when: 13 Assertion: Positive charge always moves from a higher potential point to a [1]
𝜆
a) cos𝜃 = lower potential point.
2𝑑
3𝜆 Reason: Electric potential is a vector quantity.
b) cos𝜃 =
4𝑑 a) Assertion and reason both are correct statements and reason is correct
3𝜆
c) sec𝜃 - cos 𝜃 = explanation for assertion.
4𝑑
𝜆
d) sec𝜃 - cos 𝜃 = 2𝑑 b) Assertion and reason both are correct statements but reason is not correct
explanation for assertion.
c) Assertion is correct statement but reason is wrong statement.
d) Assertion is wrong statement but reason is correct statement.
9 In an experiment of photoelectric emission for incident light of 4000A0 , the [1]
stopping potential is 2V. If the wavelength of incident light is made 3000 A0 , 14 Assertion (A): If the frequency of the applied AC is doubled, then the power [1]
factor of a series R - L circuit decreases. Reason (R): Power factor of series
then stopping potential will be 2𝑅
a) 2 Volt b) less than 2 volt c) more than 2 volt d) zero R - L circuit is given by cos𝜙 = 2 2 2 .
𝑅 +𝜔 𝐿
10 The longest wavelength in the ultraviolet region of the hydrogen spectrum is [1] a) Both A and R are true and R is the correct explanation of A.
122 nm. The shortest wavelength in the infrared region of the hydrogen b) Both A and R are true but R is not the correct explanation of A.
spectrum (to the nearest integer) is c) A is true but R is false.
a) 823 nm b) 802 nm c) 1882 nm d) 1648 nm d) A is false but R is true.
11 The dependence of binding energy per nucleon (B𝑁 ) on the mass number A [1] 15 Assertion (A): Corpuscular theory fails in explaining the velocities of light in [1]
is represented by air and water.
Reason (R): According to Corpuscular theory, the light should travel faster in
denser media than in rarer media.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) A is true but R is false.
a) b) d) A is false but R is true.
16 Assertion (A): When two semiconductor of p and n - type are brought in [1]
contact, they form p - n junction which act like a rectifier.
Reason (R): A rectifier is used to convert alternating current into direct
current.
a) Both A and R are true and R is the correct explanation of A.
b) Both A and R are true but R is not the correct explanation of A.
c) d)
c) A is true but R is false.
12 In the circuit given in the figure, an a.c. source of 200 V is connected through [1] d) A is false but R is true.
a diode D to a capacitor. The potential difference across the capacitor will be
SECTION -B
a) 283 V b) 100 V
c) 310 V d) 200 V 17 Five balls, numbered 1 to 5 are suspended using separate threads. Pairs (1, [2]
2), (2, 4), (4, 1) show electrostatic attraction, while pairs (2, 3) and (4, 5) show
repulsion. What is the nature of the charge on ball 1?
18 A galvanometer can be converted into a voltmeter of a certain range by [2]
connecting a resistance of 980𝛺 in series with it. When the resistance is 470
𝛺 connected in series, the range is halved. Find the resistance of the
galvanometer.

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 4. Point out the right statements about the validity of Kirchhoff’s Junction (I) On the basis of electron drift, derive an expression for resistivity of a
rule. conductor in terms of 3
number density of free electrons and relaxation time. On what factors does
a. The current flowing towards the junction are taken as positive. resistivity of a conductor depend?
b. The currents flowing away from the junction are taken as 2
(II) Why alloys like constantan and manganin are used for making standard
negative.
resistors?
c. bending or reorienting the wire does not change the validity of
Kirchhoff’s Junction rule. 32 1. Draw a labelled diagram of an ac generator and state its working [5]
d. All of these principle.
5. Potential difference between A and 2. How is magnetic flux linked with the armature coil changed in a
B in the circuit shown here is generator?
3. Derive the expression for a maximum value of the induced emf and
a. 4V b. 5.6V c. 2.8V state the rule that gives the direction of the induced emf.
d. 6V 4. Show the variation of the emf generated versus time as the armature
is rotated with respect to the direction of the magnetic field.
OR
30 Read the source given below and answer the following questions: A
compound microscope is an optical instrument used for observing highly i) Draw a schematic arrangement for winding of primary and secondary coils
magnified images of tiny objects. Magnifying power of a compound in a transformer when the two coils are wound on top of each other.
microscope is defined as the ratio of the angle subtended at the eye by the (ii) State the underlying principle of a transformer and obtain the expression
final image to the angle subtended at the eye by the object, when both the for the ratio of secondary to primary voltage in terms of the
final image and the object are situated at the least distance of distinct vision
• number of secondary and primary windings and
from the eye. It can be given that : m = m 𝑒 × m 𝑜 , where m 𝑒 is magnification
• primary and secondary currents.
produced by eye lens and m 𝑜 is magnification produced by objective lens.
Consider a compound microscope that consists of an objective lens of focal (iii) Write the main assumption involved in deriving the above relations.
length 2.0 cm and an eyepiece of focal length 6.25 cm separated by a distance (iv) Write any two reasons due to which energy losses may occur in actual
of 15 cm. transformers.
1. The object distance for eye - piece, so that final image is formed at the
33 1. Draw a labelled ray diagram to obtain the real image formed by an [5]
least distance of distinct vision, will be
1 astronomical telescope in normal adjustment position. Define its
a. 3.45 cm b. 5 cm c. 1.29 cm d. 2.59 cm
magnifying power.
2. How far from the objective should an object be placed in order to obtain
1 2. You are given three lenses of power 0.5 D, 4D and 10 D to design a
the condition described in part (i)?
telescope.
a. 4.5 cm b. 2.5 cm c. 1.5 cm d. 3.0 cm
a. Which lenses should be used as objective and eyepiece? Justify
3. What is the nature intermediate image formed by the objective of a
your answer.
compound microscope?
b. Why is the aperture of the objective preferred to be large?
OR
OR
How you can increase the magnifying power of a compound
A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in
microscope increase?
2
(i) a medium of refractive index 1.65,
SECTION-E
(ii) a medium of refractive index 1.33.
31 Two squares ABCD and BEFC have the side BC in common. The sides are [5]
of conducting wires with resistances as follows: AB, BE, FC and CD each 2𝛺 (a) Will it behave as a converging or a diverging lens in the two cases?
; AD, BC, EF each 1 𝛺 . A cell of emf 2 V and internal resistance 2 𝛺 is joined (b) How will its focal length change in the two media?
across AD. Find the currents in various branches of the circuit.
OR ************

269 270
16. Assertion (A): In a series LCR circuit, the impedance is minimum at the resonant 33. (a) Explain the formation of a PN junction diode and discuss its working principle. (3
frequency. marks)
Reason (R): At the resonant frequency, the inductive reactance equals the capacitive (b) Draw and describe the V-I characteristics of a PN junction diode in forward bias and
reactance, and the circuit behaves like a pure resistor. reverse bias conditions. (2 marks)
17. Assertion (A): The inductance of a solenoid depends on the number of turns and the Or
length of the solenoid. a) Explain the working of a PN junction diode as a half-wave rectifier with the help of a
Reason (R): Increasing the number of turns or decreasing the length of the solenoid circuit diagram and waveforms. (3 marks)
increases the magnetic flux linkage per unit current. (b) Describe the working of a PN junction diode as a full-wave rectifier with the help of a
18. Assertion (A): In an intrinsic semiconductor, the number of electrons in the circuit diagram and waveforms. (2 marks)
conduction band is equal to the number of holes in the valence band. 34. (a) Derive the lens maker's formula for a convex lens. (3 marks)
Reason (R): Intrinsic semiconductors are doped with impurity atoms to increase their (b) A convex lens has a focal length of 20 cm. Where should an object be placed so
conductivity. that its image is formed 40 cm from the lens? (2 marks)
Section B: (2 marks each)
19. Define electric dipole moment. Give its S.I. unit. OR
20. State Gauss's law. How is it useful in calculating the electric field due to a uniformly (a) Explain the principle of interference of light and derive the expression for the
charged spherical shell? resultant intensity when two coherent light waves interfere. (3 marks)
21. Derive the relation between current and drift velocity. (b) Two coherent sources of light produce waves with intensities I1=4 units and I2=9 units.
22. Explain the working of a photodiode. Calculate the maximum and minimum intensities observed on the screen. (2 marks)
23. Derive the expression for the capacitance of a parallel plate capacitor.
24. Write any two properties of electromagnetic waves. Section E: (4 marks each)
25. Differentiate between polar and non-polar molecules. 35. Case Study 1:
26. Explain the term 'mutual inductance' and write its unit. Read the following passage and answer the questions that follow:
OR The hydrogen spectrum consists of several series of lines in different regions of the
Explain fission in brief electromagnetic spectrum. These series are named after their discoverers: Lyman,
Balmer, Paschen, Brackett, and Pfund. Each series corresponds to electron transitions
Section C: (3 marks each) between different energy levels in the hydrogen atom.
27. Describe the principle, construction, and working of a moving coil galvanometer. Questions:
28. Using Kirchhoff's rules, calculate the current in a circuit having three resistors R 1, R2 a) Which series of hydrogen spectral lines lies in the visible region? (1 mark)
and R3 in series with a battery of emf E. b) Calculate the wavelength of the first line of the Lyman series. (Given: Rydberg
29. Explain how interference pattern is obtained in Young's double-slit experiment. constant (R = 1.097 x 107 m-1 (2 marks)
30. What are the different types of polarization of light? Explain any one type in detail. c) Why are the spectral lines of hydrogen important in astronomy? (1 mark)
31. Explain the phenomenon of total internal reflection and write its two applications.OR
36. Case Study 2:
(a) Calculate the radius of a nucleus with a mass number of 64.
Read the following passage and answer the questions that follow:
A coil of wire is connected to a galvanometer. When a bar magnet is moved towards the
(b) Determine the ratio of the radii of nuclei with mass numbers 27 and 125.
coil, the galvanometer shows a deflection. When the bar magnet is moved away from the
Section D: (5 marks each) coil, the galvanometer shows a deflection in the opposite direction. The faster the magnet
32. (a) Derive an expression for the force between two long parallel current-carrying is moved, the greater the deflection.
conductors. (3 marks) a) Name the phenomenon demonstrated in the above experiment. (1 mark)
(b) Two long parallel wires carry currents of 5 A and 10 A in opposite directions. b) State Faraday’s law of electromagnetic induction. (2 marks)
Calculate the force per unit length between them if they are separated by a distance of 2 c) What will happen if the number of turns in the coil is increased? (1 mark)
cm. (2 marks)
********

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8 The phase difference between the alternating current and e.m.f. is π/2. 14 Assertion: Bohr had to postulate that the electrons in stationary orbits
Which of the following cannot be the constituent of the circuit? around the nucleus do not radiate.
(a) C alone (b) R alone (c) R, L (d) L, C Reason: According to classical physics all moving electrons radiate
9 Whenever a magnet is moved either towards or away from a conducting 15 Assertion: A pure semiconductor has negative temperature coefficient
coil, an e.m.f. is induced, the magnitude of which is independent of of resistance.
(a) the strength of the magnetic field. Reason: In a semiconductor on raising the temperature, more charge
(b) the speed with which, the magnet is moved. carriers are released, conductance increases and resistance decreases.
(c) the number of turns in the coil. 16 Assertion: A lens, whose radii of curvature are different, is forming
(d) the resistance of the coil. the image of an object placed on its axis. If the lens is reversed,
10 Which of the following is not the property of light? the position of the image will not change.
1 1 1
(a) It requires a material medium for propagation. Reason: The focal length of a lens is given by = (𝜇 − 1) ( − ) and
𝑓 𝑅1 𝑅2
(b) It can travel through vacuum. so focal length in both the cases is same.
(c) It involves transportation of energy.
(d) It has finite speed. SECTION B
11 The magnetic flux linked with a coil (in Wb) is given by the equation: 17 Draw energy band diagram of n-type and p-type semiconductor at
Φ = 5 t2 +5t+16. The induced e.m.f. in the coil in the fourth second will temperature T>0K. Mark the donor and acceptor energy level with their
be energies.
(a) 10V (b) 108 V (c) 45 V (d) 210V 18 A proton and an electron have same kinetic energy. Which one has
12 The diagram shows the energy levels for an greater de-Broglie wavelength and why?
electron in a certain atom. Which transition 19 Under what conditions does the phenomenon of total internal reflection
shown represents the emission of a photon take place? Draw a ray diagram showing how a ray of light deviates by
with the most energy? 900 after passing through a right angled isosceles prism.
(a) III (b) IV (c) I (d) II 20 When 5 V potential difference is applied across a wire of length 0.1
m, the drift speed of electrons is 2.5 × 10–4 m/s. If the electron density
in the wire is 8 × 1028 m–3, calculate the resistivity of the material of
wire.
Questions number 13 to 16 are Assertion (A) and Reason (R) type questions.
Two statements are given – one labelled Assertion (A) and the other labelled 21 Why is that sun-glasses (goggles), which have curved surfaces, do not
Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as have any power?
given below. OR
(A) Both Assertion (A) and Reason (R) are true and Reason (R) is the Can a convergent lens in one medium behave as a divergent lens in
correct explanation of the Assertion (A). some other medium?
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the SECTION C
correct explanation of the Assertion (A).
22 (i) The radius of the innermost electron orbit of a hydrogen atom is 5.3
(C) Assertion (A) is true, but Reason (R) is false.
(D) Assertion (A) is false and Reason (R) is also false. X 10-11 m. Calculate its radius in n=3 orbit.
(ii) The total energy of an electron in the first excited state of the
13 Assertion: The kinetic energy of photoelectrons emitted from metal hydrogen atom is -3.4 eV. Find out its (a) kinetic energy and (b)
surface does not depend on the intensity of incident photon. potential energy in this state.
Reason: The ejection of electrons from metallic surface is not possible 23 Two point charges +q and -2q are placed at the vertices B and C of an
with frequency of incident photons below the threshold frequency. equilateral ∆𝐴𝐵𝐶 of side a. Obtain the expression for

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 (a) 12cm (b) 10cm (c) 20cm (d) 30cm (ii) What happens if the field is non-uniform?
(ii) The radii of curvature of the faces of a double convex lens are 10 cm and (iii) What would happen if the external field E is increasing
15 cm. If focal length is 12 cm, then refractive index of glass is (a) parallel to 𝑝 and
(a) 1.5 (b) 1.78 (c) 2.0 (d) 2.52 (b) antiparallel to 𝑝 ?
(iii) An under-water swimmer cannot see very clearly even in absolutely clear OR
water because of (i) A thin conducting spherical shell of radius R has charge Q spread uniformly
(a) absorption of light in water over its surface. Using Gauss’s theorem, derive an expression for the
(b) scattering of light in water electric field at a point outside the shell.
(c) reduction of speed of light in water (ii) Draw a graph of electric field E(r) with distance r from the center of the shell
(d) change in the focal length of eye-lens for 0 ≤ r ≤∞.
(iv) A thin lens of glass (𝜇 = 1.5) of focal length 10 cm is immersed in water (𝜇 33 (a) What is impedance?
= 1.33). The new focal length is (b) A series LCR circuit is connected to an ac source having voltage V = V m
(a) 20cm b) 40cm (c) 48cm (d) 12cm sin ωt. Derive expression for the impedance, instantaneous current and its
OR phase relationship to the applied voltage.
(iv) An object is immersed in a fluid. In order that the object becomes invisible, (c)Find the expression for resonant frequency.
it should OR
(a) behave as a perfect reflector (a) An ac source of voltage V = Vm sin ωt is connected to a series combination
(b) absorb all light falling on it of L, C and R. Use the phasor diagram to obtain expressions for impedance
(c) have refractive index one of the circuit and phase angle between voltage and current. Find the
(d) have refractive index exactly matching with that of the surrounding condition when current will be in phase with the voltage. What is the circuit
fluid. in this condition called?
(b) In a series LR circuit XL = R and power factor of the circuit is P1. When
SECTION E capacitor with capacitance C such that XL = XC is put in series, the
31 (a) Two thin lenses are placed coaxially in contact. Obtain the expression for power factor becomes P2. Calculate 𝑃1
𝑃

the focal length of this combination in terms of the focal lengths of the two 2

lenses. **********
(b) A converging lens of refractive index 1.5 has a power of 10 D. When it is
completely immersed in a liquid, it behaves as a diverging lens of focal
length 50 cm. Find the refractive index of the liquid.
OR
(a) Draw the ray diagram showing refraction of light through a glass prism and
hence obtain the relation between the refractive index m of the prism, angle
of prism and angle of minimum deviation.
(b) Determine the value of the angle of incidence for a ray of light travelling
from a medium of refractive index μ1 = √2 into the medium of refractive
index μ2 = 1, so that it just grazes along the surface of separation.
32 (i) Define torque acting on a dipole of dipole moment p placed in a uniform
electric field E. Express it in the vector form and point out the direction along
which it acts.

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24. State Gauss theorem. Using this theorem find the electric field intensity due to a called depletion layer. At the junction a potential barrier appears, which does not
charged spherical shell. allow the movement of majority charge carriers across the junction in the absence
25. State Huygens’s wave theory of light. Using this theory, prove the laws of refraction. of any biasing of the junction. The p-n junction offers low resistance when forward
26. Derive an expression for capacitance of parallel plate capacitor filled with dielectric biased and high resistance when reverse biased.
slab of dielectric constant K. (a) Does current flow when diode is reverse biased?
27. Two coils have a mutual inductance 0.005 H. The current changes in the first coil (b) What is meant by reverse bias?
according to equation I = I0 Sin ωt, where I0 = 10 A and ω = 100 π rad-1. Then what (c) Can we measure the potential barrier of p-n junction by putting a sensitive
is the maximum value of e. m. f. in the second coil? voltmeter across its terminals?
28. Explain binding energy per nucleon and its variation with mass number. (d) Explain how a potential barrier is developed in a p-n junction diode.
Derive an expression for magnetic field at a point along the axis of current (e) Draw the labelled diagram of step-up transformer. Write its principle & deduce an
carrying circular coil. expression for its working.
(f) A transformer of efficiency 90 % has turns ratio 1:10 . If the voltage across the primary
29.Case Base Study Question: is 220 V and current in the primary is 0.5A, then find the current in secondary.
OR
According to de-Broglie a moving material particle sometimes acts as a wave and (a) Draw the diagram of an ac generator and explain its principle, construction and
sometimes as a particle or a wave is associated with moving material particle which working.
controls the particle in every respect. The wave associated with moving material (b) The number of turns in the coil of AC generator is 5000, and the area of the coil
particle is called matter wave or de-Broglie wave whose wavelength called de-Broglie is 0.25 m 2. The coil is rotated at the rate of 100 cycles/sec in a magnetic field of
wavelength, is given by λ = h/mv 0.2 Wbm − 2. What is the peak value of emf generated?
31.(a) Explain the magnifying power of compound microscope, when it
i) The dual nature of light is exhibited by
produces a final image at (i) Distance of distinct vision and (ii) Infinity.
a. diffraction and photo electric effect b. photoelectric effect
(b) An object is placed in front of a concave mirror of focal length 20 cm. The image
c. refraction and interference d. diffraction and reflection
formed is three times the size of the object. Calculate two possible distances of the
ii) If the momentum of a particle is doubled, then its de-Broglie wavelength will
object from the mirror.
a. remains unchanged b. become four times c. become two times d. become half
OR
iii) If an electron and proton are propagating in the form of waves having the same λ , it (a) Draw ray diagram to show refraction of a ray of monochromatic light passing
implies that they have the same through a prism. Deduce the expression for the refractive index of glass in terms
a. Energy b. Momentum c. Velocity d. angular momentum of angle of prism and angle of minimum deviation.
iv) Velocity of a body of mass m, having de-Broglie wavelength λ , is given by relation (b) A monochromatic light is incident on an equilateral prism at an angle 30º and
a. v = λ h/m b. v = λm/h c. v = λ/hm d. v = h/ λm emerges at an angle of 75º. What is the angle of deviation produced by the prism?
30.Case Base Study Question: 32. (a) With the help of neat labeled diagram, explain the diffraction at single slit. Also
Read the following paragraph and answer the questions.
show the position of secondary maxima and secondary minima on intensity graph.
(b) Give the difference between interference and diffraction.
OR
What is fringe width? Show that bright fringes and dark fringes are equally spaced in
interference pattern. Give the difference between constructive interference and
destructive interference.
The p-n junction is a semiconductor diode. It is obtained by bringing p-type
semiconductor in close contact with n- type semiconductor. A thin layer is developed
********
at the p-n junction which is devoid of any charge carrier but has immobile ions. It is

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B: If both Assertion and Reason are correct but Reason is not a correct explanation of the Q.25 How are electromagnetic waves produced? What is the source of energy 03
Assertion. of these waves? Write mathematical expressions for electric and
C:If the Assertion is correct but Reason is incorrect. magnetic fields of an electromagnetic wave propagating along the z-
D: If both the Assertion and Reason are incorrect axis. Write any two important properties of electromagnetic waves.
Q. 13 Assertion: In Young’s experiment, the fringe width for dark fringes is 1 Q.26 How will you explain twinkling of stars? 03
different from that for white fringes. Q.27 Describe briefly, with the help of a diagram, the role of the two important 03
Reason: In Young’s double slit experiment the fringes are performed process involved in the formation of a p n - junction.
with a source of white light, then only black and bright fringes are Q.28 Briefly describe proton-neutron hypothesis of nuclear composition. 03
observed. OR
Q.14 Assertion: We cannot think of a magnetic field configuration with 1 What are uncontrolled and controlled chain reactions?
three poles. 1
Reason : A bar magnet does exert a torque on itself due to its own
field SECTION-D
Q.15 Assertion: Diamond behaves like an insulator. 1 Q.29
Reason: There is a large energy gap between valence band and 1 When light from a monochromatic source is incident on a single narrow slit, it
conduction band of diamond. gets diffracted and a pattern of alternate bright and dark fringes is obtained on
Q.16 Assertion: In series LCR circuit resonance can take place. 1 screen, called “Diffraction Pattern” of single slit. In diffraction pattern of single
Reason: Resonance takes place if inductance and capacitive 1 slit, it is found that
resistances are equal and opposite. Central bright fringe is of maximum intensity and the intensity of any secondary bright
fringe decreases with increase in its order.
SECTION-B Central bright fringe is twice as wide as any other secondary bright or dark fringe.

Q.17 Is the steady electric current the only source of magnetic field? Justify 02
your answer.
Q.18 Magnetic field lines can be entirely confined with the core of toroid, but not 02
within a straight solenoid, why?
Q.19 How are infrared waves produced? Why are these referred to as heat 02
waves? Write their one important use.
Q.20 A concave lens of refractive index 1.5 is immersed in a medium of 02
refractive index 1.65 what is the nature of the lens?
Q.21 Why are two bulbs lighting the same walls considered as incoherent 02 i) A single slit of width 0.1 mm is illuminated by a parallel beam of light of 01
sources? How do their intensities add up? wavelength 6000 A.U. and diffraction bands are observed on a screen
OR 0.5 m from the slit. The distance of the third dark band from the central
When a tiny circular obstacle is placed in the path of light from a distant bright band is
source, a bright spot is seen at the centre of shadow of the obstacle. (a) 3 mm (b) 1.5 mm (c) 9 mm (d) 4.5 mm
Explain Ii) In Fraunhofer diffraction pattern, slit width is 0.2 mm and screen is at 2 m 01
away from the lens. If wavelength of light used is 5000 A.U. then the
SECTION-C distance between the first minimum on either side the central
Q.22 Determine the distance of closest approach when an alpha particle of 03 maximum is (a) 10-1 m (b) 10-2 m (c) 2 x10-2 m (d) 2 x10-1 m
kinetic energy 4.5 MeV strikes a nucleus of Z = 80, stops and reverse III) Light of wavelength 600 nm is incident normally on a slit of width 0.2 mm. 01
its direction. The angular width of central maxima in the diffraction pattern is
Q.23 Distinguish between ‘Intrinsic’ and ‘extrinsic’ semiconductors? 03 (measured from minimum to minimum)
Q.24 A charge Q is given to three capacitors C1, C2 and C3 connected in 03 (a)6 x10-3 rad (b) 4 x 10-3 rad (c)2.4 x 10-3 rad (d)
parallel. Determine the charge on each. 4.5 x 10-3 rad

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