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िुर्ाकांक्षा सवहत ।
Mr. VIVEK SAWHNEY PGT PHYSICS PM SHRI KENDRIYA
VIDYALAYA, NMU,
लनलि पांडे JALGAON,
MAHARASHTRA
आयुक्त, केन्द्रीय लवद्यािय संगठन
 विषय सूची Unit I: Electrostatics 26 Periods

INDEX
Chapter–1: Electric Charges and Fields

Electric charges, Conservation of charge, Coulomb's law-force between two-

क्र सं पाठ का नाम पृष्ठ सं point charges, forces between multiple charges; superposition principle and
S. No. NAME OF CHAPTER PAGE NO.
continuous charge distribution.
1. ELECTRIC CHARGES AND FIELDS 1-15 Electric field, electric field due to a point charge, electric field lines, electric
dipole, electric field due to a dipole, torque on a dipole in uniform electric
2. ELECTRIC POTENTIAL AND CAPACITANCE 16-35
field.

3. CURRENT ELECTRICITY 36-68 Electric flux, statement of Gauss's theorem and its applications to find field
due to infinitely long straight wire, uniformly charged infinite plane sheet and
4. MOVING CHARGES AND MAGNETISM 69-89 uniformly charged thin spherical shell (field inside and outside).

5. MAGNETISM AND MATTER 90-107 Chapter–2: Electrostatic Potential and Capacitance

ELECTROMAGNETIC INDUCTION Electric potential, potential difference, electric potential due to a point charge,
6. 108-120
a dipole and system of charges; equipotential surfaces, electrical potential
7. ALTERNATING CURRENT 121-141 energy of a system of two-point charges and of electric dipole in an
electrostatic field.
8. ELECTROMAGNETIC WAVES 142-152
Conductors and insulators, free charges and bound charges inside a

RAY OPTICS AND OPTICAL INSTRUMENTS conductor. Dielectrics and electric polarization, capacitors and capacitance,
9. 153-176
combination of capacitors in series and in parallel, capacitance of a parallel
10. WAVE OPTICS 177-191 plate capacitor with and without dielectric medium between the plates,
energy stored in a capacitor (no derivation, formulae only).
11. DUAL NATURE OF RADIATION AND MATTER 192-213
Unit II: Current Electricity 18 Periods
12. ATOMS 214-227 Chapter–3: Current Electricity

13. NUCLEI 228-237 Electric current, flow of electric charges in a metallic conductor, drift velocity,
mobility and their relation with electric current; Ohm's law, V-I characteristics
14. SEMICONDUCTOR MATERIAL: ELECTRONIC DEVICES 238-262 (linear and non-linear), electrical energy and power, electrical resistivity and
conductivity, temperature dependence of resistance, Internal resistance of a
15. SAMPLE QUESTION PAPERS 263-284
cell, potential difference and emf of a cell, combination of cells in series and
in parallel, Kirchhoff's rules, Wheatstone bridge
 Chapter–7: Alternating Current

Alternating currents, peak and RMS value of alternating current/voltage;

CBSE QUESTION PAPER DESIGN-2024-25
reactance and impedance; LCR series circuit (phasors only), resonance,
power in AC circuits, power factor, wattless current. (Classes XI-XII)

AC generator, Transformer. Particulars Academic Session 2023-24 Academic Session 2024-25

Composition • Competency Focused Questions in the • Competency Focused Questions in the
of question form of MCQs/ Case Based Questions, form of MCQs/ Case Based Questions,
Unit V: Electromagnetic waves 04 Periods paper for Source-based IntegratedQuestions or Source-based IntegratedQuestions or
year-end
Chapter–8: Electromagnetic Waves any other type = 40% any other type = 50%
examination/
Board • Select response type questions • Select response type questions
Examination (MCQ) = 20% (MCQ) = 20%
Basic idea of displacement current, Electromagnetic waves, their
(Theory) • Constructed response questions • Constructed response questions
characteristics, their transverse nature (qualitative idea only). (Short Answer Questions/Long (Short Answer Questions/Long
Answer type Questions, as per Answer type Questions, as per
Electromagnetic spectrum (radio waves, microwaves, infrared, visible, existing pattern) = 40% existing pattern) = 30%
ultraviolet, X-rays, gamma rays) including elementary facts about their uses.

Unit VI: Optics 30 Periods

Chapter–9: Ray Optics and Optical Instruments

Ray Optics: Reflection of light, spherical mirrors, mirror formula, refraction

of light, 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 lenses in contact, refraction of light
through a prism.

Optical instruments: Microscopes and astronomical telescopes (reflecting and

refracting) and their magnifying powers.

Chapter–10: Wave Optics

Wave optics: Wave front and Huygen’s principle, reflection and refraction of
plane wave at a plane surface using wave fronts. Proof of laws of reflection
and refraction using Huygen’s principle. Interference, Young's double slit
experiment and expression for fringe width (No derivation final expression
only), coherent sources and sustained interference of light, diffraction due to
a single slit, width of central maxima (qualitative treatment only).
 MIND MAP

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
E2. Which is not possible. Since one and only one tangent can be drawn.
Therefore, our assumption is wrong.
5. Electric field contract in length which shows that opposite charges attract.
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.

2 4
 MCQ-LEVEL1 MCQ LEVEL2
1 A force of 4N is acting between two charges in air. If the space between them is 1 .The electric flux through the surface
completely filled with glass (relative permittivity = 8), then the new force will be
(a) 2N ( b) 5N (c) 0.5N (d) 0.2N (a) In figure (iv) is the largest
(b) In figure (iii) is the least
2 A charge q is placed at the center of the line joining two equal charges Q. The system (c) In figure (ii) is same as in figure (iii)
of three charges will be in equilibrium if q is equal to but is smaller than in figure (iv)
(a) –Q/2 ( b) –Q/4 (c )Q/2 (d) Q/4 (d) Is the same for all the figures. (NCERT EXEMPLAR)

3 Two point charges Q and -3Q are placed some distance apart. If the electric field at the 2 A spherical conductor of radius 10cm has a charge 3.2 x10 -7C distributed uniformly.
location of Q is E, the field at the location of -3Q is
What is the magnitude of electric field at a point 15 cm from the centre of the sphere?
(a) E (b) -E (c) E/3 (d) -E/3
(a)1.28x104N/C (b) 1.28x105N/C (c) 1.28x106N/C (d) 1.28x107N/C
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 3 A positive charge Q is uniformly distributed along a circular ring
(a) Zero (b) π/ 2 (c) π/3 (d) π of radius R. A small test charge q is placed at the centre of the
ring in the figure. Then
5 An electric dipole consists of two opposite charges of magnitude 1µC separated by a (a) If q > 0 and is displaced away from the centre in the plane of
distance of 2cm. The dipole is placed in an electric filed 10-5 V/m. The maximum torque the ring, it will be pushed back towards the centre.
(a) 10-3 Nm ( b) 2 x10-13 Nm (c) 3 x10-3 N (d) 4x10-3 Nm (b) If q < 0 and is displaced away from the centre in the plane of
the ring, it will never return to the centre and will continue moving
ASSERTION AND REASON QUESTIONS till it hits the ring.
DIRECTION: Read the two statements
(c) If q < 0, it will perform SHM for small displacement along the axis.
Assertion (A) and Reason (R) carefully to mark the correct option out of the options
given below: (d) q at the centre of the ring is in an unstable equilibrium within the plane of the ring
(a) Assertion and Reason both are correct statements and Reason is correct for q > 0.
explanation for Assertion.
(b) Assertion and Reason both are correct statements but Reason is not correct 4 Two-point charges A and B having charges + Q and -Q respectively, are placed at a
explanation for Assertion. distance apart and the force acting between them is F. If 25% charge on A is transferred
(c) Assertion is correct statement but Reason is wrong statement. to B,then the force between the charges becomes(NEET 2019)
(d) Assertion is wrong statement but Reason is correct statement
(a)4F/3 (b) F (c ) 9F/16 (d)16F/9
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 5 A hemisphere is uniformly charged positively. The electric field at a point on a diameter
field away from the centre is directed
7 Assertion: Coulombs law of force is applicable for point charges at rest. (a) perpendicular to the diameter
Reason: Coulombs law is a central force. (b) parallel to the diameter
8 Assertion: Electric charge is quantized. (c) at an angle tilted towards the diameter
Reason: Charging is because of transfer of an integral number of protons or (d) at an angle tilted away from the diameter.
electrons.
9 Assertion: If there exists coulomb attraction between two bodies, both of them may 6 The Electric field at a point is
not be charged. (a) always continuous.
Reason: In coulomb attraction two bodies are oppositely charged (b) continuous if there is no charge at that point.
10 Assertion: Surface charge density of an irregularly shaped conductor is non uniform (c) discontinuous only if there is a negative charge at that point.
Reason: Surface density defined as charge per unit area (d) discontinuous if there is a charge at that point.
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

6 8
6 An electron falls from rest through a vertical distance h in a uniform and vertically NUMERICALS LEVEL1
upward directed electric field E. The direction of electric field is now reversed, keeping
1. Given a uniform electric field E→=4×103i^ N/C. Find the flux of this field through a
its magnitude the same. A proton is allowed to fall from rest in it through the same
square of 5 cm on a side whose plane is parallel to the Y-Z plane. What would be
vertical distance h. The time of fall of the electron, in comparison to the time of fall of
the flux through the same square if the plane makes a 30° angle with the x-axis?
the proton is
(Delhi 2014)
(a) Smaller (b) 5 times greater (c) 10 times greater (d)equal
2. A sphere S1 of radius r1 encloses a net charge Q. If there
is another concentric sphere S2 of radius r2 (r2 > r,)
7 A spherical conductor of radius 10 cm has a charge of 3.2 × 10-7 C distributed uniformly.
enclosing charge 2Q, find the ratio of the electric flux
That is the magnetude of electric field at a point 15 cm from the centre of the sphere?
through S1 and S2. How will the electric flux through
(a) 1.28x105 N/C (b) 1.28x107 N/C (c) 1.28x10-9 N/C (d)1.28x1011 N/C
sphere S1 change if a medium of dielectric constant K is
introduced in the space inside S2 in place of air?
8 Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are
separated by a distance of 2 cm. If the spheres are connected by a conducting wire,
then in equilibrium condition, the ratio of the magnitudes of the electric fields at the
surface of the sphere A and B will be : NUMERICALS -LEVEL2
(A) 1 : 2 (b) 2 : 1 (c) 1 : 1 (d) 1 : 4(JEE MAINS 2022) 1. (a)Define electric flux. Write its SI
units.
(b) The electric field components due
9 Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 µC to a charge inside the cube of side
are combined to form a bigger drop. The ratio of surface density of bigger drop to the 0.1 m are as shown : Ex = ax, where
smaller drop will be : α = 500 N/C-m
(A) 1 : 4 (b) 4 : 1 (c) 1 : 8 (d) 8 : 1 (JEE MAINS 2022)
Calculate
(i) the flux through the cube, and
**************
(ii) the charge inside the cube.
CASE STUDY QUESTIONS
NUMERICALS -LEVEL3
Photocopiers work on the principle that ‘opposites attract’. Toner is a powder that 1. A hollow cylindrical box of length 1m and area of
is used to create the printed text and images on paper. The powder is negatively cross-section 25 cm2 is placed in a three
charged, and so it is attracted to something positive – the paper. The drum, which
dimensional coordinate system as shown in the
is located in the heart of a photocopier, is positively charged using static electricity.
An image of the master copy is transferred onto the drum using a laser. The light figure. The electric field in the region is given
parts of the image (the white areas on a piece of paper) lose their charge so by E→=50xi^ where E is in NC-1 and x is in metres.
become more negative, and the black areas of the image (where the text is) remain Find
positively charged.
• Net flux through the cylinder.
• Which of the following figures represent the electric field lines due to a single • Charge enclosed by the cylinder. (Delhi 2013
negative charge?
. 2. Two point charges + 3q and – 4q are placed at the
vertices ‘B’ and ‘C’ of an equilateral triangle ABC of side
‘a’ as given in the figure. Obtain the expression for

(i) the magnitude and

(ii) the direction of the resultant electric field at the vertex
A due to these two charges.

10 12
 SELF ASSESSSMENT TEST
M.M 40
UNIT-I ELECTROSTATICS
ANSWER ALL THE QUESTIONS CH:2 ELECTROSTATIC POTENTIAL AND CAPACITANCE
1. What is the work done in moving a test charge q through a distance of 1 cm along the
equatorial axis of an electric dipole? (1) GIST

2. S1and S2are two parallel concentric spheres enclosing charges Electric potential, Potential difference, electric potential due to a point charge, a dipole
Q and 2 Q respectively as shown in Fig.The ratio of the electric flux and system of charges, equipotential surfaces, electric potential energy of a system
through S1and S 2 (1) of two point in charges and of electric dipole in an electrostatic field.
Conductors and insulators, free charges and bound charges inside a conductor.
3. What is the dimensional formula for 0 ? (1) Dielectrics and electric polarization, capacitors and capacitance, combination of
capacitors in series and in parallel, capacitance of a parallel plate capacitor with and
4. Define electric flux(1) without dielectric medium between the plates; energy stored in a capacitor (no
derivation formulae only.
5. Name the physical quantity whose S.I unit is J/C.Is it a scalar or a vector quantity?(1)

6. An oil drop of 12 excess electrons is held stationary under a constant electric field of
2.55 ‫ױ‬04 V m –1in Millikan's oil drop experiment. The density of the oil is 1.26 g cm –3. MIND MAPS
Estimate the radius of the drop. Given that g = 9.81 m s–2and e = 1. 6 x10–19 C. (2)

7. What is the force between two small charged spheres having charges of 2x10 -7c and
3x10-7c placed 30 cm apart in air ? (2)

8. The sum of two point charges is 9 µc .They repel each other is force of 2 N. When
kept 30 cm apart in free space. Calculate the value of each charge. (2)

9.An electric dipole with dipole moment 4x10-9Cm is aligned at 30оwith the direction of
a uniform electric field of magnitude 5x104N/C. Calculate the magnitude of the torque
acting on the dipole (2)

10.Two charges 5x10-8c and -3x10-8C are located 16cm apart. At what points on the
line joining the two charges is the electric potential zero? (2)

11.Derive the formula for electric field of an electric dipole for the following two cases(a)
axial line (b) equatorial line. (5)

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
14 16
➢ Insertion of a dielectric reduces the electric field between the plates of a capacitor 𝟏
*Energy stored in capacitors: U= 𝟐 𝑪𝑽𝟐 =𝟐 𝑸𝑽 = 𝟐𝑪
𝟏 𝑸𝟐

➢ In a series combination of capacitor, the charges on each capacitor are same but 𝟏 𝝈𝟐
the potential difference across any capacitor is inversely proportional to its *Energy density :Ud = ϵ0 E2 =
𝟐 𝟐𝝐𝟎
capacitance.
Capacitance of a parallel plate capacitor with a dielectric medium of dielectric
➢ In a parallel combination of capacitors, the potential difference across each
constant K thickness t in between :
capacitor is same but the charged stored in any capacitor is proportional to its 𝜖0 𝐴
capacitance. Cm= 𝑡
(𝑑−𝑡+ )
𝐾
𝜀0 𝐴 𝜖0 𝐴
➢ When charges are shared between any two bodies, their potential become equal. If t = 0 then C0=
𝑑
If t = d then Cm= K
𝑑
The charges acquired are in the ratio of their capacities. No charges is lost, but ⇒ Cm = KC0
some loss of energy does occur. 𝟏 𝟏 𝟏 𝟏
*Combination of capacitors: (i) Capacitors in series: = + +
𝑪 𝑪𝟏 𝑪𝟐 𝑪𝟑
➢ The capacitance of a capacitor depends neither on Q nor on V. It depends upon
(ii) Capacitors in parallel :C =∑𝒏𝒊=𝟏 𝑪𝒊
the shape and size of the conductor.
𝟏 𝟏 𝑸𝟐
➢ The maximum electric field that a dielectric medium can withstand without break- *Energy stored in capacitors: U= 𝑪𝑽𝟐 = 𝑸𝑽 =
𝟐 𝟐 𝟐𝑪
down (of its insulating property) is called its dielectric strength; for air it is about 𝟏 𝝈𝟐
3 × 106 Vm–1 . For a separation between conductors of the order of 1 cm or so, this *Energy density :Ud = ϵ0 E2 =
𝟐 𝟐𝝐𝟎
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 *Introducing dielectric slab between the plates of the charged conductor with:
capacitance should be high enough so that the potential difference and hence the PROPERTY BATTERY CONNECTED BATTERY DISCONNECTED
electric field do not exceed the break-down limits. Put differently, there is a limit to Charge KQ0 Q0
the amount of charge that can be stored on a given capacitor without significant
Potential difference V0 V0/K
leaking. In practice, a farad is a very big unit.
Electric Field E0 E0/K
GRAPHS Capacitance KC0 KC0
Energy 𝟏 11
K 𝟐ϵ0E2(Energy is supplied 𝐾2
ϵ0E2 (Energy used for
by battery) polarization)
*On connecting two charged capacitors:
𝐶1 𝑉1 +𝐶2 𝑉2
(a) Common Potential : V= 𝑉1 +𝑉2

1 𝐶 ×𝐶
(b)Loss of energy : ΔU = 2 (𝐶 1+𝐶 ) (V1 – V2)2
1 2

3.Graph between E & C 4.Graph of E & V verses distance r

for a point charge ********

18 20
Q9.Capacitors A and B are identical. Capacitor A is charged so it stores 4 J of energy (a)All three in parallel
and capacitor B is uncharged. The capacitors are then connected in parallel. The total (b)All three in series
stored energy in the capacitors is now: (c)Two of them connected in series and the combination in parallel to the third
a) 16 J b) 8 J c) 4 J d) 2 J (d)Two of them connected in parallel and the combination in series to the third
Q10.If both the plate area and the plate separation of a parallel-plate capacitor are
doubled, the capacitance is: Q6. Three capacitors 2 µF, 3 µF and 6 µF are joined in series with each other. The
a) doubled b) halved c) unchanged d) tripled equivalent capacitance is
Q11.An electric dipole of dipole moment p is placed in a uniform electric field of (a) ½ µF (b)1 µF (c)2 µF (d)11 µF
strength E in a direction perpendicular to the field. The work done in rotating the dipole Q7. The work done in moving a unit positive test charge over a closed path in an
by an angle 900 without acceleration in a plane perpendicular to the field is: electric field is _____________.
a) pE b) –pE c). Zero d). -2pE
(a) Always 1 (b)Infinite (c) Zero (d) Negative
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 Q8. Consider a uniform electric field in the z-direction. The potential is a constant
metallic box is:
(a) for any x for a given z
a)Zero b) q c)–q d) 2q (b) for any y for a given z
Q13.In a parallel plate capacitor, the capacity increases if (c) on the x-y plane for a given z
(a) area of the plate is decreased. (d) all of these
(b) distance between the plates increases.
Q9. An electric dipole of moment p is placed in a uniform electric field E . Then
(c) area of the plate is increased.
(i) the torque on the dipole is p ×E→
(d) dielectric constantly decreases.
Q14 An electron moves from point i to point f, in the direction of a uniform electric field. (ii) the potential energy of the system is p .E→
During this displacement:
(iii) the resultant force on the dipole is zero.
Choose the correct option.
a) The work done by the field is positive and the potential energy of the electron-field (a) (i), (ii) and (iii) are correct
system increases. (b) (i) and (iii) are correct and (ii) is wrong
b) The work done by the field is negative and the potential energy of the electron-field (c) only (i) is correct
system increases. (d) (i) and (ii) are correct and (iii) is wrong
c) The work done by the field is positive and the potential energy of the electron-field Q10. The figure shows some concentric equipotential surfaces. The
system decreases. correct choice related to the electric field and its direction is-
d) The work done by the field is negative and the potential energy of the electron-field (a) E ∝ 1/ r and radially inward (b) E ∝ 1/ r2 and radially outward
system decreases.
(c) E ∝ 1/ r and radially outward (d) E ∝ 1/ r2 and radially inward
ASSERTION – REASON QUESTIONS
Directions: These questions consist of two statements, each printed as Assertion and MULTIPLE CHOICE QUESTIONS (LEVEL 3)
Reason. While answering these questions, you are required to choose any one of the Q1.Two charges 14 µC and -4 µC are placed at (-12 cm, 0,0) and (12 cm, 0,0) in an
external electric field E = (B/r2 ), where B = 1.2 x 106 N/cm2 and r is in metres.
following four responses.
The electrostatic potential energy of the configuration is
(a) Both Assertion and Reason are correct and the Reason is a correct explanation of (a) 97.9 J (b) 102.1 J (c) 2.1 J (d) -97.9 J
the Assertion.
Q2.The equivalent capacitance of the combination between A and B in the given figure
(b) Both Assertion and Reason are correct but Reason is not a correct explanation of is 4uf.Calculate capacitance of the capacitor C and charge on each capacitor if a 12V
the Assertion. battery is connected across terminals A and B.
(c) Assertion is correct, Reason is incorrect
22 24
Q8.In a certain region of 0.1 cubic metre of space ,electric potential is found to be 5V Q3. Find the expression for the capacitance of a parallel plate capacitor of area A and
throughout .What is the electric field in this region ? plate separation d if a dielectric slab of thickness t (t<d) is introduced between the
(a)0.5 v/m (b)2 V/m (c)0v/m (d)0.02 V/m plates of capacitor.
Q4. (a) Define the SI unit of capacitance.
Q9.A thin metal sheet is placed in the middle of a parallel plate capacitor. What will be (b) Obtain the expression for the capacitance of a parallel plate capacitor.
the effect on its capacitance ? Q5. A slab of material of dielectric constant K has the same area as that of the plates
(gets doubled (b)no effect (c)halved (d)becomes three times of a parallel plate capacitor but has the thickness d/2, where d is the separation
between the plates. Find out the expression for its capacitance when the slab is
Q10.Three capacitors of 3 ,3 and 6 micro farad are connected in series to a 10V
inserted between the plates of the capacitor.
source. The charge on the 3icro farad capacitor is
(a)5 µC (b)12 µC (c)15µC (d)10 µC 3 MARKS QUESTIONS (LEVEL 2)
Q1. Calculate the potential difference and the energy
*********** stored in the capacitor C2 in the circuit shown i the figure.
Given potential at A is 90 V, C1 = 20 µF, C2 = 30 µF and C3
2 MARKS QUESTIONS (Level 1) = 15 µF.
Q2. A capacitor of unknown capacitance is connected across a battery of V volts. The
Q1.Sketch equi potential surfaces for
charge stored in it is 300 µC. When potential across the capacitor is reduced by 100
(a) A negative point charge (CBSE 2001)
V, the charge stored in it becomes 100 V. Calculate the potential V and the unknown
(b) Two equal and positive charges separated by a small distance. (CBSE
capacitance. What will be the charge stored in the capacitor if the voltage applied had
2015)
increased by 100 V?
Q2.Deduce the expression for the potential energy of an electric dipole placed with its
Q3. A parallel plate capacitor is charged by a battery to a potential difference V. It is
axis at an angle θ to the external field 𝐸⃗ .Hence discuss the conditions of its stable and
disconnected from battery and then connected to another uncharged capacitor of the
unstable equilibrium. (CBSE 2008,2019,2021 Compt.)
same capacitance. Calculate the ratio of the energy stored in the combination to the
Q3.A metal plate is introduced between the plates of a charged parallel plate capacitor.
initial energy on the single 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
3 MARKS QUESTIONS (LEVEL 3)
when connected in series. Calculate their capacitances. Q1. A 200 F parallel plate capacitor having plate separation of 5 mm is charged by a
Q5.An isolated capacitor of unknown capacitance C is charged to a potential 100 V dc source. It remains connected to the source. Using an insulated handle, the
difference V. It is then connected in parallel to an uncharged capacitor of cap distance between the plates is doubled and a dielectric slab of thickness 5 mm and
acitance Co such that the potential difference across the combination become dielectric constant 10 is introduced between the plates. Explain with reason, how the
s V/3. Determine the unknown capacitance C. (i) capacitance, (ii) electric field between the plates, (iii) energy density of the capacitor
Q6.A parallel plate capacitor C with a dielectric in between the plates is charged to a will change ?
potential V by connecting it to a battery. The capacitor is then isolated. If the dielectri Q2.Two identical parallel plate capacitors A and B are
c is withdrawn from the capacitor, connected to a battery of V volts with the switch S closed.
(a) Will the energy stored in the capacitor increase or decrease? The switch is now opened and the free space between the
(b)Will the potential difference across the capacitor plates increase or decrease plates of the capacitors is filled with a dielectric of
? Give an explanation. dielectric constant K. Find the ratio of the total
Q7.A capacitor is connected across a battery .(i)Why does each plate receive a charge electrostatic energy stored in both capacitors before and
of exactly the same magnitude ?(ii)Is this true even if the plates are of different sizes? after the introduction of the dielectric.
Q8. Establish the equation for electric potential at any point in the electric field due Q3.The area of each of the plates of a parallel plate air capacitor is 7 cm2 .
to a point change by using fundamental relation. (a) Determine the maximum charge this capacitor can store without breakdown.
(b)A material of dielectric constant 2 and dielectric strength 15 x 106 V/m is inserted
into the capacitor. Find the percentage change in the maximum chargethat can be stored in
the capacitor with the dielectric material. (Take Dielectric strength of air = 3 x 106 V/m, ∈o
= 8.8 x10‐12 C2/Nm2 )

26 28
(i) before CASE STUDY BASED QUESTION
(ii) after the dielectric has been put in between its plates. An arrangement of two conductors separated by an insulating medium can be used
Q2. Two identical capacitors of plate dimensions l × b and plate separation d have di- to store electric charge and electric energy. Such a system is called a capacitor.
electric slabs filled in between the space of the plates as shown in the figure. The more charge a capacitor can store,
the greater is its capacitance. Usually, a
capacitor consists of two conductors
having equal and opposite charge +Q and
-Q. Hence, there is a potential difference
V between them. By the capacitance of a
Obtain the relation between the dielectric constants K, K1 and K2. capacitor, we mean the ratio of the charge Q to the potential difference V. By the
Q3. A parallel plate capacitor of capacitance C is charged to a potential V by a battery. charge on a capacitor we mean only the charge Q on the positive plate. Total
Without disconnecting the battery, the distance between the plates is tripled and a charge of the capacitor is zero. The capacitance of a capacitor is a constant and
dielectric medium of k = 10 is introduced between the plates is tripled and a dielectric depends on geometric factors, such as the shapes, sizes and relative positions of
medium of k = 10 is introduced between the plates of the capacitor. Explain giving the two conductors, and the nature of the medium between them. The unit of
reasons, how will the following be affected: capacitance is farad (F), but the more convenient units are µF and pF. A commonly
(i) capacitance of the capacitor used capacitor consists of two long strips or metal foils, separated by two long
(ii) charge on the capacitor strips of dielectrics, rolled up into a small cylinder. Common dielectric materials are
NUMERICALS (LEVEL 3) plastics (such as polyestors and polycarbonates) and aluminium oxide. Capacitors
Q1. A network of four capacitors each of 12μF capacitance is connected to a 500 V are widely used in radio, television, computer, and other electric circuits.
supply as shown in the figure.
1.A parallel plate capacitor C has a charge Q . The actual charge on its plates are
Determine (a) Q,Q (b) Q/2, Q/2
(a) equivalent capacitance of the network and (c) Q ,-Q (d) Q/2, -Q/2
(b) charge on each capacitor. 2.A parallel plate capacitor is charged. If the plates are pulled apart .
(a) the capacitance increases (b) the potential difference increases
Q2. A capacitor of unknown capacitance is connected across a battery of V volt. A (c ) the total charge increases (d) the charge & potential difference remains
charge of 240 pC is stored in it. When the potential across the capacitor is reduced by same
80 V, the charge stored in the capacitor becomes 80 pC. Calculate V and the unknown 3.Three capacitors of 2 , 3 & 6 µF are connected in series to a 10 V source. The
charge on the 3 µF capacitor is
capacitance. What would have been the charge in the capacitor if the voltage were
(a) 5µC (b) 10µC (c) 12µC (d) 15µC
increased by 80 V?
4.If n capacitors each of capacitance C are connected in series, then the equivalent
Q3. Find equivalent capacitance between A capacitance of the combination is
and B in the combination given below. Each (a) NC (b) n2C (c) C/n (d) C/n2
capacitor is of 2 µF capacitance.
**********

30 32
carrying an α-particle across a potential difference of one volt. UNIT II CURRENT ELECTRICITY

3MARKS QUESTIONS
CH-3 CURRENT ELECTRICITY
Q9. A charge of 24µC is given to a hollow metallic sphere of radius 0.2 m. find the Gist of the chapter
potential
Electric Current: rate of flow of electric charge
a. At the surface of the sphere
b. At a distance 0.1cm from the centre of the sphere 𝑑𝑞
Instantaneous current: 𝐼 = SI unit: ampere, scalar quantity
𝑑𝑡
c. At the centre of the sphere.
Q10. Derive the expression for electrostatic potential due to dipole .Hence ,find the Current carriers (mobile charge carriers): The charged particles whose drift in a
value of potential on axial and equatorial line of dipole. definite direction constitutes the electric current are called current carriers.

Conventional current in a metallic conductor: In metallic conductors, negatively

5 MARKS QUESTION
charged particles, namely electrons, drift under the influence of applied potential
Q11. (a)Write any two properties of equipotential surfaces. What will be the difference. This constitutes an electron current.
equipotential surface for a dipole.
(b)Two charges –q and +q, are located at points (0, 0, –a) and (0, 0, a), respectively. The direction of drift of positive charges is the direction of current. This current is
(i)What is the electrostatic potential at the points (0, 0, z) and (x, y, 0)? called conventional current. The direction of conventional current is opposite to that
(ii)Obtain the dependence of potential on the distance r of a point from the origin when of drift of electrons.
r/a >> 1.
(iii) How much work is done in moving a small test charge from the point (5,0,0) to Current Density (𝑱): it is amount of charge flowing per second per unit area
(–7,0,0) along the x-axis? Does the answer change if the path of the test charge normal to flow of charge. It is a vector quantity having the same
between the same points is not along the x-axis? direction as that of the motion of the positive charge.
𝐼
𝑗=𝐴
Q12.CASE STUDY BASED QUESTION

In general , 𝐼 = 𝐽. 𝐴

SI unit of current density = Am2

Drift velocity: the average velocity gained by the free

electrons of a conductor in the opposite direction of the
externally applied electric field

Relaxation time: the average time that elapses between

two successive collisions of an electron is called relaxation time.

Relation between drift velocity and electric field: Drift velocity of electron is given
𝑒𝐸⃗ 𝜏
by 𝑣𝑑 = −
⃗⃗⃗⃗ 𝑚
Where 𝑒 = charge on electron, m = mass of electron, 𝜏 =
𝑟𝑒𝑙𝑎𝑥𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒, 𝐸⃗ = electric field
Q1.When a dipole is placed in uniform electric field ,then
(a)It experiences torque but not force
(b)It experiences force but not torque.
(c) It experiences both force and torque.
(d) It experiences neither force not torque.
34 36
V-I characteristics 𝐸𝑒𝑞 = 𝐸1 + 𝐸2

• The variation of current (I) with voltage (V) at various temperatures for any 𝑟𝑒𝑞 = 𝑟1 + 𝑟2
device is called its V-I characteristics.
Cell in parallel
• For an ohmic device, V-I characteristic is linear.

𝐸1 𝑟2 + 𝐸2 𝑟1
𝐸𝑒𝑞 =
𝑟1 + 𝑟2
𝑟1 𝑟2
𝑟𝑒𝑞 =
𝑟1 + 𝑟2

• For a non-ohmic device, the V-I characteristic curve is non-linear.

V-I characteristic of some non-ohmic devices
Electric Power: it is the rate at which an electric appliance convert electric energy into
other forms of energy.
𝑊 𝑉2
P= 𝑡
= 𝑉𝐼 = 𝐼 2 𝑅 = 𝑅
SI unit of power: Watt
V-I characteristic of Ohmic device – Metal conductor
Electric energy: it is the total work done in maintaining an electric current for a given
Effect of temperature on resistance time.
𝑉2
• The resistivity 𝜌 of a material depends on its temperature. For a small variation 𝑊 = 𝑉𝐼𝑡 = 𝐼 2 𝑅𝑡 = 𝑡 Commercial unit: 1 𝐾𝑊ℎ = 3.6 × 106 𝐽
𝑅
of temperature,
𝜌 = 𝜌0 (1 + 𝛼 (𝑇 − 𝑇0 ), where 𝛼 = temperature coefficient of resistance of the High voltage power transmission: suppose power P is delivered to a load R via
material. transmission cables of resistance 𝑅𝑡 . If V is the voltage across load R and I the current
through it, then P = VI The power wasted in transmission cables
• The resistance of a conductor at absolute temperature T is given by the
relation𝑅𝑇 = 𝑅0 (1 + 𝛼(𝑇 − 𝑇0 ), 𝑝2 𝑅𝑡
−1 𝑃⃗𝑡 = 𝐼 2 𝑅𝑡 =
𝑉2
• SI unit of 𝛼 = ℃
1
Distinctive values of 𝜶 for metal, alloys and semiconductor: 𝑃⃗𝑡 ∝
𝑉2
1) For metals, 𝛼 is positive i.e., resistance of metals increases with the Kirchhoff’s first law or junction law(KCL): In an electric circuit, the algebraic sum
increase in temperature. of currents at any junction is zero.
Σ𝐼 = 0
Sign convention for applying junction rule:1.The current
flowing towards the junction are taken as positive.

2.The current flowing away from the junction are taken as

negative.

Variation of resistivity of copper variation of resistivity of nichrome with

temperature. with temperature Σ𝐼 = 𝐼1 + 𝐼3 − 𝐼2 − 𝐼4 = 0 or 𝐼1 + 𝐼3 = 𝐼2 + 𝐼4

2) For alloy like constantan and manganin, the temperature coefficient of

resistance is very small. So, they are used for making standard resistor.

38 40
Mind Map 0f 50mA in the circuit. Find the value of the resistance of resistor:
A. 2500Ω C. 0.4Ω
B. 400Ω D. None of these
9. Among which of the following resistance does not depend :
A. Length of conductor C. Temperature
B. Area cross-section D. Density
10. The incorrect statement among the following statement is
A. Emf of a cell is the potential difference between its positive and negative
potential electrodes in an open circuit
B. Internal resistance of dry cells is much higher than common electrolyte cells
C. The terminal potential difference of a cell can be zero.
D. When current passes from positive to negative terminal of a cell inside it,
terminal potential difference is less than its emf
11. Two wires A and B of the same material, having radii in the ratio 1:2 and carry
currents in the ratio 4:1. The ratio of drift speed of electrons in A and B is
A. 16:1 C. 1:4
B. 1:16 D. 4:1
12. Kirchhoff’s first law, i.e. Σ𝐼 = 0 at a junction, deals with the conservation of
A. Charge C. Momentum
B. Energy D. Angular momentum
13. A battery of emf 10V and internal resistance 30ohm is connected to a resistor.
The current in the circuit is 0.2 amp. The terminal voltage of the battery when
the circuit is closed is
A. 10V C. 1.5V
B. Zero D. 8.5V
14. The potential difference between the terminal of a cell in an open circuit is 2.2
V. when a resistor of 5 ohm is connected across the terminals of the cell, the
potential difference between the terminals of the cell is found to be 1.8 V. the
internal resistance of the cell is
7 9
A. Ω C. Ω
12 10
10 12
B. Ω D. Ω
9 7
15. The figure below shows currents in a part of electric circuit. The current I is

A. 1.7 A C. 1.3A
B. 3.7A D. 1 A
For Questions 16 to 20, two statements are given –one labelled Assertion (A) and
other labelled Reason (R). Select the correct answer to these questions from the
options as given below.

42 44
 14
A. Ω C. 14Ω power of 60W. if these resistances are now connected in parallel combination
3
20 D. 21Ω to the same battery, the electric power consumed will be
B. Ω A. 60 W C. 120 W
3
4. Two solid conductors are made up by of same material, have same length and B. 30 W D. 240 W
same resistance. one of them has a circular cross section of area A 1 and the 7. A heater coil is cut into two equal parts and only one part is now used in the
𝐴
other one has a square cross section area of A2. The ratio 1 is heater. The heat generated will now be.
𝐴2
A. Doubled C. One fourth
A. 1.5 C. 0.8
B. Four times D. Halved
B. 1 D. 2
8. The value of current 𝑖1 flowing from A to C in
5. The solids which have the negative temperature coefficient of resistance are
the circuit diagram is
A. Insulators and
semiconductors
A. 1 A
B. Metals
B. 4 A
C. Insulators only
D. Semiconductor only C. 5 A
D. 2 A
9. In the circuit, given in the figure, currents in
For Questions 6 to 10, two statements are given –one labelled Assertion (A)
and other labelled Reason (R). Select the correct answer to these questions
from the options as given below.
a) If both Assertion and Reason are true and Reason is correct explanation of
Assertion.
b) If both Assertion and Reason are true but Reason is not the correct
explanation of assertion
c) If Assertion is true but Reason is false. different branches and value of one resistor are shown.
d) If both Assertion and Reason are false The potential at point B with respect to the point A is
6. Assertion(A): The conductivity of an electrolyte is very low as compared to a A. +1 V C. +2 V
B. -2 V D. -1 V
metal at room temperature.
Reason(R): The number density of free ions in electrolyte is much smaller as 10. In the circuit shown, the potential difference between A and B is
compared to number density of free electrons in metals. Further, ions drift much
more slowly, being heavier.
7. Assertion(A): The dimensional formula for product of resistance and
conductance is same as for dielectric constant.
Reason(R): Both have dimensions of time constant.
8. Assertion(A): The drift velocity of electrons in a metallic wire will decrease, if
the temperature of the wire is increased.
Reason(R): On increasing temperature, conductivity of metallic wire decreases.
9. Assertion(A): Bending a wire does not affect electrical resistance. A. 6 V B. 3 V C.2 V D. 1 V
Reason(R): Resistance of wire is proportional to resistivity of material
10. Assertion(A): A person touching a high power line gets stuck with the line.
Reason(R): The current carrying wires attract the man towards it.

46 48
3. Under what condition is the heat produced in an electric circuit: LEVEL – 3
(i) Directly proportional
1. Determine the current flowing through the galvanometer G of Wheatstone
(ii) Inversely proportional to the resistance of the circuit.
4. Use Kirchhoff’s rules to obtain the balance condition in Wheatstone bridge. Bridge shown in figure.
5. In the electric network shown in figure, use Kirchhoff’s rules to calculate the 2. (a) Draw a graph showing the variation of
power consumed by the resistance 𝑅 = 4Ω. current versus voltage for a diode

(b) (i) the graph between resistance R

and temperature T for Hg is shown in
figure explain the behavior of Hg near 4 K

LEVEL - 3
1. A) Two wires of equal lengths, one of copper and the other of manganin have
the same resistance. Which wire will be thicker
B) If a wire is stretched to double its original length without loss of mass, how (iii) in which region of the graph shown in figure is
will the resistivity of the wire be influenced? the negative resistance.
2. The following graph shows the variation of terminal potential difference V,
across a combination of three cells in series
to a resistor, versus the current, I : 3. the following table gives the length of three copper
a) Calculate the emf of each cell. wires. Their diameters, and the applied potential differences across their ends.
b) For what current I, will the power Arrange the wires in increasing order according to the following:
dissipation of the circuit be maximum?
Wire no Length diameter Potential difference
1 L 3d V
2 2l D V
3 3l 2d 2V
3. Using Kirchhoff’s rules, calculate the current through 40Ω and 20Ω in the circuit
shown in below figure (i) the magnitude of the electric field within them.
(ii) The drift speed of the electrons through them, and
(iii) The current density within them.
5 MARKS QUESTIONS
LEVEL – 1
1. (a) The electron drift arises due to the force experienced by electrons in the
electric field inside the conductor. But force should cause acceleration. Why
then do the electrons acquire a steady average drift speed? (b) If the electron

50 52
 across the terminals of the cell and percentage error in the reading of the CCT BASED QUESTION
voltmeter.
3. Two aluminium wires have their lengths in the ratio 2 :3 and radii in the ration 1. Tim is a music enthusiast who wishes to create good sound effects for his
1: 3. These are connected in parallel across a battery of emf E and of negligible stereo system using his two sets of speakers at home. The first set consists of
internal resistance. Find the ratio of drift velocities of the electrons in the two two speakers of resistance 10 ohm each. The second set consists of two
wires. speakers with resistance 5 ohm and 10 ohm respectively. Initially, he connects
LEVEL – 3 the first set of two 10 ohm speakers in series to the 10 V stereo output. Later
he connects the second set of speakers such that each of them is parallel to
1. A particle of the charge 2𝜇𝐶 and mass 1.6 g is moving with a velocity 4𝑖̂ 𝑚𝑠 −1 . the first set of speakers.
At t = 0 the particle enters in a region having an electric field 𝐸⃗ (𝑖𝑛 𝑁𝐶 −1 ) =
80𝑖̂ + 60𝑗̂. Find the velocity of the particle at t = 5s (i) What is the current through each of 10 ohm speakers before the second set
2. The circuit in figure shows two cells connected in opposition to each other. Cell of speakers were connected?
𝐸1 is of emf 6V and internal resistance (ii) What is the new current through each of 10 ohm speakers after the second
2.0 Ω; the cell 𝐸2 is of emf 4V and internal set of speakers are connected?
resistance 8.0 Ω. Find the potential (iii) If the loudness of the music is directly proportional to the amount of power
difference between the points A and B. used by the speakers, how has the loudness of the first set of speakers
changed due to the introduction of the second set of speakers?
(iv) What is the impact of connecting the second set of speakers in the circuit?
***********
3. In the circuit shown in figure, with steady current,
calculate the potential difference across the
capacitor and the charge stored in it.

CASE STUDY QUESTION

Read the following text and answer the following
questions on the basis of the same:

Electric Toaster: Small Industries Service Institute takyelpat Industrial Estate Imphal
has designed an Electric toaster which is operated at 220 volts A.C., single phase
and available in four different rated capacity such as 600 W, 750 W, 1000 W and
1250 W. The heating element is made of nichrome 80/20 (80% nickel, 20%
chromium), since Nichrome does not get oxidize readily at high temperature and
have higher resistivity, so it produces more heat.
The element is wound separately on Mica sheets and fitted with body of toaster with
the help of ceramic terminals.

i.) Heating element of the toaster is made of:

(A) copper (B) nichrome (C) chromium (D) nickel

54 56
For Questions 5 to 6, two statements are given –one labelled Assertion (A) and other 1.What is the principle of the Wheatstone bridge?
labelled Reason (R). Select the correct answer to these questions from the options as 2.Name the instrument that is used as a null detector in the Wheatstone bridge.
given below. 3.Which among the following is a false statement?
a) A galvanometer is used as the null detector in a Wheatstone bridge
a) If both Assertion and Reason are true and Reason is correct explanation
b) A galvanometer is an ammeter with low resistance in series
of Assertion.
c) Wheatstone bridge is susceptible to high dc current
b) If both Assertion and Reason are true but Reason is not the correct
d) Due to the errors introduced in contact resistance, a Wheatstone bridge
explanation of assertion
cannot be used for accurate measurement
c) If Assertion is true but Reason is false.
4.PR = QS is the equation of a balanced Wheatstone bridge. Is it true or false?
d) If both Assertion and Reason are false
a) True b) False
5) Assertion(A): Though large number of free electrons are present in the metal.
Yet there is no current in the absence of electric field.
Reason(R): In the absence of electric field electrons move randomly in all
**************
directions.
6) Assertion(A): The value of temperature coefficient of resistance is positive for
metals.
Reason(R): The temperature coefficient is resistance for insulator is also
positive.
Section-B (2 Mark each)

7) A heating element using nichrome connected to a 230 V supply draws an initial

current of 3.2 A which settles after a few seconds to a steady value of 2.8 A.
What is the steady temperature of the heating element if the room temperature
is 27.0 °C and the temperature coefficient of resistance of nichrome is 1.70 ×
10–4 °C–1 ?
8) Graph showing the variation of current versus voltage foe a GaAs is shown in

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.

66 68
 Use of radial magnetic field- The angle between the normal of the plane of loop
and magnetic field θ = 90o,
𝜏 ∝ I, when radial magnetic field is used the deflection
The direction of the magnetic field at the center is perpendicular to the plane of the of coil is proportional to the current flowing through it. Hence a linear scale is
coil. used to determine the deflection of coil.
Uses of galvanometer: (i) Used to detect electric current is a circuit. (ii) Used
9. Ampere's circuital law- It states that the line integral of magnetic field B along to convert the ammeter by putting a low resistor. (iii) Used to convert voltmeter
a closed boundary of an open surface is equal to µ0-times the current (I) passing by putting a high resistor. (iv) Used as ohmmeter by making special
through the open surface with closed boundary.
arrangement
21. Current sensitivity: It is defined as the deflection of coil per unit current flowing
 NAB
in it. Current Sensitivity, S = = .
I K
22. Voltage sensitivity: It is defined as the deflection of coil per unit potential
10. Magnetic field due to infinitely long straight wire using Ampere's law- According  NAB
to Ampere’s circuital law. difference across its ends. Voltage Sensitivity, SV = V = GK
,where G is the
resistance of galvanometer.
23. Conversion of Galvanometer into Ammeter: - A galvanometer may be
11. Straight solenoid- At the axis of a long solenoid, carrying current I converted into ammeter by using very small resistance in parallel with the
B=μ0 nI , where n = N/L = number of turns per unit length. galvanometer coil. The small resistance connected in parallel is called a shunt.
Tip - When we look at any end of the coil carrying current, If the current is in If G is resistance of galvanometer, Ig is current in galvanometer for full scale
anticlockwise direction then that end of the coil behaves like north pole, and If deflection, then for conversion of galvanometer into ammeter of range I ampere,
the shunt is given by
the current is in clockwise direction then that end of the coil behaves like the
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 =
0 (i.e. is parallel to B), then the magnetic force is zero.
24. Conversion of Galvanometer into Voltmeter: - A galvanometer may be
converted into voltmeter by connecting high resistance (R) in series with the
13. Force on a moving charge in uniform magnetic field-The force on a charged
coil of the galvanometer. If V volt is the range of voltmeter formed, then series
particle moving with velocity in a uniform magnetic field is given by F =
resistance is given by
qvBsinө.
14. . The direction of this force is perpendicular to both v and B ,
When v is parallel to B ,ie ө=0, then F=0
When v is perpendicular to B , ie ө=90, then F is maximum, i.e., F=qvB

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
current then thumb gives the direction of the force acting on
the conductor.
16. Force between two parallel current-carrying
conductors- Two parallel current carrying conductors

70 72
MULTIPLE CHOICE QUESTIONS Reason (R): It gives full scale deflection for a current of the order of micro
LEVEL 1 ampere.
16 Assertion (A): A galvanometer can be converted to voltmeter by connecting
a very small resistance in series to it.
1 In a current-carrying loop, the magnetic field is strongest: Reason (R) : Voltmeter is to be connected in series with the circuit
a) At the centre of the loop 17 Name the rule which gives the direction of force, on an electron moving
b) Along the edges of the loop perpendicular to the uniform magnetic field.
c) Inside the loop (a) Fleming’s right hand Rule (b) Fleming’s left hand Rule (c) Right hand
d) Outside the loop Thumb Rule (d) Swimming Rule
2 The magnetic field inside a current-carrying conductor. 18 Which law/rule gives the direction of a magnetic field due to a conductor
(a) increases with the increase in current carrying current?
(b) decreases with the increase in current (a) Faraday's law (b) Fleming's right hand rule
(c) remains constant with the increase in current (c) Right hand thumb rule (d) Fleming's left hand rule
(d) is zero 19 According to the Right hand thumb rule, direction of which physical quantity
3 The direction of the magnetic field at the centre of a current-carrying circular is indicated by the thumb?
loop is: (a) Electric current (b) Magnetic field (c) Magnetic force (d) Motion of
(a) Along the axis of the loop conductor
(b) Parallel to the plane of the loop 20 What is the shape of magnetic field lines passing through the centre of
(c) Radially inward current carrying circular ring?
(d) Tangential to the loop (a) Circular (b) Straight line (c) Ellipse (d) no definite shape
4 Which of the following statements is correct regarding the magnetic field
around a straight current-carrying conductor?
MCQ-LEVEL 2
a) The magnetic field lines form concentric circles centred on the
conductor.
1 A circular coil of radius 4 cm and of 20 turns carries a current of 3 amperes. It
b) The magnetic field lines form straight lines parallel to the conductor.
is placed in a magnetic field of intensity of 0.5 weber/m². The magnetic dipole
c) The magnetic field lines form radial lines away from the conductor.
moment of the coil is
d) The magnetic field lines form hyperbolic curves around the conductor.
a) 0.15 ampere-m² b) 0.3 ampere-m² c) 0.45 ampere-m² d) 0.6 amp-m²
5 A current carrying closed loop of an irregular shape lying in more than one
2 A flat circular coil of 100 turns and radius 10 cm carries a current of 1 A. Then
plane whe placed in uniform magnetic field, the force acting on it
the magnetic dipole moment of the coil is A.
(a) Will be more in the plane where its larger position is covered.
a) π A·m2 b) π/2 A·m2 c) 2π A·m2 d) π/4 A·m2
(b) Is zero.
3 The strength of magnetic field at the Centre of circular coil is
(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 4 If the beams of electrons and protons move parallel to each other in the same
direction, then they
b) 4 times
a) Attract each other. b) Repel each other. c) No relation. d) Neither attracts
c) 2 times nor repel.

74 76
 3 Two α-particles have the ratio of their velocities as 3: 2 on entering the 3 A proton and a deuteron, each moving with velocity v enter simultaneously in
field. If they move in different circular paths, then the ratio of the radii of the region of magnetic field B acting normal to the direction of velocity. Trace
their paths is their trajectories establishing the relationship between the two.
a) 2 : 3 b) 3 : 2 c) 9 : 4 d) 4 : 9 4 A galvanometer of coil resistance 50 Ω shows full scale deflection for a
4 The time period of a charged particle undergoing a circular motion in a current of 5 mA. How can it be converted into a voltmeter of range 0 to 15 V?
uniform magnetic field is independent of: 5 Why is the magnetic field radial in a moving coil galvanometer? Explain how
(a) speed of the particle (b) mass of the particle it is achieved.
(c) charge of the particle (d) magnetic field of the particle
5 If an ammeter is to be used in place of a voltmeter, then we must connect LEVEL 3
with the ammeter a:
(a) low resistance in parallel (b) high resistance in parallel 1 The wire shown below carries a current I. Determine magnetic field at the
(c) high resistance in series (d) low resistance in series centre. Radius of circular section is R.
6 A particle of charge q and mass m moves in a circular orbit of radius r with
angular speed ω. The ratio of the magnitude of its magnetic moment to
that of its angular momentum depends on
(a) ω and q (b)ω, q and m (c) q and m (d) ω and m
2 To increase the current sensitivity of a moving coil galvanometer by 50%, its
Select the most appropriate answer from the options given below: resistance is increased so that the new resistance becomes twice its initial
(a) Both A and R are true and R is the correct explanation of A resistance. By what factor does its voltage sensitivity change?
(b) Both A and R are true but R is not the correct explanation of A. 3 A helium nucleus makes a full rotation in a circle of radius 0.8 m in 2 seconds.
(c ) A is true but R is false. Find the value of the magnetic field at the centre of the circle.
(d) A is false and R is also false.
3 MARKS QUESTIONS
7 Assertion (A): If an electron and proton enter a magnetic field with equal LEVEL-1
momentum, then the paths of both of them will be equally curved.
Reason (R): The magnitude of charge on an electron is same as that on 1 State the underlying principle of working of a moving coil galvanometer. Write
a proton. two reasons why a galvanometer cannot be used as such to measure current
8 Assertion (A): The torque acting on square and circular current carrying in a given circuit. Name any two factors on which the current sensitivity of a
coils having equal areas, placed in uniform magnetic field, will be same. galvanometer depends.
Reason (R): Torque acting on a current carrying coil placed in uniform 2 Using Biot-Savart law derive the expression for the magnetic field due to a
magnetic field does not depend on the shape of the coil, if the areas of the current carrying loop of radius R at a point which is at a distance of x from its
coils are same. centre along the axis of the loop.
9 Assertion (A): Electron enters into a magnetic field at an angle of 60 3 Derive an expression for a force acting per unit length between two long
degree. Its path will be Parabola. straight parallel conductors carrying current in the same direction and kept
Reason (R): Force on electron moving perpendicular to magnetic field is near each other. Hence also define one Ampere.
zero. 4 State Ampere’s circuital law. Derive an expression for magnetic field intensity
10 Assertion (A): Higher the range, lower is the resistance of ammeter. at a point due to a current carrying straight wire of infinite length.
Reason (R): To increase the range of an ammeter, additional shunt is 5 Derive an expression for the torque on a rectangular coil of area A carrying
added in series to it current I and paced in a magnetic field B which is at an angle Ɵ with the
normal to the plane of the coil.
************ LEVEL 2
1 A wire carrying a steady current is first bent in form of a circular coil of one
turn and then in form of a circular coil of two turns. Find the ratio of magnetic
fields at the centres of the two coils.

78 80
 LEVEL 3
1 (a) A uniform magnetic field B is set up along the positive x-axis. A particle of 1. Moving charge can create
charge ‘q’ and mass ‘m’ moving with a velocity v enters the field at the origin (a) Electric field (b) magnetic field
in X-Y plane such that it has velocity components both along and (c) Both electric and magnetic field (d) none of them
perpendicular to the magnetic field B. Trace, giving reason, the trajectory
followed by the particle. Find out the expression for the distance moved by 2. If a current is flowing from south to north in a straight wire what will be the
the particle along the magnetic field in one rotation. direction of magnetic field to its left side
(b) Two small identical (a) Outward (b) inward (c) Towards right (d) towards left
circular coils marked 1, 2
carry equal currents and 3. Which of the following cannot be the source of magnetic field?
are placed with their (a) Current carrying wire (b) moving electron
geometric axes (c) Moving proton (d) stationary charge
perpendicular to each other
as shown in the figure. 4. Force acting on a conductor of length 10 m carrying a current of 6A kept
Derive an expression for perpendicular to the magnetic field of 2T is
the resultant magnetic field (a) 60N (b) 120N (c) 90N (d) 100N
at O.

NUMERICALS COMPETENCY BASED QUESTION

LEVEL 1
1 A circular coil of wire consisting of 100 turns, each of radius 8 cm carries 2 1 CONVERSION OF GALVANOMETER TO VOLTMETER 4
a current of 0.4 A. What is the magnitude of magnetic field at its centre? A galvanometer can be converted into voltmeter of given range by
connecting a suitable resistance Rs in series with the galvanometer, whose
2 A long straight wire carries a current of 35 A. What is the magnitude of 2
value is given by
magnetic field at a point 20 cm from the wire? 𝑉
Rs = 𝐼𝑔 – G
3 An electron of kinetic energy 25KeV moves perpendicular to the 2
direction of a uniform magnetic field of 0.2 milli Tesla. Calculate the time where V is the voltage to be measured, Ig is the current for full scale
deflection of galvanometer and G is the resistance of galvanometer Series
period of rotation of the electron in the magnetic field?
resistor (Rs) increases range of voltmeter and the effective resistance of
4 Two parallel straight wires X and Y separated by a distance 5 cm in air 2 galvanometer. It also protects the galvanometer from damage due to large
carry current of 10 A and 5 A respectively in opposite direction as shown currents.
in diagram. Calculate the magnitude and direction of the force on a 20 Voltmeter is a high resistance instrument and it is always connected in
cm length of the wire Y. parallel with the circuit element across which potential difference is to be
measured. In order to increase the range of voltmeter n times the value of
resistance to be connected in series with galvanometer is Rs = (n-1)G

i) 10 mA current can pass through a galvanometer of resistance 25Ω. What

LEVEL 2 resistance in series should be connected through it, so that it is converted
1 into a voltmeter of 100V?
A galvanometer gives deflection of 10 division per mA. The resistance 3
a) 0.975Ω b) 99.75Ω c) 975 Ω d) 9975Ω
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?

82 84
 1. A circular loop of area 1cm2, carrying a current of 10 A is placed in a (c)Define the terms: (i) voltage sensitivity and (ii) current sensitivity of a
magnetic field of 0.1 T perpendicular to the plane of the loop. The torque galvanometer.
on the loop due to the magnetic field is 11 Lorentz forces- 4
A) zero B) 10−4 Nm C)10−2 Nm D) 1 N m

2. Relation between magnetic moment and angular velocity is

A) M ∝ ω B) M ∝ ω2 C) M ∝ √ω D) none of these

3. A current loop in a magnetic field

A) can be in equilibrium in two orientations, both the equilibrium states are
unstable
B) can be in equilibrium in two orientations, one stable while the other is
unstable
C) experiences a torque whether the field is uniform or non-uniform in all
orientations
D) can be in equilibrium in one orientation.

4. The magnetic moment of a current I carrying circular coil of radius r and

number of turns N varies as
1 1 A charge q moving with a velocity v in presence of both electric and
A) 𝑟2 B) 𝑟 C) r D) r2 magnetic fields experience a force F = q [ E + v x B ]. If electric and
magnetic fields are perpendicular to each other and also perpendicular
to the velocity of the particle, the electric and magnetic forces are in
opposite directions. If we adjust the value of electric and magnetic field
_________________________________________________________
such that magnitude of the two forces are equal. The total force on the
charge is zero and the charge will move in the fields undeflected.

1. What will be the value of velocity of the charge particle, when it moves
undeflected in a region where the electric field is perpendicular to the
magnetic field and the charge particle enters at right angles to the fields.
(a) v = E/B
(b) v = B/E
(c) v = EB
(d) v = EB/q

2. Proton, neutron, alpha particle and electron enter a region of uniform

magnetic field with same velocities. The magnetic field is perpendicular
to the velocity. Which particle will experience maximum force?
(a) proton
(b) electron
(c) alpha particle
(d) neutron

3. A charge particle moving with a constant velocity passing through a

space without any change in the velocity. Which can be true about the
region?
(a) E = 0, B = 0
(b) E ≠ 0, B ≠ 0
(c) E = 0, B ≠ 0
86 88
 UNIT III MAGNETIC EFFECTS OF CURRENT AND MAGNETISM
CH–5: Magnetism and Matter Magnetic Properties of Materials
Substances can be divided into three groups based on their magnetic properties i.e.
Gist of the chapter diamagnetic, paramagnetic, and ferromagnetic. They can be classified based on their
magnetic susceptibility.
• A magnet is a substance or object that produces a magnetic field. Diamagnetic Materials
• These days magnets have a lot of applications in areas such as electrical • The materials that develop temporary magnetization in the opposite direction
devices, motors, fans, power generation, etc. to that of the magnetic field in which they are placed are known as Diamagnetic
• All magnets exhibit magnetic force around them which is represented materials.
in magnetic field lines. • In simple words, they are repelled by magnets.
• These lines start from the north pole of the magnet to the south pole. • Their magnetic susceptibility is small and negative.
• The earth itself exhibits magnetic field lines around making it act like a magnet. • Examples of diamagnetic materials are Bismuth, Copper, Zinc, Lead, etc
Paramagnetic Materials
The properties of magnetic lines of force are as follows: The materials that develop temporary magnetization in the same direction as that of
• Magnetic field lines emerge from the north pole and merge at the south pole. the magnetic field in which they are placed are known as Paramagnetic materials.
• As the distance between the poles increases, the density of magnetic lines • They are slightly attracted by magnets.
decreases. • They have positive but very low susceptibility.
• The direction of field lines inside the magnet is from the South Pole to the North • Examples of Paramagnetic materials are Aluminium, Sodium, Calcium, etc
Pole. Ferromagnetic Materials
• Magnetic lines do not intersect with each other. The materials that develop temporary but strong magnetization in the same direction
• The strength of the magnetic lines is the same throughout and is proportional to that of the magnetic field in which they are placed are known as Ferromagnetic
to how close are the lines. materials.
• They are strongly attracted by magnets.
Magnetic field pattern of a bar magnet
• They have positive and high susceptibility.
• Examples of Ferromagnetic materials are Iron, Nickel, Cobalt, Haematite, etc

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

90 92
CONCEPT MAP/MIND MAP a) 1.2 x 10-4 T b) 2.4 x 10-4 T c) 2.4 x 104 T d) 1.2 x 104 T

LEVEL 3 MCQ
11 A short bar magnet free to rotate on horizontal plane has a magnetic moment of
0.48 J/T. Magnetic field produced by the magnet at a distance of 10 cm from the
centre of the magnet on the equatorial lines (normal bisector) of the magnet has
a direction and magnitude of
a) 0.43 G along N-S direction b) 0.38 G along N-S direction
c) 0.55 G along N-S direction d) 0.48 G along N-S direction

12 The force between two magnetic poles is F. If the distance between the poles
and pole strengths of each pole are doubled, then the force experienced is :
a) F b) F / 4 c) 2F d) F / 2

13 A cube-shaped permanent magnet is made of a ferromagnetic material with a

magnetization M of 4 x 105 A/m. The side length is 2 cm. Magnetic field due to
the magnet at a point 10 cm from the magnet along its axis is
a) 0.003T b) 0.001T c) 0.002T d) 0.004T

ASSERTION–REASON TYPE QUESTIONS

Each question contains STATEMENT – 1 (Assertion) and STATEMENT – 2 (Reason).
Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. So
select the correct choice :
Choices are:
(A)Statement – 1 is True, Statement – 2 is True; Statement – 2 is a correct
explanation
for Statement – 1.
(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a
correct
explanation for Statement – 1.
(C) Statement – 1 is True, Statement – 2 is False.
(D) Statement – 1 is False, Statement – 2 is True.

14 ASSERTION: Basic difference between an electric line and magnetic line of

force is that former is discontinuous and the latter is continuous or endless
REASON: No electric lines of forces exists inside a charged conductor but
magnetic lines do exist inside a magnet
15 ASSERTION: At neutral point, a compass needle point out in any arbitrary
direction.
REASON: Magnetic field of earth is balanced by field due to magnets at the
neutral points.
16 ASSERTION: When a magnetic dipole is placed in a non-uniform magnetic field,
only a torque acts on the dipole.
REASON: Force would not act on magnetic dipole if magnetic field were non
uniform.
17 ASSERTION : Magnetic Resonance Imaging (MRI) is a useful diagnostic tool for
producing images of various parts of human body.
REASON : Protons of various tissues of the human body play a role in MRI.

94 96
 Which magnetic property distinguishes this behaviour of the field lines due to
the two substances? LEVEL 1 (NUMERICALS)
11 Depict the behaviour of magnetic field lines when 1 Find curie constant for a sample from 𝜒 versus 1/T graph shown in fig.
(i) a diamagnetic material and
(ii) a paramagnetic material is placed in an external magnetic field.
Mention briefly the properties of these materials which explain this
distinguishing behaviour.
12 From a molecular viewpoint, discuss the temperature dependence of
susceptibility for diamagnetism, paramagnetism and ferromagnetism.

LEVEL 3 (2 M QUESTIONS)

13 Three identical bar magnets are riveted

together at the centre in the same plane, as
shown in Fig. This system is placed at rest
in a slowly varying magnetic field. It is found 2 How is magnetic force between two poles affected when strength of each pole
that the system of magnets does not show is doubled and distance between them is halved?
any motion. The north-south poles of one
magnet are shown in Fig. Determine the
poles of the remaining two.
LEVEL 2 (NUMERICALS)
1 Two short magnets P and Q are placed one over the another with their
magnetic axis mutually perpendicular to each other. It is found that resultant
LEVEL 1 (3 M QUESTIONS) magnetic field at a point on the prolongation of magnetic axis of P is inclined at
1 (i) The permeability of a magnetic material is 0.9983. Name the type of 30o with the axis. Compare the magnetic moments of the two magnets.
magnetic materials it represents. 2 A magnetised steel wire 31.4cm long has a pole strength of 0.2Am. it is bent in
(ii) The susceptibility of a magnetic material is 1.9 × 10 -5. Name the type of the form of a semicircle. Calculate its magnetic moment..
magnetic materials it represents. 3 Two identical thin bar magnets, each of length L and pole strength m are placed
(iii) The susceptibility of a magnetic material is – 4.2 × 10-6. Name the type of at right angles to each other, with the N pole of one touching the S-pole of the
magnetic materials it represents.
other. Find the magnetic moment of the system.
2 Distinguish between dia, para and ferromagnetic materials.

LEVEL 2 (3 M QUESTIONS) LEVEL 3 (NUMERICALS)

3 Derive expression for magnetic field on an axial point of a magnetic dipole 1 Two identical magnets with a length 10cm and weight 50gf each are arranged
freely with their like poles facing in a vertical glass tube. The upper magnet
4 Derive expression for magnetic field on an equatorial line of a magnetic dipole. hangs in air above the lower one so that the distance between the nearest poles
of the magnets is 3mm. Determine the pole strength of the poles of these
LEVEL 3 (3 M QUESTIONS) magnets.
5 A circular coil of N turns and radius R carries a current I. It is unwound and 2 Two identical short bar magnets each of magnetic moment 12.5Am 2 are placed
rewound to make another coil of radius R/2, current I remaining the same. at a separation of 10 cm between their centers, such that their axis are
Calculate the ratio of the magnetic moments of the new coil and the original coil perpendicular to each other. Find the magnetic field at a point midway between
6 A bar magnet of magnetic moment m and moment of inertia I (about the centre, the two magnets.
perpendicular to length) is cut into two equal pieces perpendicular to the length. 3 A bar magnet of length ‘l’ and magnetic dipole
Let T be the period of oscillations of the original magnet about an axis through moment ‘M’ is bent in the form of an arc as shown
the midpoint, perpendicular to the length, in a magnetic field B. What would be in fig. Find the new dipole moment
the similar period ‘T’ for each piece?
7 A small compass needle of magnetic moment ‘m’ is free to turn about an axis
perpendicular to the direction of uniform magnetic field ‘B’. The moment of
inertia of the needle about the axis is ‘I’. The needle is slightly disturbed from

98 100
 (iv) In a coaxial, straight cable, the central conductor and the outer
conductor carry equal
currents in opposite
direction. The magnetic
field is zero

(a) Point P
(b) for radius more than
a and less than b
(c) Inside the outer
conductor CCT
(d) Inbetween the two 1 Magnetisation and magnetic Intensity
conductors
When the atomic dipoles are aligned partially or fully, there is a magnetic moment
2 According to Neil Bohr’s atom model, in the direction of the field in any small volume of the material. The actual
the negatively charged electron is magnetic field inside material placed in a magnetic field is the sum of the applied
revolving around a positively charged magnetic field and the magnetic field due to magnetization. This field is called
nucleus in a circular orbit of radius r. magnetic intensity (H)
The revolving electron in a closed path 𝐵
constitutes an electric current. The 𝐻 = 𝜇 − 𝑀 where M is magnetization of the material, µo is the permittivity of the
𝑜
motion of the electron in anticlockwise vacuum and B is the total magnetic field. The measure that tells us how a
direction produces conventional magnetic material responds to an external field is given by a dimensionless
current in the clockwise direction. quantity is appropriately known as magnetic susceptibility: for a certain magnetic
Current, I = e/T where T is the period of revolution of the electron. If v is materials, intensity of magnetization is directly proportional to the magnetic
the orbital velocity of the electron, then Due to the orbital motion of the intensity.
electron, there will be orbital magnetic moment μl
(i) Magnetisation of a sample is
𝜇𝐿 = 𝐼𝐴, 𝑤ℎ𝑒𝑟𝑒𝐴𝑖𝑠𝑡ℎ𝑒𝑎𝑟𝑒𝑎𝑜𝑓𝑡ℎ𝑒𝑜𝑟𝑏𝑖𝑡 (a) Volume of sample per unit magnetic moment
𝑒𝑣 𝑒𝑣𝑟 𝑒 𝑒
𝜇𝑙 = 2𝜋𝑟 𝜋𝑟 2 = 2 . If m is mass of electron then 𝜇𝑙 = 2𝑚 (𝑚𝑣𝑟) = 2𝑚 𝑙 (b) Net magnetic moment per unit volume
where mvr = lcalled angular momentum of the electron about the central (c) Ratio of magnetic moment and pole strength
nucleus. Bohr hypothesized that the angular momentum of the orbiting (d) Ratio of pole strength to magnetic moment.
𝑛ℎ (ii) Identify wrongly matched quantity and unit pair
electron has only discrete values given by the equation. 𝑙 = 2𝜋
(a) Pole strength------ ----Am
(b) Magnetic susceptibility ---- dimensionless number
Substituting this in above equation magnetic moment of orbiting electron (c) Intensity of magnetisation----Am-1
is (d) Magnetic permeability---------Henry m
𝑒 𝑛ℎ 𝑛𝑒ℎ
(iii) A solenoid has core of a material with relative permeability 500 and its
𝜇𝑙 = 2𝑚 2𝜋 = 4𝜋𝑚 The minimum value of magnetic moment is (𝜇𝑙 )𝑚𝑖𝑛 = windings carrying a current of 1A. The number of turns of the solenoid
𝑒ℎ
. This value is called Bohr magneton. By substituting the values of e, is 500 per meter. The magnetization of the material is nearly
4𝜋𝑚
(a) 2.5 x 103 Am-1 (b)2.5x 105 Am-1 (c)2.0x 103Am-1 (d)2.0x 105 Am-1
h and m the value of Bohr magneton is 9.27 x 10-24 Am2.
(iv) The relative permeability of iron is 6000. Its magnetic susceptibility is
1. If an electron in an atom revolves around a nucleus in clockwise manner, the
(a) 5999 (b) 6001 (c) 6000 x 10-7 (d) 6000x107
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

102 104
 Three marks question UNIT IV ELECTROMAGNETIC INDUCTION AND ALTERNATING CURRENTS
9 A bar magnet of magnetic moment 1.5 𝐽𝑇 −1 lies aligned with the 3
direction of a uniform magnetic field of 0.22T. CH 6 ELECTROMAGNETIC INDUCTION
(a) What is the amount of work required by an external torque to Syllabus:
turn the magnet so as to align its magnetic moment Faraday's laws, induced EMF and current; Lenz's Law, Self and mutual induction.
(i) Normal to the field direction? And (ii) opposite to the
field direction? GIST
(b) What is the torque on the magnet in case (i) and (ii)
10 (a) Show that the time period (T) of oscillations of a freely 3 1. Faraday's Laws of Electromagnetic Induction:
suspended magnetic dipole of magnetic moment (m) in a
𝐼 Faraday's laws describe how a changing magnetic field can produce an electric current
uniform magnetic field (B) is given by = 2𝜋√ , where 𝐼 is a in a conductor.
𝑚𝐵
moment of inertia of the magnetic dipole.
(b) Identify the following magnetic materials: • First Law: Any change in the magnetic field within a closed loop induces an
(i) A material having susceptibility -0.00015 electromotive force (EMF) in the wire.
(ii) A material having susceptibility 10−5 • Second Law: The induced EMF is equal to the negative rate of change of the
Four marks case based question magnetic flux through the loop. Mathematically, it is expressed as:
11 According to Neil Bohr’s atom 4
model, the negatively charged •
electron is revolving around a
positively charged nucleus in a 2. Induced EMF and Current:
circular orbit of radius r. The
revolving electron in a closed • When a conductor experiences a change in magnetic flux, an EMF is induced,
path constitutes an electric generating a current if the conductor forms a closed circuit.
current. The motion of the
• The direction of the induced current is such that it opposes the change in
electron in anticlockwise
direction produces magnetic flux (Lenz's Law).
conventional current in the clockwise direction. Current, I = e/T
where T is the period of revolution of the electron. If v is the orbital 3. Lenz's Law:
velocity of the electron, then Due to the orbital motion of the
electron, there will be orbital magnetic moment μl Lenz's Law provides the direction of the induced current and EMF. It states that the
direction of the induced EMF and current will be such that it opposes the change in
𝜇𝐿 = 𝐼𝐴, 𝑤ℎ𝑒𝑟𝑒𝐴𝑖𝑠𝑡ℎ𝑒𝑎𝑟𝑒𝑎𝑜𝑓𝑡ℎ𝑒𝑜𝑟𝑏𝑖𝑡 magnetic flux that produced it. This law is a manifestation of the conservation of
𝑒𝑣 𝑒𝑣𝑟
𝜇𝑙 = 𝜋𝑟 2 = . energy.
2𝜋𝑟 2
𝑒 𝑒
If m is mass of electron then 𝜇𝑙 = 2𝑚 (𝑚𝑣𝑟) = 2𝑚 𝑙
Mathematically, Lenz's Law is represented by the negative sign in Faraday's law:
where mvr = l called angular momentum of the electron about the
central nucleus. Bohr hypothesized that the angular momentum
of the orbiting electron has only discrete values given by the
𝑛ℎ
equation. 𝑙 =
2𝜋
4. Self-Induction:
Substituting this in above equation magnetic moment of orbiting
electron is Self-induction is the phenomenon where a change in the current flowing through a coil
𝑒 𝑛ℎ 𝑛𝑒ℎ induces an EMF in the same coil.
𝜇𝑙 = 2𝑚 2𝜋 = 4𝜋𝑚 The minimum value of magnetic moment is
𝑒ℎ
(𝜇𝑙 )𝑚𝑖𝑛 = . This value is called Bohr magneton. By
4𝜋𝑚

106 108
 MCQ c) the resistance of the coil
LEVEL – 1 d) the length of the coil
1. Faraday's law of electromagnetic induction states that the induced EMF in a
circuit is directly proportional to: 22. Which of the following is not a factor affecting the inductance of a coil?
a) the resistance of the circuit a) The number of turns in the coil b) The material of the core
b) the magnetic flux through the circuit c) The cross-sectional area of the coil d) The resistance of the coil
c) the rate of change of magnetic flux through the circuit LEVEL – 2
d) the current in the circuit
1. The magnetic flux through a coil of 100 turns changes from 5 Wb to 2 Wb in 0.2
2. The unit of magnetic flux is: seconds. What is the induced EMF in the coil?
a) Tesla b) Weber c) Gauss d) Henry a) 1500 V b) 2000 V c) 2500 V d) 3000 V
3. Lenz's law is a consequence of the law of: 2. A coil is moved quickly out of a magnetic field. According to Lenz's law, the
a) conservation of energy b) conservation of charge direction of the induced current will be such that it will:
c) conservation of momentum d) conservation of mass a) oppose the increase in magnetic flux

4. The direction of induced current in a conductor moving in a magnetic field is b) support the increase in magnetic flux
given by:
c) oppose the motion of the coil
a) Fleming's right-hand rule b) Fleming's left-hand rule c) Lenz's law d)
Ampere's law d) support the motion of the coil
5. Mutual induction between two coils depends on: 3. A magnet is dropped through a coil. The direction of the induced current will be
a) the resistance of the coils b) the rate of change of current in one coil such that it will:
c) the physical dimensions of the coils d) the potential difference across the a) attract the magnet as it falls
coils b) repel the magnet as it falls
6. The SI unit of inductance is:
c) have no effect on the magnet
a) Farad b) Coulomb c) Weber d) Henry
d) both attract and repel the magnet
7. Which of the following can cause an induced EMF in a coil?
a) A steady magnetic field b) A changing magnetic field 4. In a circuit, the current changes at a rate of 2 A/s. If the inductance of the coil
c) A constant current d) A steady electric field is 3 H, what is the induced EMF?
a) 2 V b) 3 V c) 4 V d) 6 V
8. The self-inductance of a solenoid depends on:
a) the length of the solenoid b) the number of turns in the solenoid 5. A current of 5 A is established in a coil with an inductance of 4 H. If the current
is suddenly reduced to zero in 0.1 seconds, what is the induced EMF?
c) the area of cross-section of the solenoid d) all of the above a) 200 V b) 300 V c) 400 V d) 500 V
9. The induced EMF in a coil is zero when: 6. A solenoid with a length of 0.5 m and 1000 turns has a current of 2 A passing
a) the coil is moved perpendicular to the magnetic field through it. If the current changes at a rate of 4 A/s, what is the induced EMF in
b) the coil is stationary in a changing magnetic field the solenoid?
a) 2 V b) 4 V c) 6 V d) 8 V
c) the magnetic flux through the coil remains constant
7. The self-inductance of a coil is 10 H. If a current of 3 A is passing through it,
d) the magnetic field is zero what is the energy stored in the coil?
a) 30 J b) 45 J c) 60 J d) 90 J
10. The phenomenon of electromagnetic induction was discovered by:
a) Newton b) Faraday c) Maxwell d) Ampere 8. A coil with an inductance of 5 H carries a current of 4 A. If the current decreases
11. In an AC generator, the frequency of the induced EMF depends on: to 0 A in 0.2 seconds, what is the average induced EMF in the coil?
a) the speed of rotation of the coil b) the number of turns in the coil a) 10 V b) 20 V c) 40 V d) 100 V

110 112
3. Describe how an EMF is induced in a coil when the magnetic field through it change in magnetic flux. C) The induced EMF in the loop. D) The direction of
changes. the induced current using Lenz's Law.
4. What factors affect the magnitude of the induced EMF in a conductor moving
through a magnetic field? LEVEL – 2
5. State Lenz’s Law and explain its significance in determining the direction of 2. A coil of 100 turns and radius 0.05 m is placed in a magnetic field that varies
induced current.
with time according to the equation B(t)=0.01t2+0.02t, where B is in tesla and t
6. Provide an example to illustrate Lenz’s Law in a practical scenario.
7. Define self-induction and explain what is meant by the self-inductance of a coil. is in seconds.
8. What is the physical significance of the self-inductance in an electrical circuit? 1. Derive the expression for the magnetic flux through the coil as a function of
9. Define mutual induction and explain the concept of mutual inductance between time. B) Calculate the induced EMF in the coil at t=2t = 2t=2 seconds. C) Using
two coils.
Lenz’s Law, determine the direction of the induced current if the magnetic field
LEVEL – 2 is increasing.
1. A circular coil of radius 0.1 m is placed in a uniform magnetic field of 0.5 T, with
its plane perpendicular to the magnetic field. If the magnetic field changes LEVEL – 3
uniformly to 1.5 T in 0.2 s, calculate the average induced EMF in the coil.
2. A solenoid with 500 turns and a cross-sectional area of 0.01 m2 is placed in a 3. A solenoid with a self-inductance of 0.2 H is connected in series with a 10-ohm
resistor and a power supply. The current through the circuit increases uniformly
changing magnetic field. The magnetic flux through the solenoid increases from
from 0 to 5 A in 0.5 seconds. A) Calculate the induced EMF in the solenoid. B)
0.02 Wb to 0.06 Wb in 0.1 s. What is the average induced EMF in the solenoid? Determine the total voltage across the solenoid and resistor during this time. C)
3. A rectangular loop of wire is moved away from a long straight wire carrying a If another coil with a mutual inductance of 0.1 H with the solenoid is placed
nearby, calculate the induced EMF in the secondary coil during the same time
steady current. Describe the direction of the induced current in the loop and
period.
explain how Lenz’s Law applies to this situation. LEVEL-1 (NUMERICALS)
4. A coil with an inductance of 2 H has a current that increases at a rate of 3 A/s.
1. A coil of wire has 50 turns and a cross-sectional area of 0.1 m². The coil is
Calculate the induced EMF in the coil. placed in a magnetic field that changes uniformly from 0.2 T to 0.5 T in 0.1
5. wo coils are placed close to each other. A current change of 4 A/s in the first seconds. Calculate the induced EMF in the coil.
2. A straight conductor of length 1 meter is moved perpendicularly to a magnetic
coil induces an EMF of 0.8 V in the second coil. Calculate the mutual inductance
field of strength 0.2 T with a speed of 2 m/s. Calculate the induced EMF across
between the two coils. the ends of the conductor.
LEVEL – 3 3. A coil with 200 turns and a cross-sectional area of 0.05 m² is placed in a
1. A coil of 50 turns is placed in a magnetic field that changes from 0.2 T to 0.6 T magnetic field. The magnetic field changes at a rate of 0.1 T/s. Calculate the
in 0.4 seconds. The area of the coil is 0.1 m 2. Calculate the average induced induced EMF in the coil and indicate the direction of the induced current
EMF in the coil. according to Lenz’s Law.
2. Explain how Lenz’s Law applies when a metal ring is dropped into a region 4. A solenoid with 500 turns and an inductance of 2 H is connected to a circuit. If
where a magnetic field is increasing upwards. What will be the direction of the the current through the solenoid changes uniformly from 0 A to 5 A in 0.5
induced current in the ring as it enters the magnetic field? seconds, calculate the induced EMF.
3. A solenoid with an inductance of 2 H carries a current that decreases uniformly LEVEL-2 (NUMERICALS)
from 3 A to 0 A in 0.5 s. Determine the self-induced EMF in the solenoid during
1. Two coils, coil A with 500 turns and coil B with 300 turns, are placed close to
this time period.
each other. The mutual inductance between the coils is 2 H. If a current in coil
A changes from 0 to 10 A in 0.2 seconds, calculate the induced EMF in coil B.
Additionally, determine the energy transferred to coil B during this time.

114 116
 Short Answer Questions
4. What is the magnitude of the induced current (III) in the loop? 7. Explain Faraday's Law of Electromagnetic Induction. (2 marks)
A. 0.25 A B. 0.5 A C. 0.75 A D. 1.0 A
Intermediate Answer Question
8. Describe the principle of mutual induction with the help of a diagram. (3 marks)
COMPETENCY BASED
Two coils, Coil A and Coil B, are placed close to each other. Coil A has 300
Case Study-Based MCQs (4 marks)
turns and an inductance of 2 H, while Coil B has 400 turns and an inductance
of 3 H. The mutual inductance between the two coils is 1 H. Coil A is connected Read the following passage and answer the questions that follow:
to a variable power supply and a switch. Initially, there is no current in Coil A. A coil of wire is connected to a galvanometer. When a bar magnet is moved towards
At t=0, the switch is closed, and the current in Coil A increases uniformly from the coil, the galvanometer shows a deflection. When the bar magnet is moved away
0 A to 5 A in 1 second. Coil B is connected to a resistor of 2 Ω. from the coil, the galvanometer shows a deflection in the opposite direction. The
1. Calculate the rate of change of current dIA/dt in Coil A. faster the magnet is moved, the greater the deflection.
2. Determine the induced EMF εB in Coil B.
9. What is the principle demonstrated in the above experiment?
3. Calculate the induced current IB in Coil B.
a) Ohm's Law
4. Find the total energy transferred to Coil B during the 1 second. b) Faraday's Law of Electromagnetic Induction
CCT BASED c) Coulomb's Law
d) Ampere's Law
A researcher is conducting an experiment to demonstrate Lenz’s Law using a
setup that includes a strong horseshoe magnet, a copper pipe, a solenoid, a 10. What does the direction of deflection of the galvanometer indicate?
sensitive ammeter, and a small aluminium ring. The following scenarios are a) The direction of the magnetic field
being investigated: b) The direction of the induced current
c) The magnitude of the induced EMF
1. Dropping a strong magnet through a vertically oriented copper pipe. d) The strength of the magnetic field
2. Moving a magnet rapidly towards and away from the solenoid connected to the
ammeter. 11. What will happen if the number of turns in the coil is increased?
3. Placing the small aluminium ring on the top of the solenoid and turning the a) The deflection will decrease.
b) The deflection will remain the same.
current on and off in the solenoid.
c) The deflection will increase.
1. In the first scenario, describe the motion of the magnet as it falls through the d) The deflection will first increase and then decrease.
copper pipe. Explain how Lenz’s Law applies to this scenario and predict
the experimental observations. 12. Which of the following factors does NOT affect the magnitude of the induced
2. In the second scenario, what will the ammeter show when the magnet is EMF?
moved towards and then away from the solenoid? Explain your answer a) The speed of the magnet
using Lenz’s Law. b) The number of turns in the coil
3. For the third scenario, predict and explain what happens to the aluminium c) The strength of the magnetic field
ring when the current in the solenoid is suddenly turned on and off. d) The resistance of the coil
4. Consider a scenario where the copper pipe is replaced with a pipe made of
Long Answer Questions
a different non-conducting material, such as plastic. Predict how the motion 13. Derive the expression for the self-inductance of a solenoid and discuss the
of the magnet changes and explain why, based on Lenz’s Law. factors affecting it. (5 marks)

******** 14. Explain Lenz's Law with an example and describe its significance in the
conservation of energy. (5 marks)

118 120
 𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡
𝑑𝑖
𝑉 − 𝐿 = 0 (using Kirchhoff’s
𝑑𝑡 Power in AC circuit: The Power Factor:
rule)
𝑑𝑖 𝑉 𝑉𝑚 We know that, an AC voltage 𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 applied to a series LCR circuit drives a
= = 𝑠𝑖𝑛𝜔𝑡 current in the circuit given by 𝐼 = 𝐼𝑚 sin (𝜔𝑡 + 𝜑).
𝑑𝑡 𝐿 𝐿
𝑑𝑖 𝑉𝑚
∫ 𝑑𝑡 = ∫ 𝑠𝑖𝑛𝜔𝑡𝑑𝑡 Instantaneous Power = Instantaneous Voltage X Instantaneous Current
𝑑𝑡 𝐿 𝑇𝑟𝑢𝑒 𝑃𝑜𝑤𝑒𝑟 𝑃𝑎𝑣
𝑉𝑚 P = VI = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 X 𝐼𝑚 sin (𝜔𝑡 + Power Factor = 𝑐𝑜𝑠∅= =
𝑖=− 𝑐𝑜𝑠𝜔𝑡 + 𝐶 𝜑) 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑃𝑜𝑤𝑒𝑟 𝑉𝑟𝑚𝑠 𝑖𝑟𝑚𝑠
𝜔𝐿 (i) If ∅ = 00 , cos 00 = 1, then R=Z (pure
𝜋 𝑉 𝑉𝑚 𝑖𝑚
𝑖 = 𝑖𝑚 𝑠𝑖𝑛 (𝜔𝑡 − ) (𝑖𝑚 = 𝑚 ) 𝑃⃗ = [𝑐𝑜𝑠∅ − 𝑐𝑜𝑠(2𝜔𝑡 + ∅)] Resistance)
2 𝜔𝐿 2
Inductive reactance, 𝑋𝐿 = 𝜔𝐿 𝑉𝑚 𝑖𝑚 𝑉𝑚 𝑖𝑚 (ii) If ∅ = 900 , cos 900 = 0, then P=0 (pure
Current lags behind the voltage in 𝑃⃗ = 𝑐𝑜𝑠∅ = 𝑐𝑜𝑠∅ inductive or capacitive)
𝜋 2 √2 √2
phase by 2 rad. The average power consumed over a cycle is
𝑃⃗ = 𝑉𝑟𝑚𝑠 𝑖𝑟𝑚𝑠 𝑐𝑜𝑠∅
zero and current is called wattless current.
OR True power = virtual power X
Voltage leads the current in phase 𝑐𝑜𝑠∅
𝜋
by rad. 𝑃⃗ = 𝐼 2 𝑍𝑐𝑜𝑠∅
2
If circuit has all the three element R, L and C then
𝑅 𝑅
Power factor = 𝑐𝑜𝑠∅ = 𝑍 = 2 2
√(𝑅) +(𝑋𝐶 −𝑋𝐿 )

AC voltage applied to a capacitor: Transformer:

𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 Let Np and Ns be the number

𝑞 of turns in the primary and
𝑉= secondary of the transformer.
𝐶
𝑞 The voltage induced in the
𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 =
𝐶 secondary is
𝑑𝑞 𝑑 𝑑∅
𝑖= = (𝐶𝑉𝑚 𝑠𝑖𝑛𝜔𝑡) 𝜀𝑆 = −𝑁𝑆
𝑑𝑡 𝑑𝑡 𝑑𝑡
= 𝜔𝐶𝑉𝑚 𝑐𝑜𝑠𝜔𝑡 alternating flux f also induces
𝑉𝑚 𝜋 an emf, called back emf in the
= 𝑠𝑖𝑛 (𝜔𝑡 + )
1⁄ 2 primary
𝜔𝐶 𝑑∅
𝜋 𝜀𝑃 = −𝑁𝑃
= 𝑖𝑚 𝑠𝑖𝑛 (𝜔𝑡 + ) 𝑑𝑡
2 𝜀𝑆 𝑁𝑆 𝐼𝑃
1
Capacitive reactance, 𝑋𝐶 = = =
𝜔𝐶 𝜀𝑃 𝑁𝑃 𝐼𝑆
Current leads the voltage in It is a device for covert an AC at low to high voltage Energy Loss:
𝜋
phase by 2 rad. or vice versa. (i) Copper loss
OR Principal: works on Mutual induction. (ii) Eddy current loss
Voltage lags behind the current A transformer consists of two coils of insulated (iii) Flux leakage
𝜋
in phase by 2 rad. copper wire having different number of turns and (iv) Humming loss
wound on the same soft iron core. The coil to which (v) Hysteresis loss
electric energy is supplied is called the primary and
the coil from which energy is drawn is called the Efficiency of transformer,
secondary. 𝑂𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
𝜂= × 100%
To prevent energy losses due to eddy currents, a 𝐼𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
laminated core is used.
Types:
Step up Step down
𝑁𝑆 > 𝑁𝑃 , 𝜀𝑆 > 𝜀𝑃 , 𝑖𝑆 < 𝑖𝑃 𝑁𝑆 < 𝑁𝑃 , 𝜀𝑆 < 𝜀𝑃 , 𝑖𝑆 > 𝑖𝑃

122 124
MIND MAP (a) Always leads the voltage
(b) Always lags behind the voltage
(c) Is always in phase with the voltage
(d) May lead or lag behind or be in phase with the voltage
Q.11 Which of the following statements is true about the LCR circuit connected to
an AC source at resonance?
(a) voltage across R equals the applied voltage
(b) voltage across R is zero
(c) voltage across C is zero
(d) voltage across L equals the applied voltage
Q.12 What happens to the inductive reactance when the frequency of the AC
supply is increased?
(a) Increases (b) Decreases (c) Remains the same (d) Decreases
inversely
Q.13 When is the current in a circuit wattless?
(a) When the inductance of the circuit is zero
(b) When the resistance of the circuit is zero.
(c) When the current is alternating.
(d) When both resistance and inductance are zero.
Q.14 L, C and R denote inductance, capacitance and resistance respectively.
Pick out the combination which does not have the dimensions of frequency
(a) 1/RC (b) R/L (c) C/L (d) 1/√𝐿𝐶
Q.15 What will be the phase difference between virtual voltage and virtual
current, when the current in the circuit is wattless
(a) 90° (b) 45° (c) 180° (d) 60°
Q.16 The phase difference between the current and voltage of LCR circuit in
series combination at resonance is
𝜋
(a) 0 (b) 2 (c) 𝜋 (d) – 𝜋
Q.17 Power delivered by the source of the circuit becomes maximum, when
1 1
(a) 𝜔𝐿 = 𝜔𝐶 (𝑏)𝜔𝐿 = (𝑐)𝜔𝐿 = √𝜔𝐶 (𝑑)𝜔𝐿 = −
𝜔𝐶 𝜔𝐶
Q.18 When power is drawn from the secondary coil of the transformer, the
dynamic resistance
(a) Increases (b) Decreases (c) Remains unchanged
(d)Changes erratically

Q.19 A transformer is employed to

(a) Obtain a suitable dc voltage
(b) Convert dc into ac
(c) Obtain a suitable ac voltage
(d) Convert ac into dc
Q.20 Quantity that remains unchanged in a transformer is
(a) Voltage (b) Current (c) Frequency (d) None of above

126 128
 (a) 100 Ω (b) 30 Ω (c) 3.2 Ω (d) 10 Ω Q.13 Assertion: The dc and ac both can be measured by a hot wire instrument.
Q.2 An ac circuit consists of an inductor of inductance 0.5 H and a capacitor of Reason: The hot wire instrument is based on the principle of magnetic effect
capacitance 8 μF in series. The current in the circuit is maximum when the of current.
angular frequency of ac source is
Q.14 Assertion: ac is more dangerous than dc
(a) 500 rad/sec (b) 2X105 rad/sec (c) 4000 rad/sec (d) 5000 rad/sec
Q.3 An inductive circuit contains a resistance of 10 Ω and an inductance of 2.0 H. Reason: Frequency of ac is dangerous for human body.
If an ac voltage of 120 V and frequency of 60 Hz is applied to this circuit, the Q.15 Assertion: Average value of ac over a complete cycle is always zero.
current in the circuit would be nearly Reason: Average value of ac is always defined over half cycle.
(a) 0.32 A (b) 0.16 A (c) 0.48 A (d) 0.80 A Q.16 Assertion: The divisions are equally marked on the scale of ac ammeter.
Q.4 The power factor of an ac circuit having resistance (R) and inductance (L) Reason: Heat produced is directly proportional to the current.
connected in series and an angular velocity ω is Q.17 Assertion: When ac circuit contain resistor only, its power is minimum.
𝑅 𝑅 𝜔𝐿 𝑅
(a) 𝜔𝐿 (b) 2 2 2
(c) 𝑅 (d) 2 2 2 Reason: Power of a circuit is independent of phase angle.
√(𝑅 +𝜔 𝐿 ) √(𝑅 −𝜔 𝐿 )
Q.5 A telephone wire of length 200 km has a capacitance of 0.014 μF per km. If Q.18 Assertion: An electric lamp connected in series with a variable capacitor and
it carries an ac of frequency 5 kHz, what should be the value of an inductor ac source, its brightness increases with increase in capacitance.
required to be connected in series so that the impedance of the circuit is Reason: Capacitive reactance decrease with increase in capacitance of
minimum capacitor.
(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 Q.19 Assertion: An inductance and a resistance are connected in series with an
of 200 V (r.m.s.) and angular frequency 300 rad/s. When only the capacitor ac circuit. In this circuit the current and the potential difference
is removed, the current lags behind the voltage by 60 0. When only the across the resistance lag behind potential difference across the
inductor is removed the current leads the voltage by 600. The average power inductance by an angle 𝜋/2.
dissipated is Reason: In LR circuit voltage leads the current by phase angle which
(a) 50 W (b) 100 W (c) 200 W (d) 400W depends on the value of inductance and resistance both.
Q.7 A power transformer is used to step up an alternating e.m.f. of 220 V to 11
Q.20 Assertion: A capacitor of suitable capacitance can be used in an ac circuit
kV to transmit 4.4 kW of power. If the primary coil has 1000 turns, what is the
in place of the choke coil.
current rating of the secondary? Assume 100% efficiency for the transformer
Reason: A capacitor blocks dc and allows ac only.
(a) 4 A (b) 0.4 A (c) 0.04 A (d) 0.2 A
Q.8 A loss free transformer has 500 turns on its primary winding and 2500 in
secondary. The meters of the secondary indicate 200 volts at 8 amperes SA – I (2 Marks each)
under these conditions. The voltage and current in the primary is Level – 1
(a) 100 V, 16 A (b) 40 V, 40 A (c) 160 V, 10 A (d) 80 V, 20 A
Q.9 The figure shows variation of R, XL and XC Q.1 (i) Define root mean square value of an alternating current.
with frequency f in a series L, C, R circuit.
(ii) Write the relation between peak and root mean square value of alternating
Then for what frequency point, the circuit is
inductive current.
Q.2 Draw the graphs showing variation of inductive reactance and capacitive
(a) A (b) B (c) reactance with frequency of applied ac source.
C (d) All points Q.3 A lamp is connected in series with a capacitor. Predict your observation when
this combination is connected in turn across
Q.10 Which of the following plots may represent the reactance of a series LC
combination (i) AC source
(ii) a DC battery. What change would your notice in each case if the
(a) a (b) b (c) c (d) d capacitance of the capacitor is increased?
Q.4 (i) Define capacitive reactance. Write its SI unit.
(ii) Why is the use of AC voltage preferred over DC voltage? Give two reasons.
Assertion – Reason Questions: Q.5 State the principal of a transformer. How is the large scale transmission of
electric energy over long distances done with the use of transformers?
(a) If both assertion and reason are true and the reason is the correct explanation of Q.6 Mention various energy losses in a transformer.
the assertion.

130 132
 Level – 2 Level – 3
Q.1 An alternating voltage 𝑉 = 𝑉𝑚 𝑠𝑖𝑛𝜔𝑡 applied to a series LCR circuit derives a 1. A 2 μF capacitor, 100 Ω resistor and 8 H inductor are connected in series with
current given by 𝑖 = 𝑖𝑚 𝑠𝑖𝑛(𝜔𝑡 + ∅). Deduce an expression for the average a AC source.
power dissipated over a cycle. (i) What should be the frequency of the source such that current drawn in the
Q.2 When a capacitor is connected in series with a series LR circuit, the circuit is maximum? What is this frequency called?
alternating current flowing in the circuit increases. Explain why. (ii) If the peak value of emf of the source is 200 V, find the maximum current.
Q.3 State the principal of an AC generator. Obtain the expression for the emf (iii) Draw graph showing variation of amplitude of circuit current with changing
induced in a coil with labelled diagram. frequency of applied voltage in a series LCR circuit for two different values
of resistance R1 and R2 (R1>R2).
Level – 3 (iv) Define the term sharpness of resonance. Under what condition, does a
circuit become more selective?
Q.1 An inductor L of inductance XL is connected in series with a bulb B and an 2. The primary coil of an ideal step up transformer has 100 turns and
AC source. How would brightness of the bulb change when (i) number of transformation ratio is also 100. The input voltage and power are respectively
turns in the inductor is reduced. (ii) an iron rod is inserted in the inductor and 220V and 1100 W. calculate
(iii) a capacitor of reactance XC=XL is inserted in series in the circuit. Justify (i) number of turns in secondary
your answer in each case. (ii) current in primary
Q.2 Does the current in an ac circuit lag, lead, or remain in phase with the voltage (iii) voltage across secondary
frequency applied to the circuit, when (i) f=fr, (ii) f<fr and (iii) f>fr, where fr is (iv) current in secondary
the resonant frequency? (v) power in secondary
LA (5 Marks each) 3. A series LCR circuit with L= 4.0 H, C= 100 μF and R= 60 Ω is connected to a
Level – 1 variable frequency 240 V source. Calculate
Q.1 (i) Differentiate between the term inductive reactance and capacitive (i) the angular frequency of the source which drives the circuit at
reactance of an ac circuit. resonance
(ii) If an inductor and a resistor are connected in series in an ac circuit, what (ii) the current at the resonating frequency
will be the mathematical expression for the impedance of this circuit. How will (iii) the rms potential drop across the inductor at resonance.
the impedance get affected when the frequency of applied signal is decreased
and why?
Case Based questions/Source based questions:
Level –2 Q.1 When electric power is transmitted over great distances, it is economical to
Q.1 A device X is connected across as AC source of voltage 𝑉 = 𝑉𝑚 sin 𝜔𝑡. The use a high voltage and a low current to minimize the I 2R loss in the
𝜋
current through X is given as 𝑖 = 𝑖𝑚 𝑠𝑖𝑛 (𝜔𝑡 + 2 ). transmission lines. Consequently, 350-kV lines are common, and in many
(i) Identify the device X and write the expression for its reactance. areas even higher-voltage (765-kV) lines are under construction. At the
(ii) Draw graphs showing variation of voltage and current with time over one receiving end of such lines, the consumer requires power at a low voltage (for
cycle of AC, for X safety and for efficiency in design). Therefore, a device is required that can
(iii) How does the reactance of the device X vary with frequency of the AC?
change the alternating voltage and current without causing appreciable
Show this variation graphically.
(iv) Draw the phasor diagram for the device X. changes in the power delivered. The ac transformer is that device. In its
simplest form, the ac transformer consists of two coils of wire wound around
Level – 3 a core of iron. The coil on the left, which is connected to the input alternating
Q.1 A device ‘X’ is connected to an ac source. The variation of voltage, current voltage source and has N1 turns, is called the primary winding (or the
and power in one complete cycle is shown in the figure primary). The coil on the right, consisting of N 2 turns and connected to a load
resistor R, is called the secondary winding (or the secondary). The purpose
of the iron core is to increase the magnetic flux through the coil and to provide
a medium in which nearly all the flux through one coil passes through the
other coil. Eddy current losses are reduced by using a laminated core. Iron is

134 136
 (iv) What is the impedance of a capacitor with capacitance C in an ac circuit (c) If assertion is true but reason is false.
having source of frequency 50 Hz (d) If the assertion and reason both are false
(a) 1/C (b) 1/50 C (c)1/100 C (d) 1/314 C 5 Assertion: A given transformer can be used to step-up or step- 1
down the voltage.
CCT Based Question: Reason: The output voltage depends upon the ratio of the number
Q.1 An airport metal is essentially a resonant circuit. The portal you step through of turns of the two coils of the transformer.
is an inductor (a large loop of conducting wire) that is part of the circuit. The 6 Assertion: In series LCR circuit resonance can take place. 1
Reason: Resonance takes place if inductance and capacitive
frequency of the circuit is tuned to the resonant frequency of the circuit when
reactance’s are equal and opposite.
there is no metal in the inductor. Any metal on your body increases the Section – B
effective inductance of the loop and changes the current in it. When you pass 7 A resistor R and an element X are connected in series to an AC 2
through a metal detector, you become part of a resonant circuit. As you step source of voltage. The voltage is found to lead the current in phase
𝜋
through the detector, the inductance of the circuit changes, and thus the by . If X is replaced by another element Y, the voltage lags behind
4
current in the circuit changes. 𝜋
the current by .
4
(i) Identify elements X and Y.
(ii) When both X and Y are connected in series with R to the
same source, will the power dissipated in the circuit be
maximum or minimum? Justify your answer.
8 A power transmission line feeds power at 2200 V with a current of 2
5 A to step down transformer with its primary windings having 4000
turns. Calculate the number of turns and the current in the
secondary in order to get output power at 220 V.s
OR
8 A resistor of resistance 400 Ω, and a capacitor of reactance 200 Ω, 2
are connected in series to a 220V, 50 Hz ac source. If the current
is 0.49 A, find Voltage across the resistor and capacitor.
Section – C
1. What is resonance? 9 What is inductive reactance? If an AC voltage is applied across an 3
inductance L, find an expression for the current I flowing in the
2. On what factors does resonance frequency depends?
circuit. Also show the phase relationship between current and
3. For the metal detector to detect a small metal object the sharpness of the voltage in a phasor diagram.
current versus frequency graph be more or less? Justify your answer. OR
4. What is impedance of the circuit at resonance? 9 What is capacitive reactance? If an ac voltage is applied across a 3
capacitance 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.
10 In a series LCR circuit L= 10 H,C= 40 μF and R= 60 Ω are 3
connected to a variable frequency 240 V source. Calculate
(i) The angular frequency of the source which derives the
circuit at resonance.
(ii) The current at the resonating frequency.
(iii) The rms potential drop across the inductor at resonance.
Section – D
Case Study Based question.
11 An alternating current is that whose magnitude changes 4
continuously with time and direction reverses periodically and the
current that flows with same magnitude in same direction is direct
current.

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 UNIT V ELECTROMAGNETIC WAVES (d)They travel at different speeds in medium depending on their frequency
Q4. Which of the following statement is NOT true about the properties of
CH–8: Electromagnetic Waves electromagnetic waves?
(a) These waves do not require any material medium for their propagation
GIST OF CHAPTER (b) Both electric and magnetic field vectors attain the maxima and minima at the
Basic idea of displacement current, Electromagnetic waves, their characteristics, same time
their transverse nature (qualitative idea only). Electromagnetic spectrum (radio (c) The energy in electromagnetic wave is divided equally between electric and
waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including magnetic fields
elementary facts about their uses. (d) Both electric and magnetic field vectors are parallel to each other.
Q.5. Which basic oscillatory circuit is used these days to produce electromagnetic
CONTENT/ CONCEPTS- waves?
(a) LC oscillatory circuit (b) LCR circuit (c) Inductive circuit (d) Capacitive
Basic idea of displacement current
circuit
Conduction Current (ic)- Conduction current is the current, which arises due to flow
of electrons through the connecting wires in an electric circuit. Displacement current
(id)-Displacement current is the current, which arises due to time rate of change of
Q.6 What is the ratio of the speed of infrared and ultraviolet rays in a vacuum?
electric flux ( E).
(a) 1:5 (b) 2:1 (c) 1 (d) 0
Flaw in Ampere’s circuital law
Q.7 Which one of the following have the highest wavelength?
Modified Ampere’s circuital law states that the line integral of magnetic field B over
(a) radio waves (b) infrared (c) ultraviolet (d)gamma rays
a closed boundary of an open surface is equal to, times the sum of the conduction
Q.8 Electromagnetic waves carry
current (Ic) and the displacement current (Id) threading the surface.
(a) positive charge (b) negative charge (c) no charge
Maxwell’s Equations: - Following four equations, which describe the laws of
(d)both positive and negative charge
electromagnetism, are called Maxwell‟s equations
Q. 9 Which one of the following have the lowest frequency?
(i) ∮EdS . = q/∈ 0 (Gauss‟s law in electrostatics)
(a) radio waves (b) infrared (c)ultraviolet (d)gamma rays
(ii) ∮EdS . =0 (Gauss‟s law in magnetism) Q.10 Electromagnetic waves travel
(iii) ∮EdS . = d∅/𝑑𝑡 (Faraday‟s law of electromagnetic induction) (a) without medium (b) with medium (c)with medium and without medium
(iv) ∮EdS . =𝜇0 (Ic+Id)( (Ampere-Maxwell‟s circuital law) (d) in a disturbed path
ELECTROMAGNETIC SPECTRUM:
Type of Radiation Frequency Range (Hz) Wavelength Range
L-2 MCQ
Gamma-rays 10 – 10
20 24
< 10 -12
m
Q1. If the amplitude of the magnetic field is 3 × 10-6 tesla, then the amplitude of the
electric field for a electromagnetic waves is
X-rays 1017 – 1020 1 nm – 1 pm
(a) 100 V/m (b) 300 V/m (c) 600 V/m (d) 900 V/m
Q2.In an electromagnetic wave travelling in free space the rms value of the electric
Ultraviolet 1015 – 1017 400 nm – 1 nm
field is 3 V/m. The peak value of the magnetic field is,
Visible 4 x 1014 – 7.5 x 1014 750 nm – 400 nm
(a) 1.414 x10-8T (b) 1.0 × 10-8T (c) 2.828 × 10-8T (d) 2.0 × 10-8T
Q3.The direction of propagation of electromagnetic waves is along
Near-infrared 1 x 1014 – 4 x1014 2.5 μm – 750 nm (a) E (b) B (c) E.B (d)E × B
Q4.In an electromagnetic wave:
Infrared 1013 – 1014 25 μm – 2.5 μm (a) power is transmitted along the magnetic field
(b) power is transmitted along the electric field
Microwaves 3 x 1011 – 1013 1 mm – 25 μm (c) power is equally transferred along the electric and magnetic field
(d) power is transmitted in a direction perpendicular to both the fields.
Radio waves < 3 x 1011 > 1 mm

142 144
 CASE BASED - 1 QUESTIONS
ASSERTION AND REASON QUESTION
Directions: These questions consist of two statements, each printed as Assertion Read the below case and answer the questions that follow:
and Reason. While answering these questions, you are required to choose any one
LASER: Electromagnetic radiation is a natural phenomenon found in almost all area
of the following four responses.
of daily life, from radio waves to sunlight to x-rays. Laser radiation – like aii light –
(a) If both Assertion and Reason: are correct and the Reason: is a correct is also a form of electromagnetic radiation. The wave length range between 380nm
explanation of the Assertion. to 700nm is visible to human eye. Wavelength longer than780nm, optical radiation
(b) If both Assertion and Reason: are correct but Reason: is not a correct is termed infrared (IR) and is invisible to the eye. Wavelength shorter than 380nm,
explanation of the Assertion. optical radiation is termed ultraviolet (UV) and is also invisible to eye. The term
(c) If the Assertion is correct but Reason: is incorrect. ‘laser light’ refer to much broader range of the electromagnetic spectrum that just
(d) If both the Assertion and Reason: are incorrect.
the visible spectrum, anything between 150nm up to 11000nm9ie. From the UV up
Q1. Assertion: Electromagnetic waves are transverse in nature. to the far IR). The term laser is an acronym which stands for light amplification by
Reason: The electric and magnetic fields are perpendicular to each other and stimulated emission of radiation. Einstein explained the stimulated emission. In an
perpendicular to the direction of propagation. atom, electron may move to higher energy level by absorbing a photon. When the
electron comes back to the lower energy level it releases the same photon. This is
Q2. Assertion: The electromagnetic wave is transverse in nature. called spontaneous emission. This may also happen that the excited electron
absorbs another photon, releases two photons and returns to the lower energy
Reason: Electromagnetic waves propagate parallel to the direction of electric and
magnetic fields. state. This is known as stimulated emission. Laser emission is therefore a light
emission whose energy is used, in lithotripsy, for targeting and ablating the stone
Q3. Assertion: The velocity of electromagnetic waves depends on electric and inside human body organ.
magnetic properties of the medium. Apart from medical usage, laser is used for optical disk drive, printer, bar code
Reason: Velocity of electromagnetic waves in free space is constant. reader etc

Q.4 Assertion: The frequencies of incident, reflected and refracted beams of

monochromatic light incident from one medium to another are the same.
Reason: The incident, reflected and refracted rays are coplanar.

Q.5.Assertion: The earth without its atmosphere will be inhospitably cold. Q.1 What is full form of LASER? 1
a) Light amplified by stimulated emission of radiation M
Reason: All heat would escape in the absence of atmosphere. b) Light amplification by stimulated emission of radiation
c)Light amplification by simultaneous emission of radiation
Q.6 Assertion: Microwaves are better carriers of signal than optical waves. d)Light amplified by synchronous emission of radiation

Reason: Microwaves move faster than optical waves. Q.2 What is range of amplitude of LASER? 1
M
Q.7 Assertion: Gamma rays are more energetic than x rays. a)150nm-400nm b)700nm-11000nm c)Both the above d)600nm-700nm
Reason: Gamma rays are of nuclear origin but x rays are produced due to sudden
deceleration of high energy electrons while falling in the metal of high atomic Q.3 LASER is used in: 1M
number. a) Optical disk drive b)Transmitting satellite signal c)Radio communication
d) Ionization
L1-SHORT ANSWER QUESTIONS (2 MARKS)
Q.4 Lithotripsy is: 1
Q.1 Why are infrared waves called heat waves. Explain. What do you understand 2 a) An industrial application b) A medical application c)Laboratory application M
by the statement “Electromagnetic waves transport momentum”?
Q.2 Why are infrared radiations also referred as heat waves? Write the name of 2 d)Process control application
radiations which lie next to infrared radiations in the electromagnetic spectrum.

146 148
Q.1 Which wavelength of the Sun is used finally as electric energy? 1 Q.1 Solar radiation is 1
(a) radio waves (b) infrared waves (c) visible light (d) microwaves (a) transverse electromagnetic wave
(b) longitudinal electromagnetic wave
Q.2 Which of the following electromagnetic radiations have the longest 1 (c) both longitudinal and transverse electromagnetic waves
wavelength? (d) None of these
(a) X-rays (b) UV-rays (c) microwaves (d) radio waves

Q.3 Which one of the following is not electromagnetic in nature? 1 Q.2 What is the cause of greenhouse effect? 1
(a) X-rays (b) gamma rays (c) cathode rays (d) infrared rays (a) Infrared rays (b) Ultraviolet rays (c) X-rays (d) Radio waves

Q.4 (v) The decreasing order of wavelength of infrared, microwave, ultraviolet and 1 Q.3 Biological importance of ozone layer is 1
gamma rays is
(a) it stops ultraviolet rays
(a) microwave, infrared, ultraviolet, gamma rays
(b) gamma rays, ultraviolet, infrared, microwave (b) It layer reduces greenhouse effect
(c) microwave, gamma rays, infrared, ultraviolet (c) it reflects radio waves
(d) infrared, microwave, ultraviolet, gamma rays
(d) None of these
Q.4 Earth's atmosphere is richest in 1
************** (a) ultraviolet (b) infrared (c) X-rays (d) microwaves

FIVE MARKS
Q15.a) Write short notes on 1) Microwave 2) X-ray 3) Radio waves
b) Explain the Acronym LASER AND RADAR 3+
c) State the Maxwell’s law of induction. 1+
1
**********

150 152
According to new cartesian sign conventions, when the image formed is real Dispersion. The phenomenon of splitting up of white light into its constituent colours
(inverted), the magnification produced by the mirror is negative and when the image is called dispersion.
formed is virtual (erect), the magnification produced by the mirror is positive.
Spectrum. The band of seven colours obtained on the screen is called spectrum.
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 Pure spectrum. A spectrum, in which the constituent colours have sharp boundaries
aberration. and are distinctly visible, is called the pure spectrum.

2. Refraction of Light Chromatic aberration. The inability of a lens to bring the light of different colours to
focus at a single point is called chromatic aberration.
Refraction. The phenomenon of change in the path of light as it goes from one
medium to another is called refraction. Rayleigh’s law of scattering. It states that the intensity of the light of wavelength A
1
in the scattered light varies inversely as the fourth power of its wavelength. I = 4
𝜆
Laws of refraction.
Simple microscope. A convex lens of small focal length is called a simple microscope
1. The incident ray, the normal to the refracting surface at the point of incidence and
or a magnifying glass. The magnifying power of a
the refracted ray all lie in the same plane.
microscope is defined as the ratio of the angle subtended
2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction by the image at the eye to the angle subtended by the
is constant for any two- given media. It is called Snell's law. object seen directly, when both lie at the least distance
𝑠𝑖𝑛𝑠𝑖𝑛 𝑖
of distinct vision.
Mathematically- = 𝜇𝑏𝑎 𝐷
𝑠𝑖𝑛𝑠𝑖𝑛 𝑟
M=1+
𝑓
Absolute refractive index (𝜇). The absolute refractive index of a medium is defined
as ratio of the velocity of light in vacuum (c) to the velocity of light in that medium(v). Compound microscope. A
compound microscope is a two-
Real and apparent depth. When an object is placed in an optically denser medium, lens system (object lens and eye
the apparent depth of the object is always less than its real depth. lens of focal lengths f, and f,). Its
Mathematically-: 1.
𝑅𝑒𝑎𝑙 𝑑𝑒𝑝𝑡ℎ
= 𝜇𝑏𝑎 magnifying power is very large, as
𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑑𝑒𝑝𝑡ℎ compared to the simple
1 microscope.
2. Normal shift d= t (1 − )
𝜇𝑏𝑎 𝑣𝑜 𝐷
Mathematically- M = (1 + )=
𝑢𝑜 𝑓𝑒
Total internal reflection. The phenomenon of reflection of light that takes place when 𝐿𝑜 𝐷
a ray of light travelling in a denser medium gets incident at the interface of the two - 𝑓𝑜
(1 + 𝑓𝑒
)
media at an angle greater than the critical angle for that pair of media.
Astronomical telescope. It is a two-lens system and is used to observe distant
1
Mathematically 𝜇𝑏𝑎 = 𝑠𝑖𝑛 𝐶 heavenly objects. It is called refracting type astronomical telescope.

𝜇𝑏𝑎 is refractive index of the denser medium £ w.r.t. the rarer medium a and C is the Normal adjustment. When the final image is formed at infinity, the telescope is said to
𝑓𝑜
critical angle. be in normal adjustment. M = - 𝑓𝑒
Spherical refracting surface. The portion of a refracting medium, whose curved
When the final image is formed at the least distance of distinct vision, magnifying
surface forms the part of a sphere, is called spherical refracting surface. 𝑓 𝑓𝑒
power of the telescope, M = - 𝑓𝑜 (1 + )
When object is situated in the rarer medium, the relation is as follows 𝑒 𝐷

𝜇1 𝜋2 𝜇2 −𝜇1
- 𝑢
+ 𝑣
= 𝑅

When the object is situated in denser medium, the relation is as follows

𝜇2 𝜇1 𝜇1 −𝜇2
- 𝑢
+ 𝑣
= 𝑅

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

154 156
 LEVEL-1 (MCQ QUESTIONS) (a)infinity (b)zero (c) 50 cm (d)negative

1 A convex lens of power 4D and a concave lens of power 3D are placed in contact. 18 A convex lens is dipped in a liquid, whose refractive index is equal to the refractive
What is the equivalent power of the combination? index of the lens. Then its focal length will _____ .
4 3
a) 7D b) D c)1D d) D (a)become zero (b)remain unchanged (c)become infinite (d)None of these
3 4

2 An object approaches a convergent lens from the left of the lens with a uniform 19 Absolute refractive indices of glass and water are 3/2 and 4/3. The ratio of velocity
speed of light in glass and water will be

5 m/s and stops at the focus. The image (a) 4:3 (b)8:7 (c) 8:9 (d) 3:4

(a) moves away from the lens with a uniform speed 5 m/s. 20 Half of the lens is wrapped in black paper. How will it change the image
(b) moves away from the lens with a uniform acceleration. (a)Size of image is halved
(c) moves away from the lens with a non-uniform acceleration. (b)Intensity of image is halved
(d) moves towards the lens with a non-uniform acceleration. (c)There is no change in the size of image or intensity
3 The refractive index of the material of an equilateral prism is √3 .What is the angle (d)Both size and intensity of the image are changed.
of Minimum deviation?
LEVEL-2 (MCQ QUESTIONS)
(a) 45° (b) 60° (c) 37° (d) 30°
1 A student measures the focal length of a convex lens by putting an object pin at 1
4 An object is placed at the focus of the convex mirror. If its focal length is 20cm,
a distance 'u' from the lens and measuring the distance 'v' of the image pin. The
the distance of image from the mirror is
graph between 'u' and 'v' plotted by the student should look like
(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:

2 What should be increased to increase the angular magnification of a simple

6. Air bubble in water behaves as microscope?
(a) sometimes concave, sometimes convex lens a)The power of the lens b)The focal length of the lens c)Lens Aperture
(b) concave lens d)Object Size
(c) convex lens 3 What is the correct relationship
(d) always refracting surface between refractive indices n,n1 and
n2 if the behaviour of light is as shown
7 A ray of light passes from glass (μ = 1.5) to water (μ = 1.33). The value of the in the figure?
critical angle of glass is _____ . a)n1>n b)n1<n c)n1=n d)None of the above
(a) sin-1 8/9 (b) sin-1√ 8/9 (c) sin-1 ½ (d) sin-1 2/1
4 If an equiconvex lens of focal length f and power P is cut into half in thickness,
what is the focal length and power of each half?
158 160
3 Which of the following actions will lead to an increase in the magnifying power LEVEL 1 (2 M QUESTIONS)
of an astronomical telescope?
1 What is total internal reflection and what are the conditions under which it occurs?
A. Increase in the length of the telescope tube. Obtain relation between critical angle between & refractive index.
B. Interchange the objective and the eyepiece of the telescope. 2 a)A convex mirror is immersed in water of refractive index 1.33. Will the lens
behave as a converging or a diverging lens? Give reason.
C. A small piece of paper on the objective of the telescope pointed towards b) When monochromatic light travels from one medium to another its wavelength
the moon. changes but frequency remains the same. Explain.
3 Draw a ray diagram to show the image formation by a concave mirror when the
D. Increase in the focal length of the objective and decrease in the focal length
object is placed between its focus and pole.
of the eye piece. Write the value and sign of magnification in this case.
4 A real image of size p times the size of an object is formed by a concave mirror 4 A plot, between the angle of deviation (δ) and
angle of incidence (i), for a triangular prism is
of focal length f.
shown in figure:
What is the object distance from the mirror?
Explain why any given value of ‘δ’ corresponds to
A. (p+1)*f/p B. (p‐1)*f/p C. p*f/(p+1) D. p*f/(p‐1)
two values of angle of incidence. State the
5 Read the following statements carefully: significance of point P on the graph. ?
I. A drop of an oil in water or in a glass, both behave as convergent lens. 5 a)Write two differences between linear and angular magnification.

II. A water drop in air and a glass sphere in water, both behave as convergent b) Three lenses with magnifications 2, 3 and 10 form a combination. What is its
total magnification?
lens.
6 With the help of a ray diagram, obtain the relation between its focal length and
III. An air bubble in water and a water bubble in glass, both behave as a radius of curvature.
divergent lens. LEVEL-2 (2 M QUESTIONS)
IV. A frozen ice crystal inside a glass sphere and a bromine liquid drop inside a
1. How does the power & focal length of a convex lens vary, if the incident red light
glass sphere, behave as divergent lens. is replaced by violet light?
[Reference values of refractive indices of common substances: Air = 1.001; 2. A right angled isosceles glass prism is made from glass of refractive index 1.5.
Show that a ray of light incident normally on (i) one of the equal sides of this prism
Water = 1.33; ice = 1.31; Glass = 1.51; Oil = 1.4; Bromine = 1.66] is deviated through 90° (ii) the hypotenuse of this prism is deviated through 180°.
Select the correct option. 3. a)When monochromatic light is incident on a surface separating two media, the
reflected and refracted light both have the same frequency as the incident
A. Statements I and II are correct.
frequency. Explain why?
B. Statements I and III are correct. b) What are benefits of Lens Combination and making equivalent lens?
C. Statements II and III are correct. 4. An object is placed 10 cm from a lens of focal length 5 cm. Draw the ray diagrams
to show the formation of image if the lens is (i) converging, and (ii) diverging.
D. Statements II and IV are correct
6 An object is moved towards a concave mirror at a constant speed, from infinity 5 The line AB in the ray diagram represents a lens. State whether the lens is convex
or concave ?
to its focus. Which of the following statements correctly describe the
corresponding motion in the image formed by the concave mirror?

162 164
3 a)How does the angle of minimum deviation produced by a prism change with 1 A spherical convex surface of radius of curvature 20cm made of glass of refractive 2
increase in (i) the wavelength of incident light, and (ii) the refracting angle of index 1.5 is placed in air. Find the position of the image formed if a point object is
prism? placed 30cm in front of a convex surface on the principal axis?
b) A glass prism is held in water. How is the angle of minimum deviation affected?
c) When does a ray passing through a prism deviate away from its base? 2 A ray of monochromatic light is incident on the refracting face of a prism angle 3
75°. It passes through the prism and is incident on the other face at the critical
LEVEL - 3 (3 M QUESTIONS) angle. If refractive index of the prism is √2, what is the angle of incidence on the
1 i)Redraw the diagram below and mark the position of the centre of curvature of first face of the prism?
the spherical mirror used in the given set up LEVEL-3 (NUMERICALS)

1 Three rays 1,2, 3 of different colours 3

fall normally on one of the sides of
ii) State the principle of reversibility of light. an isosceles right angled prism as
shown in fig. The refractive indices
2 Which two of the following lenses L1, L2 and L3 will you select as objective and of prism for these rays are 1.39,
eyepiece for constructing the best possible (i) telescope (ii) microscope? Give 1.47 and 1.52 respectively. Find
reason to support your answer. iii)the aperture of the objective of ……….. is which of these rays get normally
preferred to be large? reflected and which get only
refracted from AC. Trace the path of rays. Justify your answer with the necessary
calculations ?
2 An angular magnification of 30X is desired for a compound microscope using an 5
objective of focal length 1.25 cm and eyepiece of focal length 5cm. How will you
set up the compound microscope?
3 a) Write the two important factors considered to increase the magnifying power of 3 i)A small telescope has an objective lens of focal length 140cm and an eyepiece 5
a refracting type telescope. of focal length 5.0cm. If this telescope is used to view a100m tall tower 3km away,
what is the height of the image of the tower formed by the objective lens?
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 ii)An astronomical telescope has focal lengths 100 & 10 cm of objective and
eyepiece lens respectively when final image is formed at least distance of distinct
i)Which one of two lenses you will select to use vision, magnification power of telescope will be?
as objective lens and why?
CASE STUDY QUESTIONS (4-Marks)
(ii) What should be the change in the distance
between the lenses to have the telescope in its A telescope is a device used to observe distant objects by their emission,
normal adjustment position? absorption, or reflection of electromagnetic radiation. Originally, it was an optical
instrument using lenses, curved mirrors, or a combination of both to observe
(iii) Calculate magnifying power of telescope in the normal adjustment position distant objects – an optical telescope. Nowadays, the word "telescope" is defined
LEVEL-1 (5 M QUESTIONS) as a wide range of instruments capable of detecting different regions of the
electromagnetic spectrum, and in some cases other types of detectors
1. a) Derive expression for the lens maker's formula, i.e., The first known practical telescopes were refracting telescopes with glass lenses
1 1 1 and were invented in the Netherlands at the beginning of the 17th century. They
= (𝜇 − 1) [𝑅1 − ] where the symbols have their usual meanings. Why is it
𝐹 𝑅2 were used for both terrestrial applications and astronomy.
known as Lens Maker’s formula.
1
166 168
 COMPETENCY BASED QUESTIONS This is the part of an eye exam people are most familiar with. You will read an eye
chart to determine how well you see at various distances. You cover one eye while
A ray of light travels from a denser to a rarer medium. After refraction, it bends the other is being tested. This exam will determine whether you have 20/20
away from the normal. When we keep increasing the angle of incidence, the angle vision or not.
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.

Your doctor will ask you to look at an

eye chart through a device called a phoroptor. The phoroptor contains different
lenses. Your doctor may check how your pupils respond to light by shining a bright
beam of light into your eye. Pupils usually respond by getting smaller. If your pupils
widen or don't respond, this may reveal an underlying problem.
Loss of side vision (peripheral vision) may be a symptom of glaucoma. This test
can find eye problems you aren't aware of because you can lose side vision
i)A ray of light travels from a medium into the water
without noticing.A test called ocular motility evaluates the movement of your eyes.
at an angle of incidence of 18°. The refractive Your ophthalmologist looks to see if your eyes are aligned. They also check that
index of the medium is more than that of water and your eye muscles are working properly.
the critical angle for the interface between the two
media is 20°. Which one of the following figures Eye pressure testing, called tonometry, measures intraocular eye pressure, or
best represents the correct path of the ray of light? IOP. Elevated IOP is one sign of glaucoma. Your ophthalmologist uses a slit-lamp
microscope to light up the front part of the eye. This includes
ii) A point source of light is placed at the bottom of the eyelids, cornea, iris and lens. This test checks for cataracts or any scars or
a tank filled with water, of refractive index µ, to a depth h. The area of the surface scratches on your cornea.
of water through which light from the source can emerge is:
i) The maximum magnification that can be obtained with a convex lens of focal
a)πh²/2(μ²-1) b) πh²/(μ²-1) length 2.5 cm is (the least distance of distinct vision is 25 cm)
a) 10 b) 0.1 c) 62.5 d)11
c) πh²/(√2√(μ²-1)) d) 2πh²/(μ²-1) ii) The magnifying power of a magnifying glass is 6. The focal length of its lens in
iii) Is the formula "Real depth/Apparent depth =µ" valid if viewed from a position metres will be, if least distance of distinct vision is 25 cm
a) 0.05 b) 0.06 c) 0.25 d) 0.12
quite away from the normal?
iii) Resolving power of human eye is:
iv) A diver in a swimming pool wants to signal his distress to a person lying on the a) 0.1 mm b) 1 mm c) 2 mm d)None of the above
edge of the pool by flashing his water proof flash light iv) In a simple microscope, if the final image is located at infinity then its magnifying
power is
a) He must direct the beam vertically upwards a) 25/f b) D/25 c) f/25 d) f/D+1
b) He has to direct the beam horizontally
c) He has to direct the beam at an angle to the vertical which is slightly less than ***********
the critical angle of incidence for total internal reflection

170 172
 A biconcave lens of power P vertically splits into two identical plano-concave parts. 1 CASE STUDY
5. The power of each part will be
13. How are rainbows formed? 4
(a) 2P (b) P/2 (c) P (d) P/√2
A prism has refractive angle 60°. When a light ray is incident at 50°, then minimum 1 The properties and behaviour of light, and how it interacts with droplets of water,
6. deviation is obtained. What is the value of minimum deviation? give rise to one of nature's most colourful meteorological events - the rainbow.
(a) 40° (b) 45° (c) 50° (d) 60° It's all in the geometry...
An object is placed in front of a concave mirror of focal length 20 cm. The image Rainbows are formed when sunlight is scattered from raindrops into the eyes of an
7. formed is three times the size of the object. Calculate two possible distances of the 2 observer.Most raindrops are spherical rather than the often depicted 'teardrop'
object from the mirror? shape and it is this spherical shape that provides the conditions for a rainbow to be
A ray of light passing from air through an equilateral glass prism undergoes seen.The position of the sun and the raindrops in relation to the observer need to
8. minimum deviation when the angle of incidence is 3/4 of the angle of prism. 2 be just right for a rainbow to form:
Calculate the speed of light in the prism. The sun needs to be behind the viewerThe sun needs to be low in the sky, at an
Three rays 1,2, 3 of different colours fall normally on one of the sides of an isosceles angle of less than 42° above the horizon. The lower the sun in the sky the more of
right angled prism as shown in fig. The refractive indices of prism for these rays are an arc of a rainbow the viewer will see
9. 1.39, 1.47 and 1.52 respectively. Find which of these rays get normally reflected Rain, fog or some other source of water droplets must be in front of the viewer
and which get only refracted from AC. Trace the path of rays. Justify your answer The size of the raindrops does not directly affect the geometry of a rainbow, but
with the necessary calculations ? 3 mist or fog tends to disperse the effect more (see fogbows).
Rainbows only appear semi-circular over level ground at sunrise or sunset, when
the sun is exactly on the horizon, the majority of the time a smaller segment of an
arc is seen. If the angles at which the light enters the droplet are correct, some of
the light that enters the droplet will be internally reflected from the inside edge of
the drop and will exit the drop, undergoing refraction again as it passes back from
water to air. Reflection by mirrors, Refraction by lenses, water give rise to many
such wonderful phenomenon in atmosphere.
10 Two parallel light rays pass through an isosceles prism of refractive index √3/2 as 3 i) An empty test tube is placed slanting in the
shown in the figure. The angle between the two emergent rays is : water and viewed from above. What will you
observe?
ii) If an equiconvex lens of focal length f and
power P is cut into half in thickness, what is the
focal length and power of each half?
CASE BASED QUESTION a)Zero b)f/2 c)f d)2f
iii) A prism has an angle 600 and refractive index √2, what is the angle of minimum
Lens maker’s formula relates to the focal length (f) of a lens to the refractive index
deviation?
of the lens and the radii of the curvature of its two surfaces. The focal length of the
a)900 b)600 c)450 d) 300
lens depends upon the refractive index of the material used for making the lens and
iv) When a thin convex lens of glass 5D is immersed in a liquid, it behaves as a
11 the radius of curvature. This formula is used by the manufacturers for making the 4
divergent lens of focal length 100 cm. What is the refractive index of the liquid?
desired lens; that’s it is called the lens maker’s formula.
a)1/3 b) 2/3 c) 3/5 d) 5/3
Limitations of the lens maker’s formula. The lens should not be thick so that the
space between the 2 refracting surfaces can be small.
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
174 176
(i) By division of wavefront: In this method the wavefront (which is the locus of points
of same phase) is divided into two parts. The examples are Young’s double slit and LEVEL 1 MCQ
Fresnel’s biprism.
(ii) By division of amplitude: In this method the amplitude of a wave is divided into 1 Idea of secondary wavelets for the. propagation of a wave was first given by
two parts by successive reflections, e.g., Lloyd’s single mirror method. (a) Newton(b) Huygens(c) Maxwell(d) Fresnel
4. Interference of Light 2 Light propagates rectilinearly, due to
Interference is the phenomenon of superposition of two light waves of same frequency (a) wave nature (b) wavelengths
and constantphase different travelling in same direction. The positions of maximum (c) velocity (d) frequency
intensity are called maxima, while those of minimum intensity are called minima.
𝒏𝑫𝝀 𝟏 𝑫𝝀 3 Which of the following is correct for light diverging from a point source?
𝒙𝒎𝒂𝒙𝒊𝒎𝒂 = 𝒙𝒎𝒊𝒏𝒊𝒎𝒂 = (𝒏 − ) (a) The intensity decreases in proportion with the distance squared.
𝒅 𝟐 𝒅
(b) The wavefront is parabolic.
𝜆𝐷 𝛽 𝜆
Linear Fringe width= β = angular fringe width=𝐷 = 𝑑 (c) The intensity at the wavelength does not depend on the distance.
𝑑
(d) None of these.
Condition for sustained interference
4 The refractive index of glass is 1.5 for light waves of λ = 6000 Å in vacuum.
(i) The two sources of light must be coherent which means the two light waves emitted
Its wavelength in glass is
by them must have a constant phase difference or in the same phase. (a) 2000 Å(b) 4000 Å(c) 1000 Å(d) 3000 Å
(ii) The two sources must emit light of the same wavelength but the amplitudes
between them should differ as little as possible. The emitted waves should be 5 The phenomena which is not explained by Huygen’s construction of
preferably of the same amplitude to get completely dark fringes. wavefront
(iii) The two sources should be very narrow. Otherwise with the increase of slit width, (a) reflection(b) diffraction(c) refraction(d) origin of spectra
the coherence property will be lost. Hence, no interference pattern will be obtained.
(iv) The two sources must lie very close to each other. Otherwise overlapping of bright
LEVEL 2 MCQ
and dark points will hinder interference. 6 A laser beam is used for locating distant objects because
5. Diffraction of Light (a) it is monochromatic(b) it is not chromatic
The bending of light from the corner of small obstacles or apertures is called diffraction (c) it is not observed(d) it has small angular spread
of light. 7 Two slits in Young’s double slit experiment have widths in the ratio 81:1. The
2𝜆𝐷 2𝜆
Linear central maxima= 2y= angular central maxima= ratio of the amplitudes of light waves is
𝑎 𝑎
(a) 3 :1(b) 3 : 2(c) 9 :1(d) 6:1
Difference between Diffraction and Interference
Interference Diffraction 8 When interference of light takes place
Interference may be defined as waves Diffraction, on the other hand, can be (a) energy is created in the region of maximum intensity
emerging from two different sources, termed as secondary waves that (b) energy is destroyed in the region of maximum intensity
producing different wavefronts. emerge from the different parts of the (c) conservation of energy holds good and energy is redistributed
same wave. (d) conservation of energy does not hold good
The contrast between maxima and The contrast between maxima and
minima is very good. minima is poor. 9 To observe diffraction, the size of the obstacle
The width of the fringes in interference The width of the fringes is not equal in (a) should beX/2, where X is the wavelength.
is equal. diffraction. (b) should be of the order of wavelength.
(c) has no relation to wavelength.
(d) should be much larger than the wavelength

10 What is the geometric shape of the wavefront that originates when a plane
wave passes through a convex lens?
a) Converging spherical b) Diverging spherical
c) Plane d) None of the above

178 180
 Reason : There will be an effect on clarity if the waves are of unequal intensity.
19 Assertion : In YDSE, if a thin film is introduced in front of the upper slit, then 2. Monochromatic light from a narrow slit illuminates two narrow slits 0.3 mm
the fringe pattern shifts in the downward direction. apart producing an interference pattern with bright fringes 1.5 mm apart on a
Reason : In YDSE if the slit widths are unequal, the minima will be completely screen 75 cm away. Find the wavelength of the light. How will the fringe width
dark. be altered if-
20 Assertion : Diffraction takes place for all types of waves mechanical or non- i) the distance of the screen is doubled
mechanical, transverse or longitudinal. ii) the separation between the slits is doubled ?
Reason : Diffraction’s effect are perceptible only if wavelength of wave is 11 A beam of light consisting of two wavelengths 6500 Ao and 5200 Ao is used to
comparable to dimensions of diffracting device. obtain interference fringes. The distance between the slits is 2.0 mm and the
LEVEL 1 (2M QUESTIONS) distance between the plane of the slits and the screen is 120 cm.
1 Write the important characteristic features by which the Interference can be a) Find position of third maxima for first wavelength.
distinguished from the observed diffraction pattern. b) Find the minimum distance at which maxima of the two wavelength coincide.
12 Monochromatic light from a narrow slit illuminates two narrow slits 0.3 mm apart
2 One of the slits of Young’s double-slit experiment is covered with a semi-
producing an interference pattern with bright fringes 1.5 mm apart on a screen
transparent paper so that it transmits lesser light. What will be the effect on the
75 cm away. Find the wavelength of the light. How will the fringe width be altered
interference pattern?
if-
3 A parallel beam of light of wavelength 600 nm is incident normally on a slit of i) the distance of the screen is doubled
width ‘a’. If the distance between the slits and the screen is 0.8 m and the distance ii) the separation between the slits is doubled ?
of 2nd order maximum from the centre of the screen is. 15 mm, calculate the
LEVEL-1 (5M QUESTIONS)
width of the slit. 1 (a) State Huygen’s principle. Using this principle draw a diagram to show how a
LEVEL 2 (2M QUESTIONS) plane wavefront incident at the interface of the two media gets refracted when it
4 (i) State the principle on which the working of an optical fibre is based. propagates from rarer to a denser medium. Hence verify Snell’s law of refraction.
(ii) What are the necessary conditions for this phenomenon to occur? (b) When monochromatic light travels from a rarer to a denser medium, explain
5 Why are coherent sources necessary to produce a sustained interference the following, giving reasons:
pattern? (i) Is the frequency of reflected and refracted light same as the frequency of
6 Write the distinguishing features between a diffraction pattern due to a single slit incident light?
and the interference fringes produced in Young’s double-slit experiment? (ii) Does the decrease in speed imply a reduction in the energy carried by light
7 In what way is diffraction from each slit related to the interference pattern in a wave ?
double-slit experiment? 2 (a) (i) ‘Two independent monochromatic sources of light cannot produce a
sustained interference pattern’. Give reason.
LEVEL 3 (2M QUESTIONS)
(ii) Light waves each of amplitude a and frequency n, emanating from two
8 When a tiny circular obstacle is placed in the path of light from a distance source, coherent light sources superpose at a point. If the displacements due to these
a bright spot is seen at the centre of the shadow of the obstacle. Explain, why? waves is given by y1 = a cos t and y2 = a cos (ωt + ϕ), what is the phase difference
9 Write the conditions under which light sources can be said to be coherent. between the two, obtain the expression for the resultant intensity at the point.
10 Why is it necessary to have coherent sources in order to produce an interference (b) In Young’s double slit experiment, using monochromatic light of wavelength,
pattern? the intensity of light at a point on the screen where path difference is, is K units.
LEVEL-1 (3M QUESTIONS)
Find out the intensity of light at a point where path difference is
1 A plane wavefront propagating in a medium of 3 (a) In Young’s double slit experiment, describe briefly how bright and dark fringes
refractive index µ1 is incident on a plane surface are obtained on the screen kept in front of a double slit. Hence obtain the
making the angle of incidence i as shown in the figure. expression for the fringe width.
It enters into a medium of refractive index µ2 (µ2> (b) The ratio of the intensities at minima to the maxima in the Young’s double slit
µ1). Use Huygens’ construction of secondary experiment is 9 : 25. Find the ratio of the widths of the two slits.
182 184
 (e) If the phase difference between the two waves reaching two slits from the (b) plane wavefront and spherical
(a) plane wavefront and plane wavefront
source slit is (i) 5π and (ii) 2π, then what will be the colour of central fringe? wavefront
9 A slit of width ‘a’ is illuminated by white light. (c) spherical wavefront and plane (d) spherical wavefront and spherical
(a) For what value of a will the first minimum for red light of λ = 650 nm be at θ = wavefront wavefront
15°?
(b) What is the wavelength λ' of the light whose first side diffraction maximum is COMPETENCY BASED
at 15°, thus coinciding with the first minimum for the red light? 1 In a double slit experiment, the two slits are 1mm apart and the screen is placed
1m away. A monochromatic light of wavelength 500nm is used. What will be the
width of each slit for obtaining ten maxima of double slit within the central maxima
LEVEL -1 (NUMERICALS)
of single slit pattern.
1 Two plane monochromatic waves propagating in the same direction with
amplitudes A and 2A and differing in phase by 𝜋/3 superimpose. Calculate the
CCT
1 In a double slit experiment , when light of wavelength 400nm was used, the
amplitude of resulting wave.
angular width of first minimum formed on a screen placed 1m away, was found
2 Two slits are made 1mm apart and the screen is placed 1m away. What is the
to be 0.2o. What will be the angular width of first minimum if entire appratus is
fringe separation when blue green light of wavelength 500nm is used?
immersed in water (µ = 4/3).

LEVEL -2 (NUMERICALS)
1 A slit of width ‘d’ is illuminated by light of wavelength 5000Å. For what value of ‘d’
will the first maximum fall at an angle of diffraction of 30o.
2 Two spectral lines of sodium D1 and D2 have wavelengths approximately 5890Å
and 5896Å. A sodium lamp sends incident plane wave on to a slit of width 2
micrometer. A screen is located 2m from the slit. Find the spacing between the
first maxima of two sodium lines as measured on the screen.
LEVEL -3 (NUMERICALS)
1 If one of the two identical slits producing interference in Young’s experiment is
covered with glass, so that light intensity passing through it is reduced to 50%,
find the ratio of the maximum intensity of the fringes in the interference pattern.

CASE BASED QUESTIONS

1 Wavefront is a locus of points which vibrate in same phase. A ray of light is
perpendicular to the wavefront. According to Huygens principle, each point of the
wavefront is the source of a secondary disturbance and the wavelets connecting
from these points spread out in all directions with the speed of wave. The figure
shows a surface XY separating two transparent media, medium-1 and medium-
2. The lines ab and cd represent
wavefronts of a light wave
travelling in medium- 1 and
incident on XY. The lines ef and
gh represent wavefronts of the
light wave in medium -2 after
refraction.
(i) Light travels as a
a) parallel beam in each medium
b) convergent beam in each medium
c) divergent beam in each medium
186 188
7 Name the phenomenon which is responsible for bending of light 2 UNIT VII-DUAL NATURE OF RADIATION AND MATTER
around sharp corners of an obstacle. Under what conditions does CH–11: DUAL NATURE OF RADIATION AND MATTER
this phenomenon take place? Give one application of this
phenomenon in everyday life
8 A parallel beam of light of 600 nm falls on a narrow slit and the 2 GIST OF CHAPTER
resulting diffraction pattern is observed on a screen 1.2 m away. It Dual nature of radiation, Photoelectric effect, Hertz and Lenard's observations; Einstein's
is observed that the first minimum is at a distance of 3 mm from photoelectric equation-particle nature of light. Experimental study of photoelectric
the centre of the screen. Calculate the width of the slit. effect, Matter waves-wave nature of particles, de-Broglie relation.
9 .(a) If one of two identical slits producing interference in Young’s 3
experiment is covered with glass, so that the light intensity passing DEFINITION & CONCEPTS: -
through it is reduced to 50%, find the ratio of the maximum and
minimum intensity of the fringe in the interference pattern. Free electrons: - In metals, the electrons in the outer shell of the atoms are loosely
(b) What kind of fringes do you expect to observe if white light is bound. They move about freely throughout the lattice of positive ions. Such loosely
used instead of monochromatic light? bound electrons are called free electrons.
10 Two wavelengths of sodium light 590 nm and 596 nm are used, in 3 Work function of a metal. The minimum energy, which must be supplied to the electron
turn, to study the diffraction taking place at a single slit of aperture so that it can just come out of a metal surface, is called the work function of the metal. It
2 × 10–4 m. The distance between the slit and the screen is 1.5 m. is denoted by W0.
Calculate the separation between the positions of the first maxima
of the diffraction pattern obtained in the two cases. Work function depends on (i) nature of the metal (ii) the conditions of its surface.
11 CASE BASED QUESTION 4 Electron emission: - The phenomenon of ejecting out the electron from metal surface
For constructive interference, the path difference is equal to is called electron emission.
integral multiple of wavelengths and resultant intensity will be
maximum at that points. While for destructive interference, the PHOTOELECTRIC EMISSION/ EFFECT: -.
path difference is (n + 1/2) multiple of wavelengths and where
The phenomenon of ejection of electrons from a metal surface, when light of sufficiently
resultant intensity is zero. When light is passed around the sharp
high frequency falls on it, is known as photoelectric effect.
edges of an obstacle it get bended and may enters into the
geometrical shadow of that obstacle such a phenomenon of light The electrons so emitted are called photoelectrons
is called as diffraction of light. In interference, there are equally
spaced alternate bright and dark bands are possible. While in
diffraction, the there is a only one bright central Maxima and
around both sides of the central Maxima the intensity of the light
decreases as we go away from that central Maxima.

Q I.) For coherent sources of light the phase

difference must be___
a) one
b) zero
c) either zero or constant
d) 90°
Q II.) If the phase difference is 0, +2π, -4π then the
interference should be
a)constructive interference
b) destructive interference
c) both a and b
d) diffraction of light
Q III.) For destructive interference
a) path difference is (n +1/2) times wavelength
b) phase difference is π, -3π, +5π
c) path difference is integral multiple of wavelengths

190 192
 The Effect of the Potential:-
When light of frequency ν is incident on a metal surface, whose work function is W
then the maximum kinetic energy of the emitted photoelectrons is given by
The photoelectric current increases with increase in
accelerating (positive) potential of collector plate. ℎ𝑣=1/2 mv2max ɸ𝑜 ⇒ 1/2 mv2max = ℎ (𝑣 − 𝑣 𝑜)
For a certain positive potential of plate A, the
This is called EINSTEIN’S PHOTOELECTRIC EQUATION. It can explain the laws of
photoelectric current becomes maximum and
photoelectric emission.
constant or saturates. This maximum value of the
photoelectric current is called saturation current. Properties of Photon:-
Saturation current corresponds to the case when all (i) In interaction of radiation with matter, radiation behaves as if it is made of particles like
the photoelectrons emitted by the emitter plate C photons.
reach the collector plate A. (ii) Each photon has energy (E= ℎ𝑣) and momentum (p=ℎ𝑣/c)
Saturation current increases with increase in intensity of incident radiation. The
(iii) All photons of a particular frequency 𝑣 or wavelength have same energy (E= ℎ𝑣=h c/
photoelectric current decreases with negative potential of collector plate.
𝝀) and same momentum (p=ℎ𝑣/c= h/ 𝝀) irrespective of intensity of radiations.
(iv) Velocity of photon in different media is different due to change in its wave length.
STOPPING POTENTIAL (𝑉0):-
At certain negative potential of the collector plate the photocurrent becomes zero. This negative (v) Rest mass of photon is zero.
potential is called STOPPING POTENTIAL (𝑉0). (vi) During collision of photon and electron energy and momentum are conserved.
The stopping potential is measure of maximum kinetic energy of photoelectron.
If stopping potential is 𝑉𝑜 then, 𝑀𝑎𝑥. 𝐾𝐸 𝑜f 𝑝ℎ𝑜𝑡𝑜 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 = 𝑒 𝑉𝑜
1/2 mv2max = eVo
⇒ 𝑒 𝑉𝑜 = ℎ𝑣 − ɸ𝑜 = ℎ (𝑣 − 𝑣 𝑜)
Where 𝑣𝑚𝑎𝗑 is the maximum velocity with which the photoelectrons are emitted

This explains why the 𝑉𝑜versus 𝑣 curve is a straight line with slope = (h/e), independent of the
Effect of intensity of incident radiation on stopping potential nature of the material.
❖ Stopping potential does not change on changing the intensity of incident radiation.
❖ The maximum kinetic energy of photoelectron thus does not depend on intensity DE-BROGLIE HYPOTHESIS.
of incident radiation. Both radiation and matter have dual nature. A moving particle of momentum p is associated
with a wave called de-Broglie wave of wavelength.

194 196
MIND MAP MULTIPLE CHOICE QUESTIONS

LEVEL 1
1. The minimum energy required to remove an electron is called

a. Stopping potential b. Kinetic energy c.Work function d.None of these

2. In which of the following, emission of electrons does not take place?
a. Thermionic emission b. X-rays emission c. Photoelectric emission d.Secondary
emission
3. Which of the following when falls on a metal will emit photo electrons?
a. UV radiations b. Infrared radiation c. Radio waves d. Microwaves
4. Which of the following metals is not sensitive to visible light?
a. Cesium b. Sodium c. Rubidium d. Cadmium
5. Photons are deflected by
a. electric field only b. magnetic field only c. electromagnetic field d.None of these
6. The emission of electrons does not occur in which of the following?

a. Photoelectric Emission b. Thermionic Emission c, Secondary Emission

d. X-Ray Emission
7. What happens to the kinetic energy of the emitted electrons when the light is
incident on a metal surface?

a. It varies with the frequency of light

b. It varies with the light intensity
c. It varies with the speed of light
d. It varies irregularly
8. A photoelectric cell is a device which
a. Converts light energy into electricity
b. Converts electricity into light energy
c. Stores Light energy
d. Stores Electricity
9. What does a cathode ray consist of?

a. Electrons b. Protons c. Photons d. Alpha particles

10. Who gave the theory of quantization of electric charge?

a. J.J Thomason b. William Crookes c. R.A Millikan d. Wilhelm Hallwachs

11. Which of the following metals is not sensitive to visible light?

a. Rubidium b. Sodium c. Caesium d. Cadmium

12. Which of the following does the wave theory of light not explain?

a. Diffraction b. Photocurrent c. Polarization d. Interference

13. Photons are deflected by

198 200
 potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the 2. Assertion: Photoelectric effect demonstrates the wave nature of light.
stopping potential is V/4. The threshold wavelength for the metallic surface is Reason. The number of photoelectrons is proportional to the frequency of light.
a. 4λ b. 5λ c. 5/2λ d. 3λ. (a) A (b) B (c) C (d) D
7. In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the 3. Assertion: When light of certain wavelength falls on a metal surface it ejects electron.
voltage is changed to 224 kV, then the de Broglie wavelength associated with the Reason: Light has wave nature.
electrons would (a) A (b) B (c) C (d) D
a. increase by 2 times b. decrease by 2 times c. decrease by 4 times 4. Assertion: As work function of a material increases by some mechanism, it requires
d. increase by 4 times. greater energy to excite the electrons from its surface.
Reason: A plot of stopping potential (V) versus frequency (v) for different materials, has
8. A particle of mass 3 × 10–6 g has the same wavelength as an electron moving with a greater slope for metals with greater work functions
velocity 6×106 m s−1. The velocity of the particle is
(a) A (b) B (c) C (d) D
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
5. Assertion: Light of frequency 1.5 times the threshold frequency is incident on
9. If a light of wavelength 330 nm is incident on a metal with work function 3.55 eV, the photosensitive material. If the frequency is halved and intensity is doubled the photo current
electrons are emitted. Then the wavelength of the emitted electron is (Take h = 6.6 × remains unchanged.
10–34 Js)
Reason: The photo electric current varies directly with the intensity of light and frequency
a. < 2.75×10−9 m b. ≥ 2.75×10−9 m c. ≤ 2.75×10−12 m d. < 2.5×10−10 m
of light.
10. A photoelectric surface is illuminated successively by monochromatic light of (a) A (b) B (c) C (d) D
wavelength λ and λ/2. If the maximum kinetic energy of the emitted photoelectrons in LEVEL 2
the second case is 3 times that in the first case, the work function at the surface of
material is 6. Assertion: The de-Broglie wavelength of a neutron when its kinetic energy is k is λ. Its
a) hc/λ b) 2hc/ λ c) hc/3λ d) hc/2λ
wavelength is 2 λ when its kinetic energy is 4k.
LEVEL 3 Reason: The de - Broglie wavelength λ is proportional to square root of the
1. In photoelectric emission, a radiation whose frequency is 4 times threshold frequency kinetic energy.
of a certain metal is incident on the metal. Then the maximum possible velocity of the (a) A (b) B (c) C (d) D
emitted electron will be 7. Assertion: In process of photoelectric emission, all emitted electrons do not have same
kinetic energy.
Reason: If radiation falling on photosensitive surface of a metal consists of different
wavelength then energy acquired by electrons absorbing photons of different wavelengths
shall be different.
(a) A (b) B (c) C (d) D
8. Assertion: Though light of a single frequency (monochromatic) is incident on a metal,
the energies of emitted photoelectrons are different.
Reason: The energy of electrons emitted from inside the metal surface, is lost in collision
with the other atoms in the metal.
(a) A (b) B (c) C (d) D

2. Two radiations with photon energies 0.9 eV and 3.3 eV respectively are falling on a 9. Assertion: The photoelectrons produced by a monochromatic light beam incident on a
metallic surface successively. If the work function of the metal is 0.6 eV, then the ratio metal surface have a spread in their kinetic energies.
of maximum speeds of emitted electrons will be Reason: The work function of the metal is its characteristics property.
a) 1:4 b) 1:3 c) 1:1 d) 1:9 (a) A (b) B (c) C (d) D
10. Assertion: Photoelectric saturation current increases with the increase in
3. A light source of wavelength 520 nm emits 1.04 × 1015 photons per second while the frequency of incident light.
second source of 460 nm produces 1.38 × 1015 photons per second. Then the ratio
Reason: Energy of incident photons increases with increase in frequency and as a result
of power of second source to that of first source is
a) 1.00 b) 1.02 c) 1.5 d) 0.98 photoelectric current increase. (a) A (b) B (c) C (d) D

202 204
4. Work function of sodium is 2.3eV. Does sodium show photo electric emission for
light of wavelength 6800A˚ 3. Figure shows a plot of 1/√V, where V is the accelerating potential, Vs. The de Broglie
5. Do all the electrons that absorb a photon come out as photoelectrons? wavelength λ in the case of two particles having same charge 'q' but different masses
m1 and m2. Which line (A or B) represents a particle of larger mass?
LEVEL 3
1.The graph shows variation of stopping potential Vo verses frequency of incident
5 MARKS QUESTIONS
radiation ϑ for two photosensitive metals A
LEVEL 1
and B. (i) Which of the two metals has 1. Draw properly labelled graphs to show the following concerning photo electric
higher threshold frequency and why? (ii) emission:
What does intercept on –ve y axis (i) Variation of photo electric current with the intensity of incident
represent? radiation.
(ii) Variation of photo electric current with accelerating
and stopping potential.
(iii) Variation of stopping potential with frequency of
2.The variation of the stopping potential (v0) with the
incident radiation.
frequency (v) of the light incident on two different
From the graph how the following can be determined. 1)
photosensitive surfaces M1 and M2 is shown in the figure.
Plank’s constant. 2) The work function of the material.
Identify the surface which has greater value of the work
Obtain Einstein s photo- electric equation.
function.
3.Show that the wavelength of electromagnetic radiation is
LEVEL 2
equal to the de-Broglie wavelength of its quantum. 2. A proton and an alpha particle are accelerated through the same potential. Which
one of the two has (i) greater value of de Broglie wavelength associated with it and
3 MARKS QUESTIONS (ii) less kinetic energy? Give reasons to justify your answer.

LEVEL 3
LEVEL 1 3. Two monochromatic radiations of frequencies v1 and v2 (V1 > v2) and having the
1. In photoelectric effect, why should the photoelectric current increase as the intensity
same intensity are, in turn, incident on a photosensitive surface to cause photoelectric
of monochromatic radiation incident on a photosensitive surface is increased?
emission. Explain, giving reason, in which case
Explain.
(i) a greater number of electrons will be emitted and
2. Light of wavelength 3500 Å is incident on two metals A and B. Which metal will yield
(ii) maximum kinetic energy of the emitted photoelectrons will be more.
more photoelectrons if their work functions are 5 eV and 2 eV respectively?
3. Plot a graph showing the variation of photo current vs collector potential for
NUMERICALS
three different intensities I1 > I2 > I3, two of which (I1 and I2) have the same
LEVEL 1
frequency ν and the third has frequency ν1 > ν.
1. What is the momentum of a photon of energy 1 MeV?
4. Show the variation of photocurrent with collector plate potential for different
2. The de-Broglie wavelength associated with an electron accelerated through a
frequencies but same intensity of incident radiation.
potential difference V is λ. What will be its wavelength when the accelerating potential
5. Define the terms (i) cut-off voltage and (ii) threshold frequency in relation to the
is increased to 4V?
Phenomenon of photoelectric effect. Using Einstein’s photoelectric equation show
3. An electron is accelerated through a potential difference of 100 volt. What is the de-
how the cut -off voltage and threshold frequency for a given photosensitive material
Broglie wavelength associated with it? To which part of the electromagnetic spectrum
can be determined with the help of a suitable plot.
does this value of wavelength correspond?
.
4. The maximum kinetic energy of a photoelectron is 3 eV. What is its stopping
potential?

206 208
 COMPETENCY BASED QUESTIONS SELF ASSESEMENT
TOPIC: DUAL NATURE OF RADIATON & MATTER
1. According to wave theory of light, the light of any frequency can emit electrons from
metallic surface provided the intensity of light be sufficient to provide necessary Marks: 25 Time: 40Min.
energy for emission of electrons, but according to experimental observations, the light
of frequency less than threshold frequency cannot emit electrons; whatever be the
General Instructions:
intensity of incident light. Einstein also proposed that electromagnetic radiation is
quantized. If photoelectrons are ejected from a surface when light of wavelength λ1 (a) All questions are compulsory
= 550 nm is incident on it. The stopping potential for such electrons is Vs =0.19. If (b) There are 25 questions in total. Q. 1 to 6 carries1 mark each. Q. 7 to 8 carry 2
photoelectrons are ejected from a surface when light of wavelength λ1 = 550 nm is marks each, Q. 9 to 10 carry 3 mark each, Q. 11 carry 4 mark and Q. 12 carry 5
incident on it. The stopping potential for such electrons is Vs =0.19. Suppose the marks.
radiation of wavelength λ2 = 190 nm is incident on the surface.

1. An electron, an alpha particle, a deuteron and a proton have the same KE. Which
i) Photoelectric effect supports quantum nature of light because
a. there is a minimum frequency of light below which no photoelectrons are emitted. one has shortest de Broglie wavelength?
b. the maximum K.E. of photoelectric depends only on the frequency of light and not a. α particle b. electron c. proton d. deuteron.
on its intensity 2. Photons of energies 1eV and 2eV are successively incident on a metallic surface of
c. even when the metal surface is faintly illuminated, the photo electrons leave the work function 0.5eV. The ratio of kinetic energy of most energetic photoelectrons in
surface immediately. the two cases will be
d. electric charge of the photoelectrons is quantized. a. 1:2 b.1:1 c. 1:3 d.1:4
3. When a metallic surface is illuminated with radiation of wavelength λ, the stopping
ii) Calculate the stopping potential Vs2 of surface.
a. 4.47 b. 3.16 c. 2.76 d. 5.28 potential is V. If the same surface is illuminated with radiation of wavelength 2λ, the
stopping potential is V/4. The threshold wavelength for the metallic surface is
iii) Calculate the work function of the surface a.4λ b. 5λ c. 5/2λ d. 3λ
a. 3.75 b. 2.07 c. 4.20 d. 3.60
4. In an electron microscope, the electrons are accelerated by a voltage of 14 kV. If the
iv) Calculate the threshold frequency for the surface voltage is changed to 224 kV, then the de Broglie wavelength associated with the
a. 500 x 1012 Hz b. 480 x 1013 Hz c. 520 x 1011 Hz d. 460 x 1013 Hz electrons would
a. increase by 2 times b. decrease by 2 times c. decrease by 4 times
2. Observations in Photoelectric Effect
1. For each metal there is a characteristic minimum frequency below which d. increase by 4 times
photoelectric effect is not observed. This is called threshold frequency. If frequency Directions: In each of the following questions, a statement of Assertion (A) is given
of light is less than the threshold frequency, there is no ejection of electrons no matter followed by a corresponding statement of Reason (R) just below it. Of the
how long it falls on surface or how high is its intensity. statements, mark the correct answer as:
2. The kinetic Energy of electrons emitted is directly proportional to frequency of (A)If both assertion and reason are true and reason is the correct explanation of
striking photons & independent of their intensity. assertion (B)If both assertion and reason are true but reason is not the correct
3. The no. of electrons that are ejected per second from metal surface depends upon explanation of assertion (C)If assertion is true and reason is false
intensity of striking radiations and doesn’t depend upon their frequency. (D)If both assertion and reason are false.
4. If frequency of incident light is more than threshold frequency, then the excess 5. Assertion: Two photons of equal wavelength must have equal linear momentum.
energy is imparted to electrons in the form of kinetic energy. Reason: Two photons of equal linear momentum will have equal wavelength.
(a) A (b) B (c) C (d) D
i) Electrons are emitted with zero velocities from metal surface when exposed to 6. Assertion: The kinetic energy of photoelectrons emitted from metal surface does
radiation of wavelength 6800Ao. Calculate (ν0 = photon’s frequency & W0 = work
not depend on the intensity of incident photon.
function)?
a. 3.21x 10 12 /sec & 9.7 x 10 -19 J Reason: The ejection of electrons from metallic surface is not possible with frequency
b. 4,14x 10 14 /sec & 2.92 x 10 -19 J of incident photons below the threshold frequency.

210 212
 UNIT VIII ATOMS AND NUCLEI - Foundation for Modern Atomic Theory : The discovery of the nucleus paved the way
for the development of the Bohr model and subsequent quantum mechanical models of
CHAPTER 12-ATOMS the atom.

Gist The gold foil experiment was crucial in advancing our understanding of atomic structure,
- Early atomic models and their limitations. Thomson’s model of atom leading to the realization that atoms have a tiny, dense nucleus surrounded by electrons,
fundamentally changing the way we understand matter at a microscopic level.
-Rutherford’s alpha ray scattering experiment
- Rutherford’s nuclear model: Electrons orbit a dense, positively charged nucleus.
-Rutherford’s model of atom .
- Bohr’s model of the atom and its postulates. - Limitations: Stability of atoms and spectrum of hydrogen couldn't be explained.

- Hydrogen atom spectrum and energy level transitions. 3. Bohr’s Model of the Atom

1. Introduction to Atomic Models

- Dalton’s Atomic Theory: Early concept

of the atom as an indivisible particle.

- Discovery of Electrons and Nucleus :

Introduction to the electron discovered by
J.J. Thomson and the nucleus
discovered by Rutherford through the
gold foil experiment.

2. Rutherford’s Model of the Atom

- Description of the gold foil experiment.

Setup of the Gold Foil Experiment - Postulates of Bohr’s theory: Quantized electron orbits, stationary states, and energy
levels.

- Energy quantization: Electrons can only occupy certain discrete orbits.

- Explanation of hydrogen spectrum: Emission and absorption spectra explained using

the concept of electronic transitions between quantized orbits.

4. Spectral Series

- Lyman Series: Transitions to n=1 (ultraviolet region).

- Balmer Series: Transitions to n=2 (visible region).

Apparatus - A source of alpha particles (helium nuclei), a thin sheet of gold foil, a - Paschen, Brackett, and Pfund Series : Transitions to n=3, 4, and 5 (infrared region).
fluorescent screen, and a detector.

Alpha Particles : High-energy particles emitted from a radioactive source, typically

radium or polonium.

214 216
MIND MAP /CONCEPT MAP 14. Who discovered the nucleus of the atom?
- A) Bohr B) Thomson C) Rutherford D) Einstein

15. Which particle has the least mass?

- A) Proton B) Neutron C) Electron D) Nucleus

16. The energy levels in an atom are:

- A) Continuous B) Quantized C) Infinite D) Non-existent

17. What is the charge of a neutron?

- A) Positive B) Negative C) Neutral D) Double positive

18. In Bohr's model, which orbit has the lowest energy?

- A) First orbit B) Second orbit C) Third orbit D) Fourth orbit

19. What is the main limitation of Rutherford’s model?

- A) Could not explain atomic spectra
- B) Could not explain the charge of the nucleus
- C) Could not explain the mass of the atom
- D) Could not explain the behavior of neutrons

20. In which region of the electromagnetic spectrum does the Lyman series lie?
- A) Visible B) Infrared C) Ultraviolet D) X-ray
Level 2
1. According to Bohr's model of the atom, which of the following statements is true about
the orbits of electrons?
- A) Electrons in higher orbits have higher energy.
- B) Electrons in lower orbits have higher energy.
- C) Electrons in all orbits have the same energy.
- D) Electrons have no defined energy in Bohr's model.

2. Which series of hydrogen spectrum lies in the ultraviolet region?

- A) Lyman series B) Balmer series C) Paschen series D) Brackett series

3. In Bohr's model, what does the quantum number \( n \) represent?

- A) Energy level of the electron
- B) Angular momentum of the electron
- C) Spin of the electron
- D) Magnetic quantum number of the electron

4. What is the fundamental assumption in Bohr's model that leads to quantization of

electron orbits?
- A) Electrons emit radiation continuously.
- B) Electrons do not radiate energy while moving in orbits.
- C) Electrons move in random paths around the nucleus.
- D) Electrons have no specific mass.

5.The energy difference between two energy levels in an atom corresponds to:
- A) The wavelength of light emitted or absorbed
- B) The number of electrons in the atom

218 220
6.For an electron orbit to be non-radiating, it should be Level 3
A) such that the angular momentum should be integral multiple of h.
B) circular in nature 1. Describe brother for atom model. What are the drawbacks of this model?
C) elliptical in nature NUMERICALS
D) none of these
Level 1
7.The ratio of the angular momentum of an electron in first orbit to that in the second 1.The ground state energy of hydrogen atom is -13.6 electron volt. What are the potential
orbit is energy of electron in the state?
A) ½ B)1/4 C) 4/1 D) 2 2.what is the energy possessed by an electron four and tends to be infinity?
3. What is the ratio of radii of orbit corresponding to the first excited state and ground
8.The ionisation energy of hydrogen atom is E. When the electron in a hydrogen atom state in hydrogen atom?
jumps from the state n = 1 to the state n = 2, the energy absorbed by it is ………………… 4. The radius of inner most electron orbit of an hydrogen atom is 5.3×10 -11 m. What is
A) 3E/4 B) 4E/3 C) E/4 D) E/3 the radius of the orbit in second excited state?
9.In the Bohr model of the atom, which of the following quantities takes quantized
Level 2
values?** 1.The energy levels of a hypothetical atom are shown below.
Which of the shown transitions will result in the emission of a
A) Linear momentum of electron B) Radius of electron orbit photon of wavelength 275 nm? Which of these transitions
correspond to emission of radiation of
C) Angular momentum of electron D) None of the above
(i) maximum and
(ii) minimum wavelength ?
10.The ionization energy of hydrogen is 13.6 eV. The energy required to remove an
electron from the second orbit of Li2+ is: 2.Find the ratio of energies of photons produced due to transition of an electron of
hydrogen atom from its
A) 13.6 Ev B) 30.6 eV C) 40.8 eV D) 122.4 eV (i) second permitted energy level to the first level, and
(ii) the highest permitted energy level to the first permitted level.

2 marks Questions 3.The ground state energy of hydrogen atom is -13.6 eV. What are the kinetic and
Level 1 potential energies of electron in this state? (All India)
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
1.The value of a ground state energy of hydrogen atom is -13.6 eV.
state in a hydrogen atom?
Q4.Why is the classical (Rutherford) model for an atom—of electron orbiting around the (i) Find the energy required to move an electron from the ground state to the first excited
nucleus—not able to explain the atomic structure? state of the atom.
Q5.What is the maximum number of spectral lines emitted by a hydrogen atom when it (ii) Determine
is in the third excited state? (a) the kinetic energy and
(b) orbital radius in the first excited state of the atom.
Level 2 (Given the value of Bohr radius = 0.53 Å)
Q1. What are the values of first and second excitation potential of hydrogen atom? 2.The energy levels of an atom are as shown here.
Q.2 The wavelength of some of the spectral lines of obtained in hydrogen spectrum are Which of them will result in the transition of a photon
1216 A0 , 6463 A0 and and 9546 A0 Which one of these wavelength belongs to the of wavelength 275 nm?
paschen series. b) Which transition corresponds to emission of radiation of maximum wavelength?
Q3.Name the series of Hydrogen spectrums lying in ultraviolet and visible regions.
3.The total energy of an electron in the first excited state of hydrogen atom is -3.4 eV.
Q4. what are results What is 4 Do you expect if alpha particle, scattering experiment is
repeatedly using a thin sheet of hydrogen in place of a gold foil? (a) What is kinetic energy of electron in this state? (ii) What is potential energy of electron
Q5.Define ionisation energy. What is its value for a hydrogen atom? in this state? (c) Which of the answers above would change if the choice of zero of
potential energy is changed?

222 224
 SELF ASSESSMENT TEST UNIT VIII ATOMS AND NUCLEI
Total marks =25 Time = 40 Mins.
Chapter–13: Nuclei
Question 1 to 6 each of 1 mark Gist of chapter
Question 7to8 each of 2 mark
Question 9to 10:each of 3 mark • Composition and size of nucleus
Question 11 of 4 mark 1)Nuclei are made up of proton and neutron. The number of protons in a nucleus
Question 12 is of 5 marks (called the atomic number or proton number) is represented by the symbol Z. The
number of neutrons (neutron number) is represented by N. The total number of neutrons
Q1.What is the main limitation of Rutherford’s model? and protons in a nucleus is called it's mass number A so A = Z + N.
- A) Could not explain atomic spectra 2) Neutrons and proton, when described collectively are called nucleons. A single
- B) Could not explain the charge of the nucleus nuclear species having specific values of both Z and N is called a nuclide.
- C) Could not explain the mass of the atom 3) Nuclides are represented as Z X A ; where X denotes the chemical symbol of the
- D) Could not explain the behaviour of neutrons element.
4) Isotopes : The atoms of element having same atomic number but different mass
Q2 The spectral lines of hydrogen were explained using: number are called isotopes. All isotopes have the same chemical properties. The
- A) Thomson’s model B) Rutherford’s model C) Bohr’s model D) Dalton’s model isotopes of some elements are the following
1
1H , 1 H 2 , 1 H 3 8 O 16 , 8 O 17 , 8 O 18 2 He
3
, 2 He 4 17 Cl 35 , 17 Cl
37
92 U
235
, 92 U
238

Q3.Two H atoms in the ground state collide inelastically. The maximum amount by which
5) Isobars : The nuclei which have the same mass number (A) but different atomic
their combined kinetic energy is reduced is
number (Z) Arecalled isobars. Isobars occupy different positions in periodic table so all
-A) 10.20 eV - B) 20.40 eV - C) 13.6 eV - D) 27.2 eV
isobars have Different chemical properties. Some of the examples of isobars are
Q4.The Bohr model for the spectra of a H - atom. 3 3 14
and 7 N 14 , 8 O 17 and 17
1H and 2 He , 6C 9F

- A) will not be applicable to hydrogen in the molecular form • Nuclear Force

(1) Nuclear forces are short range forces. These do not exist at large distances
- B) will not be applicable as it is for a He -atom.
greater
- C) is valid only at room temperature
than 10–15m.
- D) predicts continuous as well as discreeter spectral lines .
(2) Nuclear forces are the strongest forces in nature.
Directions for Assertion-Reason Type Questions (3) These are attractive force and causes stability of the nucleus.
(4) These forces are charge independent.
In each of the following questions, a statement of assertion (A) is followed by a statement (5) Nuclear forces are non-central force.
of reason (R). Mark the correct choice as: - (a) Both Assertion (A) and Reason (R) are
true and Reason (R) is the correct explanation of Assertion (A). - (b) Both Assertion (A) • POTENTIAL ENERGY CURVE
and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A). 1) shows how the potential energy of two molecules and
the force between them changes with their separation.
- (c) Assertion (A) is true but Reason (R) is false.
2) The force at any point is found from taking the gradient of
- (d) Assertion (A) is false but Reason (R) is true. the potential energy curve, in other words
Q5.Assertion (A): in alpha rays, scattering experiment, most of the alpha particle goes F = -dV/dr, where V is the potential energy.
on deflected.
Reason (R): most of the space in the atom is empty • Size of Nucleus
Q6.Assertion (A): In Bohr’s model of the atom, the angular momentum of the electron is Nuclear radius : Experimental results indicates that the nuclear radius is
quantized. proportional to A1/3, where A is the mass number of nucleus i.e. R  A 1 / 3 
Reason (R): The electron in an atom revolves in circular orbits around the nucleus under R = R0 A1 / 3 , where R0 = 1.2  10–15m = 1.2 fm.
the influence of electrostatic forces.
• Mass-energy relation
Q7.State the limitations of Bohr’s atomic model
E=mc2 E= energy, m=mass, c=speed of light

226 228
 (a) Water, in which soap does not lather (b) Compound of heavy oxygen
Fission and heavy hydrogen
fragm
(c) Compound of deuterium and oxygen (d) Water at 4°C
235U
Fissio Neutr
Neutr
n 17. The tritium which is the isotope of hydrogen contains
(a)One proton, one neutrons (b)One proton, two neutrons
Fission reaction of U235
(c)Two protons, one neutrons (d)None
92 U
235
+ 0 n1 → 92 U
236
→ 56 Ba
141
+ 36 Kr
92
+ 3 0 n1 + Q
(unstable nucleus) 18. The force between a neutron and a proton inside the nucleus is
https://upload.wikimedia.org/wikipedia/commons/a/a0/PressurizedWaterReactor.gif (a) Only nuclear attractive (b) Only Coulomb force
(c) Both of the above (d) None of these
• Nuclear Fusion 19. “Mass density” of nucleus varies with its mass number A as
P n P
(1) In nuclear fusion two or more than P 3He 4He P (a) A 2 (b) A (c) A 0 (d) 1/A
2
P H
two lighter nuclei combine to form a P P n P P P
20. The mass defect in a particular nuclear reaction is 0.3 gm. The amount of
n n n n n
single heavy nucleus. The mass of P P
P

P
energy liberated in kilowatt hours is (Velocity of light = 3  108m/s)
single nucleus so formed is less than  e +

P
the sum of the masses of parent nuclei. This
(a) 1.5  10 6 (b) 2.5  10 6 (c) 3  10 6 (d) 7.5  10 6
difference in mass results in the release of tremendous amount of energy
Level 2
Fission
fragment
1. The mass defect for the nucleus of helium is 0.0303 a.m.u. What is the binding
energy per nucleon for helium in MeV
(a) 28 (b) 7 (c) 4 (d) 1
Mind map
235U
2. Atomic power station at Tarapore has a generating capacity of 200 MW. The energy
Neutrons generated in a day by this station is
Fission
Neutrons
fragment (a) 200 MW (b) 200 J (c) 4800  10 6 J (d) 1728  10 10 J
Fig. 26.18 3. One microgram of matter converted into energy will give
(a) 90 J (b) 9  10 3 J (c) 9  10 10 J (d) 9  10 5 J
4. Mn and Mp represent the mass of neutron and proton respectively. An element
having mass M has N neutron and Z-protons, then the correct relation will be
(a) M < {N. Mn + Z. Mp} (b) M > {N. Mn + Z. Mp}
(c) M = {N. Mn + Z. Mp} (d) M = N {Mn + Mp}
5. The binding energy of deuteron 12 H is 1.112 MeV per nucleon and an  − particle 42 He
has a binding energy of 7.047 MeV per nucleon. Then in the fusion reaction
1 H +1 H →2 He + Q , the energy Q released is
2 2 4

(a) 1 MeV (b) 11.9 MeV (c)23.8 MeV (d) 931 MeV
6. Binding energy of a nucleus is
(a) Energy given to its nucleus during its formation
(b) Total mass of nucleus converted to energy units
(c) Loss of energy from the nucleus during its formation
(d) Total K.E. and P.E. of the nucleons in the nucleus
7. One requires energy E n to remove a nucleon from a nucleus and an energy ' Ee ' to
remove an electron from the orbit of an atom. Then
(a) En = Ee (b) En  Ee (c) En  Ee (d) En  E e
8. The binding energy of nucleus is a measure of its
(a) Charge (b) Mass (c) Momentum (d) Stability
9. The binding energies per nucleon for a deuteron and an  − particle arex1 and x2
respectively. What will be the energy Q released in the reaction 1 H 2 +1 H 2 →2 He 4 + Q
(a) 4 (x 1 + x 2 ) (b) 4 (x 2 − x 1 ) (c) 2(x 1 + x 2 ) (d) 2(x 2 − x 1 )

230 232
 5)Two nuclei have mass number in the ratio 1 : 3. What is the ratio of their 2. Outside a nucleus
nuclear densities? (a)Neutron is stable (b)Proton and neutron both are stable
(c) Neutron is unstable (d)Neither neutron nor proton is stable
LEVEL 2 3. Nuclear force is
short answer type ( 2 MARKS ) (a) Short range and charge dependent (b)Short range and charge independent
1) Calculate the energy equivalent of 1amu in MeV. (c) Long range and charge independent (d) Long range like electrostatic type
2) Distinguish between nuclear fission and nuclear fusion. 4. If Fpp , Fpm and Fnn are the magnitudes of net force between proton-proton, proton-
3) State the necessary condition for nuclear fission. neutron and neutron-neutron respectively, then
4)Define atomic mass unit. (a) Fpp = Fpn = Fnn (b) Fpp  Fpn = Fnn
5) Write the number of proton and neutron in 56Ba144.
(c) Fpp  Fpn  Fnn (d) Fpp  Fpn  Fnn
6)Two nuclei have mass number 3:9 what is their nuclear density ratio.
LEVEL 3
short answer type ( 2 MARKS )
1) When 92 U 235 undergoes fission. 0.1% of its original mass is changed into
energy. How much energy is released if 1 kg of 92 U 235 undergoes fission?

Level -1
Short answer type (3 MARKS)
1) Write any three characteristic properties of nuclear force.
2) Show that the nuclear density is independent of mass number.
3) Plot a graph showing the variation of potential energy of a pair of nucleons as
a function of their separation. Write its two characteristic properties.
LEVEL 2
Short answer type (3 MARKS)
1) The sun radiates energy in all directions. The average radiations received on the
earth surface from the sun is 1.4 kilowatt / m 2 .The average earth- sun distance is
1.5  10 11 metres
. Find the mass lost by the sun per day.
(1 day = 86400 seconds)
Level 3
1) Calculate the energy released in MeV in the following nuclear reaction:

Level -1
Long answer type ( 5 MARKS)
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
and nuclear fusion can be explained.
2) Calculate binding energy per nucleon of 209Bi83 nucleus. Given that mass of
209Bi83 = 55.934939u, mass of proton = 1.007825u, mass of neutron = 1.0086 MeV665
u and 1 u = 931 MeV.

234 236
 Unit IX: Electronic Devices Due to the deficiency of an electron, there is one incomplete covalent bond. The
Chapter–14: Semiconductor Electronics: Materials, vacancy that exists with the fourth covalent bond with fourth Si atom constitutes a
hole.
Devices and Simple Circuits
The semiconductor becomes deficient in electrons i.e. number of holes become more
GIST OF THE CHAPTER: than the number of electrons. Such a semiconductor is called p-type
Energy bands in conductors, semiconductors and insulators (qualitative ideas only) semiconductor. It has holes as majority carriers and electrons as minority carriers.
Intrinsic and extrinsic semiconductors- p and n type, p-n junction Semiconductor Electrical conductivity of a semiconductor:
diode - I-V characteristics in forward and reverse bias, application of junction diode The conductivity of a semiconductor is determined by the mobility (µ) of both
-diode as a rectifier. electrons and holes and their concentration. Mathematically- σ = e (neμe + nhμh)
Energy bands in solids: P-N JUNCTION.
⮚ Due to influence of high electric field between the core of the atoms and the
shared electrons, energy levels are split-up or spread-out forming energy
bands.
⮚ The energy band formed by a series of levels containing valance electrons
is called valance band and the lowest unfilled energy level just above the
valance band is called conduction band.
⮚ Filled energy levels are separated from the band of unfilled energy levels by
an energy gap called forbidden gap or energy gap or band gap.
The device obtained by bringing a p-type semiconductor crystal into close contact
with n-type semiconductor crystal is called a p-n junction. It conducts in one
direction only. It is also called a junction diode
Depletion layer.
It is a thin layer formed between the p and n-sections and devoid of holes and
electrons. Its width is about 10-8 m. A potential difference of about 0.7 V is
produced across the junction, which gives rise to a very high electric field (= 106
V/ m).
Potential Barrier:
Energy band diagram for, Conductors Semiconductors and Insulators
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. This acts as a barrier
Conductors (Metals):The conduction band and valance band partly overlap each
and hence called „potential barrier‟ .Potential barrier for Si is nearly 0.7 V and for
other and there is no forbidden energy gap in between.Large number of electrons
Ge is 0.3 V. The potential barrier opposes the motion of the majority carriers.
are available for electrical conduction , hence the resistance is low of such
materials.Even if a small electric field is applied across the metal, these free
electrons start moving.Hence metals behave as a conductor. Forward biasing:
Semiconductors: The conduction and valance bands are separated by the small The p-n junction is said to be forward biased, when the positive terminal of the
energy gap ( 1 eV) called forbidden energy gap. The valence band is completely external battery is connected to p-section and the negative terminal to n-section
filled, while the conduction band is empty at zero kelvin. The electrons cross from of the junction diode.
valence band to conduction band even when a small amount of energy is supplied. P-N JUNCTION.
The semiconductor acquires a small conductivity at room temperature. The device obtained by bringing a p-type semiconductor crystal into close contact
Insulators: Electrons, however heated, cannot practically jump to conduction band with n-type semiconductor crystal is called a p-n junction. It conducts in one
from valence band due to a large energy gap (>3 eV). Therefore, conduction is not direction only. It is also called a junction diode
possible in insulators. Depletion layer. It is a thin layer formed between the p and n-sections and devoid
of holes and electrons. Its width is about 10-8 m. A potential difference of about
INTRINSIC SEMICONDUCTORS:
0.7 V is produced across the junction, which gives rise to a very high electric field
Intrinsic Semiconductor is a pure semiconductor.
(= 106 V/ m).
238 240
2. Full wave rectifier: A rectifier which rectifies both halves of each a.c. input cycle 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.
MCQ LEVEL 1
1 The energy band gap is maximum in
(a) Metals (b) superconductors (c) insulators (d) semiconductors
2 At absolute zero, silicon (Si) acts as
(a) Non-metal (b) metal (c) insulator (d) none of these
3 When impurities are added to a pure semiconductor, the procedure is known
as
(a) Mixing (b)Doping (c)Diffusing (d)None of the above
4 Silicon is doped with which of the following to obtain P type semiconductor
(a) Phosphorus (b) Gallium (c) Germanium (d) Bismuth
5 When an intrinsic semiconductor is doped with an impurity, the
semiconductor's conductivity
TABLES (a) Increases (b) decreases (c) remains the same (d) becomes zero
1) DIFFERENCE BETWEEN INTRINSIC AND EXTRINSIC SEMICONDUCTORS 6 6. Correct order of relative values of electrical conductivity σ for different types
of solid is…….
S.NO INRINSIC SEMICONDUCTOR EXTRINSIC SEMICONDUCTOR (a) σ metal >σ semiconductor > σ insulator
(b) σ semiconductor >σ insulator >σ metal
1 Pure form of semiconductor. Impure form of semiconductor.
(c) σ semiconductor >σ metal >σ insulator
2 Conductivity is low Conductivity is higher than (d) σ insulator>σ semiconductor>σ metal
intrinsic semiconductor.
7 To create a p-type semiconductor, an pure semiconductor is doped with the
3 The no of holes is equal to In n-type, the no. of electrons is following material:
no of free electrons greater than that of the holes and a) aluminum b) Phosphorous c) Arsenic d) Sodium
in p-type, the no. holes is greater
8 The following parameters determines a p-n junction's barrier potential:
than that of the electrons.
i) type of semiconductor or material (ii) amount of doping (iii) Temperature
4 The conduction The conduction depends on the Which one of the following is correct?
depends on concentration of doped impurity (a)Both (i)and(ii) (b)Only(ii) (c)Both (ii)and(iii) (d)(i),(ii)and(iii)
temperature. and temperature. Directions: In the following questions, A statement of Assertion (A) is followed by a
statement of Reason (R). Mark the correct choice as.
A: If both Assertion and Reason are correct and the Reason is a correct explanation of
DIFFERENCE BETWEEN HALF WAVE AND FULL WAVE RECTIFIER
the Assertion.
B: If both Assertion and Reason are correct but Reason is not a correct explanation of
S.NO HALF WAVE RECTIFIER FULL WAVE RECTIFIER the Assertion.
C:If the Assertion is correct but Reason is incorrect.
1 Only half cycle of AC is Both cycles of AC are rectified.
D: If both the Assertion and Reason are incorrect
rectified.
2 Requires only one diode Requires two diodes. 9 Assertion (A): The depletion layer in the p-n junction is free from mobile charge
carriers.
3 The output frequency is equal The output frequency is double of
to input supply frequency. (F) the input supply frequency. (2F) Reason (R) : There is no electric field across the junction barrier.

4 The electric current A continuous electric current

through the load is not flow through the load.
continuous

242 244
 2 Free electrons have more mobility than free holes due to the following B: If both Assertion and Reason are correct but Reason is not a correct explanation of
reasons: the Assertion.
(a) they are light (b) they carry negative charge C:If the Assertion is correct but Reason is incorrect.
(c) They mutually collide less d) they require low energy to continue their
D: If both the Assertion and Reason are incorrect
motion
3 The energy needed for an electron to move from the valance band to the 8 Assertion (A): Electron has higher mobility than hole in a semiconductor.
conduction band in Germanium is Reason(R): The mass of electron is less than the mass of the hole.
(a) 0.12 eV (b)0.72 eV (c)7.2 eV (d)None of these 9 Assertion (A): When two semiconductor of p-type and n- type are brought in
4. For semiconductors, which of the ones that follow is the most suitable? contact, they form p-n junction which act like a rectifier.
(a) large evacuated space (b)external heating arrangement Reason(R): A rectifier is used to convert alternating current into direct current.
(c) low operating voltages (d)high power 10 Assertion (A): A p-n junction with reverse bias can be used as a photo-diode to
5 When a forward bias is applied to a p-n junction, it
measure light intensity.
(a) raises the potential barrier. (b) reduces the majority carrier current to
zero. (c) lowers the potential barrier (d)None of the above. Reason(R): In a reverse bias condition the current is small but it is more sensitive
to changes in incident light intensity.
6. In a full wave rectifier, input AC has a frequency ‘ν’. The output frequency of
current is 2 MARK QUESTIONS
(a) ν /2 (b) ν (c) 2 ν (d) None of these LEVEL-1
7 When an electric field is applied across a semiconductor, 1 Given that silicon and carbon have four valence electrons each, how may they be
(a) Electrons move from lower energy level to higher energy level in the distinguished?
conduction band 2 Draw the n- and p-type semiconductors' energy band diagrams at a temperature
(b) Electrons move from higher energy level to lower energy level in the T >0K. With their energies, show the energy levels of the donor and acceptor.
conduction band 3 Using a circuit diagram, describe how a p-n junction diode functions as a half-
(c) Holes in the valence band move from lower energy level to higher wave rectifier.
energy level 4 Distinguish between intrinsic and extrinsic semiconductors.
(d) None of the above 5 As far as we are aware, despite having a lot of holes, p-type semiconductors are
electrically neutral. Why?
Directions: In the following questions, A statement of Assertion (A) is followed by a
statement of Reason (R). Mark the correct choice as. 2 MARK QUESTIONS
A: If both Assertion and Reason are correct and the Reason is a correct explanation of LEVEL-2
the Assertion.
B: If both Assertion and Reason are correct but Reason is not a correct explanation of 1 Write differences between forward bias and reverse bias.
the Assertion. C:If the Assertion is correct but Reason is incorrect. 2 The V-I characteristic of a silicon diode is as shown
D: If both the Assertion and Reason are incorrect in the figure. Calculate the resistance of the diode
8 Assertion (A): For the same doping concentrations, n-type Si material has a at (i) I = 5 mA and (ii) V = –20V
higher conductivity than p-type Si material.
Reason (R): In a semiconductor the electrons are less tightly bounded than
holes.
9 Assertion (A): n-type semiconductors of silicon are electrically charged.
3 How does a doping agent modify a semiconductor's conductivity?
Reason(R): In n-type semiconductors, the doped atom has no more valence 4 How does temperature cause semiconductors' resistivity to decrease?
Electron than silicon.

246 248
 3. An a.c. signal is fed into two circuits X and Y ii) Draw the energy band diagram of conductor , insulator and semiconductor.
and the corresponding output in the two cases
have the wavefront shown in figure. Name the CASE STUDY/SOURCE BASED QUESTIONS
circuit X and Y. Also draw their detailed circuit LEVEL-2
diagram. 1.
CASE STUDY/SOURCE BASED QUESTIONS Full Wave Rectifier The process of
LEVEL-1 converting alternating
1. voltage/current into direct
On the basis of energy bands materials are also defined as metals, semiconductors voltage/current is called rectification.
and insulators. These semiconductors are classified as intrinsic semiconductors and Diode is used as a rectifier for
extrinsic semiconductors also. Intrinsic semiconductors are those semiconductors converting alternating
which exist in pure form. And intrinsic semiconductors have number of free electrons is current/voltage into direct
equal to number of holes. The semiconductors doped with some impurity in order to current/voltage. Diode allows
increase its conductivity are called as extrinsic semiconductors. Two types of dopants current to pass only, when it is
are used they are trivalent impurity and pentavalent impurity also. The extrinsic forward biased. So, if an alternating
semiconductors doped with pentavalent impurity like Arsenic, Antimony, Phosphorus voltage is applied across a diode, the current flows only in that part of the cycle when
etc are called as n – type semiconductors. In n type semiconductors electrons are the the diode is forward biased. This property is used to rectify the current/voltage.
majority charge carriers and holes are the minority charge carriers. When trivalent
impurity is like Indium, Boron, Aluminium etc are added to extrinsic semiconductors i) If in a p-n junction, a square input signal of 10V is applied as shown
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?
III) Why doping is necessary?
IV) Majority charge carriers in p-type semiconductor are

2.
From Bohr's atomic model, we know that the electrons have well defined energy levels
in an isolated atom. But due to interatomic interactions in a crystal, the electrons of the
outer shells are forced to have
energies different from those in ii) In figure, the input is across the terminals A and C and the output is across B
and D. Then, the output is
isolated atoms. Each energy level
splits into a number of energy levels
forming a continuous band. The gap
between top of valence band and
bottom of the conduction band in
which no allowed energy levels for
electrons can exist is called energy

250 252
 ii) Based on the V-I characteristics of the diode, we can classify diode as 2 A 10V battery is attached to 3 01
resistors and two ideal diodes as
(a) bi-directional device (b) ohmic device
shown below. What will be the
(c) non-ohmic device (d) passive element reading of the ammeter?
iii) In the case of forwarding biasing of a p-n junction diode, which one of the
following statement is correct?
a)1/6 A b)1/5 A c) 1/4 A d)3/14
(a) effective barrier potential decreases A
(b) majority charge carriers begins to flow away from junction 3 What is energy required for an electron to jump to forbidden band in Silicon 01
(c) width of depletion layer increases at room temperature?
(d) effective resistance across the junction increases a) 0.01 eV b)0.05 eV c)0.7 eV d)1.1 Ev
iv) If an ideal junction diode is connected as shown, then the value of the current I is. 4 A battery, resistance, and semiconductor device are connected in a series 01
circuit. The circuit is determined to be carrying a current. The current almost
completely disappears if the battery's polarity is switched. The apparatus
could be
a) Si Semiconductor b) Si with III-A impurity c) Si With V-
(a) 0.005 (b) 0.02 A (c) 0.01 A (d) 0.1A A impurity d) diode

2. COMPETENCY BASED QUESTIONS

When the diode is forward biased, it is found that beyond forward voltage V = Vk, 2 MARK QUESTIONS
called knee voltage, the conductivity is very high. At this value of battery biasing
1 A sample of germanium doped with pentavalent impurity is heated to 300 K. 02
for p-n junction, the potential barrier is overcome and the current increases rapidly
Determine the electron and hole counts if the pentavalent impurity
with increase in forward voltage. When the diode is reverse biased, the reverse
concentration is 12 x 1017 cm-3. Assume that the impurity atom has fully
bias voltage produces a very small current about a few microamperes which almost
ionized. Given: 2.4 x 1013 cm-3 is the inherent carrier concentration.
remains constant with bias. This small current is reverse saturation current. 36. In
2 When a forward-biased p-n junction experiences a voltage supply that 02
which of the following figures, the p-n diode is forward biased.
exceeds the potential barrier, the diffusion current increases exponentially in
i) In which of the following figures, the p-n diode is forward biased
proportion to the number of holes that diffuse into the n-region. Will the
diffusion current eventually reach zero and the hole concentration in the p-
and n-regions become equal? Give reasons for your response.
3 The threshold voltage for diodes D1 and D2 are 0.3 V and 0.7 V respectively. 02
In circuit I, both the diodes D1 and D2 are forward biased. In circuit II, D1 is
forward biased whereas D2 is reverse biased. Determine current through the
diodes in series, ID and voltage Vo in each of the two given circuits.

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
reverse bias resistance is

254 256
 potential barrier of Vo. The holes approach the pn junction with a non-zero
initial kinetic energy from either p or the n- side depending upon the nature SELF ASSESSMENT PAPER
of biasing applied. TOTAL MARKS 25
a. If the holes approach the pn junction from p-side, SECTION A
i. What type of biasing must have been applied across the pn junction?
ii. Will the kinetic energy of the holes increase or decrease while crossing the
Q MARKS
junction? Give reason for your answer.
01 Which of the following statements is correct? 01
b. If the holes approach the pn junction from n-side,
(a) Hole is an antiparticle of electron.
i. What type of biasing must have been applied across the pn junction?
ii. Will the kinetic energy of the holes increase or decrease while crossing the (b) Hole is a vacancy created when an electron leaves a covalent bond.
junction? Give reason for your answer. (c) Hole is the absence of free electrons.
3 A diode is connected in series with a 3 V battery and a 30 Ω resistor. A drift 03 (d) Hole is an artificially created particle.
current of 10 μA flows through the diode. 02 A potential barrier of 0.3 V exists across a p-n junction. If the depletion 01
(a) What is the potential drop across the diode? region is 1 µm wide, what is the intensity of electric field in this region?
(b) Is the diode forward-biased or reverse-biased? Draw a circuit diagram to
represent the above connections.

COMPETENCY BASED QUESTIONS 03 The breakdown in a reverse biased p-n junction diode is more likely to 01
5 MARK QUESTIONS occur due to
1 The image below shows a circuit with three diodes and three resistors 05 (a) large velocity of the minority charge carriers if the doping
connected to an AC source with an rms voltage V. concentration is small
What is the average power delivered over one full cycle of AC in the above (b) large velocity of the minority charge carriers if the doping
concentration is large
circuit? Show your calculations and arrive at the final answer in terms of V
and R. (Assume the diode is ideal.) (c) strong electric field in a depletion region if the doping concentration
is small
(d) none of these
04 In a full wave junction diode rectifier the input ac has rms value of 20 V. 01
The transformer used is a step up transformer having primary and
secondary turn ratio 1 : 2. The dc voltage in the rectified output is
(a) 12 V (b) 24 V (c) 36 V (d) 42 V
Directions: In the following questions, A statement of Assertion (A) is followed by a
statement of Reason (R). Mark the correct choice as.
A: If both Assertion and Reason are correct and the Reason is a correct explanation of
the Assertion.
B: If both Assertion and Reason are correct but Reason is not a correct explanation of
the Assertion.
C:If the Assertion is correct but Reason is incorrect.
D: If both the Assertion and Reason are incorrect
05 Assertion (A) : The half-wave rectifier work only for positive half cycle 01
of ac.

258 260
 charge carriers and holes are the minority charge carriers. When trivalent impurity arm PQ is F, then the magnetic force which acts on the arm QR will be
is like Indium, Boron, Aluminium etc are added to extrinsic semiconductors then p
type semiconductors will be formed. In p type semiconductors holes are majority
charge carriers and electrons are the minority charge carriers.
i) In case of p-type semiconductors__ 𝐹
a) - F b) √2𝐹 c) F d)
a) nh<< ne b) nh = ne c) nh>> ne d) nh= ne = 0 √2
3 If an a.c. main supply is given to be 220 V, the average e.m.f. during a positive [1]
ii) An intrinsic semiconductor behaves like _____ at T = 0K. half cycle will be
a) conductors b) semiconductors c) insulators d) superconductors a) 240 V b) 220√2 V c) 220 V d) 198 V
iii) If the energy band gap Eg> 3 eV then such materials are called as 4 In the given circuit, the reading of the voltmeter V1 and V 2 are 300 V each. [1]
a) conductors b) semiconductors c) insulators d) superconductors
The reading of the voltmeter V 3
iv) P- type semiconductor is obtained by adding ……… in pure semiconductor and ammeter A are respectively
a) zinc b) Magnesium c) Phosphorous d) Aluminum a) 150 V,2.2A
b) 240 V,2A
SECTION E c) 100 V,2A
11 (i) Can a slab of p-type semiconductor be physically joined to another 05 d) 220 V,2.2A
n-type semiconductor slab to form p-n junction? Justify your answer.
(ii) In a p-n junction diode, the forward bias resistance is low as 5 Figure shows a capacitor made of two circular plates each of radius 12 cm, [1]
compared to the reverse bias resistance. Give reason. and separated by 5mm. The capacitor is being charged by an external source
(not shown in the figure). The charging current is constant and equal to 0.15

A. Displacement current across the plates is

a) 0.17 A b) 0.18 A c) 0.15 A d) 0.16 A
6 A ray of light travels from the point A to B [1]
************ with a uniform speed. On its way, it is
reflected by the surface XX’. The path
followed by the ray to take least time is:

a) 1 b) 4
c) 2 d) 3

7 Which of the following principle is used in optical fiber? [1]

a) Total internal reflection b) Scattering
c) Interference d) Diffraction

262 264
 SECTION-A 26 Obtain the binding energy (in MeV) of a nitrogen nucleus(14 14
7 𝑁) , given 𝑚(7 𝑁) [3]
13 Assertion: Positive charge always moves from a higher potential point to a [1] = 14.00307 u
lower potential point. 27 State the basic assumption of the Rutherford model of the atom. Explain in [3]
Reason: Electric potential is a vector quantity. brief why this model cannot account for the stability of an atom?
a) Assertion and reason both are correct statements and reason is correct 28 An a.c. the signal is fed into two circuits X and [3]
explanation for assertion. Y and the corresponding output in the two
b) Assertion and reason both are correct statements but reason is not correct cases have the wave forms shown in the
explanation for assertion. figure. Name the circuits X and Y. Also draw
c) Assertion is correct statement but reason is wrong statement. their detailed circuit diagrams.
d) Assertion is wrong statement but reason is correct statement.
OR
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 Explain the working of PN junction diode in Forward bias with suitable circuit
2𝑅 diagram.
R - L circuit is given by cos𝜙 = 2 2 2 .
𝑅 +𝜔 𝐿 SECTION-D
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. 29 Read the source given below and answer any [4]
c) A is true but R is false. four out of the following questions: In 1942, a
d) A is false but R is true. German physicist Kirchhoff extended Ohm’s law to
complicated circuits and gave two laws, which
15 Assertion (A): Corpuscular theory fails in explaining the velocities of light in [1]
air and water. enable us to determine current in any part of such
Reason (R): According to Corpuscular theory, the light should travel faster in a circuit. According to Kirchhoff’s first rule, the
denser media than in rarer media. algebraic sum of the currents meeting at a junction
a) Both A and R are true and R is the correct explanation of A. in a closed electric circuit is zero. The current
b) Both A and R are true but R is not the correct explanation of A. flowing in a conductor towards the junction is taken as positive and the current
c) A is true but R is false. flowing away from the junction is taken as negative. According to Kirchhoff’s
d) A is false but R is true. second rule, in a closed loop, the algebraic sum of the emf’s and algebraic
sum of the products of current and resistance in the various arms of the loop
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. is zero. While traversing loop, if negative pole of the cell is encountered first,
Reason (R): A rectifier is used to convert alternating current into direct then its emf is negative, otherwise positive.
current. 1. Kirchhoff’s 1st law follows
a) Both A and R are true and R is the correct explanation of A. a. law of conservation of energy
b) Both A and R are true but R is not the correct explanation of A. b. law of conservation of charge
c) A is true but R is false. c. law of conservation of
d) A is false but R is true. momentum
SECTION -B 2. The value of current I in the given circuit
17 Five balls, numbered 1 to 5 are suspended using separate threads. Pairs (1, [2] Is
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? a. 4.5 A b. 3.7 A c. 2.0 Ad. 2.5 A
𝑛𝑑
18 A galvanometer can be converted into a voltmeter of a certain range by [2] 3. Kirchhoff’s II law is based on.
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 a. law of conservation of momentum of electron
galvanometer. b. law of conservation of charge and energy
c. law of conservation of energy
d. none of these.

266 268
 (I) On the basis of electron drift, derive an expression for resistivity of a
conductor in terms of 3 8. A charged particle moves in a magnetic field in a circular path. The time period of
number density of free electrons and relaxation time. On what factors does revolution is:
resistivity of a conductor depend? 2 a) Directly proportional to the charge
(II) Why alloys like constantan and manganin are used for making standard b) Inversely proportional to the charge
resistors? c) Directly proportional to the velocity
32 1. Draw a labelled diagram of an ac generator and state its working [5] d) Independent of the velocity
principle.
2. How is magnetic flux linked with the armature coil changed in a 9. A diode is used as?
generator? a) Rectifier b) Amplifier c) Inverter d) As an AND Gate
3. Derive the expression for a maximum value of the induced emf and
state the rule that gives the direction of the induced emf. 10. The SI unit of magnetic susceptibility is:
4. Show the variation of the emf generated versus time as the armature
a) m3 b) Unitless c) Am2 d) T-1
is rotated with respect to the direction of the magnetic field.
OR
11. In a pn junction diode, in forward bias:
i) Draw a schematic arrangement for winding of primary and secondary coils a) Junction resistance decreases
in a transformer when the two coils are wound on top of each other.
b) Width of depletion layer decreases
(ii) State the underlying principle of a transformer and obtain the expression c) Both a and b
for the ratio of secondary to primary voltage in terms of the d) None of the above
• number of secondary and primary windings and
• primary and secondary currents. 12. The energy of a photon is directly proportional to its:
(iii) Write the main assumption involved in deriving the above relations. a) Amplitude b) Frequency c) Speed d) Wavelength
(iv) Write any two reasons due to which energy losses may occur in actual
13. The work function of a metal is:
transformers.
a) The minimum energy required to remove an electron from the metal surface
33 1. Draw a labelled ray diagram to obtain the real image formed by an [5] b) The maximum energy required to remove an electron from the metal surface
astronomical telescope in normal adjustment position. Define its c) The average energy required to remove an electron from the metal surface
magnifying power.
d) None of the above
2. You are given three lenses of power 0.5 D, 4D and 10 D to design a
telescope.
a. Which lenses should be used as objective and eyepiece? Justify 14. A capacitor of capacitance C is connected to a battery of voltage V. The energy stored
your answer. in the capacitor is:
b. Why is the aperture of the objective preferred to be large?
OR
A convex lens made up of glass of refractive index 1.5 is dipped, in turn, in
(i) a medium of refractive index 1.65,
(ii) a medium of refractive index 1.33.
(a) Will it behave as a converging or a diverging lens in the two cases? 15. Assertion (A): The magnetic moment of a current-carrying loop is proportional to the
(b) How will its focal length change in the two media? current and the area of the loop.
Reason (R): The magnetic moment of a current-carrying loop is given by the product of
************ the current and the perimeter of the loop.

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33. (a) Explain the formation of a PN junction diode and discuss its working principle. (3 SECTION A
marks) Q.No. Question
(b) Draw and describe the V-I characteristics of a PN junction diode in forward bias and 1 Some charge is being given to a conductor. Then, it’s potential
reverse bias conditions. (2 marks) (a) is maximum at the surface.
Or
(b) is maximum at the centre.
a) Explain the working of a PN junction diode as a half-wave rectifier with the help of a
circuit diagram and waveforms. (3 marks) (c) remains the same throughout the conductor.
(b) Describe the working of a PN junction diode as a full-wave rectifier with the help of a (d) is maximum somewhere between the surface the and centre.
circuit diagram and waveforms. (2 marks) 2 What is the effective capacitance between X and Y?
34. (a) Derive the lens maker's formula for a convex lens. (3 marks) (a) 24 µC
(b) A convex lens has a focal length of 20 cm. Where should an object be placed so
(b) 18 µC
that its image is formed 40 cm from the lens? (2 marks)
(c) 12 µC
OR (d) 6 µC
(a) Explain the principle of interference of light and derive the expression for the 3 As the intensity of incident light increases:
resultant intensity when two coherent light waves interfere. (3 marks) (a) photoelectric current increases.
(b) Two coherent sources of light produce waves with intensities I1=4 units and I2=9 units. (b) photoelectric current decreases.
Calculate the maximum and minimum intensities observed on the screen. (2 marks)
(c) the kinetic energy of emitted photoelectrons increases.
(d) the kinetic energy of emitted photoelectrons decreases.
Section E: (4 marks each)
35. Case Study 1: 4 The Bohr model of atoms
Read the following passage and answer the questions that follow: (a) assumes that the angular momentum of electrons is quantized.
The hydrogen spectrum consists of several series of lines in different regions of the (b) predicts continuous emission spectra for atoms.
electromagnetic spectrum. These series are named after their discoverers: Lyman, (c) predicts the same emission spectra for all types of atoms.
Balmer, Paschen, Brackett, and Pfund. Each series corresponds to electron transitions (d) uses Einstein’s photoelectric equation.
between different energy levels in the hydrogen atom. 5 An electron moves along the line AB, which lies
Questions: in the same plane as a circular loop of
a) Which series of hydrogen spectral lines lies in the visible region? (1 mark) conducting wires as shown in diagram. What
b) Calculate the wavelength of the first line of the Lyman series. (Given: Rydberg will be the direction of current induced if any, in
constant (R = 1.097 x 107 m-1 (2 marks)
the loop:
c) Why are the spectral lines of hydrogen important in astronomy? (1 mark)
(a) No current will be induced
36. Case Study 2: (b) The current will be clockwise
Read the following passage and answer the questions that follow: (c) The current will be anticlockwise
A coil of wire is connected to a galvanometer. When a bar magnet is moved towards the (d) The current will change direction as the electron passes by
coil, the galvanometer shows a deflection. When the bar magnet is moved away from the 6 If number of turns, area and current through a coil are given by n,
coil, the galvanometer shows a deflection in the opposite direction. The faster the magnet A and I respectively, then its magnetic moment is given by
is moved, the greater the deflection. 𝑛𝐼
(a) nIA (b) n2IA (c) nIA2 (d)
a) Name the phenomenon demonstrated in the above experiment. (1 mark) √𝐴

b) State Faraday’s law of electromagnetic induction. (2 marks) 7 A solenoid of 1.5 m length and 4.0 cm diameter possesses 10 turns/cm. A
c) What will happen if the number of turns in the coil is increased? (1 mark) current of 5 A is flowing through it. The magnetic induction at axis inside the
solenoid is
******** (a) 2𝜋 × 10−3 T (b) 2𝜋 × 10−3 G (c) 2𝜋 × 10−5 T (d) 2𝜋 × 10−5 G

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14 Assertion: Bohr had to postulate that the electrons in stationary orbits outermost orbit only. For Si, the outermost orbit is the third orbit (n =
around the nucleus do not radiate. 3), while for Ge it is the fourth orbit (n = 4). The number of electrons
Reason: According to classical physics all moving electrons radiate in the outermost orbit is 4 (2s and 2p electrons). Hence, the total
15 Assertion: A pure semiconductor has negative temperature coefficient number of outer electrons in the crystal is 4N. The maximum possible
of resistance. number of outer electrons in the orbit is 8 (2s + 6p electrons). So, out
Reason: In a semiconductor on raising the temperature, more charge of the 4N electrons, 2N electrons are in the 2N s-states (orbital quantum
carriers are released, conductance increases and resistance decreases. number l= 0) and 2N electrons are in the available 6N p-states.
16 Assertion: A lens, whose radii of curvature are different, is forming Obviously, some p electron states are empty. This is the case of well
the image of an object placed on its axis. If the lens is reversed, separated or isolated atoms.
the position of the image will not change. (i)The energy of electrons of atoms of a substance will be same if:
1 1 1 (a) atoms are isolated. (b) atoms are closely spaced.
Reason: The focal length of a lens is given by = (𝜇 − 1) ( − ) and
𝑓 𝑅1 𝑅2
(c) atoms are excited. (d) atoms are charged.
so focal length in both the cases is same.
(ii) The overlap (or interaction) will be more felt by the electrons when they are:
(a) in the outermost orbit. (b) in the innermost orbit.
SECTION B
(c) free. (d) in any orbit.
17 Draw energy band diagram of n-type and p-type semiconductor at
(iii) For Silicon and Germanium, the outermost orbits are respectively:
temperature T>0K. Mark the donor and acceptor energy level with their
(a) n = 3 and n = 5 (b) n = 4 and n = 3
energies.
(c) n = 5 and n = 4 (d) n = 3 and n = 4
18 A proton and an electron have same kinetic energy. Which one has
(iv) In a crystal, the distance between two atoms is:
greater de-Broglie wavelength and why?
(a) 200 Å to 300 Å (b) 2 Å to 3 micron
19 Under what conditions does the phenomenon of total internal reflection
(c) 2 Å to 3 Å (d) 2 mm to 3 mm
take place? Draw a ray diagram showing how a ray of light deviates by
OR
900 after passing through a right angled isosceles prism.
(iv) The maximum possible electrons in an orbit is:
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 (a) 8 (2s + 6p electrons) (b) 8 (6s + 2p electrons)
in the wire is 8 × 1028 m–3, calculate the resistivity of the material of (c) 8 (4s + 4p electrons) (d) 8 (1s + 7p electrons)
wire. 30 Lens Maker's Formula
21 Why is that sun-glasses (goggles), which have curved surfaces, do not The lens maker's formula relates the focal length of a lens to the
have any power? refractive index of the lens material and the radii of curvature of its two
OR surfaces. This formula is called so because it is used by manufacturers
Can a convergent lens in one medium behave as a divergent lens in to design lenses of the required focal length from a glass of given
some other medium? refractive index. If the object is placed at infinity, the image will be
SECTION C formed at a focus for both double convex lens and double concave
22 (i) The radius of the innermost electron orbit of a hydrogen atom is 5.3 lens.
1 𝜇 1 1
X 10-11 m. Calculate its radius in n=3 orbit. Therefore, Len’s maker’s formula is = (𝜇2 − 1) (𝑅 − 𝑅 )
𝑓 1 1 2
(ii) The total energy of an electron in the first excited state of the when lens is placed in air 𝜇1 = 1 𝑎𝑛𝑑 𝜇2 = 𝜇𝑊 The lens maker
hydrogen atom is -3.4 eV. Find out its (a) kinetic energy and (b) 1 1 1
formula takes the form, 𝑓 = (𝜇 − 1) (𝑅 − 𝑅 ).
potential energy in this state. 1 2

23 Two point charges +q and -2q are placed at the vertices B and C of an (i) The radius of curvature of each face of biconcave lens with refractive index
equilateral ∆𝐴𝐵𝐶 of side a. Obtain the expression for 1.5 is 30 cm. The focal length of the lens in air is

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 (ii) What happens if the field is non-uniform? a) –Q/2 b) –Q/4 c) +Q/2 d) +Q/4
(iii) What would happen if the external field E is increasing 12. Calculate the mutual inductance between two coils if a current 10 A in the primary
(a) parallel to 𝑝 and coil changes the flux by 500 Wb per turn in the secondary coil of 200 turns.
(b) antiparallel to 𝑝 ? a) 10 H b) 104 H c) 1000 H d) 100 H
OR Directions: In each of the following questions No. 13 to 16, a statement of Assertion is
(i) A thin conducting spherical shell of radius R has charge Q spread uniformly given followed by a corresponding statement of Reason just below it. Of the
over its surface. Using Gauss’s theorem, derive an expression for the statements, mark the correct answer as:
electric field at a point outside the shell. (A) If both assertion and reason are true and reason is the correct explanation of
(ii) Draw a graph of electric field E(r) with distance r from the center of the shell assertion
for 0 ≤ r ≤∞. (B) If both assertion and reason are true but reason is not the correct explanation of
33 (a) What is impedance? assertion
(b) A series LCR circuit is connected to an ac source having voltage V = V m (C) If assertion is true and reason is false
sin ωt. Derive expression for the impedance, instantaneous current and its (D) If both assertion and reason are false.
phase relationship to the applied voltage.
(c)Find the expression for resonant frequency. 13.Assertion: The tyres of aircraft are slightly conducting.
OR Reason: If a conductor is connected to ground, the extra charge induced on
(a) An ac source of voltage V = Vm sin ωt is connected to a series combination conductor will flow to ground.
of L, C and R. Use the phasor diagram to obtain expressions for impedance 14. Assertion: A laminated core is used in transformers to increase eddy currents.
of the circuit and phase angle between voltage and current. Find the Reason: The efficiency of a transformer increases with increase in eddy currents.
condition when current will be in phase with the voltage. What is the circuit 15.Assertion: An electric bulb becomes dim, when the electric heater in parallel circuit
in this condition called? is switched on.
(b) In a series LR circuit XL = R and power factor of the circuit is P1. When Reason: Dimness decreases after sometime.
capacitor with capacitance C such that XL = XC is put in series, the 16.Assertion: No interference pattern is detected when two coherent sources are
𝑃 infinitely close to each other.
power factor becomes P2. Calculate 𝑃1
2
Reason: The fringe width is inversely proportional to the distance between the two
**********
sources.
17.Prove Bohr’s second postulates on the basis of De-Broglie hypothesis.
18. State distinguishing behavior of paramagnetic and diamagnetic materials.
19.With the help of Kirchhoff’s laws, obtain the condition of Wheatstone bridge.
20. Name the parts of the electromagnetic spectrum which is
21. Suitable for radar systems used in aircraft navigation.In the detection of explosives.
22. An electric dipole of length 2 cm, when placed with its axis making an angle of 60°
with a uniform electric field, experiences a torque of 8√3 Nm. Calculate the potential
energy of the dipole, if it has a charge of ± 4 nC.
23. A heating element using nichrome connected to a 230 V supply draws an initial
current of 3.2 A which settles after a few seconds to a steady value of 2.8 A. What is
the steady temperature of the heating element if the room temperature is 27.0 °C?
Temperature coefficient of resistance of nichrome averaged over the temperature
range involved is 1.70 × 10–4 °C–1.

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 called depletion layer. At the junction a potential barrier appears, which does not (c) ferromagnetism (d) both b and c
allow the movement of majority charge carriers across the junction in the absence Q..4 When two charged capacitors having capacitance and potential C1, V1 and 1
of any biasing of the junction. The p-n junction offers low resistance when forward C2, V2 respectively, are joined with the help of a wire, the common potential 1
biased and high resistance when reverse biased. will be
(a) Does current flow when diode is reverse biased?
(b) What is meant by reverse bias?
(c) Can we measure the potential barrier of p-n junction by putting a sensitive
voltmeter across its terminals?
(d) Explain how a potential barrier is developed in a p-n junction diode.
Q.5 In photoelectric effect the maximum kinetic energy of emitted electron 1
(e) Draw the labelled diagram of step-up transformer. Write its principle & deduce an depends on 1
expression for its working. (a) wavelength (b) frequency (c) intensity (d) work function
(f) A transformer of efficiency 90 % has turns ratio 1:10 . If the voltage across the primary Q.6 The number of Photons of frequency 1014 Hz in radiation of 6.62 J will be 1
is 220 V and current in the primary is 0.5A, then find the current in secondary. 1
OR
(a) Draw the diagram of an ac generator and explain its principle, construction and
working. Q.7 What is the resistance of a 40 W lamp which is lighted as full brilliance by 1
(b) The number of turns in the coil of AC generator is 5000, and the area of the coil a current of1/3 A? 1
is 0.25 m 2. The coil is rotated at the rate of 100 cycles/sec in a magnetic field of
0.2 Wbm − 2. What is the peak value of emf generated?
31.(a) Explain the magnifying power of compound microscope, when it
produces a final image at (i) Distance of distinct vision and (ii) Infinity. Q.8 Which of the following does not obey the phenomenon of mutual 1
induction? 1
(b) An object is placed in front of a concave mirror of focal length 20 cm. The image
(a)dynamo (b) transformer (c) induction coil (d) electric heater
formed is three times the size of the object. Calculate two possible distances of the Q.9 In a series combination, R = 300 Ω, L = 0 9. H, C = 2 µF, ω = 1000 rad s -1 1
object from the mirror. . The impedance of the LCR-circuit is 1
OR (a) 400 Ω (b) 500 Ω (c) 900 Ω (d) 1300 Ω
(a) Draw ray diagram to show refraction of a ray of monochromatic light passing Q.1 An electric dipole consists of a positive and negative charge of 4 µ C each 1
through a prism. Deduce the expression for the refractive index of glass in terms 0 placed at a distance of 5 mm. The dipole moment is 1
of angle of prism and angle of minimum deviation. (a) 2 x 10-8 C-m (b) 4 x 10-8 C-m (c) 6 x 10-8 C-m
(b) A monochromatic light is incident on an equilateral prism at an angle 30º and (d) 8 x 10-8 C-m
emerges at an angle of 75º. What is the angle of deviation produced by the prism? Q.1 Two solenoids of the same length having number of turns in the ratio of 2 1
32. (a) With the help of neat labeled diagram, explain the diffraction at single slit. Also 1 3: are connected in series. The ratio of magnetic fields at their centres 1
is
show the position of secondary maxima and secondary minima on intensity graph.
(a) 2:1 (b) 3:1 (c) 2:3 (d)3:2
(b) Give the difference between interference and diffraction.
Q.1 The core of a transformer is laminated, so as to 1
OR 2 (a) make it light weight (b) make it robust and strong 1
What is fringe width? Show that bright fringes and dark fringes are equally spaced in (c) increase the secondary voltage (d) reduce energy loss due to
interference pattern. Give the difference between constructive interference and eddy current
destructive interference. Directions: In the following questions, A statement of Assertion (A) is followed by a
statement of Reason (R). Mark the correct choice as.
A: If both Assertion and Reason are correct and the Reason is a correct explanation of the
******** Assertion.

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 Q.25 How are electromagnetic waves produced? What is the source of energy 03 , having n turns per unit length and carrying a steady current I .
of these waves? Write mathematical expressions for electric and (ii) An observer to the left of a solenoid of N turns each of cross-
magnetic fields of an electromagnetic wave propagating along the z- section area A observes that a steady current I in it flows in the
axis. Write any two important properties of electromagnetic waves.
clockwise direction. Depict the magnetic field lines due to the
Q.26 How will you explain twinkling of stars? 03
solenoid specifying its polarity and show that it acts as a bar
Q.27 Describe briefly, with the help of a diagram, the role of the two important 03
process involved in the formation of a p n - junction. magnet of magnetic moment m = NIA.
Q.28 Briefly describe proton-neutron hypothesis of nuclear composition. 03
OR
What are uncontrolled and controlled chain reactions?

Q.33 Give postulates of Bohr’s theory. Explain hydrogen spectrum on the basis 05
SECTION-D of Bohr’s theory.
Q.29 OR
When light from a monochromatic source is incident on a single narrow slit, it What is Hα line in the emission spectrum of hydrogen atom obtained?
gets diffracted and a pattern of alternate bright and dark fringes is obtained on Calculate the frequency of the photon emitted during this transition.
screen, called “Diffraction Pattern” of single slit. In diffraction pattern of single
slit, it is found that
Central bright fringe is of maximum intensity and the intensity of any secondary bright
fringe decreases with increase in its order.
Central bright fringe is twice as wide as any other secondary bright or dark fringe.
*************

i) A single slit of width 0.1 mm is illuminated by a parallel beam of light of 01

wavelength 6000 A.U. and diffraction bands are observed on a screen
0.5 m from the slit. The distance of the third dark band from the central
bright band is
(a) 3 mm (b) 1.5 mm (c) 9 mm (d) 4.5 mm
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
distance between the first minimum on either side the central
maximum is (a) 10-1 m (b) 10-2 m (c) 2 x10-2 m (d) 2 x10-1 m
III) Light of wavelength 600 nm is incident normally on a slit of width 0.2 mm. 01
The angular width of central maxima in the diffraction pattern is
(measured from minimum to minimum)
(a)6 x10-3 rad (b) 4 x 10-3 rad (c)2.4 x 10-3 rad (d)
4.5 x 10-3 rad

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