ST.

ARNOLD’S CENTRAL SCHOOL, PUNE

UNIT TEST-2, (2024-25)
SUBJECT–PHYSICS
STD: XII
Time Allowed: 3 Hrs M.M:70

General Instructions:
1. There are 33 questions in all. All questions are compulsory.
2. This question paper has five sections: Section A, Section B, Section C, Section D and Section E.
3. All the sections are compulsory.
4. Section A contains sixteen questions, twelve MCQ and four Assertion reasoning based of 1 mark each,
Section B contains five questions of two marks each, Section C contains seven questions of three marks
each, Section D contains two case study-based questions of 4 marks each and Section E contains three long
Answer questions of five marks each.
5. There is no overall choice. However, an internal choice has been provided in one question in section B,
one question in section C, one question in each CBQ in section D and all three questions in section E. You
have to attempt only one of the choices in such questions.
6. Use of calculators is not allowed.

Section A
1. A thin plastic rod is bent into a circular ring of radius R. It is uniformly charged with charge density . The
magnitude of the electric field at its centre is :
(A) λ/2ε0 R (B) Zero (C) λ/4πε0R (D) λ/4ε0R
2. Ten capacitors, each of capacitance 1 µF, are connected in parallel to a source of 100 V. The total energy
stored in the system is equal to :
(A) 10 -2 J (B) 10 -3 J (C) 0·5 ×10 -3 J (D) 5·0 × 10 -2 J
3. A student is asked to connect four cells, each of emf E and internal resistance r, in series. But she/he
connects one cell wrongly in series with the other cells. The equivalent emf and the equivalent internal
resistance of the combination will be :
(A) 4E and 2r (B) 4E and 3r (C) 3E and 4r (D) 2E and 4r
4. A 10 cm long wire lies along y-axis. It carries a current of 1.0 A in positive y-direction. A magnetic field
B = (5 mT) ^ j- (8 mT) ^ k exists in the region. The force on the wire is :
(A) (0·8 mN) ^ i (B) (-0·8 mN) ^ i (C) (80 mN) ^ i (D) (-80 mN) ^ i
OR
The electric power consumed by a 220 V – 100 W bulb when operated at 110 V is
(A) 25 W (B) 30 W (C) 35 W (D) 45 W
5. The displacement current flows in the dielectric of the capacitor, when the potential difference across its
plates:
(A) changes (increases/decreases) with time. (B) changes with distance.
(C) attains a constant value. (D) None of these
6. The wavelength of infrared rays is:
(A) less than that of visible light. (B) greater than, that of visible light.
(C) greater or lesser depending on the source. (D) None of these.
7. A resistor and an ideal inductor are connected in series to a 100√2 V, 50 Hz ac source. When a voltmeter is
connected across the resistor or the inductor, it shows the same reading. The reading of the voltmeter is :
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 (A) 100√2 V (B) 100 V (C) 50√2 V (D) 50 V
8. The electric and magnetic fields of electromagnetic waves are :
(A) In the same phase and perpendicular to each other.
(B) In the same phase and not perpendicular to each other.
(C) Not in the same phase but are perpendicular to each other.
(D) Neither in the same phase nor perpendicular to each other.
9. Two coils are placed near each other. When the current in one coil is changed at the rate of
5 A/s, an emf of 2 mV is induced in the other. The mutual inductance of the two coils is
(A) 0.4 mH (B) 2.5 mH
(C) 10 mH (D) 2.5 H
10. The electromagnetic waves used to purify water are
(A) Infrared rays (B) Ultraviolet rays
(C) X-rays (D) Gamma rays
11. Which of the following quantity/quantities remains same in primary and secondary coils of an ideal
transformer ? Current, Voltage, Power, Magnetic flux
(A) Current only (B) Voltage only
(C) Power only (D) Magnetic flux and Power both
12. Electromagnetic waves with wavelength 10 nm are called :
(A) Infrared waves (B) Ultraviolet rays
(C) Gamma rays (D) X-rays

For Questions 13 to 16, two statements are given, one labelled Assertion (A) and other labelled
Reason (R). Select the correct answer to these questions from the options 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
d) If both Assertion and Reason are false

13. Assertion (A): Higher the range, lower is the resistance of an ammeter.
Reason (R): To increase the range of an ammeter additional shunt is added in series to it.
14. Assertion (a): The poles of a bar magnet cannot be separated.
Reason (R): Magnetic monopoles do not exist.
15. Assertion (A) : Two long parallel wires, freely suspended and connected in series to a battery, move apart.
Reason (R) : Two wires carrying current in opposite directions repel each other.
16. Assertion (A) : The mutual inductance between two coils is maximum when the coils are wound on each
other.
Reason (R) : The flux linkage between two coils is maximum when they are wound on each other.
Section B
17. Two batteries of emfs 6 V and 3 V and internal resistances 0·8 and 0·2 respectively are connected in series
to an external resistance R, as shown in figure. Find the value of R so that the potential difference across
the 6 V battery be zero.

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 18. Derive an expression for magnetic force F acting on a straight conductor

of length L carrying current I in an external magnetic field B. Is it valid when the

conductor is in zig-zag form ? Justify.
19. Find the temperature at which the resistance of a wire made of silver will be twice its resistance at 20 0 C.
Take 200 C as the reference temperature and temperature coefficient of resistance of silver at 20 0 C = 4·0
×10 -3 K-1
OR
Define resistivity of a conductor. How does the resistivity of a conductor depend upon the following : (a)
(b) Number density of free electrons in the conductor (n) Their relaxation time (τ )

20. Two long straight wires 1 and 2 are kept as shown in the figure. The linear charge
density of the two wires are λ1 = 10µC/m and λ2 = -20µC/m. Find the net force F
experienced by an electron held at point P.

21. Draw the circuit diagram of a Wheatstone bridge. Obtain the condition when no current flows through the
galvanometer in it.
Section C

22. Three point charges Q1, Q2 and Q3 are located in x y plane at points ( d, 0), (0,
0) and (d, 0) respectively. Q 1 and Q3 are identical and Q2 is positive. What will be the
nature and value of Q1 so that the potential energy of the system is zero?
23. (a) Define the term ‘electric flux’ and write its dimensions.
(b) A plane surface, in shape of a square of side 1 cm is placed in an electric field E =
(100 N / C ) i such that the unit vector normal to the surface is given by n = 0.8
i + 0.6k. Find the electric flux through the surface.
24. electrostatics. Apply this to obtain the electric field E at a point near a uniformly charged

infinite plane sheet.

25. A bar magnet of magnetic moment 2·5 JT-1 lies aligned with the direction of a uniform magnetic field of
0·32 T. (a) Find the amount of work done to turn the magnet so as to align its magnetic moment (i) normal
to the field direction, and (ii) opposite to the field direction. (b) What is the torque on the magnet in above
cases (i) and (ii) ?

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 26. (a) (i) State Lenz's Law. In a closed circuit, the induced current opposes
the change in magnetic flux that produced it as per the law of conservation of energy.
Justify.
(ii) A metal rod of length 2 m is rotated with a frequency 60 rev/s about an
axis passing through its centre and perpendicular to its length. A
uniform magnetic field of 2T perpendicular to its plane of rotation is
switched-on in the region. Calculate the
e.m.f. induced between the centre and the end of the rod.
OR
(b) (i) State and explain Ampere's circuital law.
(ii) Two long straight parallel wires separated by 20 cm, carry 5 A and 10 A
current respectively, in the same direction. Find the magnitude and direction of
the net magnetic field at a point midway between them.

27. Consider the arrangement of two coils P and Q shown in the figure. When current in coil
P is switched on or switched off, a current flows in coil Q.
a. Explain the phenomenon involved in it.
b. Mention two factors on which the current produced in coil Q depends.
c. Give the direction of current in coil Q when there is a current in
the coil P and (i) R is increased, and (ii) R is decreased.

28. A rectangular coil of N turns and area of cross-section A is rotated at a steady angular speed in a uniform
magnetic field. Obtain an expression for the emf induced in the coil at any instant of time.
Section D
Case Study Based Questions

29. When the terminals of a cell are connected to a conductor of resistance R, an electric current flows through
the circuit. The electrolyte of the cell also offers some resistance in the path of the current, like the
conductor. This resistance offered by the electrolyte is called internal resistance of the cell (r). It depends
upon the nature of the electrolyte, the area of the electrodes immersed in the electrolyte and the
temperature. Due to internal resistance, a part of the energy supplied by the cell is wasted in the form of
heat. When no current is drawn from the cell, the potential difference between the two electrodes in known
as emf of the cell ( ). With a current drawn from the cell, the potential difference between the two
electrodes is termed as terminal potential difference (V).
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 i. Choose the incorrect statement :
(A) The potential difference (V) between the two terminals of a cell in a closed
circuit is always less than its emf ( ε), during discharge of the cell.
(B) The internal resistance of a cell decreases with the decrease in temperature
of the electrolyte.
(C) When current is drawn from the cell then V = ε-Ir.
(D) The graph between potential difference between the two terminals of the cell
(V) and the current (I) through it is a straight line with a negative slope.

ii. Two cells of emfs 2·0 V and 6·0 V and internal resistances 0·1Ω and 0·4Ω
respectively, are connected in parallel. The equivalent emf of the combination will
be:
(A) 2·0 V (B) 2·8 V
(C) 6·0 V (D) 8·0 V

iii. Dipped in the solution, the electrode exchanges charges with the
electrolyte. The positive electrode develops a potential V+ (V+ > 0), and the
negative electrode develops a potential - (V‒ ) (V‒ ≥ 0), relative to the
electrolyte adjacent to it. When no current is drawn from the
cell then :
(A) ε= V+ + V‒ >0 (B) ε= V+ − V‒ > 0
1
(C) ε= V+ + V‒ <0 (D) ε = V+ + V‒ =0

iv. (a) Five identical cells, each of emf 2 V and internal resistance 0·1Ω are connected in parallel.
This combination in turn is connected to an external resistor of 9·98 Ω. The current flowing
through the resistor is :
(A) 0·05 A (B) 0·1 A

(C) 0·15 A (D) 0·2 A

OR
(b) Potential difference across a cell in the open circuit is 6 V. It becomes 4 V when a current of
2 A is drawn from it. The internal resistance of the cell is :
(A) 1·0 Ω (B) 1·5Ω
(C) 2·0 Ω (D) 2·5Ω

30. Dielectrics play an important role in design of capacitors. The molecules of a

dielectric may be polar or non-polar. When a dielectric slab is placed in an
external electric field, opposite charges appear on the two surfaces of the slab
perpendicular to electric field. Due to this an electric field is established inside the
dielectric.

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 The capacitance of a capacitor is determined by the dielectric constant of the
material that fills the space between the plates. Consequently, the energy storage
capacity of a capacitor is also affected. Like resistors, capacitors can also be
arranged in series and/or parallel.
(i) Which of the following is a polar molecule ?
(A) 02 (B) H2
(C) N2 (D) HCP

(ii) Which of the following statements about dielectrics is correct ?

(A) A polar dielectric has a net dipole moment in absence of an external electric
field which gets modified due to the induced dipoles.
(B) The net dipole moments of induced dipoles is along the direction of the applied
electric field.
(C) Dielectrics contain free charges.
(D) The electric field produced due to induced surface charges inside a dielectric is
along the external electric field.

(iii) When a dielectric slab is inserted between the plates of an isolated charged capacitor,
the energy stored in it
(A) increases and the electric field inside it also increases.
(B) decreases and the electric field also decreases.
(C) decreases and the electric field increases.
(D) increases and the electric field decreases.

(iv) (a) An air-filled capacitor with plate area A and plate separation d has capacitance
C0. A slab of dielectric constant K, area A and thickness d/5 is inserted
between the plates. The capacitance of the capacitor will become
A [4K/(5K+1)] Co B. [(K+5)/4] Co

C [5K/(4K+1)] Co D [(K+4)/5] Co
OR
(b) Two capacitors of capacitances 2 C0 and 6 C0 are first connected
in series and then in parallel across the same battery. The ratio of energies
stored in series combination to that in parallel is
A 1/4 B 1/6
C 2/15 D 3/16

Section E

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 31. a. i) Derive an expression for potential energy of an electric dipole p in an external uniform electric field E.
When is the potential energy of the dipole (1) maximum, and (2) minimum?
ii) An electric dipole consists of point charges -1·0 pC and + 1·0 pC located at (0, 0) and (3 mm, 4 mm)
respectively in x y plane. An electric field E = (1000 V/m) i is switched on in the region. Find the torque
acting on the dipole.
OR
b. An electric dipole (dipole moment p = p^ i), consisting of charges q and q, separated by distance 2a, is
placed along the x-axis, with its centre at the origin. Derive that the potential V, due to this dipole, at a
point x, (x >> a)
Two isolated metallic spheres S1 and S2 of radii 1 cm and 3 cm respectively are charged such that both
have the same charge density (2/π) ×10-9 C / m2 . They are placed far away from each other and connected
by a thin wire. Calculate the new charge on sphere S1.
32. a. i) A resistor and a capacitor are connected in series to an ac source v = vm sin ωt. Derive an expression
for the impedance of the circuit.
ii) When does an inductor act as a conductor in a circuit ? Give reason for it.
iii) An electric lamp is designed to operate at 110 V dc and 11 A current. If the lamp is operated on 220 V,
50 Hz ac source with a coil in series, then find the inductance of the coil.
OR
b. i) Draw a labelled diagram of a step-up transformer and describe its working principle. Explain any three
causes for energy losses in a real transformer.
ii) A step-up transformer converts a low voltage into high voltage. Does it violate the principle of
conservation of energy ? Explain.
iii)A step-up transformer has 200 and 3000 turns in its primary and secondary coils respectively. The input
voltage given to the primary coil is 90 V. Calculate : (1) The output voltage across the secondary coil
(2)The current in the primary coil if the current in the secondary coil is 2·0 A.
33. (a) (i)A particle of mass m and charge q is moving with a velocity v in a magnetic field B as shown in the
figure. Show that it follows a helical path. Hence, obtain its frequency of revolution.

(ii) In a hydrogen atom, the electron moves in an orbit of radius 2 Å making 8 ×1014 revolutions per
second. Find the magnetic moment associated with the orbital motion of the electron.
OR

(b) (i) What is current sensitivity of a galvanometer ? Show how the current sensitivity of a
galvanometer may be increased. Increasing the current sensitivity of a
galvanometer may not necessarily increase its voltage sensitivity Explain.

(ii) A moving coil galvanometer has a resistance 15Ω and takes 20 mA to produce full scale
deflection. How can this galvanometer be converted into a voltmeter of range 0
to 100 V ?
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