PSEB CLASS 12 PHYSICS ANSWER KEY ( 18/9/2025)

September 2025 Physics Exam Answer Key 

Subject: Physics Class +2 (SET–A)
Maximum Marks: 70
Time: 3 Hours

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Instructions:

1. All questions are compulsory.

2. Question number 1 will carry 20 objective type questions of 1 mark each. Out of these, 17 will be multiple-choice and 3 will be True/False statements.

3. Question number 2 to 8 (total 7 questions) will carry 2 marks each. There will be 3 questions of internal choice.

4. Question number 9 to 15 (total 7 questions) will carry 3 marks each. There will be three questions of internal choice.

5. Question number 16 will be comprehension type having 5 questions.

6. Question number 17 and 18 will be carrying 5 marks each and there will be internal choice in each.

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Section – A (1 Mark each, Total 20 Marks)

Q1: Objective type questions

Multiple Choice Questions:

(i) Charging without actual contact is called:
(a) Charging by friction
(b) Charging by conduction
(c) Charging by induction
(d) None of these

(ii) The units of linear charge density are:
(a) C/m
(b) C/m²
(c) C/m³
(d) unit less

(iii) A 
(a) Charge
(b) Potential
(c) Capacitance
(d) None of these

(iv) 1 kWh is equal to:
(a) 36 × 100000J
(b) 36 × 10⁶ J
(c) 746 watt
(d) 150 ergs

(v) Which of the following statements is correct about electric current?
(a) Current has magnitude and direction. Therefore, it is vector.
(b) Current has only magnitude but no direction. Therefore, it is scalar.
(c) Current has both magnitude and direction but does not follow vector laws, so it is scalar.
(d) None of these

(vi) Standard resistance wire is made of alloy constantan/manganin because:
(a) Low resistivity, low temperature coefficient
(b) High resistivity, low temperature coefficient
(c) High resistivity, high temperature coefficient
(d) Low resistivity, high temperature coefficient

(vii) A bar magnet in a uniform magnetic field experiences:
(a) A torque but not a force
(b) A force but not a torque
(c) Both a force and torque
(d) Neither a force nor torque

(viii) Resistance of an ideal voltmeter is:
(a) Zero
(b) Very low
(c) Very large
(d) Infinite

(ix) Magnetic dipole moment of a current-carrying coil is equal to:
(a) nIA
(b) IA
(c) 2πIA
(d) None

(x) In an LCR series AC circuit, the current:
(a) Always lags voltage
(b) Always leads voltage
(c) Always in phase
(d) May lag or lead voltage

(xi) Which is wrong for magnetic flux?
(a) Proportional to number of lines
(b) Scalar quantity
(c) SI unit Weber (Wb)
(d) Flux is a vector quantity

(xii) The law “magnitude of induced emf equals time rate of change of magnetic flux” is:
(a) Ampere’s law
(b) Faraday’s law
(c) Lenz’s law
(d) Gauss’s law

(xiii) Electromagnetic waves can be produced by:
(a) Stationary charges
(b) Steady currents
(c) Accelerated charges
(d) None

(xiv) Relation between magnitudes of electric and magnetic fields in EM waves:
(a) E₀ = B₀
(b) E₀ = cB₀
(c) E₀ = B₀/c
(d) E₀ = c/B₀

(xv) Waves used to take photographs in fog/smoke:
(a) X-rays
(b) Infrared rays
(c) Ultraviolet rays
(d) γ-rays

(xvi) Electric field lines never form closed loops due to:
(a) Conservative nature of electric field
(b) Non-conservative nature
(c) Attraction of charges
(d) Repulsion of charges

(xvii) Kirchhoff’s first and second laws are based on conservation of:
(a) Energy and momentum
(b) Energy and charge
(c) Charge and energy
(d) Momentum and charge

True / False Questions:

(xviii) Magnetic susceptibility is slightly negative for diamagnetic material.
(xix) Transformer is based on conservation of linear momentum.
(xx) Welders wear special glass goggles to protect eyes from UV rays of arcs.

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Section – B (2 Marks each)

Q2. Why does a capacitor block direct current (DC)?

Q3. Derive an expression for torque on an electric dipole in uniform electric field.

Q4. Find drift velocity of electrons in conductor when electric field strength = 200 V/m, mobility = 4.5 × 10⁻⁴ m²/Vs.

OR

(i) 5 cells of emf 5V and internal resistance 2Ω are connected in parallel. Find total emf and internal resistance.

(ii) In given circuit (diagram shown), write values of I₁ and I₂.

Q5. What are ohmic and non-ohmic materials? Give examples.

OR

Calculate resistance of manganin wire of length 100 m, cross-sectional area 0.1 mm², resistivity 60 × 10⁻⁸ Ωm.

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Section – C (3 Marks each)

Q6. How can you convert a moving coil galvanometer (resistance G) into (i) an ammeter, (ii) a voltmeter?

Q7. Find electric force between two protons inside a nucleus (distance = 10⁻¹⁵ m).

OR

Two charges +3 × 10⁻⁶ C and −2 × 10⁻⁶ C are placed 15 cm apart. At what point is potential zero?

Q8. (i) A plane EM wave travels in +z direction. What are directions of E and B?
(ii) What physical quantity is same for X-rays, red light, and radiowaves?

Q9. Derive relation between current and drift velocity.

Q10. Two cells of emf E₁, E₂ and resistances r₁, r₂ in parallel. Derive equivalent emf and resistance.

Q11. In the circuit (figure given), r = internal resistance. Define emf and terminal potential difference. Derive relation of r in terms of E, V, R.

Q12. Using Ampere’s circuital law, derive B at point P due to long straight conductor.

OR

A bent wire carrying current 60A, radius 2 cm, angle 240°. Find B at centre.

Q13. A 100-turn coil of radius 10 cm carries current 1A. Find B at centre.

OR

A particle of charge 3.2 × 10⁻¹⁹ C, mass 6.8 × 10⁻²⁷ kg describes circle radius 0.45 m in B = 1.2 T. Find speed, frequency, kinetic energy.

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Section – D (3 Marks each)

Q14. By drawing phasor diagram, derive impedance (Z) of LCR circuit and phase difference.

OR

Metal rod of length 1 m rotated with f = 50 rev/s in uniform magnetic field (B), one end at centre and other at circumference. Find emf induced.

Q15. Define coefficient of self-induction of coil. Write SI unit, dimensions, and definition.

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Section – E (Comprehension Type, 5 sub-questions)

Q16. Passage on diamagnetic substances given. Answer:

1. Give two examples.

2. How does diamagnetic sample behave near magnet?

3. State approximate relative permeability and susceptibility.

4. Effect of temperature on susceptibility?

5. Diamagnetism is ______ property of all substances.

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Section – F (5 Marks each)

Q17. State Gauss’s theorem. Derive E due to thin spherical shell:
(a) Inside, (b) Outside, (c) On surface. Draw graph of E vs r.

OR

Define capacitance, SI unit. Derive capacitance of parallel plate capacitor with and without dielectric.

Q18. Derive torque expression for dipole in electric field. Discuss stable/unstable equilibrium.

OR

Derive potential due to dipole at any point. Special cases: axial and equatorial lines.

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Answer Key — Physics Class +2 (September 2025) — 

Section A — Objective (Q1)

(i) Charging without actual contact is called — (c) Charging by induction
(ii) Units of linear charge density — (a) C/m
(iii) After disconnecting battery and moving plates apart which increases — (b) Potential
(iv) 1 kWh = (b) 3.6 × 10⁶ J
(v) Correct statement about electric current — (c) (current has magnitude & direction but does not follow vector laws → treated as scalar)
(vi) Standard resistance wire made of manganin/constantan because — (b) High resistivity and low temperature coefficient
(vii) Bar magnet in uniform field experiences — (a) A torque but not a force
(viii) Resistance of ideal voltmeter — (d) Infinite
(ix) Magnetic dipole moment of coil — (a) nIA
(x) In LCR series AC circuit current — (d) May lag behind or lead the voltage
(xi) Wrong statement for magnetic flux — (d) Magnetic flux is a vector quantity (this is wrong; flux is scalar)
(xii) Law: induced emf = time rate of change of flux — (b) Faraday’s law
(xiii) Electromagnetic waves produced by — (c) Accelerated charges
(xiv) Relation between E and B magnitudes in EM wave — (b) E₀ = c B₀
(xv) Waves used to photograph in fog/smoke — (b) Infrared rays
(xvi) Electric field lines never form closed loops due to — (a) Conservative nature of electric field
(xvii) Kirchhoff’s 1st & 2nd laws based on conservation of — (c) Charge and energy respectively

True / False:
(xviii) Magnetic susceptibility slightly negative for diamagnetics — True
(xix) Transformer based on conservation of linear momentum — False (it’s based on electromagnetic induction)
(xx) Welders use goggles/face-masks to protect from UV — True

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Section B — 2-mark questions (Q2–Q5)

Q2. Why a capacitor blocks DC?
Short answer: After a transient charging current, charges on plates become constant and no further current passes through dielectric — so steady DC cannot pass; capacitor blocks DC but allows changing currents (AC/transients).

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Q3. Torque on an electric dipole in uniform E-field
Answer / expression: For dipole moment $p$ and field $E$, angle $\theta$ between them, torque magnitude

$$\boxed{\tau = pE\sin\theta}$$

Vector form $\boldsymbol{\tau}=\mathbf{p}\times\mathbf{E}$.

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Q4. Drift velocity from mobility
Given $E=200\ \mathrm{V/m},\ \mu=4.5\times10^{-4}\ \mathrm{m^2/Vs}$

$$v_d=\mu E = 4.5\times10^{-4}\times200 = 9.0\times10^{-2}\ \mathrm{m/s}=0.09\ \mathrm{m/s}.$$

Q4 OR (i) 5 identical cells (each 5 V, internal r = 2 Ω) in parallel:
Equivalent emf $E_{\rm eq}=5\ \mathrm{V}$.
Equivalent internal resistance $r_{\rm eq}= \dfrac{2}{5}=0.4\ \Omega.$

Q4 OR (ii) Circuit currents (diagram): central horizontal current = (sum of entering minus leaving as per diagram). (If you need explicit I₁,I₂ values paste a clearer crop of that diagram; earlier we found central I = −1 A from visible branch numbers.)

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Q5. Ohmic vs Non-ohmic material (with examples)

• Ohmic: obeys Ohm’s law $V\propto I$; V–I linear. Example: metallic resistor (copper wire, constant-temperature resistor).

• Non-ohmic: V–I non-linear; resistance depends on V or T. Examples: diode, filament lamp, thermistor.

Q5 OR Resistance of manganin wire:
Given $L=100\ \mathrm{m},\ A=0.1\ \mathrm{mm^2}=1.0\times10^{-7}\ \mathrm{m^2},\ \rho=60\times10^{-8}\ \Omega\cdot\mathrm{m}=6.0\times10^{-7}\ \Omega\cdot\mathrm{m}.$

$$R=\rho\frac{L}{A}=\frac{6.0\times10^{-7}\times100}{1.0\times10^{-7}}=600\ \Omega.$$

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Section C — 3-mark questions (Q6–Q13)

Q6. Convert moving coil galvanometer (resistance $G$):
(i) To ammeter: connect shunt $R_s$ in parallel so that for required FSD current $I$ and galvanometer FSD $I_g$,

$$R_s=\frac{I_g G}{I-I_g}.$$

(ii) To voltmeter: connect series resistance $R_s$ so that for required voltage $V$,

$$R_s=\frac{V}{I_g}-G.$$

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Q7. Electric force between two protons in nucleus
Given $q=1.6\times10^{-19}\ \mathrm{C},\ r=10^{-15}\ \mathrm{m}$. Coulomb:

$$F = \frac{1}{4\pi\varepsilon_0}\frac{q^2}{r^2}=9\times10^9\frac{(1.6\times10^{-19})^2}{(10^{-15})^2}\approx 2.3\times10^2\ \mathrm{N}.$$

(≈ 230 N)

Q7 OR Two charges +3×10⁻⁶ C and −2×10⁻⁶ C, separation 0.15 m: potential zero point on line found by

$$\frac{3}{x}=\frac{2}{0.15-x}\Rightarrow x=0.09\ \mathrm{m}$$

i.e. 9 cm from +3 μC charge.

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Q8. (i) If wave travels along +z, then $\mathbf{E}$ and $\mathbf{B}$ are perpendicular to +z and to each other (example: $E$ along +x, $B$ along +y so $E\times B$ points +z).
(ii) Quantity same for X-rays, red light, radio waves: speed in vacuum (c = 3×10⁸ m/s).

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Q9. Relation between current and drift velocity

$$\boxed{I = n e A v_d}$$

where $n$=number density, $e$=charge, $A$=area, $v_d$=drift velocity.

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Q10. Cells E₁,r₁ and E₂,r₂ in parallel
Equivalent internal resistance:

$$r_{\rm eq}=\frac{r_1 r_2}{r_1+r_2}.$$

Equivalent emf:

$$E_{\rm eq}=\frac{\dfrac{E_1}{r_1}+\dfrac{E_2}{r_2}}{\dfrac{1}{r_1}+\dfrac{1}{r_2}}.$$

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Q11. Emf and terminal potential difference (cell with internal resistance r)
Definition: EMF $E$ is work per unit charge done by source in moving charge around internal chemical forces (open-circuit voltage). Terminal p.d. $V$ across external terminals under load. Relation:

$$V=E-Ir \quad\Rightarrow\quad r=\frac{E-V}{I}.$$

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Q12. Ampere’s circuital law — B due to long straight wire

$$\boxed{B=\dfrac{\mu_0 I}{2\pi r}}$$

(At distance $r$ from an infinite straight current $I$.)

Q12 OR (bend arc) Bent arc of angle $\theta$ (radians), radius $R$, current $I$:

$$B=\frac{\mu_0 I \theta}{4\pi R}.$$

For given: $I=60\ \mathrm{A},\ R=0.02\ \mathrm{m},\ \theta=240^\circ=4\pi/3$ rad:

$$B=\frac{\mu_0 \cdot 60 \cdot (4\pi/3)}{4\pi\cdot0.02}=\frac{\mu_0\cdot60}{3\cdot0.02}\approx 4.0\times10^{-3}\ \mathrm{T}\ (\text{approx}).$$

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Q13. 100-turn coil, radius 0.10 m, I = 1 A
Magnetic field at centre (N turns):

$$B=\frac{\mu_0 N I}{2R}=\frac{4\pi\times10^{-7}\cdot100\cdot1}{2\cdot0.1}\approx6.28\times10^{-4}\ \mathrm{T}.$$

Q13 OR (particle in B): Given $q=3.2\times10^{-19}C,\ m=6.8\times10^{-27}kg,\ r=0.45m,\ B=1.2T$.

(i) Speed from centripetal force $qvB = mv^2/r$ → $v=\dfrac{qBr}{m}$:

$$v\approx\frac{3.2\times10^{-19}\cdot1.2\cdot0.45}{6.8\times10^{-27}}\approx2.5\times10^7\ \mathrm{m/s}.$$

(ii) Frequency $f=\dfrac{v}{2\pi r}\approx\frac{2.5\times10^7}{2\pi\times0.45}\approx8.8\times10^6\ \mathrm{Hz}.$

(iii) Kinetic energy $=\tfrac12 m v^2\approx2.1\times10^{-12}\ \mathrm{J}.$

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Section D — 3-mark / 5-mark (Q14–Q15)

Q14 (LCR impedance & phase)
Series LCR impedance:

$$\boxed{Z=\sqrt{R^2+(X_L-X_C)^2}},\quad X_L=\omega L,\ X_C=\frac{1}{\omega C}.$$

Phase angle (voltage relative to current):

$$\tan\phi=\frac{X_L-X_C}{R}.$$

If $X_L>X_C$ → circuit inductive (V leads I). If $X_C>X_L$ → circuit capacitive (V lags I).

Q14 OR (rotating rod + ring emf)
Emf between centre and rim for rod rotating with angular speed $\omega$ in axial B:

$$\boxed{\varepsilon = \tfrac12 B \omega R^2.}$$

With $R=1\ \mathrm{m},\ \omega=2\pi f=100\pi\ \mathrm{rad/s}$ → $\varepsilon=50\pi B$ volts.

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Q15. Coefficient of self-induction (self-inductance) L
Definition: $L=\dfrac{\text{flux linkage }\lambda}{I}$. SI unit: henry (H). Dimension: $[L]=M^{1}L^{2}T^{-2}I^{-2}$ (or $\mathrm{kg\ m^2 s^{-2} A^{-2}}$). (Also $\mathcal{E} = -L \dfrac{dI}{dt}$.)

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Section E — Comprehension (Q16)

(Answers from passage)

1. Two examples: Copper, Gold (also Bismuth, Antimony, Helium, Neon, Argon, water, alcohol).

2. Behaviour near magnet: Weakly repelled; induced magnetization opposite to applied field.

3. Approximate relative permeability & susceptibility: $\mu_r$ slightly less than 1; susceptibility $\chi$ small and slightly negative.

4. Effect of temperature: Susceptibility essentially independent of temperature (diamagnetism not temperature-dependent).

5. Diamagnetism is the universal property of all substances.

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Section F — 5-mark questions (Q17–Q18)

Q17. Gauss’s law + field of thin spherical shell
Gauss’s law:

$$\oint\mathbf{E}\cdot d\mathbf{A}=\frac{Q_{\rm enc}}{\varepsilon_0}.$$

For thin spherical shell of radius $R$ and total charge $Q$:

• Inside $r<R:\quad E=0.$

• On surface $r=R:\quad E=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{R^2}.$

• Outside $r>R:\quad E=\dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{r^2}.$
  Graph: $E=0$ for $r<R$; jump at $r=R$; then $E\propto1/r^2$ for $r>R.$

Q17 OR (capacitance)
Capacitance $C=Q/V$, SI unit farad (F). Parallel plate (vacuum):

$$C=\frac{\varepsilon_0 A}{d}.$$

With dielectric constant $K$:

$$C=\frac{K\varepsilon_0 A}{d}.$$

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Q18. Torque on electric dipole and equilibrium
Torque magnitude: $\tau=pE\sin\theta$, vector $\tau=\mathbf{p}\times\mathbf{E}$.

• Stable equilibrium: dipole aligned with field ($\theta=0$) — small perturbation produces restoring torque.

• Unstable equilibrium: dipole anti-aligned ($\theta=\pi$) — small perturbation leads to increasing displacement.

Q18 OR (potential of dipole)
Potential at distance $r$ (far field) and angle $\theta$:

$$V(r,\theta)=\frac{1}{4\pi\varepsilon_0}\frac{p\cos\theta}{r^2}.$$

On axial line ($\theta=0$): $V=\dfrac{1}{4\pi\varepsilon_0}\dfrac{p}{r^2}.$
On equatorial line ($\theta=90^\circ$): $V=0$ (dipole approx).

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