Current Electricity: Class 12 Important Questions with Answers

Practice set: test yourself

Try every question before looking at the answers below. 64 or more out of 80 means you are ready for the board.

C. Very short answer (1 mark each)

1. Define relaxation time.
2. How does $v_d$ change if the temperature of a metal rises (V fixed)?
3. A wire is stretched to 3 times its length. New R?
4. Write the SI unit of mobility.
5. Why are connecting wires made of copper?
6. When is the terminal voltage greater than the emf?
7. Give one example of a non-ohmic device.
8. Write the relation between j, σ and E.
9. What is 1 kWh in joules?
10. Two resistors 2 Ω and 3 Ω in parallel: equivalent?

D. Short answer I (2 marks each)

1. Derive $I=neA{v}_d$.
2. Distinguish between emf and terminal voltage (two points).
3. A 100 W, 220 V bulb runs on 110 V. Find its power.
4. State Kirchhoff's rules and their basis.
5. A cell gives 0.5 A in 4 Ω and 0.25 A in 9 Ω. Find ε and r.
6. Why is electricity transmitted at high voltage?
7. Show that ρ ∝ 1/τ for a metal. How does τ change with temperature?
8. Find the resistance of a copper wire 2 m long, area 1 mm² (ρ = $1.7\times 10^{-8}$ Ω m).

Rough work

E. Short answer II (3 marks each)

1. Derive the expression for the resistivity of a metal in terms of n, e, τ and m.
2. Derive the equivalent emf and internal resistance of two cells in series. When is a series combination useful?
3. Find the currents in a circuit where a 6 V cell (r = 1 Ω) and a 4 V cell (r = 1 Ω) are in parallel (+ to +) across a 2 Ω resistor.
4. A copper wire of area 1 mm² carries 2 A. Find $v_d$ ($n=8.5\times 10^{28}$ m⁻³) and the time to drift 1 m.
5. Derive the balance condition of a Wheatstone bridge using Kirchhoff's rules.
6. A heater coil is cut into two equal halves and only one half is used on the same supply. How does the heat produced change?

F. Long answer (5 marks each)

1. Derive $v_d=eE\tau /m$ and $\vec{j}=\sigma \vec{E}$. A wire of length 2 m, area 2 mm², carries 4 A when 0.4 V is applied: find ρ and σ.
2. Derive the emf and internal resistance of two cells in parallel. Three identical cells (1.5 V, 0.3 Ω) are in parallel across 1.9 Ω: find the current and the terminal voltage.
3. State Kirchhoff's rules. In a Wheatstone bridge AB = 10 Ω, BC = 20 Ω, CD = 30 Ω, DA = 15 Ω, find whether it is balanced; if 4 V is applied across AC, find the current from the cell.
4. Explain the temperature dependence of resistivity of metals and semiconductors with graphs. A wire is 2.5 Ω at 20 °C and 3.0 Ω at 120 °C: find α and the temperature where R = 3.5 Ω.

G. HOTS (higher-order thinking)

1. Why does a bulb glow almost immediately when switched on although electrons drift so slowly?
2. Two wires of the same material, one thick and one thin, are in series. In which is the drift speed larger? Why?
3. Why does the brightness of car headlights drop when the starter motor is used?
4. Can the potential difference across a cell be zero while current flows through it? When?

20 MCQs

1. The SI unit of current density is
   (a) A m² (b) A/m (c) A/m² (d) C/m²
2. Resistivity of a wire depends on
   (a) its material (b) its area (c) its length (d) the current
3. Drift velocity is of the order of
   (a) 1 m/s (b) $10^5$ m/s (c) $3\times 10^8$ m/s (d) $10^{-4}$ m/s
4. $\rho =$
   (a) $n{e}^2\tau /m$ (b) $m/n{e}^2\tau$ (c) $m/ne\tau$ (d) $ne\tau /m$
5. A wire stretched to double length: R becomes
   (a) 2R (b) 4R (c) R/4 (d) R/2
6. With T rising, the resistivity of a semiconductor
   (a) increases (b) becomes zero (c) stays same (d) decreases
7. Terminal voltage of a cell (ε, r) giving current I is
   (a) ε − Ir (b) ε (c) ε + Ir (d) Ir
8. Maximum current from a cell (ε, r) is
   (a) ε (b) εr (c) ε/r (d) r/ε
9. Kirchhoff's loop rule is based on conservation of
   (a) charge (b) momentum (c) mass (d) energy
10. Balanced Wheatstone bridge
    (a) $R_1{R}_2=R_3{R}_4$ (b) $R_1/R_2=R_4/R_3$ (c) $R_1+R_2=R_3+R_4$ (d) $R_1=R_3$
11. Material for heater coils
    (a) copper (b) silver (c) nichrome (d) aluminium
12. Two identical cells in parallel: emf and r
    (a) ε, r/2 (b) 2ε, 2r (c) ε, 2r (d) 2ε, r/2
13. A 60 W, 220 V bulb has resistance about
    (a) 3.7 Ω (b) 807 Ω (c) 13 200 Ω (d) 220 Ω
14. Mobility of electrons is
    (a) $m/e\tau$ (b) $e/m\tau$ (c) $e\tau /m$ (d) $eE\tau /m$
15. If V across a wire is doubled, $v_d$
    (a) halves (b) stays same (c) quadruples (d) doubles
16. Equivalent of 3 Ω, 6 Ω in parallel
    (a) 2 Ω (b) 9 Ω (c) 4.5 Ω (d) 1.5 Ω
17. Power dissipated in R carrying I
    (a) $I^{2}R$ (b) $I{R}^2$ (c) $I/R$ (d) $R/I^2$
18. Conductivity of a metal is
    (a) $m/n{e}^2\tau$ (b) $e\tau /m$ (c) $ne/m$ (d) $n{e}^2\tau /m$
19. When a cell is charged, V is
    (a) less than ε (b) greater than ε (c) zero (d) equal to ε
20. Equivalent resistance of a balanced bridge of 4 equal R (with G of R)
    (a) R/2 (b) 2R (c) R (d) 4R

1 (c) · 2 (a) · 3 (d) · 4 (b) · 5 (b) · 6 (d) · 7 (a) · 8 (c) · 9 (d) · 10 (b) · 11 (c) · 12 (a) · 13 (b) · 14 (c) · 15 (d) · 16 (a) · 17 (a) · 18 (d) · 19 (b) · 20 (c)

Assertion–Reason (6)

(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.

1. A: The resistance of a metal increases with temperature. R: The relaxation time decreases as temperature rises.
2. A: Current is a scalar. R: It has a direction.
3. A: The drift speed is independent of the area of the wire when V is fixed. R: $v_d=eV\tau /ml$.
4. A: The terminal voltage of a cell can exceed its emf. R: This happens when the cell is being charged.
5. A: Alloys are used for standard resistors. R: Alloys have low resistivity.
6. A: Kirchhoff's junction rule is based on conservation of charge. R: Charge does not accumulate at a junction in the steady state.

Key: 1 (a) · 2 (b) · 3 (a) · 4 (a) · 5 (c) · 6 (a)

Answers to the practice set