Alternating Current: 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 rms current.
2. What is the average of ac over a cycle?
3. Why does a capacitor allow ac to pass?
4. What is impedance?
5. When is the power factor zero?
6. Write the transformer ratio.
7. Name two energy losses in a transformer.
8. What is the peak of 220 V rms?
9. Write the condition for resonance.
10. Which current is called wattless?

D. Short answer I (2 marks each)

1. Show that a pure inductor consumes no average power.
2. Derive $X_C=1/\omega C$ and the phase of i in a capacitor.
3. Draw phasors for R, L and C circuits.
4. Explain why power is transmitted at high voltage.
5. A 100 Ω resistor and 0.3 H inductor are in series on 220 V, 50 Hz. Find Z and I.
6. Define resonant frequency. On what does it depend?
7. Explain how a capacitor improves the power factor.
8. A 1:10 step-up transformer gets 2 kW at 200 V. Find the primary current and output voltage.

Rough work

E. Short answer II (3 marks each)

1. Derive the average power in an ac circuit and define the power factor.
2. Derive the current in a pure inductor on ac and its phase. Draw the graph of $X_L$ against ν.
3. Derive the condition for resonance and show that the circuit is purely resistive then.
4. An LCR circuit has R = 10 Ω, X_L = 30 Ω, X_C = 20 Ω on 100 V. Find Z, I, φ and P.
5. Explain the working of a transformer and derive $v_s/v_p=N_s/N_p$.
6. A 60 W, 120 V bulb is to be run on 240 V, 50 Hz with a capacitor in series. Find C.

F. Long answer (5 marks each)

1. Using phasors, derive Z and φ for a series LCR circuit. R = 300 Ω, L = 0.9 H, C = 2 μF on 50 V, ω = 1000 rad/s: find Z, I and the voltages across each element.
2. Describe a step-up transformer: principle, construction, theory and four energy losses. A transformer of 90% efficiency steps 220 V to 2200 V with input 4.4 kW: find the currents.
3. Discuss resonance in a series LCR circuit with a graph. Show how R changes the sharpness. Find ν₀ for L = 10 mH and C = 0.1 μF.

G. HOTS (higher-order thinking)

1. Why can't a transformer be used with dc? What would happen if dc were applied to its primary?
2. A bulb in series with a capacitor glows on ac. What happens if a dielectric is inserted in the capacitor?
3. Can the voltage across the inductor in a series LCR circuit exceed the source voltage? When?
4. Why is the core of a transformer laminated, and why soft iron?

20 MCQs

1. rms value of $v_m\sin \omega t$
   (a) $v_m$ (b) $v_m/2$ (c) $v_m/\sqrt{2}$ (d) $\sqrt{2}{v}_m$
2. Average of ac over a full cycle
   (a) zero (b) $0.637v_m$ (c) $v_m$ (d) $v_m/\sqrt{2}$
3. In a pure inductor the current
   (a) leads by π/2 (b) leads by π (c) in phase (d) lags by π/2
4. $X_C$ equals
   (a) ωC (b) 1/ωC (c) ωL (d) 1/ωL
5. Impedance of series LCR
   (a) R + X_L + X_C (b) $\sqrt{R^2+(X_L-X_C{)}^2}$ (c) $\sqrt{R^2+X_L^2+X_C^2}$ (d) $R(X_L-X_C)$
6. At resonance
   (a) φ = 90° (b) Z is maximum (c) I is minimum (d) $X_L=X_C$
7. Resonant frequency
   (a) $1/2\pi \sqrt{LC}$ (b) $2\pi \sqrt{LC}$ (c) $\sqrt{L/C}$ (d) $1/LC$
8. Power factor of a pure capacitor
   (a) 1 (b) 0.5 (c) zero (d) 0.707
9. Average power
   (a) VI (b) VI sin φ (c) VI tan φ (d) VI cos φ
10. Peak value of 220 V rms
    (a) 155 V (b) 311 V (c) 220 V (d) 440 V
11. A transformer works on
    (a) self-induction (b) Joule heating (c) mutual induction (d) magnetic effect
12. In a step-up transformer
    (a) voltage increases (b) current increases (c) $N_s<N_p$ (d) power increases
13. Eddy current loss is reduced by
    (a) thick wire (b) laminated core (c) soft iron (d) more turns
14. $X_L$ at 50 Hz for 0.1 H
    (a) 3.14 Ω (b) 5 Ω (c) 31.4 Ω (d) 314 Ω
15. A circuit with $X_L>X_C$ is
    (a) capacitive (b) resistive (c) at resonance (d) inductive
16. For dc, $X_L$ is
    (a) zero (b) infinite (c) R (d) ωL
17. Wattless current flows when φ =
    (a) π/2 (b) π/4 (c) π (d) 0
18. Same quantity in both coils of an ideal transformer
    (a) current (b) voltage (c) turns (d) flux and power
19. R = 3 Ω, X = 4 Ω: power factor
    (a) 0.75 (b) 0.6 (c) 0.8 (d) 1
20. C doubled, frequency halved: $X_C$
    (a) doubles (b) halves (c) unchanged (d) four times

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: A capacitor blocks dc. R: Its reactance is infinite for dc.
2. A: At resonance the current is in phase with the voltage. R: At resonance $X_L=X_C$.
3. A: An inductor consumes no average power. R: The current through it lags the voltage by π/2.
4. A: A step-up transformer increases power. R: It increases voltage.
5. A: Power is transmitted at high voltage. R: High voltage reduces current and I²R loss.
6. A: The rms value of ac is less than its peak value. R: rms = peak/√2 for sinusoidal ac.

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

Answers to the practice set