Home › Free notes › Class 12 Physics › Alternating Current

Alternating Current – Class 12 Physics notes, important questions and MCQs

NCERT Class 12 Physics, chapter 7. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Alternating current varies sinusoidally. Resistors, inductors and capacitors respond differently, giving impedance, resonance and power factor; transformers change AC voltage.

AC basics

I = I₀ sin ωt; rms values I_rms = I₀/√2, V_rms = V₀/√2.
Inductive reactance X_L = ωL; capacitive reactance X_C = 1/(ωC).
Impedance of LCR series circuit Z = √[R² + (X_L − X_C)²].

Resonance, power and transformer

Resonant frequency ω₀ = 1/√(LC); at resonance Z = R and current is maximum.
Average power P = V_rms I_rms cos φ; cos φ = R/Z (power factor).
Transformer: V_s/V_p = N_s/N_p = I_p/I_s (ideal); step-up raises voltage.

Key terms

rms value: effective value of AC that produces the same heat as DC
Power factor: cos φ, ratio of true power to apparent power
Impedance: total opposition to AC in an LCR circuit, Z = √[R² + (X_L − X_C)²]

Formulas

I_rms = I₀/√2
Z = √[R² + (X_L − X_C)²]
ω₀ = 1/√(LC)
V_s/V_p = N_s/N_p

Important questions with answers

Why is the average power consumed by a pure inductor zero?2 marks

In a pure inductor the current lags the voltage by 90°, so the power factor cos 90° = 0. Energy stored in the magnetic field in one quarter cycle is returned in the next.

What is resonance in a series LCR circuit? Write the resonant frequency and the current at resonance.3 marks

Resonance occurs when X_L = X_C, i.e. ωL = 1/ωC. Then Z = R (minimum) and current is maximum, I = V/R. Resonant frequency ω₀ = 1/√(LC), f₀ = 1/(2π√(LC)). Used in tuning radios.

Explain the working of a step-up transformer and list its energy losses. A transformer steps 220 V up to 2200 V and the primary has 100 turns; find the secondary turns and the primary current if the secondary supplies 2 A (ideal transformer).5 marks

AC in the primary produces a changing flux in the soft iron core; this flux links the secondary and induces emf by mutual induction. Vₛ/Vₚ = Nₛ/Nₚ; with more secondary turns, voltage steps up and current steps down. Losses: copper (I²R) loss in windings, eddy-current loss (reduced by laminated core), hysteresis loss (soft iron), flux leakage. Nₛ = 100 × 2200/220 = 1000 turns. Ideal: VₚIₚ = VₛIₛ, so Iₚ = 2200 × 2/220 = 20 A.

Quick revision

X_L increases with frequency; X_C decreases.
Resonance: X_L = X_C.
Transformers work only on AC.

Exam tips

In a pure inductor or capacitor, average power is zero (wattless current).
Transformers work only on AC; for an ideal transformer Vₛ/Vₚ = Nₛ/Nₚ = Iₚ/Iₛ.

Practice MCQs

rms value of AC with peak 10 A is about
1. 7.07 A
2. 10 A
3. 14.1 A
4. 5 A
Show answer
Answer: (a) 7.07 A. 10/√2.
A transformer works on
1. AC only
2. DC only
3. both equally
4. neither
Show answer
Answer: (a) AC only. Needs changing flux.
Capacitive reactance as frequency increases
1. increases
2. decreases
3. stays same
4. becomes infinite
Show answer
Answer: (b) decreases. X_C = 1/(ωC).
At resonance in an LCR circuit, impedance equals
1. R
2. X_C
3. X_L
4. zero
Show answer
Answer: (a) R. X_L = X_C cancel.
Peak voltage of 220 V (rms) mains is about
1. 311 V
2. 220 V
3. 156 V
4. 440 V
Show answer
Answer: (a) 311 V. √2 × 220.
A step-up transformer has 100 primary and 500 secondary turns. With 220 V input, output is
1. 1100 V
2. 44 V
3. 220 V
4. 500 V
Show answer
Answer: (a) 1100 V. 220 × 5.
Average power in a purely inductive AC circuit is
1. maximum
2. V_rms I_rms
3. zero
4. I²R
Show answer
Answer: (c) zero. cos 90° = 0.
Resonant frequency of an LC circuit with L = 1 mH and C = 1 µF is about
1. 5 kHz
2. 50 kHz
3. 500 Hz
4. 1 kHz
Show answer
Answer: (a) 5 kHz. 1/(2π√(10⁻⁹)) ≈ 5033 Hz.

All chapters of Class 12 Physics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.