Last Updated: 11 May 2026
Chapter 7 ‘Alternating Current’ is a high-yield Class 12 Physics topic worth 8-10 marks in CBSE 2027 boards, with at least 1 long-answer question almost every year. RC/LC/RLC circuit problems also feature heavily in JEE/NEET, making this a multi-purpose chapter.
AC Voltage and Current
- Instantaneous: V = V₀ sin(ωt), I = I₀ sin(ωt – φ)
- Peak: V₀, I₀
- RMS (effective): V_rms = V₀/√2 = 0.707 V₀
- Average over full cycle: 0
- Average over half cycle: (2/π) × V₀ = 0.637 V₀
AC Through Pure Components
| Component | Phase | Reactance/Resistance |
|---|---|---|
| Resistor (R) | I in phase with V | R (Ω) |
| Inductor (L) | I lags V by π/2 | X_L = ωL = 2πfL |
| Capacitor (C) | I leads V by π/2 | X_C = 1/ωC = 1/(2πfC) |
RLC Series Circuit
- Impedance: Z = √(R² + (X_L – X_C)²)
- Phase angle: tan φ = (X_L – X_C)/R
- Power factor: cos φ = R/Z
Resonance
- Occurs when X_L = X_C → ω_r = 1/√(LC), f_r = 1/(2π√(LC))
- At resonance: Z = R (minimum), current = maximum
- Q-factor: Q = ω_r L / R = (1/R)√(L/C); sharpness of resonance
- Bandwidth: Δω = R/L; Q = ω_r / Δω
Power in AC Circuit
- Average power: P_avg = V_rms × I_rms × cos φ
- Apparent power: V_rms × I_rms
- Wattless current: when cos φ = 0 (pure L or pure C)
LC Oscillations
Energy oscillates between L and C:
- Initial energy in C: (1/2)CV₀²
- Frequency of oscillations: ω = 1/√(LC)
- Charge: q(t) = q₀ cos(ωt)
AC Generator (Dynamo)
- Based on electromagnetic induction (Faraday’s law).
- EMF induced: ε = ε₀ sin(ωt), where ε₀ = NBAω.
- Slip rings make it AC; commutator makes it DC.
Transformer
- Step-up: more turns in secondary; Step-down: fewer turns in secondary.
- Turns ratio: V_s/V_p = N_s/N_p = I_p/I_s (for ideal transformer).
- Energy losses: Cu loss (I²R), Iron loss (eddy currents + hysteresis), Flux leakage.
- Power transmission at high voltage to reduce I²R loss.
NCERT Diagrams to Master
- Phasor diagram for RLC series
- Resonance curve (I vs ω)
- AC generator schematic
- Transformer schematic + EMF-time graph
- LC oscillation energy plot
Internal Links
FAQ
Marks weightage of AC chapter?
8-10 marks (Section B + 1 numerical in Section D).
Most-asked derivation?
Average power in AC circuit and Q-factor derivation — both appeared in 2023 and 2025 boards.
Is transformer numerical asked?
Yes — every alternate year. Practice turns-ratio and efficiency problems.
Practice Quiz
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