CBSE Class 12 Physics: Alternating Current — Complete Notes 2026

AC Voltage and Current

• AC: current direction reverses periodically; v = V₀ sin(ωt); i = I₀ sin(ωt + φ) where φ is phase difference
• V₀ = peak voltage, V_rms = V₀/√2; I_rms = I₀/√2; household voltage: 220 V rms (peak = 311 V)
• Frequency f = ω/2π; India: 50 Hz; USA: 60 Hz

AC Through Resistor, Inductor, Capacitor

• R: current in phase with voltage; Vᴿ = IR; no phase difference
• L: current lags voltage by π/2 (90°); inductive reactance Xₗ = ωL; Vₗ = IXₗ
• C: current leads voltage by π/2; capacitive reactance Xc = 1/ωC; Vc = IXc

Series LCR Circuit

• Impedance Z = √(R² + (Xₗ−Xc)²); tan φ = (Xₗ−Xc)/R
• Current I = V/Z; power P = VᵢI_rms cos φ where cos φ is power factor
• Phasor diagram: draw V_R along horizontal; V_L upward; V_C downward; resultant = applied V

Resonance in LCR Circuit

• Resonance: Xₗ = Xc → Z = R (minimum); current maximum I = V/R
• Resonant frequency ω₀ = 1/√(LC); f₀ = 1/(2π√LC)
• Q factor (Quality factor) = ω₀L/R = 1/(ω₀CR); sharp resonance = high Q; bandwidth = ω₀/Q

Power in AC Circuits

• Average power P = V_rms × I_rms × cos φ (cos φ = power factor)
• Pure R: φ = 0, cos φ = 1, P = V_rms × I_rms (maximum); pure L or C: φ = 90°, cos φ = 0, P = 0
• Wattless current: component of current not contributing to power; present in L and C circuits

Transformers

• Step-up: Ns > Np → Vs > Vp; step-down: Ns < Np → Vs < Vp
• Turns ratio: Vs/Vp = Ns/Np = Ip/Is (power conservation: VsIs = VpIp at 100% efficiency)
• Losses: copper (I²R in windings), core/iron (eddy currents + hysteresis); minimised by laminating core

CBSE Board Focus

• AC: 7–9 marks in CBSE; phasor diagram, LCR resonance, transformer derivation most important
• Numericals: find Z, I, resonant frequency, turns ratio — all common in CBSE Board
• Power factor: define, explain wattless current, why it matters for energy efficiency