Class 12 Physics Chapter 7 Alternating Current – Revision Notes

Alternating current brings resistors, inductors, and capacitors together under a sinusoidal voltage, and this Class 12 Physics Chapter 7 summary traces that idea through rms values, reactance, resonance, and the Q-factor.

Last Updated: September 10, 2026

RMS and Peak Values

• For a sinusoidal signal of peak value A₀: A_rms=A₀/√2≈0.707A₀.

AC Through R, L, and C

• Resistor: voltage and current in phase; X_R=R.
• Inductor: current lags voltage by 90°; reactance X_L=2πfL=ωL.
• Capacitor: current leads voltage by 90°; reactance X_C=1/(2πfC)=1/(ωC).
• Average power over a cycle is zero for a pure L or pure C circuit (current and voltage 90° out of phase).

Series LCR Circuit and Resonance

• Impedance Z=√(R²+(X_L−X_C)²); power factor cosφ=R/Z.
• Resonance occurs when X_L=X_C, at ω_r=1/√(LC); impedance is then minimum (Z=R) and current is maximum.
• Q-factor Q=(1/R)√(L/C) measures the sharpness of resonance — a higher Q means a narrower, sharper resonance peak.

Average Power in AC Circuits

• P_avg=V_rmsI_rmscosφ; maximum (=V_rmsI_rms) at resonance, where cosφ=1.

LC Oscillations and Transformers

• An ideal (resistance-free) LC circuit oscillates at ω=1/√(LC), with energy continuously exchanged between the capacitor and inductor, total energy conserved.
• A transformer changes ac voltage using the turns ratio: V_s/V_p=N_s/N_p; high-voltage transmission reduces line power loss (I²R) for a given power delivered.

One-Line Summary

An ac circuit’s response depends on frequency through the reactances of L and C, peaking (resonating) when these reactances cancel, with the Q-factor describing how sharply.