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 23, 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.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

What is the difference between direct current and alternating current?
Direct current flows in one constant direction, while alternating current periodically reverses direction and varies in magnitude, typically following a sinusoidal pattern with time, which is the form of current supplied to homes.

What is the significance of the rms value of an alternating current?
The rms value of an alternating current is the equivalent steady direct current that would produce the same heating effect in a resistor, making it the practical value used to rate household appliances and electrical equipment.

Written by Satish

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