Chapter 7 — Alternating Current

Alternating Current (AC) is a current whose magnitude and direction vary sinusoidally with time; it is the dominant form of electrical power because AC voltages can be efficiently stepped up or down using transformers, enabling economical long-distance transmission.

Class 12 Physics Chapter 7 covers alternating current (AC) circuits in depth. It explains AC voltage applied to resistors, inductors, and capacitors, introducing key concepts like inductive reactance (XL = ωL), capacitive reactance (XC = 1/ωC), and impedance (Z = √[R² + (XC − XL)²]) for series LCR circuits. The chapter covers phasor diagrams, resonance (ω₀ = 1/√LC), power factor (cos φ), and the transformer principle (Vs/Vp = Ns/Np), explaining how step-up and step-down transformers enable efficient power transmission across long distances.

1. 01In a pure resistor, voltage and current are in phase; rms current I = im/√2 = 0.707 im and rms voltage V = vm/√2 = 0.707 vm.
2. 02In a pure inductor, current lags voltage by π/2; inductive reactance XL = ωL (unit: ohm); average power over a full cycle is zero.
3. 03In a pure capacitor, current leads voltage by π/2; capacitive reactance XC = 1/ωC (unit: ohm); average power over a full cycle is zero.
4. 04In a series LCR circuit, impedance Z = √[R² + (XC − XL)²] and resonance occurs at ω₀ = 1/√LC, where current amplitude is maximum (im = vm/R).
5. 05Average power in an AC circuit is P = VI cos φ, where cos φ is the power factor; in purely inductive or capacitive circuits cos φ = 0, giving zero net power (wattless current).
6. 06A transformer changes AC voltage using mutual induction: Vs/Vp = Ns/Np; step-up transformers increase voltage and reduce current for efficient long-distance power transmission.