Chapter 7 — Alternating Current

Chapter 7 of the Class 12 Physics NCERT textbook, "Alternating Current", covers alternating current — a current whose magnitude and direction vary sinusoidally with time — which dominates electrical power because AC voltages can be efficiently stepped up or down using transformers, enabling economical long-distance transmission.

• How AC differs from DC — The chapter examines current that continually reverses direction, introducing rms values so that time-varying quantities can be compared meaningfully with steady DC ones.
• Reactance and impedance — Inductors and capacitors respond to AC differently from resistors, introducing frequency-dependent reactance and combining into impedance that governs current in an LCR circuit.
• Resonance and power — At resonance the circuit responds most strongly, while the power factor explains why purely reactive elements carry 'wattless' current that transfers no net energy over a cycle.
• Transformers and transmission — Using mutual induction, transformers step voltage up or down. This lets power travel long distances at high voltage and low current, the key reason AC dominates the grid.

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.