Alternating Current

The mains supply in your home is not a steady voltage but a sine wave — and this chapter, a dependable 4-7 Board marks and a fixture in JEE/NEET, is the physics of circuits driven by it. We start with an AC source across a resistor, where current and voltage are in phase, and meet the root-mean-square (rms) values that make AC power formulas look exactly like DC ones ($I = i_m/\sqrt{2}$; the '220 V' mains is rms, with peak 311 V). Phasors — rotating vectors for oscillating quantities — then unlock the reactive elements: a pure inductor, where current lags the voltage by 90 degrees with reactance $X_L = \omega L$, and a pure capacitor, where current leads by 90 degrees with $X_C = 1/\omega C$, both consuming zero average power. Combining all three in the series LCR circuit gives the impedance $Z = \sqrt{R^2 + (X_C - X_L)^2}$ and phase angle $\tan\phi = (X_C - X_L)/R$, and at the resonant frequency $\omega_0 = 1/\sqrt{LC}$ the impedance collapses to R and the current peaks — the principle behind radio tuning and airport metal detectors. Average power is $P = VI\cos\phi$, introducing the power factor and the strange 'wattless current' that flows without dissipating. The chapter closes with the transformer — mutual induction put to work, $v_s/v_p = N_s/N_p$ — and the grand story of why electrical power crosses the country at high voltage. Every formula, phasor diagram and exam-favourite numerical is covered.