AC voltage: v = $V_{0}$ sin(ωt); $V_{0}$ = peak voltage; ω = 2πf = angular frequency.

RMS value: V_rms = $V_{0}$/√2 ≈ 0.707$V_{0}$; this is the "DC equivalent" used for all power calculations and equipment ratings.

Mean value (half cycle): V_mean = 2$V_{0}$/π ≈ 0.637$V_{0}$; used for rectified DC average. RMS > Mean always for sinusoidal waveforms.

Pure resistor (AC): V and I in phase (φ = 0); P = V_rms I_rms > 0. R does not depend on frequency.

Pure inductor: X_L = ωL = 2πfL; I lags V by 90°; P = 0 (wattless); energy stored and returned from magnetic field; X_L increases with frequency.

Pure capacitor: X_C = 1/(ωC) = 1/(2πfC); I leads V by 90°; P = 0 (wattless); energy stored and returned from electric field; X_C decreases with frequency.

Mnemonic ELI the ICE man: In L, E leads I (E-L-I); in C, I leads E (I-C-E).

Series LCR: Z = √($R^{2}$ + (X_L − X_C)^{2}); tan φ = (X_L − X_C)/R; Z is the generalisation of resistance to AC.

Resonance: X_L = X_C; f_{0} = 1/(2π√LC); Z = R (minimum — NOT zero); I_max = V_rms/R; φ = 0; power factor = 1.

Voltage magnification: At resonance, V_L = V_C = Q × V_supply where Q = ω_{0}L/R is the quality factor; individual reactive voltages can greatly exceed supply.

Power: P = V_rms I_rms cos φ = I_r$ms^{2}$ R = V_r$ms^{2}$ R/$Z^{2}$; power factor cos φ = R/Z; only R consumes power.

Wattless current: I_rms sin φ — flows in circuit but dissipates no power; exchanges energy with reactive components.

Transformer: V_s/V_p = N_s/N_p; I_s/I_p = N_p/N_s (INVERSE of voltage ratio); V_s I_s = V_p I_p (ideal).

High-voltage transmission: Using step-up transformers reduces transmission current by factor k = N_s/N_p; power loss $I^{2}$R reduces by $k^{2}$, demonstrating the economic importance of transformers.

AC generator: NBAω sin(ωt); 3000 rpm at 50 Hz (India); slip rings give AC, commutator gives DC.

Induction motor: Rotating magnetic field induces eddy currents in rotor → rotation; no electrical connection to rotor (brushless, robust).