• Tags: power-factor, wattless, apparent
• Difficulty: Moderate

Average power P = $V_{rms}$$I_{rms}$cos(phi), where cos(phi) = $\frac{R}{Z}$ is the power factor. Three types of power: (1) Real/active power P = VIcos(phi) (in watts) — actual energy dissipated. (2) Reactive power $Q_r$ = VIsin(phi) (in VAR) — energy oscillating between source and reactive elements. (3) Apparent power S = VI (in VA) — the product VI without considering phase. Relation: $S^2$ = $P^2$ + $Q_r^2$. The wattless current is I*sin(phi) — it flows but dissipates no power. For pure R: cos(phi) = 1 (maximum power transfer). For pure L or pure C: cos(phi) = 0 (zero power — completely wattless). At resonance: cos(phi) = 1. Power companies aim for cos(phi) close to 1 to minimize wattless current (which still causes $I^{2R}$ losses in transmission lines).