Power & Power Factor

Instantaneous power in an AC circuit: p(t) = v(t)·i(t). For sinusoidal v and i with phase difference φ: p(t) varies, but ITS AVERAGE matters.

Average power: P_avg = V_rms · I_rms · cos φ. The factor cos φ is called the POWER FACTOR.

Pure R: cos φ = 1 ⇒ full power delivered.

Pure L or C: cos φ = 0 ⇒ no power dissipated (wattless current — energy oscillates but doesn't transfer net).

Mixed circuit: cos φ = R/Z. Higher reactance ⇒ smaller cos φ ⇒ less real power for same current.

Real power (W) vs apparent power (VA): P = V_rms·I_rms·cos φ (real), S = V_rms·I_rms (apparent). Reactive power Q = V_rms·I_rms·sin φ (VAR).

Power factor correction: industries add capacitors in parallel with inductive loads to bring cos φ close to 1. Lowers I for the same P → reduces transmission losses.