AC through Capacitor

A pure capacitor lets the current jump first, voltage builds up. Driven by v = V₀ sin(ωt), current is i = (V₀/X_C) sin(ωt + π/2).

Current LEADS voltage by 90°. When V is zero (about to rise), I is at its peak.

Capacitive reactance: X_C = 1/(ωC) = 1/(2πfC). Units: Ω. FALLS with frequency.

At DC (f = 0): X_C → ∞ (capacitor BLOCKS DC after charging). At very high f: X_C → 0 (capacitor passes AC like a wire).

Average power: P_avg = 0 (cos(π/2) = 0). Like an inductor, no net energy dissipation.

Phasor: I leads V by 90° — current phasor is 90° counter-clockwise from voltage phasor.

Capacitors store energy in the electric field — energy goes back and forth between source and capacitor.