AC through Resistor

When AC voltage v = V₀ sin(ωt) drives a pure resistor R, the current is i = (V₀/R) sin(ωt).

V and I are IN PHASE — they peak, zero, and reverse together. Phase angle φ = 0.

Peak current: I₀ = V₀/R. RMS current: I_rms = V_rms/R = I₀/√2.

Average power: P_avg = V_rms · I_rms = V_rms²/R = I_rms²·R — exactly like a DC formula but with rms values.

Resistors dissipate energy continuously — instantaneous power p(t) = v·i = (V₀²/R) sin²(ωt) ≥ 0.

On a phasor diagram, V and I phasors point in the SAME direction.

Resistors do not store energy; they dissipate it as heat (Joule heating).