RMS Values

Root-mean-square (rms) value of an AC quantity is the DC equivalent that delivers the SAME average power to a resistor.

For sinusoidal AC: V_rms = V₀/√2 and I_rms = I₀/√2.

Mean voltage over a full sine cycle is ZERO (positive and negative halves cancel) — that's why ⟨V²⟩ is used.

Average power: P_avg = V_rms·I_rms = V_rms²/R = I_rms²·R (matches DC form).

rms is what AC meters display by default. '230 V mains' means 230 V rms.

Average over a half-cycle (magnitude only): |V|_avg = 2V₀/π ≈ 0.637 V₀ — DIFFERENT from rms.

For NON-sinusoidal waveforms: rms must be computed from the specific waveform. For a square wave amplitude V₀: V_rms = V₀ (no factor of √2).