• Tags: AC, peak, RMS, frequency
• Difficulty: Foundation

Alternating current varies sinusoidally: V(t) = V_0 sin(omegat) and I(t) = I_0 sin(omegat + phi). The peak value V_0 is the maximum instantaneous voltage. The RMS (root-mean-square) value V_rms = V_0/sqrt(2) ≈ 0.707V_0 is defined such that an AC source of V_rms delivers the same power to a resistor as a DC source of voltage V_rms. For Indian household supply: V_rms = 220 V, so V_0 = 220sqrt(2) = 311 V, f = 50 Hz, T = 1/50 = 0.02 s, omega = 2pi50 = 100pi ≈ 314 rad/s. The mean value of V over a full cycle is zero (positive and negative halves cancel). The mean value over a half cycle is 2V_0/pi ≈ 0.637*V_0. JEE often tests the relationship between peak, RMS, and mean values. Remember: RMS > mean (for half cycle) always for a sinusoidal wave.