• 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 $V_{rms}$ = $\frac{V_0}{sqrt}$(2) ≈ 0.707*$V_0$ 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 2*$V_0$/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.