The effective value (RMS) of an AC sine wave is how many times the peak value?

• A. 0.5 times peak
• B. 1.0 times peak
• C. 1.414 times peak
• D. 0.707 times peak

Answer: (D)

RMS value represents the heating effect of an AC signal, and for a sine wave this is the peak value divided by √2. If the instantaneous voltage is v(t) = Vp sin(ωt), calculating the RMS involves squaring, averaging over a full cycle, and taking the square root. The average value of sin² over a cycle is 1/2, so the RMS becomes Vp · sqrt(1/2) = Vp/√2 ≈ 0.707 Vp. This is why the effective or "DC-equivalent" value is about 70.7% of the peak. The other fractions (0.5, 1.0, or 1.414 times the peak) don’t reflect the actual average of the squared sine waveform.