The peak value of an AC sine wave is how many times its RMS value?

• A. 1.414 times RMS
• B. 0.707 times RMS
• C. 1.0 times RMS
• D. 2.0 times RMS

Answer: (A)

For a sine wave, the RMS value is the square root of the average of the squared instantaneous voltage. If the waveform is v(t) = Vp sin(ωt), then Vrms = Vp / √2. Rearranging gives the peak value Vp = √2 × Vrms, which is about 1.414 times the RMS value. So the peak value is approximately 1.414 times the RMS value.

This relationship matters because RMS corresponds to the heating effect (power), while peak value is what you’d see as the maximum voltage. The other relationships don’t fit: 0.707 times RMS would be Vrms/√2, not the peak; 1.0 times RMS would mean peak equals RMS, which isn’t true for a sine; 2.0 times RMS would double the RMS, also incorrect for a sine wave.