The peak value equals what times the RMS value for a sine wave?

The peak value equals what times the RMS value for a sine wave?

• A. 0.707 x RMS
• B. 2 x RMS
• C. 1.0 x RMS
• D. 1.414 x RMS

Answer: (D)

For a sine wave, the RMS value is the effective value that would produce the same heating as a DC voltage. If the voltage is v(t) = Vp sin(ωt), then Vrms = Vp / √2 because the average of sin^2 over a cycle is 1/2. Rearranging gives Vp = √2 × Vrms. Since √2 is about 1.414, the peak value is approximately 1.414 times the RMS value.

For a sine wave, the RMS value is the effective value that would produce the same heating as a DC voltage. If the voltage is v(t) = Vp sin(ωt), then Vrms = Vp / √2 because the average of sin^2 over a cycle is 1/2. Rearranging gives Vp = √2 × Vrms. Since √2 is about 1.414, the peak value is approximately 1.414 times the RMS value.