For a sine wave, what is the relationship between peak and RMS values?

For a sine wave, what is the relationship between peak and RMS values?

• A. peak = 0.707 x RMS
• B. peak = RMS
• C. peak = 1.414 x RMS
• D. peak = 2 x RMS

Answer: (C)

For a sine wave, the RMS value is the effective DC value that would produce the same heating effect. If the peak amplitude is Vp, the RMS value is Vrms = Vp / √2 because the average of sin^2 over a full cycle is 1/2. Rearranging gives Vp = Vrms × √2 ≈ 1.414 × Vrms. So the peak is about 1.414 times the RMS. That makes the correct relationship peak ≈ 1.414 × RMS. The other options would imply incorrect factors (for a sine wave, RMS is not equal to the peak, nor is it half or double the peak).

For a sine wave, the RMS value is the effective DC value that would produce the same heating effect. If the peak amplitude is Vp, the RMS value is Vrms = Vp / √2 because the average of sin^2 over a full cycle is 1/2. Rearranging gives Vp = Vrms × √2 ≈ 1.414 × Vrms. So the peak is about 1.414 times the RMS. That makes the correct relationship peak ≈ 1.414 × RMS. The other options would imply incorrect factors (for a sine wave, RMS is not equal to the peak, nor is it half or double the peak).