For a sine wave with peak value 424.2 V, its RMS value is approximately which?

For a sine wave with peak value 424.2 V, its RMS value is approximately which?

• A. 424.2 V
• B. 212.1 V
• C. 311.8 V
• D. 299.7 V

Answer: (D)

For a sinusoidal voltage, the RMS value is the peak value divided by the square root of 2. This comes from the definition of RMS and the fact that the average of sin^2 over a cycle is 1/2, so Vrms = Vp/√2. With a peak of 424.2 V, Vrms ≈ 424.2 / √2 ≈ 424.2 / 1.414 ≈ 299.7 V. So the RMS value is about 299.7 V—the closest option. The other numbers don’t fit because they correspond to the peak value or to different factors of the peak.

For a sinusoidal voltage, the RMS value is the peak value divided by the square root of 2. This comes from the definition of RMS and the fact that the average of sin^2 over a cycle is 1/2, so Vrms = Vp/√2.

With a peak of 424.2 V, Vrms ≈ 424.2 / √2 ≈ 424.2 / 1.414 ≈ 299.7 V.

So the RMS value is about 299.7 V—the closest option. The other numbers don’t fit because they correspond to the peak value or to different factors of the peak.