If a sine wave has an average value of 90 V, the peak value is approximately what?

If a sine wave has an average value of 90 V, the peak value is approximately what?

• A. 90
• B. 141.5
• C. 128.6
• D. 100

Answer: (B)

For a sine wave, the average value taken over a half cycle relates to the peak value by a factor of 2/π. If the instantaneous peak is Vpeak, the average over the positive half-cycle is (2/π) × Vpeak. Setting this average equal to 90 V gives Vpeak = 90 × (π/2) ≈ 141.37 V, which rounds to about 141.5 V. Context: the RMS value would be Vpeak/√2, so with Vpeak ≈ 141.5 V, Vrms ≈ 100 V. The full-cycle average is zero, so 90 V wouldn’t be the average over a full cycle.

For a sine wave, the average value taken over a half cycle relates to the peak value by a factor of 2/π. If the instantaneous peak is Vpeak, the average over the positive half-cycle is (2/π) × Vpeak. Setting this average equal to 90 V gives Vpeak = 90 × (π/2) ≈ 141.37 V, which rounds to about 141.5 V.

Context: the RMS value would be Vpeak/√2, so with Vpeak ≈ 141.5 V, Vrms ≈ 100 V. The full-cycle average is zero, so 90 V wouldn’t be the average over a full cycle.