An AC voltage has an average (mean) value of 72 V. Its RMS value is approximately what?

• A. 72
• B. 60.0
• C. 113.2
• D. 80.03

Answer: (D)

RMS is the effective DC value that would produce the same heating as the AC waveform. For a sine wave, the average value of the rectified (absolute) voltage is Vavg = 2 Vpeak / π, while the RMS value is Vrms = Vpeak / √2. The ratio Vrms / Vavg for a sine wave is π / (2√2) ≈ 1.1107. So Vrms ≈ Vavg × 1.1107. With Vavg = 72 V, Vrms ≈ 72 × 1.1107 ≈ 80.0 V. Therefore the RMS value is about 80 V.