What is the formula to find the average voltage of an AC circuit?

The average voltage of an alternating current (AC) circuit can be calculated using the formula that involves the peak voltage. In an AC waveform, particularly a sinusoidal waveform, the average voltage can be derived from the peak voltage by taking into account the shape of the waveform.

For a sinusoidal AC waveform, the average value over one complete cycle is not simply the peak value; instead, it is given by multiplying the peak value by a factor that accounts for the waveform shape. The correct factor for a full sine wave is approximately 0.637. This factor represents how much of the peak voltage is averaged out over time. In mathematical terms, it is derived from the integration of the sine function over one cycle, divided by the time period.

In contrast, other options present different factors that correspond either to other values in AC analysis, such as the root mean square (RMS) value, which is 0.707 of the peak value for a sine wave, or the peak voltage multiplied by √2 for instantaneous or peak voltages in different contexts. None of these accurately describe the average value of voltage for a sinusoidal waveform, making 0.637 x peak value the appropriate choice for this question.