Question

The root mean square (RMS) value of an alternating voltage applied to a full-wave rectifier is \( \frac{V_0}{\sqrt{2}} \). Then the root mean square value of the rectified output voltage is:

Hint:

In a full-wave rectifier, the RMS value of the output voltage is the same as the RMS value of the input AC voltage, as it retains the waveform's overall power distribution.

Answer 1

For a full-wave rectifier, the rectified output voltage waveform consists of the absolute values of the input AC voltage waveform. The RMS value of the output voltage is calculated as: \[ V_{\text{rms}} = \sqrt{\frac{1}{T} \int_0^T V_{\text{rectified}}^2 \, dt} \] Since the full-wave rectifier converts both halves of the alternating current waveform into positive polarity, the RMS value remains the same as that of the input AC voltage waveform: \[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} \] Thus, the RMS value of the rectified output voltage is \( \frac{V_0}{\sqrt{2}} \).