Concept:Form Factor (\( \text{FF} \)) is the ratio of the Root Mean Square (RMS) value to the average (DC) value of a periodic waveform.
Formula:$$\text{FF}_{\text{half-wave}} = \frac{V_{\text{rms}}}{V_{\text{dc}}} = \frac{V_m / 2}{V_m / \pi} = \frac{\pi}{2} \approx 1.5708$$
Solution:- For a half-wave rectifier, \( V_{\text{rms}} = \frac{V_m}{2} \) and \( V_{\text{dc}} = \frac{V_m}{\pi} \).
- Calculating the ratio: \( \text{FF} = \frac{V_m/2}{V_m/\pi} = \frac{\pi}{2} \approx 1.57 \).
Why other options are incorrect:- Option A: 1.11 (\( \pi / 2\sqrt{2} \)) is the Form Factor of a full-wave rectifier or pure AC sine wave.
- Option C: 0.707 is \( 1/\sqrt{2} \), the RMS factor of a full sine wave.
- Option D: 2.00 is the peak-to-average ratio of a square wave.
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