Concept:Because a half-wave rectifier delivers one charging pulse per input cycle, the filter capacitor charges and discharges at the same fundamental frequency as the AC input.
Formula:$$f_{\text{ripple, half-wave}} = f_{\text{input}} = 50\text{ Hz}$$
Solution:- The capacitor charges once every \( T = \frac{1}{50}\text{ s} = 20\text{ ms} \).
- Therefore, the fundamental frequency of the residual ripple across the load matches the input frequency of \( 50\text{ Hz} \).
Why other options are incorrect:- Option A: 25 Hz would imply frequency division, which does not occur here.
- Option B: 100 Hz is the ripple frequency for a full-wave rectifier driven by a 50 Hz input.
- Option D: 0 Hz represents an ideal, theoretically infinite filter capacitor with zero ripple.
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