Question

An AC voltage \( V = 0.5 \sin (100\pi t) \) volt is applied, in turn, across a half-wave rectifier and a full-wave rectifier. The frequency of the output voltage across them respectively will be:

• A. 25 Hz, 50 Hz
• B. 25 Hz, 100 Hz
• C. 50 Hz, 50 Hz
• D. 50 Hz, 100 Hz

Hint:

A half-wave rectifier retains the same frequency as the input AC, whereas a full-wave rectifier doubles the frequency.

Answer 1

The Correct Option is D

Rectifier Frequency Response Analysis
- Input AC voltage: \[ V = 0.5 \sin(100\pi t) \] - Standard AC signal form: \[ V = V_0 \sin(2\pi f t) \] By comparison: \[ 2\pi f = 100\pi \] \[ f = \frac{100\pi}{2\pi} = 50 \text{ Hz} \] 

Output Frequency of Half-Wave Rectifier: 
- A half-wave rectifier passes only one half-cycle of the input AC voltage. 
- The output voltage maintains the input's fundamental frequency, which is 50 Hz. Full
-Wave Rectifier Output Frequency: 
- A full-wave rectifier inverts the negative half-cycles, doubling the output frequency. 
- Therefore, the output frequency is: \[ 2 \times 50 = 100 \text{ Hz} \] Consequently, the output for a half-wave rectifier is 50 Hz, and for a full-wave rectifier, it is 100 Hz.