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

Understanding Rectifier Frequency Response 
- The given AC voltage is: \[ V = 0.5 \sin(100\pi t) \] - The general form of an AC signal is: \[ V = V_0 \sin(2\pi f t) \] Comparing, we get: \[ 2\pi f = 100\pi \] \[ f = \frac{100\pi}{2\pi} = 50 \text{ Hz} \] 

Half-Wave Rectifier Output Frequency: 
- A half-wave rectifier allows only one half-cycle of the input AC voltage. 
- The output voltage still follows the same fundamental frequency as the input, i.e., 50 Hz. Full
-Wave Rectifier Output Frequency: 
- A full-wave rectifier inverts the negative half-cycles, making the output frequency twice the input frequency. 
- Thus, the frequency of the output becomes: \[ 2 \times 50 = 100 \text{ Hz} \] Thus, the correct answer is 50 Hz for the half-wave rectifier and 100 Hz for the full-wave rectifier.