Question

For a single-phase full-wave uncontrolled rectifier with a purely \( R \) load, the form factor is:

• A. \( \frac{2\sqrt{2}}{\pi} \)
• B. \( \frac{2}{\pi} \)
• C. \( \frac{\pi}{2\sqrt{2}} \)
• D. \( \frac{\pi}{2} \)

Hint:

The form factor helps analyze rectifier performance by comparing RMS and average voltage values. For a full-wave rectifier, \( FF = \frac{2\sqrt{2}}{\pi} \).

Answer 1

The Correct Option is A

Step 1: The form factor (\( FF \)) of a rectifier is defined as the ratio of the RMS value of output voltage to the average output voltage: \[ FF = \frac{V_{\text{rms}}}{V_{\text{avg}}} \] Step 2: For a single-phase full-wave uncontrolled rectifier with a purely resistive (\( R \)) load: - The RMS value of the output voltage is: \[ V_{\text{rms}} = \frac{V_m}{\sqrt{2}} \] - The average output voltage is: \[ V_{\text{avg}} = \frac{2V_m}{\pi} \] Step 3: Calculating the form factor: \[ FF = \frac{V_{\text{rms}}}{V_{\text{avg}}} = \frac{\frac{V_m}{\sqrt{2}}}{\frac{2V_m}{\pi}} \] \[ FF = \frac{V_m}{\sqrt{2}} \times \frac{\pi}{2V_m} = \frac{\pi}{2\sqrt{2}} \] \[ FF = \frac{2\sqrt{2}}{\pi} \] Step 4: Thus, the correct form factor is \( \frac{2\sqrt{2}}{\pi} \).