The value of form factor in case of half wave rectifier is

Options

A. `1.11`
B. `1.57`
C. `1.27`
D. `0.48`

Answer

To find the value of the form factor in the case of a half wave rectifier, we will follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Form Factor**:
The form factor (FF) is defined as the ratio of the root mean square (RMS) value of the current (I_rms) to the average value of the current (I_avg).
\[ \text{Form Factor (FF)} = \frac{I_{rms}}{I_{avg}} \]

2. **Determine the RMS Current for a Half Wave Rectifier**:
For a half wave rectifier, the RMS current (I_rms) is given by:
\[ I_{rms} = \frac{I_0}{2} \]
where \(I_0\) is the peak current.

3. **Determine the Average Current for a Half Wave Rectifier**:
The average current (I_avg) for a half wave rectifier is given by:
\[ I_{avg} = \frac{I_0}{\pi} \]

4. **Substitute the Values into the Form Factor Formula**:
Now, substituting the expressions for I_rms and I_avg into the form factor equation:
\[ FF = \frac{I_{rms}}{I_{avg}} = \frac{\frac{I_0}{2}}{\frac{I_0}{\pi}} \]

5. **Simplify the Expression**:
Simplifying the above expression:
\[ FF = \frac{I_0}{2} \cdot \frac{\pi}{I_0} = \frac{\pi}{2} \]

6. **Calculate the Numerical Value**:
Now, substituting the value of \(\pi\) (approximately 3.14):
\[ FF = \frac{3.14}{2} \approx 1.57 \]

7. **Conclusion**:
Therefore, the value of the form factor in the case of a half wave rectifier is approximately 1.57.

### Final Answer:
The value of the form factor in case of a half wave rectifier is 1.57.