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 for a half-wave rectifier, we can 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 output current to the average (DC) value of the output current. Mathematically, it is expressed as:
\[ \text{Form Factor (FF)} = \frac{I_{\text{RMS}}}{I_{\text{average}}} \]

2. **Identify the RMS and Average Values for Half-Wave Rectifier**:
For a half-wave rectifier:
- The RMS current (\(I_{\text{RMS}}\)) is given by:
\[ I_{\text{RMS}} = \frac{I_0}{2} \]
- The average current (\(I_{\text{average}}\)) is given by:
\[ I_{\text{average}} = \frac{I_0}{\pi} \]

3. **Substituting the Values into the Form Factor Formula**:
Now, substitute the expressions for \(I_{\text{RMS}}\) and \(I_{\text{average}}\) into the form factor formula:
\[ \text{FF} = \frac{I_{\text{RMS}}}{I_{\text{average}}} = \frac{\frac{I_0}{2}}{\frac{I_0}{\pi}} \]

4. **Simplifying the Expression**:
When we simplify the above expression, the \(I_0\) terms cancel out:
\[ \text{FF} = \frac{I_0}{2} \cdot \frac{\pi}{I_0} = \frac{\pi}{2} \]

5. **Calculating the Numerical Value**:
Now, we can calculate the numerical value of \(\frac{\pi}{2}\):
\[ \text{FF} \approx \frac{3.14}{2} \approx 1.57 \]

6. **Conclusion**:
Therefore, the value of the form factor for a half-wave rectifier is approximately \(1.57\).

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