The form factor for a sinusoidal `A.C` is

Options

A. `2 sqrt(2)`
B. `pi : 2 sqrt(2)`
C. `sqrt(2) : 1`
D. `1 : sqrt(2)`

Explanation

To find the form factor for a sinusoidal alternating current (A.C.), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Form Factor**:
The form factor is defined as the ratio of the root mean square (RMS) value to the average value of the current (or voltage) over one complete cycle.

\[ \text{Form Factor} = \frac{\text{RMS Value}}{\text{Average Value over Half Cycle}} \]

2. **Identify the RMS and Average Values**:
For a sinusoidal current (or voltage), the RMS value \(I_{\text{rms}}\) and the average value \(I_{\text{avg}}\) can be expressed in terms of the peak value \(I_0\):
- The RMS value is given by:
\[ I_{\text{rms}} = \frac{I_0}{\sqrt{2}} \]
- The average value over half a cycle is given by:
\[ I_{\text{avg}} = \frac{2}{\pi} I_0 \]

3. **Substitute the Values into the Form Factor Formula**:
Now, substituting the expressions for \(I_{\text{rms}}\) and \(I_{\text{avg}}\) into the form factor formula:
\[ \text{Form Factor} = \frac{I_{\text{rms}}}{I_{\text{avg}}} = \frac{\frac{I_0}{\sqrt{2}}}{\frac{2}{\pi} I_0} \]

4. **Simplify the Expression**:
Cancel \(I_0\) from the numerator and denominator:
\[ \text{Form Factor} = \frac{1/\sqrt{2}}{2/\pi} = \frac{\pi}{2\sqrt{2}} \]

5. **Final Result**:
Therefore, the form factor for a sinusoidal A.C. is:
\[ \text{Form Factor} = \frac{\pi}{2\sqrt{2}} \]

### Conclusion:
The form factor for a sinusoidal A.C. is \(\frac{\pi}{2\sqrt{2}}\).