If an AC main supply is given to be `220V`. What would be the average e.m.f during a positive half cycle?

Options

A. `198V`
B. `386V`
C. `256V`
D. None of these

Explanation

To find the average e.m.f during the positive half cycle of an AC supply given as 220V, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The AC main supply voltage is given as \( V_{rms} = 220V \).

2. **Relate RMS Voltage to Maximum Voltage**:
- The relationship between the root mean square (RMS) voltage and the maximum voltage (\( V_m \)) is given by:
\[ V_{rms} = \frac{V_m}{\sqrt{2}} \]
- Rearranging this formula gives us:
\[ V_m = V_{rms} \times \sqrt{2} \]

3. **Calculate the Maximum Voltage**:
- Substitute \( V_{rms} = 220V \) into the equation:
\[ V_m = 220V \times \sqrt{2} \approx 220V \times 1.414 \approx 311.08V \]

4. **Calculate the Average Voltage for the Positive Half Cycle**:
- The average value of the voltage during the positive half cycle is given by:
\[ V_{avg} = \frac{V_m}{\pi} \]
- Substitute \( V_m \approx 311.08V \):
\[ V_{avg} = \frac{311.08V}{\pi} \approx \frac{311.08V}{3.14159} \approx 99.06V \]

5. **Final Answer**:
- Therefore, the average e.m.f during the positive half cycle is approximately \( 99.06V \).

### Summary:
The average e.m.f during the positive half cycle of an AC supply of 220V is approximately \( 99.06V \).

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