The peak voltage of an ac supply is 440 V, then its rms voltage is

Options

A. `31.11 V`
B. `311.1 V`
C. `41.11 V`
D. `411.1V`

Explanation

To find the RMS (Root Mean Square) voltage from the peak voltage of an AC supply, we can use the relationship between the two. The formula to convert peak voltage (Vm) to RMS voltage (Vrms) is given by:

\[ V_{rms} = \frac{V_m}{\sqrt{2}} \]

### Step-by-Step Solution:

1. **Identify the Peak Voltage (Vm)**:
The problem states that the peak voltage (Vm) is 440 V.

2. **Use the Formula for RMS Voltage**:
We will substitute the peak voltage into the formula:
\[ V_{rms} = \frac{V_m}{\sqrt{2}} = \frac{440 \, V}{\sqrt{2}} \]

3. **Calculate \(\sqrt{2}\)**:
The value of \(\sqrt{2}\) is approximately 1.414.

4. **Perform the Division**:
Now we will divide 440 V by 1.414:
\[ V_{rms} = \frac{440 \, V}{1.414} \approx 311.1 \, V \]

5. **Conclusion**:
Therefore, the RMS voltage of the AC supply is approximately 311.1 V.

### Final Answer:
The RMS voltage is approximately **311.1 V**.