V(rms )= 220volt , the peak voltage of the source is

Options

A. 305 V
B. 310 V
C. 311 V
D. 315 V

Explanation

To find the peak voltage (V₀) from the given root mean square voltage (Vₘₛ), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Value**:
We know that the root mean square voltage (Vₘₛ) is given as 220 volts.
\[ V_{rms} = 220 \, \text{volts} \]

2. **Use the Relationship Between Vₘₛ and V₀**:
The relationship between the peak voltage (V₀) and the root mean square voltage (Vₘₛ) is given by the formula:
\[ V_{rms} = \frac{V_0}{\sqrt{2}} \]

3. **Rearrange the Formula to Solve for V₀**:
To find the peak voltage (V₀), we can rearrange the formula:
\[ V_0 = V_{rms} \times \sqrt{2} \]

4. **Substitute the Given Value**:
Now, substitute the value of Vₘₛ into the equation:
\[ V_0 = 220 \, \text{volts} \times \sqrt{2} \]

5. **Calculate √2**:
The value of \(\sqrt{2}\) is approximately 1.414.
\[ V_0 = 220 \, \text{volts} \times 1.414 \]

6. **Perform the Multiplication**:
Now, calculate the product:
\[ V_0 \approx 220 \times 1.414 \approx 311.08 \, \text{volts} \]

7. **Round the Result**:
For practical purposes, we can round this to:
\[ V_0 \approx 311 \, \text{volts} \]

### Final Answer:
The peak voltage (V₀) of the source is approximately **311 volts**.

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