What is the maximum value of an ac voltage whose rms value is 220 V?

Answer

To find the maximum value of an AC voltage given its RMS (Root Mean Square) value, we can use the relationship between the two values. The formula that relates the RMS value (Vrms) to the maximum value (V0) is:

\[ V_{rms} = \frac{V_0}{\sqrt{2}} \]

### Step-by-step Solution:

1. **Identify the given RMS value**:
The RMS value provided in the question is \( V_{rms} = 220 \, V \).

2. **Use the formula to express V0**:
Rearranging the formula to find the maximum value \( V_0 \):
\[ V_0 = V_{rms} \times \sqrt{2} \]

3. **Substitute the RMS value into the equation**:
Substitute \( V_{rms} = 220 \, V \) into the equation:
\[ V_0 = 220 \times \sqrt{2} \]

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

5. **Perform the multiplication**:
Now, multiply \( 220 \) by \( 1.414 \):
\[ V_0 = 220 \times 1.414 \approx 311.08 \, V \]

6. **Conclusion**:
The maximum value of the AC voltage is approximately \( 311.08 \, V \).

### Final Answer:
The maximum value of the AC voltage is approximately \( 311.08 \, V \).

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