The maximum voltage in DC circuit is 282 V. the effective voltage in AC circuit will be

Options

A. 200 V
B. 300 V
C. 400 V
D. 564 V

Answer

To solve the problem of finding the effective voltage in an AC circuit given the maximum voltage in a DC circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept**: The effective voltage (or RMS voltage) in an AC circuit is related to the maximum voltage (V0) in a DC circuit. The relationship is given by the formula:
\[ V_{\text{RMS}} = \frac{V_0}{\sqrt{2}} \]

2. **Identify Given Values**: From the problem, we know that the maximum voltage \( V_0 \) in the DC circuit is 282 V.

3. **Substitute the Value**: Plug the value of \( V_0 \) into the formula:
\[ V_{\text{RMS}} = \frac{282 \, \text{V}}{\sqrt{2}} \]

4. **Calculate \( \sqrt{2} \)**: The value of \( \sqrt{2} \) is approximately 1.41.

5. **Perform the Division**: Now, calculate:
\[ V_{\text{RMS}} = \frac{282}{1.41} \]

6. **Final Calculation**: Performing the division gives:
\[ V_{\text{RMS}} \approx 200 \, \text{V} \]

7. **Conclusion**: Therefore, the effective voltage in the AC circuit is approximately 200 V.

### Final Answer:
The effective voltage in the AC circuit is **200 V**.

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