The amplitude of an alternating voltage is 110 V. Its rms value will be:

Options

A. `77.8 V`
B. `70.7 V`
C. `102.2 V`
D. `112 V`

Explanation

To find the RMS (Root Mean Square) value of an alternating voltage given its amplitude, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The amplitude (peak voltage) of the alternating voltage, \( V_0 = 110 \, V \).

2. **Recall the Formula for RMS Voltage**:
- The relationship between the RMS voltage \( V_{RMS} \) and the peak voltage \( V_0 \) is given by the formula:
\[ V_{RMS} = \frac{V_0}{\sqrt{2}} \]

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

4. **Substitute the Values into the Formula**:
- Now, substitute \( V_0 = 110 \, V \) into the formula:
\[ V_{RMS} = \frac{110 \, V}{1.414} \]

5. **Perform the Division**:
- Calculate the value:
\[ V_{RMS} \approx \frac{110}{1.414} \approx 77.79 \, V \]

6. **Round the Result**:
- When rounding \( 77.79 \, V \) to one decimal place, we get \( 77.8 \, V \).

7. **Conclusion**:
- Therefore, the RMS value of the alternating voltage is \( 77.8 \, V \).

### Final Answer:
The RMS value of the alternating voltage is \( 77.8 \, V \).

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