The amplitude of an alternating voltage is 120 V. What will be its rms value?

Options

A. 84.8V
B. 70.7V
C. 56.5V
D. 101.3V

Explanation

To find the RMS (Root Mean Square) value of an alternating voltage when the amplitude (peak value) is given, we can use the formula:

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

where:
- \( V_{rms} \) is the RMS value,
- \( V_0 \) is the peak value (amplitude).

### Step-by-Step Solution:

1. **Identify the given amplitude (peak value)**:
- The problem states that the amplitude of the alternating voltage is \( V_0 = 120 \, V \).

2. **Use the RMS formula**:
- We will apply the formula for RMS value:
\[ V_{rms} = \frac{V_0}{\sqrt{2}} \]

3. **Substitute the given value into the formula**:
- Plugging in the value of \( V_0 \):
\[ V_{rms} = \frac{120 \, V}{\sqrt{2}} \]

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

5. **Perform the division**:
\[ V_{rms} = \frac{120 \, V}{1.414} \approx 84.85 \, V \]

6. **Round the answer**:
- Rounding \( 84.85 \, V \) gives us approximately \( 84.8 \, V \).

### Final Answer:
The RMS value of the alternating voltage is approximately \( 84.8 \, V \).