The frequency of an alternating voltage is `50` cycles/sec and its amplitude is `120V`. Then the r.m.s value of voltage is

Options

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

Explanation

To find the root mean square (r.m.s) value of an alternating voltage, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Amplitude (V_max) = 120 V
- Frequency = 50 Hz (not needed for r.m.s calculation)

2. **Understand the Relationship Between Amplitude and r.m.s Value:**
- The r.m.s value (V_rms) of an alternating voltage is related to its maximum value (V_max) by the formula:
\[ V_{rms} = \frac{V_{max}}{\sqrt{2}} \]

3. **Substitute the Given Amplitude into the Formula:**
- Using the formula, we substitute V_max:
\[ V_{rms} = \frac{120 V}{\sqrt{2}} \]

4. **Calculate the r.m.s Value:**
- First, calculate \(\sqrt{2}\):
\[ \sqrt{2} \approx 1.414 \]
- Now, divide 120 V by \(\sqrt{2}\):
\[ V_{rms} = \frac{120 V}{1.414} \approx 84.85 V \]

5. **Final Answer:**
- The r.m.s value of the voltage is approximately:
\[ V_{rms} \approx 84.85 V \]

### Summary:
The r.m.s value of the alternating voltage with an amplitude of 120 V is approximately 84.85 V.