The equation of an alternating vottage is V `= 100sqrt(2)` sin `100pit` volt. The RMS value of vollage and frequeny, will be respectively

Options

A. 100 V, 50 Hz
B. 50 V, 100 Hz
C. 150 V, 50 Hz
D. 200 V, 50 Hz

Answer

To solve the problem, we need to find the RMS (Root Mean Square) value of the voltage and the frequency from the given equation of the alternating voltage.

### Step-by-Step Solution:

1. **Identify the Given Equation**:
The equation of the alternating voltage is given as:
\[ V = 100\sqrt{2} \sin(100\pi t) \text{ volts} \]

2. **Compare with the General Form**:
The general form of the alternating voltage is:
\[ V = V_0 \sin(\omega t) \]
where \( V_0 \) is the peak value and \( \omega \) is the angular frequency.

3. **Extract Values**:
From the comparison, we can identify:
- Peak Voltage \( V_0 = 100\sqrt{2} \)
- Angular Frequency \( \omega = 100\pi \)

4. **Calculate the RMS Value**:
The RMS value of the voltage is given by the formula:
\[ V_{rms} = \frac{V_0}{\sqrt{2}} \]
Substituting the value of \( V_0 \):
\[ V_{rms} = \frac{100\sqrt{2}}{\sqrt{2}} = 100 \text{ volts} \]

5. **Calculate the Frequency**:
The relationship between angular frequency \( \omega \) and frequency \( f \) is given by:
\[ \omega = 2\pi f \]
Substituting the value of \( \omega \):
\[ 100\pi = 2\pi f \]
Dividing both sides by \( 2\pi \):
\[ f = \frac{100\pi}{2\pi} = 50 \text{ Hz} \]

6. **Final Results**:
Therefore, the RMS value of the voltage is \( 100 \text{ volts} \) and the frequency is \( 50 \text{ Hz} \).

### Summary:
- RMS Voltage: \( 100 \text{ volts} \)
- Frequency: \( 50 \text{ Hz} \)