If an alternating voltage is represented as v = 300 sin 600 t then the arms value of the voltage and the frequency are respectively :

Options

A. 141 V, 628 Hz
B. 100 V, 50 Hz
C. 100V,100 Hz
D. None of these

Answer

To solve the problem, we need to find the RMS (Root Mean Square) value of the voltage and the frequency from the given alternating voltage equation \( v = 300 \sin(600t) \).

### Step-by-Step Solution:

1. **Identify the Peak Voltage**:
The given voltage equation is \( v = 300 \sin(600t) \). Here, the coefficient of the sine function (300) represents the peak voltage \( V_0 \).
\[ V_0 = 300 \, \text{volts} \]

2. **Calculate the RMS Voltage**:
The RMS value of an AC voltage is given by the formula:
\[ V_{\text{RMS}} = \frac{V_0}{\sqrt{2}} \]
Substituting the value of \( V_0 \):
\[ V_{\text{RMS}} = \frac{300}{\sqrt{2}} \approx \frac{300}{1.414} \approx 212.16 \, \text{volts} \]

3. **Determine the Angular Frequency**:
The angular frequency \( \omega \) is given in the equation as 600 rad/s. We know that:
\[ \omega = 2\pi f \]
Setting \( \omega = 600 \):
\[ 600 = 2\pi f \]

4. **Calculate the Frequency**:
Rearranging the equation to solve for \( f \):
\[ f = \frac{600}{2\pi} \]
Substituting the value of \( \pi \) (approximately 3.1416):
\[ f \approx \frac{600}{2 \times 3.1416} \approx \frac{600}{6.2832} \approx 95.5 \, \text{hertz} \]

5. **Final Results**:
The RMS value of the voltage is approximately \( 212.16 \, \text{volts} \) and the frequency is approximately \( 95.5 \, \text{hertz} \).

### Summary of Results:
- RMS Voltage: \( 212.16 \, \text{volts} \)
- Frequency: \( 95.5 \, \text{hertz} \)