A generator produces a time varying voltage given by `V=240 sin 120 t,` where `t` is in second. The rms voltage and frequency are

Options

A. `170V` and `19 Hz`
B. `240 V` and `60 Hz`
C. `170V` and `60 Hz`
D. `120 V` and `19 Hz`

Explanation

To find the RMS voltage and frequency from the given voltage equation \( V = 240 \sin(120t) \), we can follow these steps:

### Step 1: Identify the peak voltage (\( V_0 \))
From the equation \( V = 240 \sin(120t) \), we can see that the coefficient of the sine function represents the peak voltage:
\[ V_0 = 240 \, \text{V} \]

### Step 2: Calculate the RMS voltage (\( V_{rms} \))
The RMS voltage is calculated using the formula:
\[ V_{rms} = \frac{V_0}{\sqrt{2}} \]
Substituting the value of \( V_0 \):
\[ V_{rms} = \frac{240}{\sqrt{2}} \approx \frac{240}{1.414} \approx 169.71 \, \text{V} \approx 170 \, \text{V} \]

### Step 3: Identify the angular frequency (\( \omega \))
From the equation \( V = 240 \sin(120t) \), we can see that the coefficient of \( t \) is the angular frequency:
\[ \omega = 120 \, \text{rad/s} \]

### Step 4: Calculate the frequency (\( f \))
The frequency can be calculated from the angular frequency using the formula:
\[ f = \frac{\omega}{2\pi} \]
Substituting the value of \( \omega \):
\[ f = \frac{120}{2\pi} \approx \frac{120}{6.283} \approx 19.1 \, \text{Hz} \approx 19 \, \text{Hz} \]

### Final Result
Thus, the RMS voltage and frequency are:
\[ V_{rms} \approx 170 \, \text{V}, \quad f \approx 19 \, \text{Hz} \]

---