The emf generated by ac generator is given by `epsi=epsi_0sin210pit` . What is the frequency of emf?

Options

A. 115 Hz
B. 100 Hz
C. 105 Hz
D. 110 Hz

Explanation

To find the frequency of the emf generated by the AC generator given by the equation \( \epsilon = \epsilon_0 \sin(210 \pi t) \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Angular Frequency (ω)**:
The standard form of the equation for the emf generated by an AC generator is:
\[ \epsilon = \epsilon_0 \sin(\omega t) \]
In our case, we have:
\[ \epsilon = \epsilon_0 \sin(210 \pi t) \]
By comparing both equations, we can see that:
\[ \omega = 210 \pi \]

2. **Calculate the Time Period (T)**:
The time period \( T \) is related to the angular frequency \( \omega \) by the formula:
\[ T = \frac{2\pi}{\omega} \]
Substituting the value of \( \omega \):
\[ T = \frac{2\pi}{210 \pi} \]
Here, the \( \pi \) cancels out:
\[ T = \frac{2}{210} = \frac{1}{105} \text{ seconds} \]

3. **Calculate the Frequency (f)**:
The frequency \( f \) is the reciprocal of the time period:
\[ f = \frac{1}{T} \]
Substituting the value of \( T \):
\[ f = \frac{1}{\frac{1}{105}} = 105 \text{ Hz} \]

### Conclusion:
The frequency of the emf generated by the AC generator is \( 105 \text{ Hz} \).

### Final Answer:
The correct option is **105 Hz**.