An ac. generator generates an e.m.f.'e' given by: e = 311 sin (100 `pit`) volt.
The frequency of emf generated by a.c generator is:

Options

A. 60 Hz
B. 55 Hz
C. 50 Hz
D. 70 Hz

Explanation

To find the frequency of the e.m.f. generated by the AC generator, we start with the given equation for the e.m.f.:

\[ e = 311 \sin(100 \pi t) \, \text{volts} \]

### Step 1: Identify the angular frequency (ω)
The standard form of the equation for an alternating current (AC) generator is:

\[ e = e_0 \sin(\omega t) \]

where \( \omega \) is the angular frequency in radians per second. By comparing the given equation with the standard form, we can see that:

\[ \omega = 100 \pi \, \text{radians/second} \]

### Step 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 \( \omega \):

\[ T = \frac{2\pi}{100 \pi} \]

### Step 3: Simplify the time period
Now, we simplify the expression:

\[ T = \frac{2}{100} = \frac{1}{50} \, \text{seconds} \]

### Step 4: Calculate the frequency (f)
The frequency \( f \) is the reciprocal of the time period \( T \):

\[ f = \frac{1}{T} \]

Substituting the value of \( T \):

\[ f = \frac{1}{\frac{1}{50}} = 50 \, \text{Hz} \]

### Conclusion
Thus, the frequency of the e.m.f. generated by the AC generator is:

\[ \boxed{50 \, \text{Hz}} \]

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