An A.C. generator generating an e.m.f of `epsilon =300 sin (100pi)` t is connected to a series combination of `16muF` capacitor, 1 H inductor and 100 `Omega` resistor. What is the frequency of A.C.?

Options

A. 100 Hz
B. 50 Hz
C. 300 Hz
D. 25 Hz

Explanation

To find the frequency of the alternating current (A.C.) generated by the A.C. generator, we can follow these steps:

### Step 1: Identify the given equation
The equation for the electromotive force (e.m.f) generated by the A.C. generator is given as:
\[ \epsilon = 300 \sin(100\pi t) \]

### Step 2: Compare with the standard form
The standard form of the A.C. voltage equation is:
\[ \epsilon = E_0 \sin(\omega t) \]
where \(E_0\) is the peak voltage and \(\omega\) is the angular frequency.

From the given equation, we can identify:
- \(E_0 = 300\) volts
- \(\omega = 100\pi\) rad/s

### Step 3: Calculate the frequency
The relationship between angular frequency (\(\omega\)) and frequency (\(f\)) is given by:
\[ \omega = 2\pi f \]
To find the frequency \(f\), we can rearrange the equation:
\[ f = \frac{\omega}{2\pi} \]

### Step 4: Substitute the value of \(\omega\)
Now, substituting the value of \(\omega\):
\[ f = \frac{100\pi}{2\pi} \]

### Step 5: Simplify the expression
The \(\pi\) terms cancel out:
\[ f = \frac{100}{2} = 50 \text{ Hz} \]

### Conclusion
The frequency of the alternating current is:
\[ \boxed{50 \text{ Hz}} \]