If a capacitor of `8 mu F` is connected to a 220 V, 100 Hz ac source and the current passing through it is 65 mA, then the rms voltage across it is

Options

A. `129.4 V`
B. `12.94 V`
C. `1.294 V`
D. 15 V

Explanation

To find the RMS voltage across a capacitor connected to an AC source, we can follow these steps:

### Step 1: Identify the given values
- Capacitance (C) = 8 µF = \(8 \times 10^{-6}\) F
- Frequency (f) = 100 Hz
- Current (I_rms) = 65 mA = \(65 \times 10^{-3}\) A

### Step 2: Calculate the capacitive reactance (X_c)
The formula for capacitive reactance is given by:
\[ X_c = \frac{1}{2 \pi f C} \]
Substituting the values into the formula:
\[ X_c = \frac{1}{2 \pi \times 100 \times 8 \times 10^{-6}} \]
Calculating this:
\[ X_c = \frac{1}{2 \pi \times 100 \times 8 \times 10^{-6}} \approx 199 \, \Omega \]

### Step 3: Calculate the RMS voltage (V_rms)
The formula for RMS voltage across the capacitor is:
\[ V_{rms} = I_{rms} \times X_c \]
Substituting the values:
\[ V_{rms} = 65 \times 10^{-3} \times 199 \]
Calculating this:
\[ V_{rms} \approx 12.94 \, V \]

### Final Answer
The RMS voltage across the capacitor is approximately **12.94 V**.

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