The energy stored in a capacitor of capacitance `100 muF` is 50 J. Its potential difference is

Options

A. 50 V
B. 500 v
C. 1000 V
D. 1500 V

Answer

To find the potential difference across a capacitor given its capacitance and the energy stored, we can use the formula for the energy stored in a capacitor:

\[ U = \frac{1}{2} C V^2 \]

Where:
- \( U \) is the energy stored in the capacitor (in joules),
- \( C \) is the capacitance (in farads),
- \( V \) is the potential difference (in volts).

### Step-by-Step Solution:

1. **Identify the given values**:
- Energy stored, \( U = 50 \, \text{J} \)
- Capacitance, \( C = 100 \, \mu\text{F} = 100 \times 10^{-6} \, \text{F} = 10^{-4} \, \text{F} \)

2. **Substitute the values into the energy formula**:
\[ 50 = \frac{1}{2} \times (100 \times 10^{-6}) \times V^2 \]

3. **Multiply both sides by 2 to eliminate the fraction**:
\[ 100 = (100 \times 10^{-6}) \times V^2 \]

4. **Divide both sides by \( 100 \times 10^{-6} \)**:
\[ V^2 = \frac{100}{100 \times 10^{-6}} = \frac{100}{10^{-4}} = 100 \times 10^{4} = 10^{6} \]

5. **Take the square root of both sides to solve for \( V \)**:
\[ V = \sqrt{10^{6}} = 1000 \, \text{V} \]

### Final Answer:
The potential difference across the capacitor is \( 1000 \, \text{V} \).

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