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 1: Write down the known values
Given:
- \( U = 50 \, \text{J} \)
- \( C = 100 \, \mu\text{F} = 100 \times 10^{-6} \, \text{F} \)

### Step 2: Substitute the known values into the energy formula
Substituting the values into the formula:

\[ 50 = \frac{1}{2} \times (100 \times 10^{-6}) \times V^2 \]

### Step 3: Simplify the equation
Multiply both sides by 2 to eliminate the fraction:

\[ 100 = (100 \times 10^{-6}) \times V^2 \]

### Step 4: Divide both sides by \( 100 \times 10^{-6} \)
To isolate \( V^2 \):

\[ V^2 = \frac{100}{100 \times 10^{-6}} = \frac{100}{0.0001} = 10^6 \]

### Step 5: Take the square root of both sides
Now, taking the square root to find \( V \):

\[ V = \sqrt{10^6} = 1000 \, \text{V} \]

### Conclusion
The potential difference across the capacitor is:

\[ V = 1000 \, \text{V} \]