Find the energy stored in a capacitor of capacitance `100muF ` when it is charged to a potential difference of 20 V.

Options

A. `0.02 J`
B. `0.04 J`
C. `0.01 J`
D. `0.05 J`

Explanation

To find the energy stored in a capacitor, we can use the formula:

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

where:
- \( U \) is the energy stored in the capacitor,
- \( C \) is the capacitance of the capacitor,
- \( V \) is the potential difference across the capacitor.

### Step 1: Identify the given values
- Capacitance \( C = 100 \, \mu F = 100 \times 10^{-6} \, F \)
- Potential difference \( V = 20 \, V \)

### Step 2: Substitute the values into the formula
Now we can substitute the values of \( C \) and \( V \) into the energy formula:

\[ U = \frac{1}{2} (100 \times 10^{-6} \, F) (20 \, V)^2 \]

### Step 3: Calculate \( V^2 \)
First, calculate \( V^2 \):

\[ V^2 = (20 \, V)^2 = 400 \, V^2 \]

### Step 4: Substitute \( V^2 \) back into the equation
Now substitute \( V^2 \) back into the equation for \( U \):

\[ U = \frac{1}{2} (100 \times 10^{-6}) (400) \]

### Step 5: Calculate \( U \)
Now perform the multiplication:

\[ U = \frac{1}{2} (100 \times 400 \times 10^{-6}) = \frac{1}{2} (40000 \times 10^{-6}) = 20000 \times 10^{-6} \, J \]

### Step 6: Convert to Joules
Finally, convert \( 20000 \times 10^{-6} \, J \) to standard form:

\[ U = 0.02 \, J \]

### Final Answer
The energy stored in the capacitor is:

\[ U = 0.02 \, J \]

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