A capacitor of capacitance `1 muF` is charged by a battery, and the energy stored is U.
If the capacitor is charged to 30 V, the energy stored U, is :

Options

A. `450 muJ`
B. `150 muJ`
C. `300 muJ`
D. `500 muJ`

Explanation

To solve the problem of finding the energy stored in a capacitor, we can follow these steps:

### Step 1: Understand the given values
We are given:
- Capacitance \( C = 1 \mu F = 1 \times 10^{-6} F \)
- Voltage \( V = 30 V \)

### Step 2: Use the formula for energy stored in a capacitor
The energy \( U \) stored in a capacitor is given by the formula:
\[ U = \frac{1}{2} C V^2 \]

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ U = \frac{1}{2} \times (1 \times 10^{-6} F) \times (30 V)^2 \]

### Step 4: Calculate \( V^2 \)
First, calculate \( V^2 \):
\[ 30^2 = 900 \]

### Step 5: Substitute \( V^2 \) back into the equation
Now substitute \( 900 \) back into the energy formula:
\[ U = \frac{1}{2} \times (1 \times 10^{-6}) \times 900 \]

### Step 6: Perform the multiplication
Calculating the multiplication:
\[ U = \frac{1}{2} \times 900 \times 10^{-6} \]
\[ U = 450 \times 10^{-6} \text{ Joules} \]

### Step 7: Convert to microjoules
Since \( 1 \text{ Joule} = 10^6 \text{ microjoules} \), we can write:
\[ U = 450 \text{ microjoules} \]

### Conclusion
Thus, the energy stored in the capacitor is:
\[ U = 450 \mu J \]

### Final Answer
The correct option is **450 microjoules**.

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