A battery does 200 J of work in charging a capacitor. The energy stored is

Options

A. 200 J
B. 100 J
C. 50 J
D. 400 J

Answer

To find the energy stored in the capacitor when a battery does 200 J of work in charging it, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between work done and energy stored**:
The work done by the battery (W) in charging the capacitor is related to the energy (U) stored in the capacitor. The formula for the energy stored in a capacitor is:
\[ U = \frac{1}{2} CV^2 \]
where \(C\) is the capacitance and \(V\) is the voltage across the capacitor.

2. **Relate work done to energy stored**:
The work done by the battery in charging the capacitor is equal to the energy stored in the capacitor plus any energy lost in the process. However, for an ideal capacitor, the energy stored is half of the work done by the battery:
\[ U = \frac{1}{2} W \]

3. **Substitute the given value of work done**:
Here, the work done by the battery is given as 200 J. Therefore, we can substitute this value into the equation:
\[ U = \frac{1}{2} \times 200 \, \text{J} \]

4. **Calculate the energy stored**:
Now, perform the calculation:
\[ U = 100 \, \text{J} \]

5. **Conclusion**:
The energy stored in the capacitor is 100 J.

### Final Answer:
The energy stored in the capacitor is **100 J**.