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 a capacitor when a battery does 200 J of work in charging it, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Work Done by the Battery**:
The work done (W) by the battery in charging the capacitor is given as 200 J. This work done is equal to the charge (Q) multiplied by the voltage (V) across the capacitor.
\[ W = Q \times V \]
Here, we have:
\[ W = 200 \, \text{J} \]

2. **Energy Stored in the Capacitor**:
The energy (U) stored in a capacitor can be calculated using the formula:
\[ U = \frac{1}{2} C V^2 \]
However, we can also express this in terms of charge (Q) and voltage (V). Since \( Q = C \times V \), we can substitute this into the energy formula:
\[ U = \frac{1}{2} Q V \]

3. **Substituting Work Done into the Energy Formula**:
From the work done by the battery, we know that \( Q \times V = 200 \, \text{J} \). Therefore, we can substitute this into our energy formula:
\[ U = \frac{1}{2} (Q \times V) = \frac{1}{2} \times 200 \, \text{J} \]

4. **Calculating the Energy Stored**:
Now, we can calculate the energy stored in the capacitor:
\[ U = \frac{1}{2} \times 200 = 100 \, \text{J} \]

5. **Conclusion**:
Thus, the energy stored in the capacitor is:
\[ U = 100 \, \text{J} \]

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