Assertion : When an uncharged capacitor is charged by a battery only `50%` of the energy supplied is stored in the capacitor.
Reason : Rest `50%` is lost.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question, we need to analyze the assertion and the reason provided regarding the energy stored in a capacitor when charged by a battery.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
The assertion states that when an uncharged capacitor is charged by a battery, only 50% of the energy supplied is stored in the capacitor.

2. **Understanding the Reason**:
The reason provided states that the rest 50% of the energy is lost.

3. **Energy Supplied by the Battery**:
When a capacitor of capacitance \( C \) is charged by a battery of voltage \( V \), the total charge \( Q \) on the capacitor is given by:
\[ Q = CV \]
The work done (or energy supplied) by the battery to charge the capacitor is:
\[ W = Q \cdot V = CV \cdot V = CV^2 \]

4. **Energy Stored in the Capacitor**:
The potential energy \( U \) stored in a capacitor is given by the formula:
\[ U = \frac{1}{2} CV^2 \]

5. **Calculating the Energy Loss**:
To find the energy lost, we can compare the energy supplied by the battery to the energy stored in the capacitor:
- Energy supplied by the battery: \( CV^2 \)
- Energy stored in the capacitor: \( \frac{1}{2} CV^2 \)

The energy lost can be calculated as:
\[ \text{Energy lost} = \text{Energy supplied} - \text{Energy stored} = CV^2 - \frac{1}{2} CV^2 = \frac{1}{2} CV^2 \]

6. **Conclusion**:
From the above calculations, we see that indeed only 50% of the energy supplied by the battery is stored in the capacitor, while the other 50% is lost (usually as heat due to resistance in the circuit). Therefore, both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer:
- Both the assertion and reason are true, and the reason is the correct explanation for the assertion.

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