STATEMENT 1: Energy stored in the capacitor is less than the energy battery during the charging of capacitor. because
STATEMENT-2: Some of the energy is converted into heat.

Options

A. Statement-1 is True , Statement-2 is True , Statement-2 is a correct explanation for Statement-1.
B. Statement-1 is True , Statement-2 is True , Statement-2 is NOT a correct explanation for Statement-1.
C. Statement-1 is True , Statement-2 is False
D. Statement-1 is False , Statement-2 is True

Answer

To solve the question, we need to analyze the two statements provided:

**Statement 1:** Energy stored in the capacitor is less than the energy provided by the battery during the charging of the capacitor.

**Statement 2:** Some of the energy is converted into heat.

### Step-by-Step Solution:

1. **Understanding the Energy Stored in a Capacitor:**
The energy (U) stored in a capacitor with capacitance \( C \) and voltage \( V \) is given by the formula:
\[ U = \frac{1}{2} C V^2 \]

2. **Understanding the Energy Provided by the Battery:**
When a battery provides charge \( Q \) to the capacitor, the work done (W) by the battery is given by:
\[ W = Q \cdot V \]
Since the charge \( Q \) on the capacitor is related to capacitance and voltage by \( Q = C V \), we can substitute this into the work done:
\[ W = C V \cdot V = C V^2 \]

3. **Comparing the Two Energies:**
Now we compare the energy stored in the capacitor and the energy provided by the battery:
- Energy stored in the capacitor: \( U = \frac{1}{2} C V^2 \)
- Energy provided by the battery: \( W = C V^2 \)

From this, we can see that:
\[ W - U = C V^2 - \frac{1}{2} C V^2 = \frac{1}{2} C V^2 \]
This shows that the energy provided by the battery is greater than the energy stored in the capacitor.

4. **Understanding Energy Loss:**
The difference in energy \( \frac{1}{2} C V^2 \) represents the energy that is lost in the circuit, primarily due to resistive heating (Joule heating) in the wires and components during the charging process.

5. **Conclusion:**
- **Statement 1** is true: The energy stored in the capacitor is indeed less than the energy provided by the battery.
- **Statement 2** is also true: The energy loss due to heat explains why the energy stored in the capacitor is less than the energy supplied by the battery.

### Final Answer:
Both statements are true, and Statement 2 provides the correct explanation for Statement 1.

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