Statement-1: If the plates of a capacitor are connected through a conducting wire, then its capacitance becomes infinite.
Statement-2: The capacitors cannot be charged.

Options

A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for statement-1
B. Statement-2 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 analyze the statements given in the question, we will break down the reasoning step by step.

### Step-by-Step Solution:

1. **Understanding Capacitance**:
- Capacitance (C) of a capacitor is defined as the ratio of the charge (Q) stored on one plate to the potential difference (V) between the plates. Mathematically, it is given by:
\[ C = \frac{Q}{V} \]

2. **Connecting the Plates with a Wire**:
- When the plates of a capacitor are connected by a conducting wire, they are effectively short-circuited. This means that there is no potential difference (V) across the plates because the wire allows charges to move freely between the plates.

3. **Effect on Charge**:
- Since the plates are shorted, any charge that might have been present on the plates will redistribute until both plates have the same potential. Therefore, the charge on the plates becomes zero, leading to:
\[ Q = 0 \]

4. **Calculating Capacitance After Shorting**:
- Substituting \(Q = 0\) into the capacitance formula:
\[ C = \frac{Q}{V} = \frac{0}{V} = 0 \]
- Hence, the capacitance becomes zero, not infinite.

5. **Electric Field Between the Plates**:
- The electric field (E) between the plates of a capacitor is given by:
\[ E = \frac{\sigma}{\epsilon_0} \]
- Where \(\sigma\) is the surface charge density. After shorting the plates, \(\sigma\) becomes zero, leading to:
\[ E = 0 \]

6. **Conclusion on Statements**:
- **Statement 1**: "If the plates of a capacitor are connected through a conducting wire, then its capacitance becomes infinite." - This statement is **False**; the capacitance becomes zero.
- **Statement 2**: "The capacitors cannot be charged." - This statement is **True**; the capacitor cannot be charged because the potential difference is zero.

7. **Final Evaluation**:
- Both statements are not correct in the context of the explanation. Statement 2 is true, but it does not explain why Statement 1 is false. Therefore, the correct conclusion is that Statement 1 is false and Statement 2 is true, but Statement 2 does not correctly explain Statement 1.

### Final Answer:
- **Answer**: Statement 1 is false, Statement 2 is true, but Statement 2 is not the correct explanation for Statement 1.