Assertion : If the distance between parallel plates of a capacitor is halved and dielectric constant is made three times, then the capacitance becomes 6 times.
Reason : Capacity of the capacitor depends upon the nature of the material between the plates.

Options

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

Answer

To solve the problem, we need to analyze the assertion and the reason provided regarding the capacitance of a capacitor.

### Step-by-Step Solution:

1. **Understanding Capacitance Formula**:
The capacitance \( C \) of a parallel plate capacitor is given by the formula:
\[ C = \frac{A \cdot \varepsilon}{d} \]
where:
- \( A \) is the area of the plates,
- \( \varepsilon \) is the permittivity of the material between the plates, given by \( \varepsilon = \varepsilon_0 \cdot k \), where \( \varepsilon_0 \) is the permittivity of free space and \( k \) is the dielectric constant,
- \( d \) is the distance between the plates.

2. **Initial Conditions**:
Let the initial capacitance be \( C_0 \):
\[ C_0 = \frac{A \cdot \varepsilon_0 \cdot k}{d} \]

3. **New Conditions**:
According to the assertion, the distance \( d \) is halved, and the dielectric constant \( k \) is tripled. Thus, the new distance \( d' = \frac{d}{2} \) and the new dielectric constant \( k' = 3k \).

4. **Calculating New Capacitance**:
The new capacitance \( C \) can be calculated as:
\[ C = \frac{A \cdot \varepsilon_0 \cdot k'}{d'} = \frac{A \cdot \varepsilon_0 \cdot (3k)}{\frac{d}{2}} = \frac{A \cdot \varepsilon_0 \cdot 3k \cdot 2}{d} = \frac{6A \cdot \varepsilon_0 \cdot k}{d} \]
Thus, we can express \( C \) in terms of \( C_0 \):
\[ C = 6 \cdot C_0 \]

5. **Conclusion on Assertion**:
The assertion states that the capacitance becomes 6 times, which we have confirmed to be true.

6. **Analyzing the Reason**:
The reason states that the capacity of the capacitor depends upon the nature of the material between the plates. While it is true that the dielectric constant \( k \) (which is related to the material) affects capacitance, the formula shows that capacitance also depends on the area \( A \) and the distance \( d \). Therefore, the statement is misleading since capacitance is not solely dependent on the nature of the material but also on these other factors.

7. **Final Answer**:
- **Assertion**: True
- **Reason**: False