Assertion (A): When the distance between the parallel plates of a parallel plate capacitor is halved and the dielectric constant of the dielectric used is made three times, then the capacitance becomes three times.
Reason (R ): Capacitance does not depend on the nature of material.

Options

A. Both A and R are true and R is the correct explanation of A
B. Both A and R are true but R is NOT the correct explanation of A
C. A is true but R is false
D. A is false and R is True

Explanation

To solve the question, we need to analyze both the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Capacitance Formula**:
The capacitance \( C \) of a parallel plate capacitor is given by the formula:
\[ C = \frac{k \epsilon_0 A}{d} \]
where:
- \( k \) is the dielectric constant,
- \( \epsilon_0 \) is the permittivity of free space,
- \( A \) is the area of the plates,
- \( d \) is the distance between the plates.

2. **Initial Conditions**:
Let the initial dielectric constant be \( k \), the area of the plates be \( A \), and the distance between the plates be \( d \). The initial capacitance \( C_{\text{initial}} \) can be expressed as:
\[ C_{\text{initial}} = \frac{k \epsilon_0 A}{d} \]

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

4. **Calculating Final Capacitance**:
Substitute the new values into the capacitance formula:
\[ C_{\text{final}} = \frac{k' \epsilon_0 A}{d'} = \frac{3k \epsilon_0 A}{\frac{d}{2}} = \frac{3k \epsilon_0 A \cdot 2}{d} = \frac{6k \epsilon_0 A}{d} \]
This can be rewritten as:
\[ C_{\text{final}} = 6 \cdot C_{\text{initial}} \]

5. **Analyzing the Assertion**:
The assertion states that the capacitance becomes three times, but we found that the capacitance actually becomes six times the initial capacitance. Therefore, the assertion is **false**.

6. **Analyzing the Reason**:
The reason states that capacitance does not depend on the nature of the material. This is misleading because capacitance does depend on the dielectric constant \( k \), which is a property of the material used. However, it does not depend on the specific type of conductive material used for the plates. Therefore, the statement about capacitance not depending on the nature of the material is **partially true**, but not entirely accurate in this context.

7. **Conclusion**:
Since the assertion is false and the reason is true (in a limited sense), we conclude that:
- Assertion (A) is **false**.
- Reason (R) is **true**.

### Final Answer:
- The assertion is false, and the reason is true.