Assertion: If the distance between parallel plates of a capacitor is halved and dielectric constant is made three times, then the capacitor becomes `6` times.
Reason: Capacity of the capacitor does not depend upon the nature of the meterial.

Options

A. If both assertion and reason are true and reson is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If the assertion is true but the reason are false.
D. If both the assertion and reason are false.

Explanation

To solve the problem, we need to analyze both the assertion and the reason provided in the question regarding the capacitor.

### Step 1: Understanding the Assertion
The assertion states that if the distance between the parallel plates of a capacitor is halved and the dielectric constant is made three times, then the capacitance becomes 6 times.

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

### Step 2: Initial Capacitance
Let the initial capacitance be:
\[ C_1 = \frac{k \varepsilon_0 A}{d} \]

### Step 3: New Capacitance After Changes
If the distance \( d \) is halved, then \( d' = \frac{d}{2} \). If the dielectric constant is tripled, then \( k' = 3k \).

The new capacitance \( C_2 \) can be calculated as:
\[ C_2 = \frac{k' \varepsilon_0 A}{d'} = \frac{3k \varepsilon_0 A}{\frac{d}{2}} = \frac{3k \varepsilon_0 A \cdot 2}{d} = \frac{6k \varepsilon_0 A}{d} \]

### Step 4: Comparing Capacitances
Now, we can compare the new capacitance \( C_2 \) with the initial capacitance \( C_1 \):
\[ C_2 = 6 \cdot \frac{k \varepsilon_0 A}{d} = 6C_1 \]
Thus, the assertion is true.

### Step 5: Understanding the Reason
The reason states that the capacity of the capacitor does not depend upon the nature of the material. This statement is misleading. While the capacitance does depend on the area and distance, it also depends on the dielectric constant \( k \), which is a property of the material.

### Conclusion
- The assertion is **true**: The capacitance becomes 6 times.
- The reason is **false**: The capacitance does depend on the nature of the material through the dielectric constant.

### Final Answer
- Assertion: True
- Reason: False