Capacitance of a parallel plate capacitor can be increased by

Options

A. increasing the distance between the plates
B. decreasing the distance between the plates
C. decreasing the area of plates
D. increasing the thickness of the plates

Explanation

To determine how to increase the capacitance of a parallel plate capacitor, we start with the formula for capacitance:

\[ C = \frac{K \epsilon_0 A}{d} \]

where:
- \( C \) is the capacitance,
- \( K \) is the dielectric constant,
- \( \epsilon_0 \) is the permittivity of free space,
- \( A \) is the area of the plates, and
- \( d \) is the distance between the plates.

### Step-by-Step Solution:

1. **Understand the Formula**: The capacitance \( C \) is directly proportional to the area \( A \) of the plates and inversely proportional to the distance \( d \) between the plates.

2. **Analyze the Proportional Relationships**:
- Since \( C \propto A \), increasing the area \( A \) of the plates will increase the capacitance.
- Since \( C \propto \frac{1}{d} \), decreasing the distance \( d \) between the plates will also increase the capacitance.

3. **Evaluate the Options**:
- **Increasing the distance between the plates**: This will decrease the capacitance, so this option is incorrect.
- **Decreasing the distance between the plates**: This will increase the capacitance, so this option is correct.
- **Decreasing the area of the plates**: This will decrease the capacitance, so this option is incorrect.
- **Increasing the thickness of the plates**: The thickness does not affect the capacitance directly, so this option is also incorrect.

4. **Conclusion**: The capacitance of a parallel plate capacitor can be increased by decreasing the distance between the plates.

### Final Answer:
The capacitance of a parallel plate capacitor can be increased by **decreasing the distance between the plates**.

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