Which of the following methods will reduce the capacitance of a parallel plate capacitor ?

Options

A. Converting another capacitor in series with this
B. Reducing the potential difference between the plates
C. Introducing a dielectric slab between the plates
D. Introducing a metal pltes of suitable thickness

Answer

To determine which method will reduce the capacitance of a parallel plate capacitor, we can analyze the options provided based on the formula for capacitance.

### Step-by-Step Solution:

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

2. **Analyzing Option A: Connecting Another Capacitor in Series**:
When capacitors are connected in series, the equivalent capacitance \( C_{eq} \) is given by:
\[ \frac{1}{C_{eq}} = \frac{1}{C_1} + \frac{1}{C_2} \]
For two capacitors of the same capacitance \( C \):
\[ C_{eq} = \frac{C \cdot C}{C + C} = \frac{C}{2} \]
This shows that connecting another capacitor in series reduces the capacitance to half. Thus, Option A reduces capacitance.

3. **Analyzing Option B: Reducing the Potential Difference**:
The capacitance \( C \) is independent of the potential difference \( V \). It is a property determined by the physical characteristics of the capacitor (area and distance between plates). Therefore, reducing the potential difference does not affect the capacitance. Thus, Option B does not reduce capacitance.

4. **Analyzing Option C: Introducing a Dielectric Slab**:
When a dielectric slab is inserted between the plates, the capacitance increases. The new capacitance \( C' \) is given by:
\[ C' = K \cdot \frac{\epsilon_0 A}{D} \]
where \( K \) is the dielectric constant (greater than or equal to 1). Thus, Option C does not reduce capacitance.

5. **Analyzing Option D: Introducing a Metal Plate**:
Introducing a metal plate effectively reduces the distance between the plates. The capacitance with a metal plate of thickness \( T \) is given by:
\[ C'' = \frac{\epsilon_0 A}{D - T} \]
Since \( D - T < D \), the capacitance increases. Thus, Option D does not reduce capacitance.

### Conclusion:
The only method that reduces the capacitance of a parallel plate capacitor is **Option A: Connecting another capacitor in series**.