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 will analyze each option provided in the question.

### Step-by-Step Solution:

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

2. **Option 1: Converting Another Capacitor in Series**:
When two 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 identical capacitors \( C \):
\[ \frac{1}{C_{eq}} = \frac{1}{C} + \frac{1}{C} = \frac{2}{C} \]
Thus, \( C_{eq} = \frac{C}{2} \). This shows that the capacitance is reduced when capacitors are connected in series.

3. **Option 2: Reducing the Potential Difference Between the Plates**:
The potential difference \( V \) does not affect the capacitance \( C \) of the capacitor. Capacitance is a function of the physical characteristics of the capacitor (area, distance, and dielectric). Therefore, this option does not reduce capacitance.

4. **Option 3: Introducing a Dielectric Slab Between the Plates**:
When a dielectric is introduced, the capacitance increases according to:
\[ C' = K \cdot C \]
where \( K \) is the dielectric constant (greater than 1). This means that introducing a dielectric slab increases the capacitance, not reduces it.

5. **Option 4: Introducing a Metal Plate of Suitable Thickness**:
Placing a metal plate between the capacitor plates effectively creates two capacitors in series (the original capacitor and the capacitor formed by the metal plate and one of the original plates). This also results in an increase in capacitance, as the effective distance between the plates is reduced.

### Conclusion:
The only method that will reduce the capacitance of a parallel plate capacitor is **Option 1: Converting another capacitor in series with this**.