In a parallel plate capacitor , the capacity increases if

Options

A. area of the plate is decreased
B. distance between the plates increases
C. area of the plate is increased
D. dielectric constant decreases.

Explanation

To solve the question regarding how the capacity of a parallel plate capacitor increases, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Capacitance**:
The capacitance \( C \) of a parallel plate capacitor is given by the formula:
\[ C = \frac{K \varepsilon_0 A}{d} \]
where:
- \( C \) is the capacitance,
- \( K \) is the dielectric constant,
- \( \varepsilon_0 \) is the permittivity of free space,
- \( A \) is the area of one of the plates, and
- \( d \) is the distance between the plates.

2. **Analyze the Factors Affecting Capacitance**:
- From the formula, we can see that capacitance \( C \) is directly proportional to the area \( A \) of the plates and inversely proportional to the distance \( d \) between them.
- This means that if the area \( A \) increases, the capacitance \( C \) increases, and if the distance \( d \) decreases, the capacitance \( C \) also increases.

3. **Evaluate the Options**:
- **Option 1**: If the area of the plates is decreased, this would lead to a decrease in capacitance. Thus, this option is incorrect.
- **Option 2**: If the distance between the plates increases, this would lead to a decrease in capacitance. Thus, this option is also incorrect.
- **Option 3**: If the dielectric constant \( K \) is increased (assuming a dielectric material is introduced), the capacitance will increase since \( C \) is directly proportional to \( K \). This option is correct.

4. **Conclusion**:
The capacity of a parallel plate capacitor increases if:
- The area of the plates increases, or
- The distance between the plates decreases, or
- The dielectric constant \( K \) increases.

### Final Answer:
The capacity of a parallel plate capacitor increases if the area of the plates is increased or the distance between the plates is decreased.

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