The capacitance of a parallel plate capacitor can be increased by

Options

A. increasing the area of the plates.
B. decreasing the distances between the plates.
C. using a dielectric of higher permittivity.
D. all the above.

Answer

To solve the question regarding how to increase the capacitance of a parallel plate capacitor, we will analyze the factors that affect capacitance based on the formula for a parallel plate capacitor.

### Step-by-step Solution:

1. **Understand the Formula for Capacitance**:
The capacitance \( C \) of a parallel plate capacitor is given by the formula:
\[ C = \frac{A \epsilon_0}{d} \]
where:
- \( C \) is the capacitance,
- \( A \) is the area of one of the plates,
- \( \epsilon_0 \) is the permittivity of free space (a constant related to the dielectric material),
- \( d \) is the distance between the plates.

2. **Analyze the Effect of Increasing the Area of the Plates**:
- From the formula, we see that capacitance \( C \) is directly proportional to the area \( A \).
- Therefore, if we **increase the area of the plates**, the capacitance will also **increase**.
- **Conclusion**: This option is correct.

3. **Analyze the Effect of Decreasing the Distance Between the Plates**:
- The formula shows that capacitance \( C \) is inversely proportional to the distance \( d \).
- Thus, if we **decrease the distance between the plates**, the capacitance will **increase**.
- **Conclusion**: This option is also correct.

4. **Analyze the Effect of Using a Dielectric of Higher Permittivity**:
- The capacitance \( C \) is directly proportional to the permittivity \( \epsilon_0 \).
- If we use a dielectric material with a higher permittivity, the capacitance will **increase**.
- **Conclusion**: This option is correct as well.

5. **Conclusion**:
- Since all three options (increasing area of the plates, decreasing distance between the plates, and using a dielectric of higher permittivity) lead to an increase in capacitance, the correct answer is:
\[ \text{D. All of the above} \]