The capacitance of a capacitor depends on

Options

A. Charge
B. Voltage
C. Only on geometrical dimensions and material in space between plates of the capacitor
D. None of these

Answer

To determine the factors on which the capacitance of a capacitor depends, we can analyze the relationship between charge, voltage, and the physical characteristics of the capacitor.

### Step-by-Step Solution:

1. **Understanding Capacitance**:
- Capacitance (C) is defined as the ratio of the charge (Q) stored on one plate of the capacitor to the voltage (V) across the plates. Mathematically, it is expressed as:
\[ C = \frac{Q}{V} \]
- This equation shows that capacitance is a measure of how much charge a capacitor can store per unit voltage.

2. **Identifying Constants**:
- In the equation \(C = \frac{Q}{V}\), both charge (Q) and voltage (V) can vary, but capacitance (C) is a constant for a given capacitor under specific conditions. Thus, capacitance does not depend on the charge or voltage directly.

3. **Factors Affecting Capacitance**:
- The capacitance of a capacitor is influenced by its physical characteristics:
- **Area of the Plates (A)**: The larger the area of the plates, the greater the capacitance. This is because a larger area allows more charge to be stored.
- **Distance Between the Plates (d)**: The capacitance decreases as the distance between the plates increases. This is because a larger distance reduces the electric field strength.
- **Dielectric Material**: The presence of a dielectric material between the plates affects capacitance. The dielectric constant (ε) of the material increases the capacitance compared to a vacuum.

4. **Capacitance Formula**:
- The capacitance can be expressed with the formula:
\[ C = \frac{\varepsilon A}{d} \]
- Here, \( \varepsilon \) is the permittivity of the dielectric material (which includes the permittivity of free space, \( \varepsilon_0 \), and the dielectric constant of the material).

5. **Conclusion**:
- From the analysis, we conclude that the capacitance of a capacitor depends on:
- The area of the plates (A)
- The distance between the plates (d)
- The dielectric material between the plates (ε)

### Final Answer:
The capacitance of a capacitor depends on the geometrical dimensions (area and distance between plates) and the dielectric material between the plates.