The capacity of a parallel plate condenser depends upon

Options

A. the type of metal used for the thickness of plates
B. the potential applied across on the plates
C. the separation between the plates
D. All of these

Answer

To determine what the capacity (capacitance) of a parallel plate capacitor depends on, we can analyze the relationship between charge, potential difference, and the physical characteristics of the capacitor.

### Step-by-Step Solution:

1. **Understanding the Capacitor**:
A parallel plate capacitor consists of two conductive plates separated by a distance. When a voltage (potential difference) is applied across the plates, one plate accumulates positive charge (Q) and the other accumulates negative charge (-Q).

2. **Electric Field Calculation**:
The electric field (E) between the plates of a parallel plate capacitor can be derived from the surface charge density (σ) and is given by:
\[ E = \frac{\sigma}{\epsilon_0} \]
where \(\sigma = \frac{Q}{A}\) (Q is the charge on one plate and A is the area of the plates) and \(\epsilon_0\) is the permittivity of free space.

3. **Potential Difference**:
The potential difference (V) across the plates is related to the electric field and the separation (d) between the plates:
\[ V = E \cdot d \]
Substituting for E, we have:
\[ V = \frac{Q}{\epsilon_0 A} \cdot d \]

4. **Capacitance Definition**:
The capacitance (C) of the capacitor is defined as the ratio of charge (Q) to the potential difference (V):
\[ C = \frac{Q}{V} \]
Substituting the expression for V, we get:
\[ C = \frac{Q}{\frac{Q \cdot d}{\epsilon_0 A}} = \frac{\epsilon_0 A}{d} \]

5. **Conclusion on Dependence**:
From the final expression \(C = \frac{\epsilon_0 A}{d}\), we can see that the capacitance depends on:
- **Area (A)** of the plates: Larger area increases capacitance.
- **Distance (d)** between the plates: Greater distance decreases capacitance.
- **Permittivity (\(\epsilon_0\))**: This is a constant for free space, but if a dielectric material is used, the capacitance will depend on the dielectric constant of that material.

### Final Answer:
The capacity of a parallel plate condenser depends on:
- The area of the plates (A)
- The separation between the plates (d)
- The type of dielectric material used between the plates (if any)