A parallel plate capacitor is filled with a uniform dielectric , maximum charge that can be given to it does not depends upon

Options

A. Dielectric constant of the dielectric
B. Dielectric strenth of the dielectric
C. Separtion between the plates
D. Area of the plates

Answer

To solve the problem, we need to analyze the factors affecting the maximum charge that can be stored in a parallel plate capacitor filled with a uniform dielectric.

### Step-by-Step Solution:

1. **Understanding the Capacitor**: A parallel plate capacitor consists of two plates separated by a distance \(d\). When a dielectric material is inserted between the plates, it affects the capacitor's ability to store charge.

2. **Key Parameters**:
- \(q\): Charge on the plates.
- \(A\): Area of the plates.
- \(d\): Separation between the plates.
- \(k\): Dielectric constant of the material.
- \(\epsilon_0\): Permittivity of free space.

3. **Charge Density**: The charge density \(\sigma\) on the plates is given by:
\[ \sigma = \frac{q}{A} \]

4. **Electric Field**: The electric field \(E\) between the plates of the capacitor filled with a dielectric is given by:
\[ E = \frac{\sigma}{k \epsilon_0} = \frac{q}{k A \epsilon_0} \]

5. **Dielectric Strength**: The maximum electric field strength that the dielectric can withstand without breaking down is denoted as \(E_0\).

6. **Maximum Charge**: The maximum charge \(q_{\text{max}}\) that can be stored in the capacitor is determined by the dielectric strength:
\[ E_0 = \frac{q_{\text{max}}}{k A \epsilon_0} \]
Rearranging this gives:
\[ q_{\text{max}} = k A \epsilon_0 E_0 \]

7. **Factors Affecting Maximum Charge**: From the equation \(q_{\text{max}} = k A \epsilon_0 E_0\), we can see that the maximum charge depends on:
- The dielectric constant \(k\)
- The area of the plates \(A\)
- The dielectric strength \(E_0\)

8. **Independence from Separation**: The maximum charge \(q_{\text{max}}\) does not depend on the separation \(d\) between the plates. This is because the formula does not include \(d\) as a variable.

### Conclusion:
Thus, the maximum charge that can be given to a parallel plate capacitor filled with a uniform dielectric does not depend on the separation between the plates.