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. Separation between the plates
D. Area of the plates

Answer

To solve the question regarding the maximum charge that can be given to a parallel plate capacitor filled with a uniform dielectric, we need to analyze the factors that influence this maximum charge.

### Step-by-Step Solution:

1. **Understanding the Capacitor with Dielectric**:
A parallel plate capacitor consists of two plates separated by a distance, and when a dielectric material is introduced between the plates, it affects the capacitor's ability to store charge.

2. **Dielectric Constant (k)**:
The dielectric constant (k) is a measure of how much the dielectric material reduces the electric field within the capacitor. It is a crucial factor in determining the capacitance of the capacitor when a dielectric is present.

3. **Capacitance with Dielectric**:
The capacitance (C) of a parallel plate capacitor filled with a dielectric is given by:
\[ C = \frac{k \epsilon_0 A}{d} \]
where:
- \( \epsilon_0 \) is the permittivity of free space,
- \( A \) is the area of the plates,
- \( d \) is the separation between the plates.

4. **Maximum Charge (Q)**:
The maximum charge (Q) that can be stored in the capacitor is given by:
\[ Q = C \cdot V \]
where \( V \) is the voltage across the capacitor. Substituting the expression for capacitance, we have:
\[ Q = \frac{k \epsilon_0 A}{d} \cdot V \]

5. **Factors Affecting Maximum Charge**:
From the equation \( Q = \frac{k \epsilon_0 A}{d} \cdot V \), we can see that the maximum charge depends on:
- The dielectric constant (k),
- The area of the plates (A),
- The voltage (V),
- The separation between the plates (d).

6. **Identifying the Independent Factor**:
The question asks for the factor that does not affect the maximum charge. Among the factors listed, the maximum charge does not depend on the **separation (d)** of the plates. This is because, while the capacitance is inversely proportional to the separation, the maximum charge is influenced by the voltage applied, which can be adjusted independently of the separation.

### 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.

### Final Answer:
The maximum charge that can be given to the capacitor does not depend on the separation of the plates (d).

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