If in a parallel capacitor, which is connected to a battery we fill in whole space of its plates, then which of the following increases?

Options

A. Q and V
B. V and E
C. E and C
D. Q and C

Explanation

To solve the question regarding the effect of filling the space between the plates of a parallel plate capacitor with a dielectric while it is connected to a battery, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Capacitor Configuration**:
- A parallel plate capacitor consists of two conductive plates separated by a distance \( D \). When connected to a battery, it maintains a constant potential difference \( V \).

2. **Capacitance of a Parallel Plate Capacitor**:
- The capacitance \( C \) of a parallel plate capacitor without a dielectric is given by the formula:
\[ C = \frac{\varepsilon_0 A}{D} \]
where \( \varepsilon_0 \) is the permittivity of free space, \( A \) is the area of the plates, and \( D \) is the separation between the plates.

3. **Effect of Inserting a Dielectric**:
- When a dielectric material with dielectric constant \( k \) is inserted between the plates, the capacitance increases to:
\[ C' = kC \]
- This means that the new capacitance \( C' \) is greater than the original capacitance \( C \).

4. **Charge on the Capacitor**:
- The charge \( Q \) stored in the capacitor is related to capacitance and potential difference by the equation:
\[ Q = CV \]
- Since the capacitor is connected to a battery, the potential difference \( V \) remains constant.

5. **Impact of Increased Capacitance**:
- With the dielectric inserted, the new charge \( Q' \) on the capacitor becomes:
\[ Q' = C'V = (kC)V = k(Q) \]
- This indicates that the charge \( Q' \) also increases because \( C' > C \).

6. **Conclusion**:
- Therefore, when a dielectric is introduced into a parallel plate capacitor connected to a battery, the capacitance \( C \) and the charge \( Q \) both increase, while the potential difference \( V \) remains constant.

### Final Answer:
The quantities that increase when a dielectric is filled in the space between the plates of a parallel plate capacitor connected to a battery are:
- Capacitance \( C \)
- Charge \( Q \)