If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then

A. the charge stored in it, increases.

B. the energy stored in it, decreases.

C. its capacitance increases.

D. the ratio of charge to its potential remains the same.

E. the product of charge and voltage increases.

Choose the most appropriate answer from the options given below:

The correct option is A, C and E only.

Let us analyze the behavior of the parallel plate capacitor step-by-step when its plates are moved closer to each other while it remains connected to a battery:

1. Potential Difference (Voltage, V):
Since the capacitor remains connected to the battery, the potential difference $V$ across its plates remains constant (i.e., $V=\text{constant}$).

2. Capacitance (C):
The capacitance of a parallel plate capacitor is given by the formula:
$C=\frac{{\epsilon }_{0}A}{d}$
where ${\epsilon }_0$ is the permittivity of free space, $A$ is the area of the plates, and $d$ is the separation between the plates. When the plates are moved closer, the distance $d$ decreases. Since capacitance is inversely proportional to $d$, the capacitance $C$ increases. Therefore, statement C is correct.

3. Charge Stored (Q):
The charge stored in the capacitor is given by:
$Q=CV$
Since $C$ increases and $V$ is constant, the charge $Q$ must increase. Therefore, statement A is correct.

4. Energy Stored (U):
The electrostatic energy stored in the capacitor is given by:
$U=\frac{1}{2}C{V}^2$
Since $C$ increases and $V$ is constant, the stored energy $U$ increases. Therefore, statement B (which says energy decreases) is incorrect.

5. Ratio of Charge to Potential (Q/V):
By definition, the ratio of charge to potential is the capacitance:
$\frac{Q}{V}=C$
Since $C$ increases, this ratio must also increase. Therefore, statement D is incorrect.

6. Product of Charge and Voltage (Q × V):
The product is $Q\times V$. Since the charge $Q$ increases and the voltage $V$ remains constant, their product $QV$ increases. Therefore, statement E is correct.

Based on this analysis, the statements A, C and E are correct, making the most appropriate option A, C and E only.