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:

NEET 2024, Medium
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Given $V^{\prime \prime}=V=$ Constant

($i$)

$C^{\prime}=\frac{\varepsilon_0 A}{d^{\prime}}, C=\frac{\varepsilon_0 A}{d}$

$d^{\prime}>d$

$ C^{\prime}>C$

Hence, final capacitance greater than initial capacitance,

($ii$)

$U^{\prime}=\frac{1}{2} C^{\prime} V^2$

$U=\frac{1}{2} C V^2$

$U^{\prime}>U$

Hence final energy is greater than initial energy

($iii$)

$\frac{Q^{\prime}}{V^{\prime}}=C^{\prime} \text { and } \frac{Q}{V}=C$

$\frac{Q^{\prime}}{V^{\prime}} \neq \frac{Q}{V}$

($iv$) Product of charge and voltage

$X^{\prime}=Q^{\prime} V=C^{\prime} V^2$

$X=Q V=C V^2$

$X^{\prime}>X$

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