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Physics · 2025 · 3 marks
CBSE 2025 · Region 5 · Set 2 · Q24
A capacitor of plate area A and plate separation d is charged by a battery to voltage V. The battery is disconnected and plates are slowly pulled…
A capacitor of plate area A and plate separation d is charged by a battery to voltage V. The battery is disconnected and plates are slowly pulled apart till the separation becomes 2d. Find the value of :
(a)
potential difference between the plates,
(b)
electric field between the plates,
(c)
work done in pulling the plates apart.
Marking-scheme solution
As the battery is disconnected, the charge remains the same:
$\displaystyle C^{\prime}=\frac{C}{2}$
(a)
$\displaystyle q^{\prime}=q$
$\displaystyle C V=C^{\prime} V^{\prime}$
$\displaystyle C V=\frac{C}{2} V^{\prime}$
$\displaystyle V^{\prime}=2 V$
(b)
$\displaystyle E^{\prime}=\frac{V^{\prime}}{d^{\prime}}$
$\displaystyle =\frac{2 V}{2 d}$
$\displaystyle =\frac{V}{d}=E$
(c)
$\displaystyle W=U^{\prime}-U$
$\displaystyle =\frac{1}{2} \times \frac{C}{2} \times(2 V)^{2}-\frac{1}{2} C V^{2}$
$\displaystyle =\frac{1}{2} C V^{2}$
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