A battery is used to charge a parallel plate capacitor till potential difference between plates beco

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2. Electric Potential and Capacitance

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A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

A

$2$

B

$\frac{1}{4}$

C

$\frac{1}{2}$

D

$1$

(AIEEE-2007)

Solution

Required ratio

$=\frac{\text { Energy stored in capacitor }}{\text { Workdone by the battery }}=\frac{\frac{1}{2} C V^{2}}{C e^{2}}$

where $C=$ Capacitance of capacitor

$V=$ Potential difference

$e=\mathrm{emf}$ of battery

$=\frac{\frac{1}{2} C e^{2}}{C e^{2}}=\frac{1}{2} \quad(\because V=e)$

Standard 12

Physics

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