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Q.

An uncharged capacitor C is connected to a battery through a resistance R. Show that by the time the capacitor gets fully charged, the energy dissipated in R is the same as the energy stored in C.

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a

U/2

b

U

c

U/3

d

2/3 U

answer is B.

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Detailed Solution

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Charge supplied by the battery,

$q = C V$

Energy supplied by the battery,

$E = q V = C V^{2}$

Energy stored in the capacitor,

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

$∴$ Energy dissipated across R in the form of heat

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

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An uncharged capacitor C is connected to a battery through a resistance R. Show that by the time the capacitor gets fully charged, the energy dissipated in R is the same as the energy stored in C.