Question

An uncharged capacitor is fully charged with a battery. The ratio of energy stored in the capacitor to the work done by the battery in this process is
(1) 1:2
(2) 2:1
(3) 1:1
(4) 2:3​

Answer 1

answer : option (1) 1 : 2

an uncharged capacitor of capacitance C is fully charged with a battery of EMF ε.

then stored in capacitor, Q = Cε

now workdone by the battery in this process , W = charge stored in capacitor × EMF of battery

= Qε = Cε²

energy stored in the capacitor, U = 1/2 Cε²

so ratio of energy stored to the workdone by this process = (1/2Cε²)/(Cε²) = 1/2

hence option (1) is correct choice.

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Answer 2

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an uncharged capacitor of capacitance C is fully charged with a battery of EMF ε.

then stored in capacitor, Q = Cε

now workdone by the battery in this process , W = charge stored in capacitor × EMF of battery

= Qε = Cε²

energy stored in the capacitor, U = 1/2 Cε²

so ratio of energy stored to the workdone by this process = (1/2Cε²)/(Cε²) = 1/2

hence option (1) is correct choice