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Electrostatic Potential And Capacitance

Question
CBSEENPH12037443

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. What will be the ratio of the energy stored in the capacitor and the work done by the battery?

Solution

Consider, E as the emf of the battery.
Then, charge gained by the battery is q=CE
and,
Work done by the battery is given by, W=qE
                                                       
                                                       =CE×E=CE2 

Now, energy stored in the capacitor-U=12CE2
Therefore, the ratio of energy stored in the capacitor and work done by the battery is,
 
                    12CE2CE2=12

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