Obtain the expression for the energy stored in a capacitor connected across a dc battery. Hence define energy density of the capacitor.

 

 

Answers (1)

Let the charge on the capacitor is increased by dq amount then,

Then, the work done  :-

dU=Vd{Q}'=\frac{{Q}'}{C}\; d{Q}'

On integrating it, we have

\int_{O}^{U}dU=\frac{1}{C}\int_{O}^{Q}{Q}'d\;{Q}'

U=\frac{1}{2}\left [ \frac{Q^{2}}{C} \right ]^{Q}_{O}

U=\frac{1}{2}\frac{Q^{2}}{C}

We know, C=\frac{Q}{V}

            U=\frac{1}{2}CV^{2}

            U=\frac{1}{2}QV

\therefore This is the work done is stored as energy on the capacitor 

Electrical energy stored per unit volume is known as energy density.

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