The energy stored in a capacitor of capacity | vedclass

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(B) The energy stored in a capacitor is the work done in charging it.If a capacitor of capacity $C$ is charged to a potential $V$,the work done $dW$ t

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$\frac{1}{2} CV^2$

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(B) The energy stored in a capacitor is the work done in charging it.If a capacitor of capacity $C$ is charged to a potential $V$,the work done $dW$ to bring an additional charge $dq$ is given by $dW = V' dq$,where $V' = q/C$.Integrating this from $0$ to $Q$ (where $Q = CV$):$U = \int_{0}^{Q} \frac{q}{C} dq = \frac{1}{C} \left[ \frac{q^2}{2} \right]_{0}^{Q} = \frac{Q^2}{2C}$.Substituting $Q = CV$,we get $U = \frac{(CV)^2}{2C} = \frac{1}{2} CV^2$.

The energy stored in a capacitor of capacity $C$ which has been raised to a potential $V$ is given by

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