Question

Derive an expression for energy sored in a capacitor.​

Answer 1

Explanation:

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Answer 2

Answer:

During the charging of a capacitor, work has to be done to add charge to the capacitor against its potential. This work is stored in the capacitor as electrical energy.

Suppose during the charging of capacitor it's potential at any instant is given by:

$\rm \implies V = \dfrac{q}{C}$

Small amount of work done in adding a charge dq is given by:

$\rm \implies dW = \dfrac{q}{C} dq$

Total work done in giving a change Q to the capacitor is:

$\rm \implies \int\limits^W_0dW = \int\limits^Q_0 \dfrac{q}{C} dq \\ \\ \rm \implies W = \dfrac{ {q}^{2} }{2C} \Big|_0^Q\\ \\ \rm \implies W = \dfrac{ {Q}^{2} }{2C}$

$\therefore$ Energy stored in capacitor (U):

$\boxed{ \bold{U= \dfrac{ {Q}^{2} }{2C} = \dfrac{1}{2}CV^2 = \dfrac{1}{2}QV}}$