Question

establish an expression for electrical energy of a capacitor of capacity c and charged to potential v​

Answer 1

Electric Energy of Capacitors:

• Let the work done to add a very small amount of charge dq to the capacitor be dW.

$dW = V \: dq$

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

• So, total work will be :

$\displaystyle \implies\int_{0}^{W} dW = \dfrac{1}{C} \int_{0}^{q} q \: dq$

$\displaystyle \implies W = \dfrac{ {q}^{2} }{2C}$

$\displaystyle \implies W = \dfrac{ {(CV)}^{2} }{2C}$

$\displaystyle \implies W = \dfrac{1}{2} C{V}^{2}$

[Hence Proved]