Question

deduce a relation for the energy stored in a charged capacitor?​

Answer 1

ENERGY IN CAPACITOR:

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

$dW = V \times dq$

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

$\implies dW = \dfrac{1}{C} (q \: dq)$

Integrating on both sides :

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

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

So, energy stored is :

$\boxed{E = \dfrac{ {q}^{2} }{2C} }$