drive an expression for energy stored in a charged capacitor .Express it in different forms.

Dear student,

Let's consider a capacitor of capacitance C and potential difference V between the plates.
Let's say the charge on one plate be +q and -q on the other.
Suppose the capacitor is being charged gradually.
Now, at any stage the charge on the capacitor is q.
Therefore, the potential difference = q/C
Small amount of work done in giving n additional charge dq to the capacitor is
dW = q*dq/C
Total work done in giving a charge Q to the capacitor  is
W = ∫dW
W = ₀∫^{​​​​Q}​​​ ​​​​(q/C)*dq
 W = Q²/2C
Then, Energy E is
E= Q²/2C = QV/2 = CV²/2

Regards,
Meritnation