Derive an expression for the energy stored in a capacitor.

Explanation

Expression for the energy stored in a capacitor: Consider an uncharged capacitor of capacitance C' and its initial will be zero. Now it is connected across a battery for changing then the final potential difference across the capacitor be V and final charge on the capacitor be Q.
`:.` Average potential difference `V_(A) = (O + V)/(2) = (V)/(2)`
Hence workdone to move the charge `Q = W = V_(A) xx Q = (VQ)/(2)`
This is stored as electrostatic potential energy U
`:. U = (QV)/(2)`
We know Q = CV then U can be written as given below.
`U = (QV)/(2) = (1)/(2) CV^(2) = (Q^(2))/(2C)`
`:.` Energy stored in a capacitor
`U = (QV)/(2) = (1)/(2) CV^(2) = (1)/(2) (Q^(2))/(C )`