Derive the expression for energy stored in a charged capacitor.

Explanation

Let .C. be the capacitance of a parallel plate capacitor . By defination ` C =Q /V ` . By defination amount of work done to raise the charge by . dq . is dW = V dq .
`i.e., d W = (q) /(C ) dq `
Where .q. is the instantaneous value of charge on the conductor .
Total work in charging the capacitor is given by ,
` W = int _(q=0) ^(q=Q) dW `
`i.e., W = int _(q=0) ^(q=Q) ((q)/(C ))dq `
`i.e, W =(1 )/(C ) [(q^(2))/(2)]_(0)^(Q)`
Or ` W=(1)/(2) (Q^(2))/(C )` , amount of work done is stored in the form of energy .
therefore ` E= (1)/(2) ((Q^(2))/(C ))`
Using `Q=CV , E =(1)/(2) CV ^(2)` , where .V. is the maximum voltage supplied to a capacitor .