Write different expression for the energy stored in a capacitor.

Explanation

The capacitance of a capacitor is defined as the ratio of magnitude of the charge on the capacitor plate to the potential difference between the plates.
i.e., `c=(q)/(V)`
Expression for energy stored in a capacitor.
Let C be capacitance of a capacitor. if q is the charge on the capacitor plate at any time t, then
Potential, `V=(q)/(C)`
Let an additional charge dq be transferred to the conductor. work done in transferring the charge dq
`W=Vdq`
`=(q)/(C)dq` . . . (1)
Total energy can be obtained by integrating (1),
`W=int_(0)^(Q)(q)/(C)dq`
or `W=(1)/(C)int_(0)^(Q)qdq`
`=(1)/(C)[(q^(2))/(2)]_(0)^(Q)`
or `W=(1)/(2C)Q^(2)`
Thus work done is called energy E stored in the capacitor i.e., `E=(Q^(2))/(2C)`
But `V=(Q)/(C)`
`impliesQ=CV`
`therefore E=(1)/(2C)xxC^(2)V^(2)`
`E=(1)/(2)CV^(2)` . . (2)
Again `C=(Q)/(V)`
Substituting in equation (2), we get
`C=(1)/(2)xx(QV^(2))/(V)`
`E=(1)/(2)QV`
Form of Energy
The energy in the charged capacitor is in the form of potential energy. it resides in the form of electric field between the plates of the capacitor.