In this topic, you study Energy Stored in a Capacitor – Derivation, Diagram, Formula & Theory.
The process of charging a capacitor can always be regarded as the process of transfer of charge from one plate to another. This transfer of charge can only be done against the opposition due to potential difference or counter e.m.f. established between the plates. Hence, charging of a capacitor always involves expenditure of energy on the part of charging agency. This energy is stored in the form of potential energy in the electric field set up in the dielectric medium.
When the capacitor is discharged, its electric field collapses and thereby energy stored in it is released. Now, let us consider the case of a capacitor having capacitance of C farads and charged to a voltage of V vo ts. At any stage during charging, let the charge on the capacitor be q coulombs. Then, corresponding potential difference across the capacitor plates will be
By definition, this obviously means that the work done in shifting a charge of one coulomb from one plate to another is v joules. Now, if the charge on the capacitor is further increased by a small amount dq coulomb, then the work done must be
dw v dq dq joules
This work is ultimately stored in the form Of potential energy in the electric field of the capacitor. Therefore, the total energy stored in the capacitor when it is finally charged to Q coulombs is
Example 3.16: A 100 “F capacitor is charged to 500 V. Calculate the energy stored in the capacitor.
Solution: From Equation (3.33),
Energy stored,
joules