# Energy Stored in Capacitor

## Energy Stored in a Capacitor

In this article, we will discuss about the energy stored in a capacitor and derive the equation for the calculating the energy stored in the capacitor.

### How energy stored in a capacitor?

Work done by the battery defines the energy stored in a capacitor.

The energy which is stored by a capacitor is the electric potential energy and is described by the available voltage and charge on the capacitor.

### Energy stored in a capacitor equation

When switch is closed, it connects the battery to the capacitor, there is no charge buildup because there is zero voltage across the capacitor. Here in this case the voltage on capacitor is proportional to charge.

V = q / C

V is the voltage on the capacitor. Energy per unit charge is represented by the voltage, therefore the work to move a charge matter dq from the negative plate to the positive plate is given by V dq. The voltage V is proportional to the total charge which is present on the capacitor.

Energy stored is given by;

dU = Vdq = (q / C) dq

When the whole battery voltage available across the capacitor then the Q is amount of stored charge, the stored energy is derived from the integral:

Based on the definition of capacitance C=Q/V, the above given energy expression can be written in three equivalent forms by using permutations.

### How to calculate energy stored in a capacitor?

Below example will help us to better understand how to calculate the energy stored in a capacitor.

Example:

If the capacitance of a capacitor is 100 F, which is charged to a potential of 100 V, Calculate the energy stored in this capacitor.

Solution:

We have a capacitor of 100F capacitance, which is charged to a potential of 100 V. Calculation of energy stored in a capacitor can be perform by below equation;

U = (1/2)CV²

Substituting the values, we get

U = (1/2) x 100 x (100)²

U = 500000 J

U = 500 x 10³

### Conclusion

Energy stored in a capacitor is defined by the battery. Hence, the energy available at capacitor is described by the voltage (V) and charge (q) on the capacitor.