# Energy Stored in a Capacitor

The dramatization that is usually seen in movies where medical personnel uses a defibrillator to pass an electric current through a patient’s heart to get it to beat normally uses the energy stored in a capacitor. Less dramatic application of the energy stored in the capacitor lies in the use of capacitors in microelectronics, such as handheld calculators.

## How do we calculate the energy stored in a capacitor?

The energy stored in a capacitor is nothing but the electric potential energy and is related to the voltage and charge on the capacitor. If the capacitance of a conductor is C, then it is initially uncharged and it acquires a potential difference V when connected to a battery. If q is the charge on the plate at that time, then

$q=CV$

The work done is equal to the product of the potential and charge. Hence, W = Vq

If the battery delivers a small amount of charge dQ at a constant potential V, then the work done is

$dW=Vdq=\frac{q}{C}dq$

Now, the total work done in delivering a charge of an amount q to the capacitor is given by

$W=\int_{0}^{q}\frac{q}{C}dq=\frac{1}{C}\frac{q^2}{2}=\frac{1}{2}\frac{q^2}{C}$

Therefore the energy stored in a capacitor is given by

$U=\frac{1}{2}\frac{q^2}{C}$

Substituting $q=CV$ in the equation above, we get

$U=\frac{1}{2}CV^2$

The energy stored in a capacitor is given by the equation $U=\frac{1}{2}CV^2$.

Let us look at an example, to better understand how to calculate the energy stored in a capacitor.

Example: If the capacitance of a capacitor is 50 F charged to a potential of 100 V, Calculate the energy stored in it.

Solution:

We have a capacitor of capacitance 50 F that is charged to a potential of 100 V. The energy stored in the capacitor can be calculated as follows

$U=\frac{1}{2}CV^2$

Substituting the values, we get

$U=\frac{1}{2}50(100)^2=250\times 10^3\,J$

### Applications of Capacitor Energy

Following are a few applications of capacitor energy:

• A defibrillator that is used to correct abnormal heart rhythm delivers a large charge in a short burst to a person’s heart. Applying large shocks of electric current can stop the arrhythmia and allow the body’s natural pacemaker to resume its normal rhythm. A defibrillator uses the energy stored in the capacitor.

• The audio equipment, uninterruptible power supplies, camera flashes, pulsed loads such as magnetic coils and lasers uses the energy stored in the capacitors

• Super capacitors are capable of storing a large amount of energy and can offer new technological possibilities