Energy Stored in a Capacitor Derivation, Formula and Applications

Energy stored in a capacitor

The energy U stored in a capacitor of capacitance C, with charge Q and voltage V is

The electric energy density (energy per unit volume) in a region with electric field is (1/2) ϵ_oE² / 2

How to calculate the energy stored in a capacitor?

Consider a capacitor of capacitance C, completely uncharged in the beginning. Charging process of capacitor requires the expenditure of energy because while charging a capacitor charge is transferred from the plate at lower potential to plate at higher potential. Now if we start charging the capacitor by transporting a charge dQ from negative plate ti the positive plate then work is done against the potential difference across the plate. If q is the amount of charge on the capacitor at any stage of charging process and φ is the potential difference across the plates of capacitor then magnitude of the potential difference is φ=q/C. Now work dW required to transfer dq is

To charge the capacitor starting from the uncharged state to some final charge Q work required is Integrating from 0 to Q

which is the energy stored in the capacitor and can also be written as

we see that the total work done is equal to the average potential V/2 during the charging process, multiplied by the total charge transferred.

If C is measured in Farads, Q in coulombs and V in volts the energy stored would in Joules. A parallel plate capacitor of area A and separation d has capacitance

Electric field in the space between the plates is

Putting above values of V and C

If u denotes the energy per unit volume or energy density then

The result for above equation is generally valid even for the electrostatic field that is not constant in space.

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 use the energy stored in the capacitors.
• Super capacitors are capable of storing a large amount of energy and can offer new technological possibilities.