Electrical Engineering ⇒ Topic : Energy Stored in a Capacitor

Energy Stored in a Capacitor

Charging a capacitor means transferring electrons from one plate of the capacitor to the other. This involves expenditure of energy because electrons have to be moved against the *opposing forces. This energy is stored in the electrostatic field set up in the dielectric medium. On discharging the capacitor, the field collapses and the stored energy is released.

                                                                       figure (a)

Consider a capacitor of C farad being charged from a d.c. source of V volts as shown in Figure (a). Suppose at any stage of charging, the charge on the capacitor is q coulomb and p.d. across the plates is v volts.

At this instant, v joules (by definition of v) of work will be done in transferring 1 C of charge from one plate to the other. If further small charge d_q is transferred, then work done is

Total work done in raising the potential of uncharged capacitor to V volts is

This work done is stored in the electrostatic field set up in the dielectric.

Energy stored in the capacitor is

Note that an ideal (or pure) capacitor does not dissipate or consume energy; instead, it stores energy

ENERGY STORED IN A CAPACITOR

When a capacitor is charged, charging agency supplies energy. If a capacitor be uncharged, little work is to be done in transferring energy from one plate to another. Next instalment of charge is to be carried against the repulsive force due to charge from one plate to another.Let the potential difference across the plates be y at any stage of charging and it is equal to the work done in shifting one coulomb of charge from one plate to another. The work done for transferring additional charge d_q is given by

For a capacitor of plate area A and dielectric thickness d, energy per unit volume of dielectric medium is given by

                                                                  ............... (1)

Capacitor is a device in which electrical energy can be stored. Consider a capacitor which is charged progressively from zero charge to a value q. Let the final potential across the capacitor plates be V. At any instant during the process of charging, let q be the charge and let the corresponding potential be V.

If d_q be the additional charge placed on the capacitor, then the work required to do so will be

Then, the total work done during the process of charging (w) will be given as

Therefore, the energy stored in a capacitor = work done (w) and is given by

where q is expressed in coulombs, C in farads and V in volts.