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Energy Stored in a Capacitor

The energy stored in a capacitor is said to reside in the dielectric permeated by the electric field. Figure 2-17 shows a simple capacitor in which a charge of q coulombs is stored in the electric field. The top plate carries a net charge of +q coulombs and the bottom plate a net charge of - q coulombs. The voltage between the top plate and bottom plate of the capacitor is v volts.

Figure 2-17. Capacitor with a charge

If a differential charge +dq is carried from the bottom plate to the top plate, there will be a differential increase of energy dw.

E = electric field intensity at some point between the plates in volts per meter

Then dF = force on the differential charge dq expressed in newtons


The differential energy required to carry the differential charge from the bottom plate to the top plate is given by the line integral along any path between the plates


When Eq. 2-47 is substituted in Eq. 2-48 the result is


However, the line integral of the electric field intensity along any path from one plate to the other gives the voltage between plates; hence


Substitution of Eq. 2-50 in Eq. 2-49 yields


In order to determine the energy required to store a charge q in the field of a capacitor when the capacitor is initially uncharged, Eq. 2-51 is integrated as follows


but from Eq. 2-25 we get


and from Eqs. 2-52 and 2-53 there results


Making use of Eq. 2-53 in 2-54, we obtain the more commonly used expression for energy stored in a capacitor, i.e.


Last Update: 2011-01-08