Energy stored in capacitor derivation

Energy stored in Capacitor

A charged Capacitor is a store of electrical potential energy.

To find the energy stored in a capacitor, let us consider a capacitor of capacitance C, with a potential difference V between the plates.

There is  a charge +q on one plate and –q on the other.

Suppose the capacitor is charged gradually. At any stage ,the charge on the capacitor is q.

Potential of capacitor =q/C.

Small amount of work done in giving an additional charge dq to the capacitor is

dW=q/C *dq

total work done in giving a charge Q to the capacitor is q.

Q=Q

W=1/C Q2/2

Energy stored in the capacitor

U=W=1/2 Q2/C

Put                                           Q=CV

U=1/2 (CV)2/C =1/2 CV2

Put                                              CV=Q

U=1/2 QV

Thus,                    U=1/2 Q2/C =1/2 CV2=1/2 QV

When Q is in coulomb,V is in Volt ,C is in fared .Energy U is in joule.

Energy stored in a capacitor is in the form of electric field energy in the charged capacitor and it resides in the dielectric medium between the plates.

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