# derivation for energy stored in a capacitor?

Energy Stored in a Charged Capacitor

The energy of a charged capacitor is measured by the total work done in charging the capacitor to a given potential.

Let us assume that initially both the plates are uncharged. Now, we have to repeatedly remove small positive charges from one plate and transfer them to the other plate.

Let

q →Total quantity of charge transferred

V →Potential difference between the two plates

Then,

qCV

Now, when an additional small charge dqis transferred from the negative plate to the positive plate, the small work done is given by, The total work done in transferring charge Qis given by,  This work is stored as electrostatic potential energy Uin the capacitor.   • 7

Its simple

Energy is the work done in moving a charge dq in the capacitor

C=q/V

w=Vd

dw=Q/C*dq

w=q^2/2c

q=cv

w=c^2v^2/2c

w=cv^2/2

• 19

considering an intermediate state,

word done in moving a charde dq from one plate to the other is given by,

dw = (Q/C).dq

or, w = intergral {Q.dq}/C = Q2/2C

• -13
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