To understand this concept we have to think that some outside agency is pulling the negatively charged electrons from the positively charged plate of the capacitor and sending them to the negative plate of it. This small amount of work is done by battery. So, this energy is stored inside the capacitor in the form of electrostatic energy. Then this energy is stored as chemical energy in the capacitor.
In this case the electric potential of conductor is given by: q/C
So the work done to charge the condenser up to a little amount is given by:
dW= q/C X dq
Total work done can be found by applying the integration on the above expression.
After integration we get
W=Q 2C X 2
Total energy packed up inside the conductor
U=W=Q2/2 C
Substitute the value of Q as CV
Because Q=CV.
After substituting the value we get:
U=(CV)2/2C = CV2/2 —–2.14
Now put CV=Q.
Then the result is :
U= QV/2
So
U=Q2/2C=CV2/2=QV/2
Energy will be in joules when the other quantities such as q , V and C will be in Coulomb , volt and farad respectively.
