Energy stored in a capacitor

 




 

1) Suppose a capacitor has capacitance C


2) Say q amount of charge is delivered to the system.


3) Then potential due q to amount of charge in the capacitor is

 

4) Now as conductor 1 has already have charge q, so if you add small infinitesimal amount of charge dq, is added to the capacitor, work has to be done



5) That amount of work is

dw = V dq

putting the value of V


6) Now on charging the capacitor from q= 0 to the charge

q = Q the total work done is




 




This work done will be stored in the capacitor as energy.


7) Therefore energy of the capacitor is as we know Q = CV