KEAM 2014 Physics and Chemistry Paper

By energy stored in a charged conductor
Suppose, a conductor of capacity C is charged to a potential V and Q the charge on conductor at a instant.
The potential of the conductor
V=‌

Q

C

Now, work done in bringing a small charge dQ at this potential is,dW=VdQ=‌

Q

C

dQ
∴ Total work done in charging it from 0 to Q is,
W=

Q

∫

0

dW=

Q

∫

0

‌

Q

C

dQ
=‌

1

2

‌

Q2

C

This work is stored as the potential energy.
U=‌

1

2

‌

Q2

C

 (∵Q=VC)
U=‌

1

2

CV2=‌

1

2

QV