Question

Prove that
"The ratio of change in potentials of conductors after connecting two charged conductors is inversely proportional to their capacitances".

Answer 1

Energy stored in a capacitor : A capacitor is a device to store energy. The process of charging up a capacitor involves the transferring of electric charges from its one plate to another.The work done in charging the capacitor is stored as its electrical potential energy. Consider two insulated conductor A and B of capacitance C

1

,C

2

and carrying charges Q

1

and Q

2

. Let V

1

and V

2

be their respective potentials.

Q

1

=C

1

V

2

and Q

2

=C

2

V

2

If connect with wire charge flow higher to lower potential

Total charge on system Q

1

+Q

2

Total capacitance C

1

+C

2

V=

C

Q

=

C

1

+C

2

Q

1

+Q

2

=

C

1

+C

2

C

1

V

1

+C

2

V

2

V∝

C

1

+C

2

1

Electric field distance curve by uniformly charged non- conducting sphere.

E outside (r>r

0

)

E=

r

2

KQ

E inside (r<r

0

)

E=

r

0

3

KQ.r