The ratio of the capacitance of two conductors A and B is 2: 3. The conductor A gains a certain amount of charge and shares it with B. Compare the initial energy of A with the total energy of A and B.

Explanation

Let the capacitance of the conductor A be 2C and that of the conductor B be 3C.
The amount of charge gained by A is Q.
Let common potential of A and B after sharing of charge be V.
`:. " " V= (Q)/(2C+3C)= (Q)/(5C)`
Energy of the conductor A before sharing of charge,
`E_A=(1)/(2)*(Q^2)/(2C)=(Q^2)/(4C)`
Total energy of the conductors A and B after sharing the charge,
`E=(1)/(2)(2C+3C)V^2= (1)/(2)xx5Cxx((Q)/(5C))^2 = (Q^2)/(10C)`
The required ratio `= (E_A)/(E)= ((Q^2)/(4C))/((Q^2)/(10C))= (5)/(2)`.