A capacitor of capacity `C_(1)` is charged to the potential of `V_(0)`. On disconnecting with the battery, it is connected with a capacitor of capacity `C_(2)` as shown in the adjoining figure. The ratio of energies before and after the connection of switch S will be

Options

A. `(C_1+C_2)//C_1`
B. `C_1//(C_1+C_2)`
C. `C_1C_2`
D. `C_1//C_2`

Answer

A

Explanation

`U_i=1/2C_1V_0^2" & "Q=CV_0`
`U_f=1/2(Q^2)/(C_(eq))=(C_1^2V_0^2)/(2(C_1+C_2))` [as Q = constant]
`U_i/U_f =(C_1V_0^2)/(C_1^2V_0^2)xx(C_1+C_2)=((C_1+C_2))/(C_1)`