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Question
A capacitor of capacity C1 is charged to the potential of V0. On disconnecting with the battery, it is connected with an uncharged capacitor of capacity C2 as shown in the adjoining figure. Find the ratio of energies before and after the connection of switch S.
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Solution
Before the connection of switch S,
Initial energy `U_i = 1/2C_1V_0^2 + 1/2C_2O^2 = 1/2C_1V_0^2`
After the connection of switch S,
common potential V = `(C_1V_1 + C_2V_2)/(C_1 + C_2) = (C_1V_0)/(C_1 + C_2)`
Final energy = `U_f = 1/2(C_1 + C_2) (C_1V_0)^2/(C_1 + C_2)^2 = 1/2 (C_1^2V_0^2)/((C_1 + C_2))`
`U_f : U_i = C_1/((C_1 + C_2))`
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