What amount of heat will be generated in the circuit shown in Fig. after the swich `Sw` is shifted from position 2 ?

Explanation

Initally, the charge on the right plate of the capacitor, `q = C (xi_(1) - xi_(2))` and finally, when swiched to the position, 2 charge on the same plate of capacitor ,
`q' = C xi_(1)`
So, `Delta q = q' = C xi_(2)`
Now, from energy conservation,
`Delta U +` Heat liberated `= A_(cell)`, when `Delta U` is the electrical energy.
`(1)/(2) C xi_(1)^(2) - (1)/(2) C (xi_(1) - xi_(2))^(2)` + Heat libreated `= Delta q xi_(1)`
as only the cell with `e.m.f xi_(1)` is responsible for redistribution of teh charge. So, `C xi_(1) xi_(2) - (1)/(2) C xi_(2)^(2) ` + Heat libreated `= C xi_(2) xi_(1)`.
Hence heat liberated `= (1)/(2) C xi_(2)^(2)`