Find charge flown through battery and heat generated in the circuit after shifting switch from `S_1" to "S_2.`

Explanation

Initially
For node x (x-v)2c+(x-v)c+(x+0)c=0
`rArr 4x=3v rArr x=(3v)/(4)`

(x'-0)C+(x'-0)2C+(x'-V)C+=0
`rArr x'=V/4`
So now charge on capacitor
Sor charge flow from battery
`Q=((3CV)/(4)-(CV)/(4))=(CV)/(2)`
So heat generated
`triangleH=QV-[{1/2C((3V)/(4))^(2)+1/2(2C)(V/4)^(2)+1/2Cxx (V/4)^(2)}-{1/2C(V/4)^(2)+1/2(2C)(V/4)^(2)+1/2 xx C xx ((3V)/(4))^(2)}`
`triangleH=QV=(CV^(2))/(2)`