Four capacitors of capacitance `C`, `2C`, `3C` & `4C` respectively are connected as shown in figure. Battery is deal and all the connected wires have no resistance capcitance or inductance. Initially the switch `S` is open. If at `t=0` switch `S` is closed
The work done by battery after closing, switch is

Options

A. `(CE^(2))/(5)`
B. `(2CE^(2))/(105)`
C. `(CE^(2))/(105)`
D. `(CE^(2))/(35)`

Explanation

Initial and final charges on capacitors are shown in figure (`a`) and (`b`) respectively charge flown through `AB` is `(CE)/(5)` work done by battery
`=W_(b)=(Q_(take)-Q_(take))E`
Heat produced `=W_(b)-DeltaU=(CE^(2))/(105)J`