Please solve Q no 16

 

Initially capacitors C1 and C2 are charged in the loop ABEF , before switch S is closed.

 

By considering capacitance of C1 and C2 are 2μF and by applying Kirchoff's voltage law for the loop ABEF ,

 

we have,   -10 + [q / (2×10^-6)] -10 + [q / (2×10^-6)]  = 0   

 

Hence charge on each of capacitors C1 and C2 ,     q = 20 × 10^-6 C

 

Hence potential across each capacitance = q/C = 20 × 10^-6 / 2× 10^-6 = 10 V

 

When switch is closed, capacitor C3 is charged in the loop BGDE.

 

By Kirchoff's voltage in the loop BGDE,  -20 + [q / (2×10^-6)] -10 = 0   

 

Hence charge on capacitor C3 ,   q = 60× 10^-6 C

 

To charge the capacitors, workdone by battery,  q × V = 60× 10^-6 × 20 = 1200 μJ

 

Energy stored in capacitor = (1/2)CV² = (1/2)×2× 10^-6 × 30 × 30 = 900 μJ

 

Heat energy produced in the circuit = (1200 - 900 ) μJ = 300 μJ  = 0.3 mJ