In the circuit shown switch S is kept open for long time. Switch is closed at t = 0, find total heat produced after closing the switch

Before closing the switchQ=CeqV=C1C2C1+C2V1-V2Q=65×1μCInitial energy stored capacitors = Q22C1+Q22C2=6522×3+6522×2=35μJAfter closing the switch Q2=10μCQ1=18μCFinal energy stored in capacitorU=12×362+12×252U=79μJWork done by batteries = 6Q1−Q+5Q+Q2=156.8μJH= work done by battery - change in potential energy of capacitors =156.8−79−35=78.4μJ