Answer :

Given, capacitance of a, b, c, d capacitors are 10 μF each.


The voltage of the DC battery is 100V


Formula used


Energy stored in a capacitor can be calculated from the relation,



Or,



Where C represents the capacitance, V is the potential difference across the capacitor and Q is the charge in the capacitor.


And, effective capacitance of capacitors C1 and C2 arranged in series is



And those connected in parallel is


Considering three capacitors)


The capacitors b and c are in parallel. For simplification, we reduce it into capacitor bc as shown,



and the capacitance of bc is, from eqn.4



By substituting the values,



Now the whole arrangement is a series connection and charges in each capacitor will be the same.


To find out effective capacitance of this arrangement, we find equivalent capacitance, Cad between a and d initially, by eqn.3



By substituting the values,



Now the total capacitance considering Cadand Cbc in series, using eqn.3,


Or,



The capacitors a ,d and the parallel arrangement will have same charge,Q in it, which can be calculated as,



Where,


Ceff= Capacitance, V= Potential difference=100V


By substitution, we get , Q as



The energy stored in a and d are same due to the same capacitance value and the same charge accumulation. So energy stored in a and d are, from eqn.2



Or,



In the parallel arrangement, the charge, Q=400μC will be splitted in half as the two branches are symmetrical. So each capacitors b and c will have Q=200μC amount of charge.


Hence, by the energy relation, eqn.2 , the energy in each capacitors b and c, will be,



Or,



Hence 8mJ will be stored in the capacitors a and d , while 2mJ will be stored in b and c.


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