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(A) For the series combination of $10$ capacitors of value $C_1$,the equivalent capacitance is $C_{eq1} = \frac{C_1}{10}$.The energy stored in the fir

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$\frac{C_1}{5}$

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(A) For the series combination of $10$ capacitors of value $C_1$,the equivalent capacitance is $C_{eq1} = \frac{C_1}{10}$.The energy stored in the first combination is $U_1 = \frac{1}{2} C_{eq1} (4V)^2 = \frac{1}{2} \left( \frac{C_1}{10} \right) (16V^2) = \frac{16}{20} C_1 V^2 = \frac{4}{5} C_1 V^2$.For the parallel combination of $8$ capacitors of value $C_2$,the equivalent capacitance is $C_{eq2} = 8C_2$.The energy stored in the second combination is $U_2 = \frac{1}{2} C_{eq2} V^2 = \frac{1}{2} (8C_2) V^2 = 4 C_2 V^2$.Given that $U_1 = U_2$,we have $\frac{4}{5} C_1 V^2 = 4 C_2 V^2$.Dividing both sides by $4V^2$,we get $C_2 = \frac{C_1}{5}$.

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