Three identical capacitors connected in series have net capacitance ' x '. Then they are connected in parallel. The ratio of energy stored in series configuration to that in parallel configuration is (if both configurations are connected to the same source)

Step-by-step solution

Let the capacitance of each identical capacitor be C . In series configuration, the equivalent capacitance is C_s = C 3 . In parallel configuration, the equivalent capacitance is C_p = 3C . The energy stored in a capacitor configuration connected to a voltage source V is given by U = 1 2 C_ eq V^2 . For the series configuration, the energy stored is U_s = 1 2 C_s V^2 = 1 2 ( C 3 ) V^2 . For the parallel configuration, the energy stored is U_p = 1 2 C_p V^2 = 1 2 (3C) V^2 . The ratio of energy stored in series to th