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)

Let the capacitance of each identical capacitor be $C$.

In series configuration, the equivalent capacitance is $C_s = \dfrac{C}{3}$.

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 $U = \dfrac{1}{2} C_{eq} V^2$.

For the series configuration, the energy stored is $U_s = \dfrac{1}{2} C_s V^2 = \dfrac{1}{2} \left(\dfrac{C}{3}\right) V^2$.

For the parallel configuration, the energy stored is $U_p = \dfrac{1}{2} C_p V^2 = \dfrac{1}{2} (3C) V^2$.

The ratio of energy stored in series to that in parallel is:

$\dfrac{U_s}{U_p} = \dfrac{\dfrac{1}{2} \left(\dfrac{C}{3}\right) V^2}{\dfrac{1}{2} (3C) V^2} = \dfrac{\dfrac{C}{3}}{3C} = \dfrac{1}{9}$

Thus, the required ratio is $1:9$.

Answer: $1:9$