Answer
$C = 6.0~\mu F$
Work Step by Step
We can write the expression for the energy stored in a capacitor:
$U = \frac{CV^2}{2}$
When there are two capacitors, the smallest capacitance occurs when the capacitors are in series, and the largest capacitance occurs when the capacitors are in parallel.
The second largest energy stored occurs when the capacitor of larger capacitance is connected individually.
We can find the larger capacitance:
$\frac{CV^2}{2} = 300~\mu J$
$C = \frac{(2)(300~\mu J)}{V^2}$
$C = \frac{(2)(300~\mu J)}{(10~V)^2}$
$C = 6.0~\mu F$
