Answer
$C = 59.0~\mu F$
Work Step by Step
We can find the value of the capacitance:
$I_C~X_C = V_C$
$\frac{I_C}{\omega_d~C} = V_C$
$I_C = V_C~\omega_d~C$
$C = \frac{I_C}{V_C~\omega_d}$
$C = \frac{0.620~A}{(30.0~V)(350~rad/s)}$
$C = 59.0~\mu F$
