Answer
$L = 0.138~H$
Work Step by Step
We can find the value of the inductance:
$I_L = \frac{V_L}{X_L}$
$I_L = \frac{V_L}{\omega_d~L}$
$L = \frac{V_L}{\omega_d~I_L}$
$L = \frac{30.0~V}{(350~rad/s)(0.620~A)}$
$L = 0.138~H$
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