Answer
$L = 2.50~mH$
Work Step by Step
We can state the expression for the current:
$i = (1.60)~sin~(2500 t+0.680)$
Note that: $~~i = (1.60)~sin~(\omega t+0.680)$
Therefore, $~~\omega = 2500~rad/s$
We can find the inductance $L$:
$\omega = \frac{1}{\sqrt{L~C}}$
$\omega^2 = \frac{1}{L~C}$
$L = \frac{1}{\omega^2~C}$
$L = \frac{1}{\omega^2~C}$
$L = \frac{1}{(2500~rad/s)^2~(64.0\times 10^{-6}~F)}$
$L = 2.50~mH$
