Answer
$L=32.2 \mathrm{mH}$.
Work Step by Step
Since $f=8000 \mathrm{~Hz}$, then $\omega_d=2 \pi(8000) \mathrm{rad} / \mathrm{s}$. The net reactance is therefore
$
X_L-X_C=\omega_d L-\left(\omega_d C\right)^{-1}=707 \Omega .
$
We are also told that the resonance frequency is $6000 \mathrm{~Hz}$, which means
$
C=\frac{1}{\omega^2 L}=\frac{1}{(2 \pi f)^2 L}=\frac{1}{4 \pi^2 f^2 L}=\frac{1}{4 \pi^2(6000 \mathrm{~Hz})^2 L} .
$
Substituting this for $C$ in our previous expression we obtain an equation that can be solved for the self-inductance.
The result is $L=32.2 \mathrm{mH}$.
