$9\mathrm{.}40$ a$.$ The source voltage in the circuit in Fig. P$9\mathrm{.}40$ is $v_g=96cos10,000tV.$ Find the values of $L$ such that $i_g$ is in phase with $v_g$ when the circuit is operating in the steady state.

b$.$ For the values of $L$ found in $($a$),$ find the steady$-$state expressions for $i_g.$

Figure P$9\mathrm{.}4$n