An electrical component has voltage drop $v=V_m \sin (\omega t)$, when the current through it is $i=I_m \sin (\omega t-\theta)$. What is the average power dissipated over a half cycle corresponding to $\omega$ ?

For the circuit shown in the figure, the source frequency is 5000 rad/sec. The mutual inductance between the magnetically coupled inductors is 5 mH with their self inductances being 125 mH and 1 mH. The Thevenin’s impedance, $Z_{th}$, between the terminals P and Q in $\Omega$ is ______________ (rounded off to 2 decimal places).