$(25$ points$)$ Assume $v_s(t)=6cos(500t)V$ and $Z=R+jx$ in Figure $5.$

Figure $5$: Circuit for Problem $5.$

$($a$)$ Find the Thevenin equivalent circuit with respect to the port $(a,b)$ and calculate $V_{Thh}$ and $Z_{Th}.$

$($b$)$ Determine the values of $R$ and $x$ so that maximum average power is delivered to $Z.$

$($c$)$ Find the maximum average power.

SOLVE ASAP