For the circuit shown below in Figure $8$:

Figure $8.$ Circuit for Problem $7.$

$($a$)$ Find the phasor$-$domain Thevenin model parameters $V_{TH}$ and $Z_{TH}$ with respect to nodes A and B $.$

$($b$)$ Find the value of $Z_L$ that, when connected to nodes A and B $,$ dissipates the maximum amount of power from the above circuit.

$($c$)$ With the constraint that the load be purely resistive, find the value of $R_L$ that, when connected to nodes A and B $,$ dissipates the maximum amount of power from the above circuit.

$($d$)$ Compute the average power delivered to the load for parts $($b$)$ and $($c$)$ make it really easy for me to figure out which average load power quantity is for the load of part $($b$)$ and which average load power quantity is for the load of part $($c$).$ Is the average load power for part $($c$)$ greater than, the same as$,$ or less than the average load power for part $($b$),$ and is this consistent with what you have learned on this

topic? Discuss POWER ANSWERS SHOULD BE $2\mathrm{.}2$ and $2\mathrm{.}5.$