Part a)

Determine R_o so that the maximum possible power is delivered to the 8 W resistor.

First, the power absorbed by the 8 W resistor is

P = 8 I₈²

With a small amount of thought, hopefully it is evident that setting R_o = 0 W will maximize the current I₈, thus maximizing the power.

For a more mathematical development of this result, see problem 4-71 from the sixth edition text.

Part b)

With R_o = 0, the entire 24 volts is across the 8 W resistor. The maximum power that can be delivered to the 8 W resistor is thus

P = 24² / 8

P = 72 W

NOTE: In part a) it was easier to see the answer by considering the current through the resistor, but in part b) it was easier to calculate the power using the voltage, thus the use of the two different forms for calculating the power absorbed by a resistor: P = I² R in part a) and V² / R in part b).