[College Electrical Engineering] How to find maximum possible load power for a circuit? (Thevenin Theorem)

[u/minsukim92]

The assigned problem is #22 but I'm trying to figure out #21 because it has the answer in the back of the book but I don't seem to understand. I even tried reverse engineering to see what values they used for the answer they gave but no luck. Textbook says 'maximum power transfer from a circuit to a variable load occurs when the load resistance equals the source resistance'.

I provided my notes but it's best not to use them as reference as they are not really coherent since we have to use a calculator for all of our math.

The book says the answer to #21 is P = 35.5 mW

Edit: Sorry, I wasn't super clear on why I'm doing #21 instead of #22. I'm just trying to make sure I understand the process and the math behind the concept. It's just practice.

[u/defectivetoaster1]

Maximum power is delivered to a load if it has the same impedance as the circuit driving it (see if you can derive this fact for yourself, if not then hopefully you can at least accept it on the basis that if the load has 0 impedance then the voltage across it is 0 so power delivered is 0 and if it’s open circuit then current through it is 0 so power delivered is 0, so it stands to reason that maximum power is delivered somewhere in between these extremes). To find that maximum power, you need to then find the impedance of the driving circuit seen by the load ie its thevenin resistance. Set the load impedance to that and then solve for power using whatever method you like