Max Power Transfer to Ro: Percentage Explained

[orangeincup]

Homework Statement

The variable resistor R in the ciruit is adjusted for maximum power to Ro. what percentage of total power developed in circuit is transferred to R.

Homework Equations

i=V/R

The Attempt at a Solution

So my goal is to put a "fake" charge across v/2(the dependent source) of 1A facing upwards. The R0 is at the very top of the circuit(the one with no value, above 7.)

Since I know i3=-1A I need equations for i1 and i2

5i1-2i2=217
-2i1+10i2=0

Solving for i1/i2..
i2=9.3A
i1=47.1A

From here, I know I need Vab which is V across the 1 ohm resistor minus V across the 3 ohm resistor

1(i2-i3)+3(i1-i3)=vab
1*10.3+3*47.1=vab
151.69=vab

151.69V/1A=151.69 ohms

The answer is meant to be 3, I also solved it the other way(calculating for Voc and Isc) and got 3 ohms for my answer. I don't know what I did wrong using this method.

 

[gneill]

The variable resistor R in the ciruit is adjusted for maximum power to Ro. what percentage of total power developed in circuit is transferred to R.

I don't see any variable resistor R in the diagram. Is it one of the existing resistors in the diagram? Does Ro have a value?
It's pretty difficult to make out the current labels on your diagram.

So my goal is to put a "fake" charge across v/2(the dependent source) of 1A facing upwards. The R0 is at the very top of the circuit(the one with no value, above 7.)

I don't see what placing a fixed current supply across the variable current supply will do for you. It doesn't seem to be a valid approach. Can you justify it?

 

[orangeincup]

The variable resistor R0 is above the 7Ohm, in the top part which is unmarked.

I am following the method I found online and in this video:

He places a "fake" current across so he calculate the voltage and solve for Rth based on the ratio, maybe I am doing it wrong.

 

[gneill]

Yes, well, I'm not going to watch a 20 minute video. Sorry.

But I'll bet he put the "fake" supply across the output terminals where the load would go. This technique serves to stimulate controlled sources when looking for the Thevenin resistance when all the independent sources have been suppressed.