Max Power Circuit Homework: Find Max Power w/o Load Resistance

[camino]

Homework Statement

http://img63.imageshack.us/img63/80/circuit1.jpg

Homework Equations

P = (I^2)(R)

The Attempt at a Solution

First, I turned the 2A and 4A current sources into voltage sources by V = IR. So (2A)(10Ω) = 20V and (4A)(12Ω) = 50V

Then I had the circuit simplified into 4 loops, then applied mesh current analysis and got the following:

I1= 3.1374A
I2= -0.2125A
I3= -5.7941A
I4= 0.1874A

(I started loop 1 in the bottom left square and went clockwise in numbering.)

Now, I'm not sure how to find max power if I don't know the resistance of the load.

Please help! If there is an easier/better way to do this please explain!

 

[waht]

Under what conditions you will get max power transfer from a source with resistance Rs to a load Rl?

How Rs and Rl are related?


Knowing that, can you find Rs?

(R as it appears looking into a-b ) without Rl