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

 

[Mene]

I would suggest using the maximum power transfer theorem to find the maximum power without knowing the load resistance. This theorem states that the maximum power will be transferred from a source to a load when the load resistance is equal to the source resistance. In this case, the source resistance is the equivalent resistance of the circuit, which can be found by combining all the resistors in parallel. Once the equivalent resistance is found, the maximum power can be calculated using the equation P = (V^2)/R, where V is the voltage across the equivalent resistance.

Another approach could be to use a variable resistor as the load and measure the power at different resistance values until the maximum power is reached. This would require some trial and error, but it would give a more accurate result.

Additionally, it is important to consider the limitations of the circuit components. For example, the voltage sources may have a maximum output power that could affect the maximum power transfer. It is also important to consider the power rating of the resistors to ensure they can handle the maximum power.

In conclusion, there are different approaches to finding the maximum power without knowing the load resistance. The maximum power transfer theorem and experimental methods can be used to find a solution, but it is important to consider the limitations and accuracy of these methods.