How Do You Determine Thevenin Equivalent Circuits and Maximize Power Transfer?

[jdawg]

Homework Statement

Find the Thevenin equivalent circuit for the circuit shown. You will need to find V_OC and then use the test source method to find the Thevenin resistance. Using the Thevenin equivalent circuit,determine the load resistor that results in maximum power transferred to that load resistor and the amount of that power.

Homework Equations

The Attempt at a Solution

(Fig.1)[/B]I'm a little stuck on this problem. I first used mesh analysis to find V_OC, which came out correct: V_OC=2.5V.
But I tried to do it with node voltage analysis as well to see if it would work also and it came out a little messed up:
(VA-5)/7 +VA/10=0
VA=2.94V
Is there a reason why node voltage doesn't work in this situation or am I just doing it wrong?
(Fig.2) I tried letting I_Test=1A and used mesh analysis:
i2=I_Test=1
0.2(V2)-(5ohm)(i1)+5v-(7ohm)(i1)-(10ohm)(i1-i2)=0
Substituted and did some algebra:
i1=0.705
I am super confused at this point :(
Is there an advantage to using a test voltage source vs using a test current source?
Should I have let V_Test=2.5V instead?

 

[jdawg]

Oops I forgot to take out the independent voltage source for the test method! I let V_test=2.5v and found I_test=0.467 so R_th=6ohms! I feel like I understand the test method now, could someone explain how I messed up with the node voltage equation in the Fig. 1 section?

 

[gneill]

Oops I forgot to take out the independent voltage source for the test method! I let V_test=2.5v and found I_test=0.467 so R_th=6ohms! I feel like I understand the test method now, could someone explain how I messed up with the node voltage equation in the Fig. 1 section?

You didn't account for the controlled source in the node equation. You need all sources active if you want to find the open circuit voltage.

 

[jdawg]

Thanks!