How to Correctly Calculate R Thevenin in a Circuit Analysis?

[TipTip]

The question is find R Thevenien using Voltage test source across terminals a and b of the following circuit:

http://img255.imageshack.us/img255/8660/rthevenen.png

I did it by adding a 20 test voltage source and used mesh to get the following 4 equations of the 4 meshes ( I deactivated the 480 V independent source to be able to use test voltage method)

M1:6(x-t) + 40(x-y)+4x=0
M2: 40(y-x)+20=0
M3: 80(z-t) - 20q +2z-20=0
M4:4t + 8(t-z) +6(t-x)=0
q=x-t

I R thevenen to be 11.55 but actually the correct answer is 12 ohms.

Where is my mistake.

 

[The Electrician]

I don't see 4 meshes; I only see 3 meshes.

You need to explain in more detail what you are doing. What are x and y? I don't see anything labeled x and y on your schematic. You should tell me what they are, and don't expect me to figure it out for myself.

I would have used the nodal method, and select the node labeled b to be the reference (ground).

Then you can inject a test current of 1 amp into node a, and the voltage there will be equal to the Thevenin resistance (setting the 480 volt source to zero, of course).