Thevenin Theorem Help

[MonkeySage]

http://i1016.photobucket.com/albums/af282/anthonysherer90/VthRth_zpsvmjcu4mj.png


I'm supposed to determine Vth and Rth, however I'm not sure how to start. I understand that 1Ω is in series with 18Ω and 1Ω which are in parallel with each other.

[Rockphed]

There are several ways to do this.

First, the thevenin and norton resistance are the same, so short your voltage source, open your current source, and find the resistance between A and B. You need to do this no matter what other method you use.

You are looking for thevenin voltage, so setting up 2 mesh currents to find the voltage at the node where 1Ω, 1Ω, and 8Ω meet will get you that (remember, when the output is an open circuit, there is no voltage drop across the final 1Ω resistor).

Alternatively, you could put a short between A and B and find the current between them. Then you change the norton current to a thevenin voltage by multiplying it by your thevenin resistance.

Finally, you could use successive source transformations to work from left to right combining branches until you are left with your thevenin voltage source and resistance. The first step would be:



.-----8Ω----T---1Ω---oA
.|..........|
10Ω........1Ω
.|..........|
20V........5V
.|..........|
.--------------------oB