(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the Thevenin resistance.

http://i.imgur.com/XoEfy.png

2. Relevant equations

Rth =Vex/Iex

3. The attempt at a solution

I found that the thevenin voltage is 869.304mV. I read in my textbook that in order to find the thevenin resistance in a circuit that contains a dependent source an external source is required, then the circuit can be solved using any method possible. So I added an external source to my circuit and then I tried using node-voltage to solve it, but I am stuck.

kcl Node 1: [itex]\frac{V1}{70}[/itex] + [itex]\frac{V1-V3}{13}[/itex] + 5V2 = 0

kcl node 2: -5V2 + [itex]\frac{V2}{50}[/itex] + [itex]\frac{V2 -V3}{18}[/itex] = 0

kcl node 3: [itex]\frac{V3-V2}{18}[/itex] + [itex]\frac{V3-V1}{13}[/itex] + [itex]\frac{V3}{16}[/itex] - Iex = 0

I ended up with Rth = -1.24118

I know this isn't right. Even if it was right, I don't know how I can find Vex using that information.

Can someone tell me what I'm doing wrong?

Edit: I think I should use mesh current. I'll try that now.

Using mesh current I ended up with 1.99 as Rth. None of my answers are right. I built the circuit and the resistance is supposed to be 12 ohms.

I think it may just be my algebra that's messing my answers up. I had 4 equations for the mesh current analysis.

70I1 + 5Vx + 50(I1-I2) = 0

16(I2-I3) + 50(I2-I1) + 18(I2-14) = 0

Vex + 16(I3-I2)=0

18(I4-I2)-5Vx + 13I4=0

Vx = 50(I1-I2)

I think I overcomplicated this by using an external source. It would have been fine if I just tried to find the short circuit current parallel to the 16 ohm resistor.

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# Homework Help: Finding Thevenin equivalent circuit

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