Finding Thevenin Equivalent circuit (Voc)

[Runner 1]

Homework Statement

[PLAIN]http://dl.dropbox.com/u/9699560/EE%20Problem.jpg

(I added the text V1, V2, and Voc to the image).
I'm only trying to find Voc because I got the wrong answer. I got Isc correct.

Homework Equations

Basic node voltage analysis techniques.

The Attempt at a Solution

Let the bottom-most node be the ground (reference node).

$\begin{array}{rcl}<br /> \dfrac{v_1}{2} + \dfrac{v_1-v_2}{3} & = & 0 \\<br /> <br /> \dfrac{v_2-v_1}{3} + \dfrac{v_2-v_{oc}}{5} & = & 10 \\<br /> <br /> \dfrac{v_{oc}-v_2}{5} & = & \dfrac{v_x}{4} \\<br /> <br /> v_1 & = & v_x<br /> \end{array}$

These simplify to:

$\begin{array}{rcl}<br /> 5v_1 - 2v_2 + 0v_{oc} & = & 0 \\<br /> -5v_1 + 8v_2 - 3v_{oc} & = & 150 \\<br /> 5v_1 + 4v_2 - 4v_{oc} & = & 0<br /> \end{array}$

in matrix form:

$\left[\begin{array}{rrrr}<br /> 5 & -2 & 0 & 0 \\<br /> -5 & 8 & -3 & 150 \\<br /> 5 & 4 & -4 & 0<br /> \end{array}\right]$

Solving, this gives:

$\begin{array}{cc}<br /> v_1 & = & 40\, V\\<br /> v_2 & = & 100\, V\\<br /> v_{oc} & = & 150\, V<br /> \end{array}$

However, 150 V is not the correct answer for Voc. Does anyone know where I have made a mistake?

Thanks!

 

[gneill]

150V for Voc looks good to me. Perhaps an error in the book?

 

[Runner 1]

Okay, I was being a little tricky here because I didn't want to bias anyone with the answer key's method for the solution, but perhaps the difference between my setup and theirs is where the flaw is. Here is how the key does it:

[PLAIN]http://dl.dropbox.com/u/9699560/ee%20problem%202.jpg

It solves the system with mesh analysis -- but it should give the same result either way (node or mesh), shouldn't it?

 

[gneill]

Yes, it should get the same answer using mesh analysis. There's at least one error in the answer key's workings (I stopped reading after spotting the first error).

Note the indicated directions for the mesh currents, then look at the first equation of the solution. Note any problems?

 

[Runner 1]

Okay, thank you.

This question is from a test I took this morning. When I stated "The problem needs to be solved using node voltage analysis, not mesh analysis", that was my own instruction so that responses to my original post would determine the solution in the same manner I did it (because I assumed I was wrong -- not the instructor). On the actual test, either method was acceptable.

I'm still kind of uncertain what error is in the answer key's solution -- is it the fact that Voc is added to the first equation?

 

[gneill]

I'm still kind of uncertain what error is in the answer key's solution -- is it the fact that Voc is added to the first equation?

Nope. Voc being there is fine. It's the polarity of the 5*I2 term. The solution shows that I1 and I2 flow in opposite directions (clockwise versus counterclockwise), so the I2 term MUST have an opposite sign to the I1 terms in the same equation

 

[Runner 1]

Ah, I see it now! Thank you. I suppose I will email the professor.