Finding Thevenin Equivalent circuit (Voc)

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Discussion Overview

The discussion revolves around finding the Thevenin equivalent circuit, specifically focusing on the open-circuit voltage (Voc) in a given electrical problem. Participants are analyzing their approaches to solving the problem using node voltage analysis and comparing it with a mesh analysis method presented in an answer key.

Discussion Character

  • Homework-related
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant presents their calculations for Voc, arriving at a value of 150 V, but expresses uncertainty about its correctness.
  • Another participant agrees with the 150 V result but suggests there may be an error in the answer key.
  • A participant introduces the answer key's method, which uses mesh analysis, and questions whether both methods should yield the same result.
  • Another participant confirms that both methods should produce the same answer and identifies an error in the answer key's workings.
  • One participant clarifies that their instruction to use node voltage analysis was to avoid biasing responses, noting that both methods were acceptable on the test.
  • There is uncertainty about the specific error in the answer key, with one participant suggesting it might relate to the inclusion of Voc in the first equation.
  • Another participant corrects this notion, indicating that the error lies in the polarity of the current terms in the equation.

Areas of Agreement / Disagreement

Participants generally agree on the calculated value of 150 V for Voc, but there is disagreement regarding the correctness of the answer key's solution and the specific nature of its errors. The discussion remains unresolved regarding the exact mistake in the answer key.

Contextual Notes

Participants express uncertainty about the correctness of their calculations and the answer key, indicating potential limitations in their understanding of the problem setup and the methods used.

Runner 1
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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} &amp; = &amp; 0 \\<br /> <br /> \dfrac{v_2-v_1}{3} + \dfrac{v_2-v_{oc}}{5} &amp; = &amp; 10 \\<br /> <br /> \dfrac{v_{oc}-v_2}{5} &amp; = &amp; \dfrac{v_x}{4} \\<br /> <br /> v_1 &amp; = &amp; v_x<br /> \end{array}

These simplify to:

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

in matrix form:

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

Solving, this gives:

\begin{array}{cc}<br /> v_1 &amp; = &amp; 40\, V\\<br /> v_2 &amp; = &amp; 100\, V\\<br /> v_{oc} &amp; = &amp; 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!
 
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150V for Voc looks good to me. Perhaps an error in the book?
 
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?
 
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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?
 
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?
 
Runner 1 said:
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
 
Ah, I see it now! Thank you. I suppose I will email the professor.
 

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