How to Find Thevenin Equivalent Resistance?

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Discussion Overview

The discussion revolves around finding the Thevenin equivalent resistance for a given circuit involving resistors and voltage sources. Participants explore various methods and approaches to solve the problem, including superposition and circuit simplification techniques.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant outlines their approach to finding the Thevenin equivalent resistance, mentioning the use of superposition to calculate open-circuit voltage (Voc) and short-circuit current (Isc).
  • Another participant suggests an alternative method of suppressing all sources to find the equivalent resistance looking into the network, indicating that determining the short-circuit current is not necessary.
  • A participant expresses uncertainty about identifying which resistors are in series or parallel due to the circuit's configuration and requests further guidance.
  • One participant notes that the voltage sources isolate certain loops in the circuit, allowing for simplification by eliminating specific components without affecting the Thevenin equivalent.
  • Another participant highlights the formation of a supernode due to equal voltage sources, suggesting that this could lead to further simplifications by allowing some resistors to be combined in parallel and eliminating one voltage source.

Areas of Agreement / Disagreement

Participants present multiple approaches and methods for finding the Thevenin equivalent resistance, indicating that there is no consensus on a single method. The discussion remains exploratory with various viewpoints and techniques being shared.

Contextual Notes

Participants express uncertainty regarding the configuration of the circuit and the relationships between components, which may affect their calculations and approaches. There are unresolved aspects related to the identification of series and parallel resistors.

jgv115
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Homework Statement


zP88WtX.gif

Where R1 = 2.4k, R2 = 2.9k, Vs1=7V, Vs2=7v and Is = 4mA

For this circuit I need to find the Thevenin Equivalent resistance.

Homework Equations


The Attempt at a Solution



*Just a heads up, all my loop analysis stuff is going clockwise*

I've tried everything to try to solve this problem but I still can't get it. Here's what I've tried:

To find Rth I need Voc and Isc.

So to find Voc I used superposition:

If I short circuit Vs1 and Vs2, I get Vo(1) = 2.4k * 4mA = 9.6V

If I open circuit Is and short circuit Vs2 and use loop analysis:

2.4k(i1) + 7 +2.9k(i1) = 0
Solving for i1 = -0.001321A
Therefore Vo(2) = 2.9k * i1 = 3.83V

Then I open circuit Is and short circuit Vs1 wouldn't Vo(3) just be Vs2 = 7V?

Am I on the right track or have I completely gone off course? Any help is appreciated!
 
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The other way to find Vth is to suppress all the sources and find the equivalent resistance looking into the network at the output terminals; you don't have to determine the short circuit current.
 
Hi gneill,

I've thought about doing that but because of the way the circuit is built, I don't quite understand which resistors are in series/parallel with other resistors.

Can you give me some tips/hints?
 
Notice that Vs1 and Vs2 "isolate" the top two loops from the bottom two loops.

Any current provided by Is flows only in Vs1 and Vs2; it can't reach the bottom resistors.

If you eliminate the top two resistors and Is, the behavior at the Vo terminals is unaffected; the Thevenin equivalent is the same with the top two loops gone, and that's an easier calculation.
 
A hint: The voltage sources keep the potential differences between the middle three nodes at fixed values. In other words, what's called a supernode is formed by those nodes. As luck would have it the two voltage sources have the same value! And with the way they're oriented, the leftmost node must always have the same potential as the rightmost (Vo). So they are electrically the same node! There's your opportunity to not only put some resistors in parallel, but to eliminate one of the voltage supplies completely :wink:

attachment.php?attachmentid=63103&stc=1&d=1382184273.gif
 

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gneill, may I ask what software you use to annotate the OP's image?
 
The Electrician said:
gneill, may I ask what software you use to annotate the OP's image?

Sure. I use an old version of Visio. I copy/paste to Visio, mark it up, then copy/paste to Paint to save it as a gif. (Visio can create gifs directly, but it uses a filter of some sort that is tedious to use. With paint there are no options, just "Save as". Actually takes much less time!)
 

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