What alternative methods can be used for solving nodal analysis equations?

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Discussion Overview

The discussion revolves around alternative methods for solving nodal analysis equations in electrical circuits. Participants explore various approaches, including the use of least common multiples and software simulations, while addressing specific calculation errors and uncertainties in their results.

Discussion Character

  • Homework-related
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant shares their attempt at solving nodal analysis equations using Cramer's rule but encounters errors in their calculations.
  • Another participant requests clarification on the nodal equations being used, indicating a lack of understanding of the provided data.
  • A suggestion is made to use least common multiples to simplify calculations, which may reduce computational errors.
  • Participants discuss the calculation of Vx and its relationship to V2, with differing interpretations of the equations leading to confusion.
  • One participant reports obtaining a specific voltage value (13.62 V) but questions its accuracy compared to others' results.
  • Another participant expresses uncertainty about their calculations, suggesting that errors may lie in the current equations for the nodes.
  • Multiple participants report arriving at the same value for Vx (-34.90443 V) but express frustration over the correctness of their answers.
  • One participant mentions using a Spice simulation as an alternative method, noting discrepancies in current source polarities that may affect results.
  • Concerns are raised about potential coding errors in automated homework systems that could lead to incorrect feedback on answers.

Areas of Agreement / Disagreement

Participants generally agree on the calculations for V2 and the value of Vx, but there is uncertainty regarding the correctness of their answers and the potential for errors in the problem setup. Multiple competing views and methods are presented without a clear consensus.

Contextual Notes

Participants express limitations in their understanding of the nodal equations and the implications of using different methods, such as least common multiples and software simulations. There are unresolved issues regarding the accuracy of the provided values and the potential for errors in the automated homework system.

Who May Find This Useful

This discussion may be useful for students and practitioners interested in electrical engineering, particularly those working on nodal analysis and seeking alternative methods for solving related equations.

Mark Nussbaum

Homework Statement


upload_2017-9-22_20-28-5.png

upload_2017-9-22_20-28-51.png

Homework Equations


using nodal analysis

The Attempt at a Solution


https://imgur.com/a/UNEDH
the excel sheet is the matrix i set up then used cramer's rule. I think i got the method down but i just can't find the error so hopefully i overlooked something.
The equation i used to find Vx= V2/90 and tried both (+) and (-) answers to check if it was a sign issue.
 
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I'm not sure what your printout is revealing since I don't know what the numbers represent. Can you write out the nodal equations that you are using?
 
Sorry I missed your link. Let me withhold my comments until I look it over further
 
First of all, have you considered using least common multiples? This would make the results a lot easier and the numbers are a good deal smaller to work with.

For example, your Node 1 resistances are 40, 25 and 150. The least common multiple is 600. So you multiply through both sides of the equation by 600 instead of 150,000 which you used. I don't know if this will affect your answers or not but the numbers are not so big this way. Your nodal equation is correct, but I favor using least common multiples. I suspect you are introducing computational errors by using the product of the three resistances instead of the least common multiple.

The other point is calculating Vx. You said you took V2/90. This would be appropriate for Ix but not for Vx. From your sketch, Vx = V2.
 
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Ah thank you that was a terrible oversight... still have the wrong answer so going to try using least common multiples and see if that cleans up the calculations.
 
I ended up with the same answer of
V2 = 34.9044309296265 (tried both positive and negative for the sake of it)
This is not the correct answer so apparently something else is wrong in my solution although I can't imagine what after trying two calculations with the same answer.
My best guess would be one of the current equations for my nodes...
 
I took the matrix inverse and multiplied it by the 4 current values. The result was 13.62 V. Is that close to what you expect?
 
I tried to do the same calculation in excel and couldn't get the same answer you did I got the same 39.90443 answer would you mind showing the numbers that you used to get 13.62V
I got
node 1: -2400 = 43V1 - 15V2 - 4V3 + 0V4
node 2: 0 = -9V1 + 19V2 - 6V3 + 0V4
node 3: 900 = -2V1 - 5V2 + 37V3 - 30V4
node 4: 200 = 0V1 + 0V2 - 20V3 + 21V4
upload_2017-9-23_3-33-46.png

matrix array.
upload_2017-9-23_3-33-58.png

inverse array and multiply with currents.
 
I get Vx = -34.90443

What are you given as the correct answer?
 
  • #10
Mark,
I agree with your 4 nodal equations so I may have made an error when I computed the inverse or did the multiplication.
 
  • #11
The Electrician said:
I get Vx = -34.90443

What are you given as the correct answer?
sadly it doesn't give a correct answer even when I have run out of attempts I have to manage to find it and put it in still and it will tell me its correct...
 
  • #12
Mark Nussbaum said:
sadly it doesn't give a correct answer even when I have run out of attempts I have to manage to find it and put it in still and it will tell me its correct...
Have you tried other methods, than just Nodal analysis. I used a Spice simulation, and also got -34.904 volts. I first got a different answer, but had one of the current sources +6 Amps instead of -6 as in the problem. I am wondering why they had the polarities like that. Sources pointing different ways, some positive, some negative. Then the voltage measurement has positive on the bottom... Weird. Can you email the professor for advice or technical assistance? That's one bad thing about these automated homework assignments. One coding error and everybody is getting it wrong.
 
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  • #13
I'm quite certain that you have the correct result for V2. Did you try putting in the other 3 node voltages? Maybe someone confused voltages in the problem answer. Occasionally, course materials make a mistake; this may be one of those times.
 
  • #14
I emailed him and in fact the correct answer is indeed -34.9044V it appeared to be some sort of coding error but is fixed now thanks all for your help.
 
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  • #15
scottdave said:
Have you tried other methods, than just Nodal analysis. I used a Spice simulation, and also got -34.904 volts. I first got a different answer, but had one of the current sources +6 Amps instead of -6 as in the problem. I am wondering why they had the polarities like that. Sources pointing different ways, some positive, some negative. Then the voltage measurement has positive on the bottom... Weird. Can you email the professor for advice or technical assistance? That's one bad thing about these automated homework assignments. One coding error and everybody is getting it wrong.
I'll have to take a look at Spice Simulation it sounds very helpful for troubleshooting the problems.
 

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