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

[Mark Nussbaum]

Homework Statement

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.

 

[magoo]

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?

 

[magoo]

Sorry I missed your link. Let me withhold my comments until I look it over further

 

[magoo]

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.

 

[Mark Nussbaum]

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.

 

[Mark Nussbaum]

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...

 

[magoo]

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?

 

[Mark Nussbaum]

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

matrix array.

inverse array and multiply with currents.

 

[The Electrician]

I get Vx = -34.90443

What are you given as the correct answer?

 

[magoo]

Mark,
I agree with your 4 nodal equations so I may have made an error when I computed the inverse or did the multiplication.

 

[Mark Nussbaum]

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...

 

[scottdave]

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.

 

[The Electrician]

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.

 

[Mark Nussbaum]

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.

 

[Mark Nussbaum]

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.