This still seems to be a class exercise.

 

Only thing I can think of as an approach would be a spread sheet. But I haven't a clue how to construct it.

While I haven't been giving this much thought, a "V-Lookup" function in Excel MIGHT solve the problem. You input each of the points you want to calculate - - - no - - - wait - - - OK, forget I mentioned it. If somewhere in the middle of the grid, imagine points AA - AB for instance, the entire grid MUST be calculated in. I don't see a solution. For AA & AB "ALL" other resistors continue to influence the resistance of AA - AB. It's doable with four points but with thousands of points - it'll take a math whiz to even begin to suggest a solution.

My advice, forget about this problem. It's, as far as I can tell, unsolvable.

 

While I haven't been giving this much thought, a "V-Lookup" function in Excel MIGHT solve the problem. You input each of the points you want to calculate - - - no - - - wait - - - OK, forget I mentioned it. If somewhere in the middle of the grid, imagine points AA - AB for instance, the entire grid MUST be calculated in. I don't see a solution. For AA & AB "ALL" other resistors continue to influence the resistance of AA - AB. It's doable with four points but with thousands of points - it'll take a math whiz to even begin to suggest a solution.

My advice, forget about this problem. It's, as far as I can tell, unsolvable.

Of course it's solvable. Given enough time, you can solve it by hand. You just need to devise an algorithm to automate the process.

 

This still seems to be a class exercise.

Possibly. The TS has stated that it isn't, but such claims are not always above board.

But, if it is a class exercise, the students appear to be operating far more open-loop than usual.

 

Consider that the TS is identified as a student. Of course this could be a MENSA exercise, I understand that occasionally they solve non-solvable equations just for fun, much like I occasionally repair non-repairable devices just for kicks. Some folks assemble difficult "Jigsaw" puzzles, which is strictly for their entertainment.

 

Thanks all for your valuable feedbacks. I guess I will have to use some kind of simulation software (i dont know which one yet) that would make a giant network of resistors with 10000 nodes. Then, I would apply voltage across any 2 nodes and find current and thus find effective resistance.

I am however trying to figure out how can I make this process automated so that I could find effective resistance between every 2 nodes possible without doing manually.

First form the admittance matrix for your network. Then do some linear algebra.
See: https://en.wikipedia.org/wiki/Laplacian_matrix
Also: https://en.wikipedia.org/wiki/Resistance_distance

Here is a worked example: https://www.physicsforums.com/threa...ctrical-circuits-networks.939813/post-5951075

 

And I am wondering what sort of real world application this would apply to.

See the references in this article: https://en.wikipedia.org/wiki/Resistance_distance

The physical chemistry people use it.

 

I found the physical chemistry class to be a bit challenging as taught where I studied. Useful concepts but killer math, as I recall.

 

Consider that the TS is identified as a student. Of course this could be a MENSA exercise, I understand that occasionally they solve non-solvable equations just for fun, much like I occasionally repair non-repairable devices just for kicks. Some folks assemble difficult "Jigsaw" puzzles, which is strictly for their entertainment.

Just because someone is a student doesn't mean that everything they do is related to an assignment -- good students spent more time pondering and solving problems that are not assigned than they do ones that are.

It would be interesting to have more info one what is motivating this problem, just out of curiosity and perhaps to give better guidance or suggest alternative approaches that might prove more useful, but there's no requirement that they provide it.

 

Amazing @The Electrician . Thanks a lot
I tried to understand the worked example.
I have a question. What did you do in the end once you find the pseudo inverse ?

 

@The Electrician . Also, will this method work because all my resistors do not have same resistance value, which was the case in the worked example you shared.
I am sorry if I am not understanding it properly . I have limited knowledge in electric circuits.
Thank you for your patience !

 

@The Electrician . Also, will this method work because all my resistors do not have same resistance value, which was the case in the worked example you shared.
I am sorry if I am not understanding it properly . I have limited knowledge in electric circuits.
Thank you for your patience !

The resistors don't have to be all one value. The matrix of resistance values has the same dimensions as the admittance matrix. Once you have the pseudoinverse, you then build the final matrix by doing some arithmetic with 4 values from the pseudoinverse for each value in the final matrix.

Study the line in my example that starts "R=Table......."; that's where the arithmetic happens.

What math app do you have to do all this linear algebra? I used Mathematica.

I have to be away until later this evening. Let me know if you need any more help.

 

13rajendra, have you had getting this to work? What math software are you using? Does it provide the pseudoinverse?

It may be possible to avoid having to compute the pseudoinverse. Tell us how you are doing.

 

I actually managed to get it worked for a 4 node network. I am very hopeful that this will also work for 10000 node circuit as well. Thank you very much @The Electrician . Great help indeed . However I wanna know more about it , i mean i wanna know how does it work. Is there any article explaining it?

 

I actually managed to get it worked for a 4 node network. I am very hopeful that this will also work for 10000 node circuit as well. Thank you very much @The Electrician . Great help indeed . However I wanna know more about it , i mean i wanna know how does it work. Is there any article explaining it?

This method works for any number of nodes as long as you have capability for the necessary number crunching.

Check the references to this article: https://en.wikipedia.org/wiki/Resistance_distance

For example, this one: https://web.archive.org/web/2012032.../cca2002/v75-n2/CCA_75_2002_633_649_KLEIN.pdf

A network of 100 resistors has an admittance matrix of 10000 elements (it's 100x100). A network with 10000 resistors leads to a really big matrix!!

You haven't answered my question about what math software you're using to do all this number crunching.

And of course, others reading this thread are wondering what the purpose of this is; is it a secret?

 

I'm using R to do it. Its for my course project where i am analyzing a huge network with edges.. im planning to use effective conductance as a measure of how connected two nodes are.

 

I'm using R to do it. Its for my course project where i am analyzing a huge network with edges.. im planning to use effective conductance as a measure of how connected two nodes are.

R is a programming language usually used for statistics computations. Your 10000x10000 matrix will have 100 million elements. I wonder if some other app such as MATLAB, which is especially good for linear algebra math might be better able to handle your problem. I would think most educational institutions would have MATLAB available on their network for student use.

The admittance matrix with which this method begins has elements that are conductances, not resistances. The final result is a matrix of resistances, which of course can be easily reciprocated to get conductance.

The admittance matrix which you'll need to create from your network will be singular, which is why the pseudoinverse is the usual next step in the method.

However, there is a trick. If you simply add a constant (with a value about the same magnitude as the rough average of the other elements of the admittance matrix to avoid numerical problems) to any one element of the admittance matrix, it will no longer be singular. You can then simply invert it (the ordinary inverse, not the pseudoinverse). Then proceed using the inverse where you previously used the pseudoinverse. It will work just as well. Give it a try. Tell us how it's all going.

 

I'm using R to do it. Its for my course project where i am analyzing a huge network with edges.. im planning to use effective conductance as a measure of how connected two nodes are.

Is this a standard technique (using effective conductance)? Does your instructor know how to solve your problem, but didn't tell you how because they wanted you to research it for yourself?

 

What I find now that is interesting is that this is far from a new challenge. The first time I saw this question posed was in a Q and A section of an electronics magazine back in about 1964, while I was in High School. It has been repeated many times since then. In one college class years later one instructor showed that the solution could exist as an infinite series, if the network extended that far. At that point the instructor also showed that there would not be an exact solution to an infinite series. That is a valid conclusion, based on a rational evaluation.
Thus the answer depends on how close you need to be to exact.

 

What I find now that is interesting is that this is far from a new challenge. The first time I saw this question posed was in a Q and A section of an electronics magazine back in about 1964, while I was in High School. It has been repeated many times since then. In one college class years later one instructor showed that the solution could exist as an infinite series, if the network extended that far. At that point the instructor also showed that there would not be an exact solution to an infinite series. That is a valid conclusion, based on a rational evaluation.
Thus the answer depends on how close you need to be to exact.

Are you thinking of this problem: https://physics.stackexchange.com/q...-of-resistors-whats-the-equivalent-resistance

That's not 13rajendra's problem. I've never seen 13rajendra's problem posed in popular electronics magazines. I have seen the infinite resistor grid problem, and the cube of resistors problem, but never 13rajendra's problem.