Electronics > Beginners
Resistance across a 1k resistor cube.
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The Electrician:
A general solution to this sort of problem is provided by graph theory:
https://en.wikipedia.org/wiki/Resistance_distance

This provides a comprehensive and compact way to compute the resistance from every node to every other node:







rs20 and kirr got the correct result.
rs20:

--- Quote from: The Electrician on April 23, 2018, 07:14:58 pm ---In reply #18 you seemed not absolutely certain that your formula was perfectly correct:

...

I thought I'd give you another dataset to test.  :)

--- End quote ---

Why do you think I suddenly sounded so much more confident? In other words, thanks for the extra test  :)  :-+


--- Quote from: The Electrician on April 23, 2018, 07:22:20 pm ---A general solution to this sort of problem is provided by graph theory:
https://en.wikipedia.org/wiki/Resistance_distance

--- End quote ---

Fascinating! Haven't had a chance to absorb this yet, but I'm a bit blown away that such a general solution can be expressed so compactly in with fairly standard-looking matrix operations.


--- Quote from: Kirr on April 23, 2018, 01:20:49 pm ---Correct about public domain and closed source. I'll probably clean it up enough for opening some day. However I'm also curious about adding symbolic solution to the solver. My only worry is that it can quickly grow out of control and turn out enormous in the end. Would be interesting to see memory requirement and speed on larger networks. Perhaps we could collaborate on this.

--- End quote ---

You don't need the code to be 100% utterly perfectly formatted and coded before open sourcing it! I understand this is a common hesitation, I certainly share it. But anyway, I'm certainly keen to collaborate!


--- Quote from: Kirr on April 23, 2018, 01:20:49 pm ---I guess the final expanded formula is unique for each network, so should be identical (other than order of terms in each sum).

--- End quote ---

Indeed, I suspect you're right about this. But a non-expanded or multi-step calculation (in which there are "temporary variables" or "intermediate values") might give a more compact representation. I'm not sure if all this is any use for anything, but at the very least it could be interesting as a purely academic exercise.

Also, your tool can simply refuse to give closed-form solutions for sufficiently large networks :-)
hamster_nz:

--- Quote from: rs20 on April 24, 2018, 04:32:47 am ---
--- Quote from: The Electrician on April 23, 2018, 07:22:20 pm ---A general solution to this sort of problem is provided by graph theory:
https://en.wikipedia.org/wiki/Resistance_distance

--- End quote ---

Fascinating! Haven't had a chance to absorb this yet, but I'm a bit blown away that such a general solution can be expressed so compactly in with fairly standard-looking matrix operations.

--- End quote ---

If you want a trip down "old school computer magazine lane" check out this 1986 Byte magazine section:

https://archive.org/stream/byte-magazine-1986-07/1986_07_BYTE_11-07_Engineers_Toolbox#page/n167/mode/2up

It walks you though why matrix operations can model this problem, and eventually builds up to modeling a 741 OpAmp on a Commodore 64 (giving results with 1% that of SPICE!)

It almost deserves a thread of it's own :D
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