Electronics > Beginners
Is it possible to know all voltages/amps in a grid or matrix of resistors?
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Beamin:
I just thought of this: What if you had a large grid of 1k resistors (can't make an ascii diagram for some reason) but rows or horizontal and vertical resistors
each resistor is connected to three other resistors. And you had a 10X10 or 1000X1000 or infinately big grid. How would you figure out the voltages? Is there an elegant math problem for this that could go up to infinate resistors? What would happen if it was a cube or if say you added 1V@1A to each corner? Or put +1 one one corner -1 on opposite corner and ground in the middle? I don't know where to start figuring this out because there would be so many values that change based on other values as every path is connected. My resistors are in storage so I can't build one to test at the moment so I will have to do this expirament in my head. Is this what a differential equation is in real life when your varibles change based on the other variables ie a+b+c=d if b=d+c? There must be a name for thisproblem so I can have a start point for google.
JimRemington:
These are standard problems and there are elegant ways to solve them. Google "solve resistor grid", for example.
MK14:
This video, seems to discuss what you are asking, to a reasonable extent.

StillTrying:

--- Quote from: Beamin on June 06, 2018, 03:43:00 pm ---And you had a 10X10 or 1000X1000 or infinately big grid. How would you figure out the voltages?
--- End quote ---

I'd be doing a lot of copying and pasting in LTSpice. >:D
rstofer:
Here is the solution for a finite grid and it is easily solved with MATLAB among other tools:
http://www.wiete.com.au/conferences/2wctee/papers/15-13-Zegarmistrz-P.pdf

The infinite grid is a little more difficult and hand-wavy because spooky stuff happens out at infinity.
http://www.mathpages.com/home/kmath668/kmath668.htm

Nothing new here, the finite grid is discussed in just about every EE101 class.

Sometimes the grid is wrapped around, like a sphere or just a cube
http://physicstasks.eu/285/the-resistance-of-a-wire-cube
http://www.rfcafe.com/miscellany/factoids/kirts-cogitations-256.htm

Really, these are just exercises in finding symmetry and creating the matrix.
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