Electronics > Beginners
Resistance across a 1k resistor cube.
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Kirr:

--- Quote from: drussell on April 22, 2018, 04:44:16 pm ---A cube is bad enough, but how about this one from xkcd #730?  https://xkcd.com/730/  :)
--- End quote ---
Yep, this always comes up (as well as infinite grid). Since there are no apparent symmetries, I guess the easiest calculation is via tedious elimination of nodes one after another - Automated here - tick "Explain each step" to see the steps in detail. (Feel free to try it manually before checking the answer). :)

I am curious about optimizing this calculation, because simple brute force process doesn't scale too well. Exploiting symmetries is one way. Another is noticing repetitions, and simplifying them before solving the entire structure (Example). Have to find time to do more experiments with this.
The Electrician:
Do a google search with the phrase "resistor cube equivalent resistance"

Three good ones are:

https://sites.google.com/site/physicsassignmenthelp/video-tutorials/how-to-find-equivalent-resistance-of-resistor-cube

http://web.physics.ucsb.edu/~lecturedemonstrations/Composer/Pages/64.42.html

http://cosinekitty.com/resistor_cube.html
The Electrician:
For extra credit, using these designators and values for the cube resistors, calculate the exact resistance between nodes A and G, showing the result as an improper fraction.  >:D



Kirr:

--- Quote from: The Electrician on April 23, 2018, 10:45:26 am ---For extra credit, using these designators and values for the cube resistors, calculate the exact resistance between nodes A and G, showing the result as an improper fraction.  >:D
--- End quote ---
When ready, click to verify your answer, or to give up :)
rs20:

--- Quote from: The Electrician on April 23, 2018, 10:45:26 am ---For extra credit, using these designators and values for the cube resistors, calculate the exact resistance between nodes A and G, showing the result as an improper fraction.  >:D

--- End quote ---

I already provided the arbitrary resistance closed-form formula back in message #18. Subbing in the values you wrote, the answer is: 6195184/1328873 Ohms.


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