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  • EEVblog #25 – The Infinite Resistor Puzzle

    Posted on August 15th, 2009 EEVblog 16 comments

    The Infinite Resistor Puzzle

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    • http://www.youritronics.com Florin

      pretty cool, I always like to do it this way. Measuring things instead of doing the math.

    • http://www.danielbjohnson.net Daniel

      Not asking for a video, but did you get a measurement for a 2×2 diagonal? And was that in 1+1=2% tolerance? (for some reason I think it would be under 2.9999999% tolerance no matter where you are in the grid.)

      Your grid reminded me of these LED Cubes people have been building.

      If you haven’t seen one: http://www.youtube.com/watch?v=Pq0dPLPeQpY

      • http://www.alternatezone.com/eevblog admin

        8.683K for 2×2
        It’ll always be +/-1%
        The LED cubes are cool

    • http://www.alternatezone.com/eevblog admin

      The ever-knowledgable Don Sauer has provided a really neat Excel Spresdsheet tool to play around with and visualize the Infinite Resistor problem.

      http://www.alternatezone.com/stuff/ResistorCalcTool.pdf
      and
      http://www.alternatezone.com/stuff/ResistorCalcTool.xlsx

      Dave.

      • SB

        Hey,

        That excel tool you mentioned for this problem.. the link is down. Can anyone send it to me. I’d really appreciate that.

        Thanks

    • Evan

      Would similar results be obtained with a triangular grid?

    • Stephen

      I dropped out of an electrical engineering degree because I got so dam fed of doing calculations and spending no time in the lab I enjoyed this video a lot good to see the physical applications for once.

    • http://www.bidouille.org/ vic

      Wow congratulations for actually building an “infinite grid” :D. I think doing the math and seeing Pi appear out of nowhere (as it likes to do) is really amazing too.

      Here’s another problem : is it possible to build a grid where the resistance between any 2 nodes is always the same ? Try to use a finite number of dimensions :P

      • whitis

        @vic: Same resistance from every point to every point is easy enough: Solder up a grid of inifinite resistors, like Daves (10M or larger will do). From each node connect a 1K resistor pointing backwards. Then build another grid of zero ohm resistors and connect the free ends of the 1K resistors to the nodes in that grid. Any point to any point on the front is 2K. Build another layer and you can make the same true for the back, as well.

        If you are sneaky, before you build it you will take your 10M and zero ohm resistors, chuck them up in a lathe and put down a base coat of epoxy that matches the body color of your 1K resistors, then color code them all 1K. That will have people scratching their heads.

        You can also build a giant 3D cube such that each of the six faces (except the edges, but people won’t be surprised to see a difference there) have your desired property.

        There are real world applications for this topology and variations on it which provide bulk resistivity in 1 or 2 out of 3 axes.
        – Zebra strips for connecting LCD displays
        – Motor brushes which short out adjacent commutator segments to a lesser extent.
        – Antistatic mats which dissipate static but put less load between points on live circuit boards than regular bulk resistive material.
        – Material that selectively dissipates e-fields while reflecting m-fields.
        – transformer and motor core laminations do something similar, but one axis has permeability, while it limits electrical conductivity and eddy currents in other directions.
        – litz wire – reduce skin effect.
        – bed of nails test fixture

        Some practical applications can be built out of conductive fibers with an insulating coating combined like the fibers in a fiber optic bundle.

    • nick

      When, can we see the grid in a frame?

      • http://www.eevblog.com EEVblog

        Well, if I don’t do it soon it’s going to get eventually mangled just being tossed around my bench!

    • http://teque5.com Teque5

      Obligatory XKCD Infinite Resistor Comment: http://xkcd.com/356/

    • Nasma

      This is the best thing I’ve seen all year.

    • http://www.soasystem.com shafri

      1) do 3×3 grid, measure
      2) do 5×5 grid, measure
      3) do 7×7 grid, measure
      4) do 9×9 grid, measure


      n) do until you satisfy or run out of resistor
      n+1) plot in graph
      n+2) extrapolate
      n+3) you will have a better idea on how this
      infinitum goes in practical.

      ps: just my 2 cents. i dont do it, i dont have resistor, i’m quite lazy, i got another more interesting things to do. nice video though, nice playing around. sometimes. :)

      • aa851210529

        That’s called Richardson Extrapolation. They use this sort of thing in numerical simulations where you double the grid resolution a couple times, then extrapolate to infinite resolution. Since your input wasn’t perfect you don’t get a perfect answer out of the method, but you can typically increase the quality of your answer by a single order. Very useful concept.

    • en4rab

      I realise this comment comes rather late but i have only just found this video.
      Would it be possible to more closely approximate the infinite resistor network by connecting a resistor and a wire between the top row and the bottom row of your grid, and the same for the sides, its kind of hard to explain what im thinking but like the game pac man, you go off one side and appear on the other :)

      My thinking is this should create a virtual infinite network but i suspect my thinking is incorrect.