Resistor Cube Properties

Discussion in 'Math' started by MrAl, May 27, 2017.

  1. MrAl

    Thread Starter AAC Fanatic!

    Jun 17, 2014
    5,365
    1,150
    Hello there,

    I started working on the resistor cube problem that we started thinking about in the resistor grid thread. Here are some results:
    Code (Text):
    1.  
    2.  
    3.   Resistor Mesh Cube
    4.   ------------------
    5.  
    6.   N    V            R
    7.   1  4.000000  8.333333
    8.   2  3.255814  10.238095
    9.   3  2.967581  11.232493
    10.   4  2.813628  11.847100
    11.   5  2.718043  12.263726
    12.   6  2.653020  12.564298
    13.   7  2.605965  12.791168
    14.   8  2.570354  12.968384
    15.   9  2.542474  13.110588
    16.   10  2.520060  13.227196
    17.   20  2.418082  13.785033
    18.   25  2.397487  13.903444
    19.  
    20.   N is the number of resistors on one edge, so number of nodes on one edge is N+1.
    21.   V is the voltage at the corner across one resistor that goes to ground.
    22.   R is the total resistance across two opposite 3d corners.
    23.   10v is applied to one corner, 0v to the oppositve corner.
    24.   Note that the "opposite corner" is across the center of the cube not just across one surface.
    25.   The solution with applied voltage across opposite corners of just one surface is a different problem.
    26.   All resistors in the cube are 10 ohms each.
    27.  
    28.  
    The only problem i ran into was that i was not able to verify the results for N>2 because i did not have any secondary method to calculate these values yet. They do look reasonable though, and the cube grid node values all look reasonable with the characteristic 1/2 Vcc showing up across a surface internal to the cube as expected (the 2d grid showed this behavior across the minor diagonal).

    If anyone wants to try to verify any of these values that would be great.
     
    Last edited: May 27, 2017
  2. MrAl

    Thread Starter AAC Fanatic!

    Jun 17, 2014
    5,365
    1,150

    Hello there,

    Was that by any chance the coding for how to get free advertising :)

    I did not revisit this problem yet since the time of the first writing as i have gotten involved with other things since then.
    I suppose i could set up a regular 3d Nodal analysis but didnt get to do anything like that yet. The current method i use is to solve a discrete version of Laplace's equation in three dimensions as that is the fastest and requires the least storage.
    If i get a chance maybe next week i might be able to verify some of those numbers using a regular Nodal type analysis.
    The cube is a little interesting to me because it is like a discrete version of a solid piece of conductive material.
     
    Last edited by a moderator: Dec 16, 2017
    GopherT likes this.
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