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): Resistor Mesh Cube ------------------ N V R 1 4.000000 8.333333 2 3.255814 10.238095 3 2.967581 11.232493 4 2.813628 11.847100 5 2.718043 12.263726 6 2.653020 12.564298 7 2.605965 12.791168 8 2.570354 12.968384 9 2.542474 13.110588 10 2.520060 13.227196 20 2.418082 13.785033 25 2.397487 13.903444 N is the number of resistors on one edge, so number of nodes on one edge is N+1. V is the voltage at the corner across one resistor that goes to ground. R is the total resistance across two opposite 3d corners. 10v is applied to one corner, 0v to the oppositve corner. Note that the "opposite corner" is across the center of the cube not just across one surface. The solution with applied voltage across opposite corners of just one surface is a different problem. All resistors in the cube are 10 ohms each. 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.
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.