0---r---....---r---r---r---r---r---r---....---r---r---0 | | | | | | | | r r r r r r r r | | | | | | | | . . . . . . . . . . . . . . . . | | | | | | | | r r r r r r r r | | | | | | | |
0---r---....---r---r---r---r---r---r---....---r---r---0 | | | | | | | | r r r r r r r r | | | | | | | |
0---r---....---r---r---r---r---r---r---....---r---r---0 | | | | | | | | r r r r r r r r | | | | | | | |
0---r---....---r---r-A-r-B-r---r---r---....---r---r---0 | | | | | | | | r r r r r r r r | | | | | | | |
0---r---....---r---r---r---r---r---r---....---r---r---0 | | | | | | | | r r r r r r r r | | | | | | | |
0---r---....---r---r---r---r---r---r---....---r---r---0 | | | | | | | | r r r r r r r r | | | | | | | | . . . . . . . . . . . . . . . . | | | | | | | | r r r r r r r r | | | | | | | |
0---r---....---r---r---r---r---r---r---....---r---r---0 | | | | | | | | | | | | | | | | r r r r r r r r | | | | | | | | | | | | | | | | 0 0 0 0 0 0 0 0
This is a 2D resistive grid which expands in all directions. The potential at infinite is 0 as indicated in above schematic. Find the equivalent resistence between point A and B as shown in figure above. I found out experimentally by constructing a huge grid and applying a voltage source between A and B. Then I measured the current and took ratio of voltage and current to give me equvivalent resistence. It comes out to be approximately r/2. But how can we do it analytical. does anyone have any clue how to start? Thanks.