So, I was walking through the engineering building here and came accross a chalk board that often has random stuff on it. Its basically a chalkboard for whatever you want to write. Sometime’s there are quotes written there, sometimes tick-tac-toe games, and sometimes some funny drawings. Today there was a brainteaser — specifically a circuit analysis brain teaser. Here’s a sketch of what was on the board:
This is an infinite grid of resistors (all of value “R”) – the elipsis implying that in all directions the circuit continues indefinitely, and the n is just saying this goes on til some “nth” resistor at infinity.
TASK:
Find the thevenin equivalent circuit across terminals a and b (essentially whats the thevenin resistance looking into those terminals).

I would like to be able to say this is an incredibly hard problem that I found the solution to, all Good Will Hunting style, but its just a brainteaser for circuit theory — there is a trick to it, and its neat, but other than that it’s not really anything all that impressive.

It took me a few minutes of thinking but I came up with a solution and it is now posted on the board.

I will state up from that there is a very easy, intuitive, almost no math solution to this problem. There is also a second, more complicated, mathematical solution. I was not clever enough to think of the elegant simple solution, and instead found the more complicated solution. Wasted work, if you ask me. I only found out about the simple solution because when I got back to lab I googled the problem to see if there were any solutions i could check my answer off of (and to see if there were more solutions). Thursday I will post both solutions. Best of luck.

EDIT: I drew only one “cell” of the grid, and drew elipsis to show it goes on forever in all directions, but to make it clear, the overall topology is a huge square grid that is infinite in extent in all directions, as shown below: