☑ Infinite 1 Ohm Resistor Grid Problem

What about a practical one. In one of the xkcd comics titled nerd sniping there is an interesting problem presented as a way to involuntarily distract certain types of people physicists mathematicians etcbeing an electrical engineer i wanted to try and solve this problem in a more typical engineering way than to use math and symbolic.

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Infinite Grid Of Resistors

64 42 Resistor Cube

Xkcd and electronics infinite 1 ohm resistor grid problem.

Infinite 1 ohm resistor grid problem. On an infinite square grid of perfect one ohm resistors what is the equivalent resistance between two points that are a knights move from each other. However with an infinite grid there are infinite paths and infinite combinations therefore their equivalent. As all you members of the ineffable all can see the problem is not trivial.

However given my lack of expertise with basic electronics it could even be an easy one. Xkcd and electronics infinite 1 ohm resistor grid problem. On this infinite grid of ideal one ohm resistors whats the equivalent resistance between the two marked nodes.

With a link to the source. For example two 1 ohm resistors in parallel will be the equivalent of 12 ohm but even the combination of a 1 ohm resistor and a 1 mohm resistor will give an equivalent resistance below 1 ohm albeit a very tiny amount less than 1. It goes on this infinite grid of ideal one ohm resistors what is the equivalent between the two marked nodes just the image assuming the two marked nodes are where a generator capable of producing an infinitely large current is hooked up is there a theoretical solution to this problem.

Im not really sure if there is an answer for this question. Start date aug 12 2009. Infinite grid of resistors solution by simulation.