Famous question from IE Irodov :For Finding resistance?



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Consider a infinite square mesh each side made up of 100 Ohm resistors. What will be the resistance measured across one 100 Ohm resistor somewhere in the middle of the mesh.

Famous question from IE Irodov :For Finding resistance?windows explorer

The answer: 50 Ω .

Funny. I hadn't heard of I. E. Irodov, ever. Still, I learned about this problem long ago, back in the '70s. Moreover, I knew which the solution was, because it was given along with the problem statement. I quote:

"4.30 A "puzzle problem" that circulated among electrical engineers some years ago was this: An infinite number of 1 Ω resistors are connected together to form a two-dimensional infinite net with square meshes. That is, at every node leads from four resistors join. What is the equivalent resistance between a node and one of its four nearest neighbor nodes? This problem is a startling example of the power of symmetry and superposition. Using superposition shrewdly, you can do it in your head, almost. Try it any other way and you will appreciate the elegance of the first solution. The answer, by the way, is 0.5 Ω, but we will not spoil the puzzle by telling you what states of current flow to superpose."

This is taken from Electricity and Magnetism, volume 2, Berkeley Physics Course, published 1965. Written by Edward Mills Purcell, recipient of the Nobel Prize in Physics, 1952.

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