[Brain Teaser] Infinite Grid of 1 Ohm Resistors

xheavenlyx

@xheavenlyx-CbvN62 • Oct 26, 2024

Oct 26, 2024

1.5K

On an infinite grid of ideal one ohm resistors, what is the equivalent resistance across the two given points?

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A clearer image:

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ISHAN TOPRE

@ishan-nohePN • May 9, 2011

I guess 2R. 😀
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Harshad Italiya

@harshad-ukH5ww • May 9, 2011

I think it will be R only.
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xheavenlyx

@xheavenlyx-CbvN62 • May 9, 2011

Hmm. I will wait for about 2 more days before I try to solve it myself or post the answer (from another source).
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everett.pattison

@everettpattison-3yhnjP • May 10, 2011

I am guessing that it will be approaching zero but never reaching it because all the resistors in parallel will continuously reduce the resistance lower and lower and lower.
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xheavenlyx

@xheavenlyx-CbvN62 • May 10, 2011

Ishutopre, godfather give your proofs in a bit more detail.
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silverscorpion

@silverscorpion-iJKtdQ • May 10, 2011

Is the first image from xkcd? I remember something like this in one of the cartoons there.. 😀

Anyway, in the second diagram, are the nodes across which you want the effective resistance same as in first pic?
I'm working on it. Will post my answer later!!
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PraveenKumar Purushothaman

@praveenkumar-66Ze92 • May 10, 2011

It would be sqrt(R)
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xheavenlyx

@xheavenlyx-CbvN62 • May 10, 2011

Yes silver the first one is from xkcd, thats where I got the question from. It was from Physicist Sniping. I will look for the comic and post it here. And Praveen, please provide proof and calculations with your answer. We need a discussion too 😀
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PraveenKumar Purushothaman

@praveenkumar-66Ze92 • May 10, 2011

xheavenlyx
Yes silver the first one is from xkcd, thats where I got the question from. It was from Physicist Sniping. I will look for the comic and post it here. And Praveen, please provide proof and calculations with your answer. We need a discussion too 😀
Er... Its a wild guess of resistance across a square is the square root of the resistance... Am I right? Got this logic from my physics book of 10th std... 😛
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xheavenlyx

@xheavenlyx-CbvN62 • May 10, 2011

xkcd: Nerd Sniping - one of the best geek comic strip I've come across in the recent times. Check it out and share your comment below.

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PraveenKumar Purushothaman

@praveenkumar-66Ze92 • May 10, 2011

You mean to say that guy is dead??? Lorry foooom???
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maraitamilan

@maraitamilan-YIpgyG • May 11, 2011

1/R(total) = 1/R1 + 1/R2 + 1/R3 ....... + 1/Rn here n tends to infinity so the resistance across the network may be infinite am i right???????? 😀
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xheavenlyx

@xheavenlyx-CbvN62 • May 11, 2011

Yea if you kill a physicist you get 2 points, one mathematician 3 points. Try it at your local university.

Thanks maraitamilan, I will keep your answer in mind.
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PraveenKumar Purushothaman

@praveenkumar-66Ze92 • May 11, 2011

xheavenlyx
Yea if you kill a physicist you get 2 points, one mathematician 3 points. Try it at your local university.

Thanks maraitamilan, I will keep your answer in mind.
Adoppaavingala (oh my god fellas), this is too much... But yeah, funny too! 😀
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amar.amar

@amaramar-EBl7G3 • May 13, 2011

is it 3R....
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amar.amar

@amaramar-EBl7G3 • May 13, 2011

dis might b wrong yaar as ur calculating between two points ther must b a resistance value,,,wel if this is right it should b 0 since u calculated 1/R(total)
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