An infinite network (XKCD) - is it not clear?

  • Thread starter OJFord
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Hi, unless I'm missing something here, it seems to me that the answer is that it is infinite, and that that is pretty intuitive.

Is that not the case?

nerd_sniping.png



I would think it could be simplified to view as two parallel and infinite resistances, giving ∞2/2∞, which simplifies to half infinity, which is of course really (in as much as it is) still infinite.
 

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  • #2
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I have no solution, but the resistance cannot be larger than 1.5 Ohm, since there are two independent paths of 3 resistors between the points. The other parallel paths can only lower the resistance. So it's definitely finite.

The forum page of this comic will no doubt contain the correct answer.
 
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  • #3
Filip Larsen
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I think it is intuitive that the resistance can not be infinite.

With some hand-waving: whenever you have a parallel circuit the equivalent resistance is lower than any of the branch resistance, so the resistance between any to adjacent nodes must be less than 1 Ohm. This means you have a path between the two marked nodes as a series of three networks that can be replaced with a resistor less than 1 Ohm, totaling less than 3 Ohm.

The exact solution, I seem to remember from years back, is a bit harder to obtain. Found a derivation [1] that may be of some use (haven't read it thoroughly enough to say if it is correct or not).

[1] http://mathpages.com/home/kmath668/kmath668.htm
 
  • #4
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I have no solution, but the resistance cannot be larger than 1.5 Ohm, since there are two independent paths of 3 resistors between the points. The other parallel paths can only lower the resistance. So it's definitely finite.
I think it is intuitive that the resistance can not be infinite.

With some hand-waving: whenever you have a parallel circuit the equivalent resistance is lower than any of the branch resistance, so the resistance between any to adjacent nodes must be less than 1 Ohm.
[1] http://mathpages.com/home/kmath668/kmath668.htm

Right, that was stupid of me. Thank you both - and for the link.

I see why it was comic-worthy now, the answer is certainly not trivial!
 

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