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I was looking through Physics Olympiad problems and I found this. This question asks: Find the equivalent resistance between the points A and B, all the arms have equal resistance $R$.

I understand that the network is self similar and I can take the resistance of the whole network as a Variable and the solve for it, but I can't seem to understand how to do so for A and B. Any hints or suggestions to how to approach this would be highly appreciated. Thank you in advance.

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closed as off-topic by John Rennie, Jon Custer, Kyle Kanos, Yashas, Emilio Pisanty Sep 13 '17 at 14:08

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Homework-like questions should ask about a specific physics concept and show some effort to work through the problem. We want our questions to be useful to the broader community, and to future users. See our meta site for more guidance on how to edit your question to make it better" – John Rennie, Jon Custer, Kyle Kanos, Yashas, Emilio Pisanty
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Is it infinite in all directions? $\endgroup$ – NickD Sep 11 '17 at 17:39
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    $\begingroup$ No, just along its length(as per the dotted lines). $\endgroup$ – Tausif Hossain Sep 11 '17 at 17:40
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    $\begingroup$ Welcome to Physics! Please note that this is not a homework help site. Please see this Meta post on asking homework questions and this Meta post for "check my work" problems. $\endgroup$ – Kyle Kanos Sep 12 '17 at 10:02
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    $\begingroup$ Well this is not a homework question but one from an Olympiad which I was curious about and it's about a conceptual difficulty on how to solve these problems with infinite network of resistors. $\endgroup$ – Tausif Hossain Sep 12 '17 at 11:19
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A hint. Would it make any difference if you joined (with a wire of zero resistance) each junction on the top row to the junction directly below it on the bottom row?

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  • $\begingroup$ Geometrical symmetry -> Current pattern symmetry & Resistance symmetry -> Potential Symmetry $\endgroup$ – AHB Sep 11 '17 at 20:01
  • $\begingroup$ For a wire with zero resistance I think it would make a difference as then current flow through the wires then instead of taking the math through the network. Correct me if I'm wrong and please elaborate. $\endgroup$ – Tausif Hossain Sep 12 '17 at 9:59
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    $\begingroup$ By symmetry a junction on the bottom line is at the same potential as the junction directly above it on the top line. Therefore you may merge these corresponding points, to make a 'ladder' consisting of just the top line modified resistor values), the middle line (with resistor values unchanged) and with the bridging resistances modified) . I've left the values of the modified resistors for you to decide – it's very easy to do. $\endgroup$ – Philip Wood Sep 12 '17 at 18:13
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    $\begingroup$ I'd be interested to know why my answer attracted a negative vote. Questioner asked for hints and suggestions and was given a hint. Follow it through and the question becomes much simpler to deal with. $\endgroup$ – Philip Wood Sep 12 '17 at 18:58
  • $\begingroup$ @PhilipWood Not my vote, but for questions that are in flagrant defiance of the homework guidance, providing answers can be seen as encouraging future questions of similar quality. $\endgroup$ – Emilio Pisanty Sep 13 '17 at 14:10

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