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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.

Tausif Hossain
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1 Answers1

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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?

Philip Wood
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  • Geometrical symmetry -> Current pattern symmetry & Resistance symmetry -> Potential Symmetry – AHB Sep 11 '17 at 20:01
  • 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. – Tausif Hossain Sep 12 '17 at 09:59
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    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. – Philip Wood Sep 12 '17 at 18:13
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    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. – Philip Wood Sep 12 '17 at 18:58
  • @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. – Emilio Pisanty Sep 13 '17 at 14:10
  • EP I take your point, but I think this is a rather special case. This question calls for a use of principles (two in particular) that may be of interest to some of the wider community; it is not a routine homework-type question. Indeed it isn't homework at all, though I know that your case isn't damaged by this distinction. – Philip Wood Sep 15 '17 at 08:15