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We have an infinite net of regular hexagons. Each side of hexagons has a resistance R. What is the resistance between two opposite vertexes of hexagon(s)?
Actually, I think I misread your question. I was taking the resistance between adjacent vertices, not opposite. Is that correct?This is a misunderstanding. :) I have already solved this problem. I was only trying to represent it to the people, who are interested in it. But I suppose I wrote this problem in the wrong forum section... Dick, please, if you have the answer, write me a private message. We'll check the result ;)
I wasn't saying that the opposite vertex was easy. It looks hard, I'm still thinking about it. I was saying the other vertex in between is nearly as easy as the adjacent.If it so easy for you, please, write me your answer :) We will check.
I occasional found this thread. The problem is very interesting ... But I don't quite understand why you get 1/3 amp out if you input 1 amp in? Any new idea and anyone explains this to me?That's a variation on an old problem with an infinite net of squares. Picture pushing 1 amp into the circuit at a vertex and taking it out at infinity. 1/3 amp flows through each resistor away from the vertex. Then forget that and picture taking 1 amp out of the circuit and feeding it in at infinity. Now we have 1/3 amp flowing through each resistor into the vertex. Now add the two, putting the 1 amp in at one vertex and taking it out at an adjacent one. Now the total going to infinity is zero, there is a total of 2/3 amp flowing through the connecting resistor and a total of 1 amp flowing between the two vertices through the whole network. What's the voltage across the two vertices? What's the total resistance?
That's too complicate to me.