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Infinite resistors circuit

  1. Mar 5, 2014 #1
    1. The problem statement, all variables and given/known data
    Calculate the equivalent resistance of the resistor chain shown in the figure between the points a) A and B; b) A and C the resistor chain is infinite in both directions and each resistor has a resistance of R.
    41137ec21c802ca3495bb5597.gif


    2. Relevant equations



    3. The attempt at a solution
    I have solved the b) part. It is the part a) which I face trouble with. How do I approach this?

    Any help is appreciated. Thanks!
     
  2. jcsd
  3. Mar 5, 2014 #2

    ehild

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    Gold Member

    You have the equivalent resistance of both the chain to the left from A and the one to the right from B. Replace the chains with their equivalent resistances in the figure.

    ehild
     
  4. Mar 5, 2014 #3
    I would add point D just below B and consider the sub-chains to the left of AC and to the right of BD (with the resistor between A and C or B and C). These sub-chains should have equal resistances. Then the entire ABDC loop can be represented as four resistors.
     
  5. Mar 5, 2014 #4
    By the way, if you solved part (b) in some other way, you can obtain the equivalent resistance of each sub-chain from that result, and then solve part (a).
     
  6. Mar 5, 2014 #5
    Thanks ehild and voko! That did the trick. :)

    I solved the part b) with the same method but couldn't observe that you could do the same with a). :redface:
     
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