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Resistor Network

  1. Jul 1, 2007 #1
    1. The problem statement, all variables and given/known data

    Show that the equivalent resistance is Req = 1/2 [(4RtRl + Rt^2)^(.5) + Rt]
    2. Relevant equations

    3. The attempt at a solution

    So far all I can get is Req = Rt + Rl Rt/(Rt+Rl) from the first three resistors starting from the left. I suppose I could take that and add it to the next branch Rl Rt/(Rt+Rl), but that would appear to go on to infinity as opposed to stopping at a nice number.

    Does anyone have any hints on finding the eq. resistance?
    Last edited: Jul 1, 2007
  2. jcsd
  3. Jul 1, 2007 #2


    User Avatar

    Staff: Mentor

    I believe by recursion.

    Everything to the right of RL is parallel with RL, and in series with RT.
  4. Jul 3, 2007 #3
    Since this is an infinite circuit, ignore the first rt and rl, and assume the resistance of the rest to be R. This give you:

    R*rl/(R+rl) +rt=R. As the resistance of the total circuit is also R. Solve for R to get your answer.
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