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Homework Help: Short in Wires with 2 Different Resistances

  1. Feb 8, 2010 #1
    1. The problem statement, all variables and given/known data
    An underground telephone cable, consisting of a pair of wires, has suffered a short somewhere along its length (at point P in the Figure). The telephone cable is 6.00 km long, and in order to determine where the short is, a techician first measures the resistance between terminals AB; then he measures the resistance across the terminals CD. The first measurement yields 10.00 Ohm; the second 95.00 Ohm. Where is the short? Give your answer as a distance from point C.



    2. Relevant equations
    I = V/R
    Vtotal = I (R1 + R2)
    ohm = V/A


    3. The attempt at a solution
    Honestly, I have no idea where to even start with this question. I would know how to calculate the total voltage, but this problem doesn't give any voltage, and I don't know what length the ohm refers to? Also, it doesn't even look like AB are attached or CD are attached. Can someone help get me started? Thanks!!! I attached a picture of the problem.
     

    Attached Files:

  2. jcsd
  3. Feb 8, 2010 #2

    rl.bhat

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    The resistance of a wire is proportional to the length of the wire.
    If x km is the distance of the short from C, then
    95 ohm = k*2x.
    Similarly write down the expression for the resistance across AB and solve for x.
     
  4. Feb 8, 2010 #3
    What is k? The 8.98*10^9 constant?
     
  5. Feb 8, 2010 #4
    and did you use 2x because there are two wires?
     
  6. Feb 8, 2010 #5

    rl.bhat

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    Νο. You know that
    R = ρ*L/A. So k = ρ/Α, which is constant for a given wire.
     
  7. Feb 8, 2010 #6
    Oh, I knew the resistance = ro*length / pi r^2, but i didn't know what Resistance is ro*length over area?
     
  8. Feb 8, 2010 #7
    Sorry, I'm still completely confused. I'm not sure what I'm solving for using the second equation...
     
  9. Feb 8, 2010 #8

    rl.bhat

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    At P thew wires are short. If the CP = x. Length of the wire CPD = 2x. So the esiatance of this wire is
    R(CD) = (ρo/A)*2x. Similarly
    R(AB) = (ρo/A)*2(L-x).
    Solve these two equations to find x.
     
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