Short circuit problem

  • #1

Homework Statement



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 4.00 km long, and in order to determine where the short is, a technician first measures the resistance between terminals AB; then he measures the resistance across the terminals CD. The first measurement yields 15.00 Ω; the second 105.00 Ω. Where is the short? Give your answer as a distance from point C. Assume that the telephone wires are of uniform diameter.


Homework Equations


I'm sure which equations to use.
R=sigmaL/A, I=V/R

The Attempt at a Solution


I'm not sure how to start on this problem. I know a short circuit is when the resistance is equal to zero, but if it is zero than length ends up being zero due to the linear relationship. I don't get this problem. Please help in any way that you can.
 

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Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
8
If AP is nearly equal to BP and is equal to x, Then what is the resistance across AB?
What is the length CP and DP? What is the resistance across CD?
 
  • #3
R=sigma(x)/A, but area is not given either. I really don't understand.
 
  • #4
2,042
311
there's a short between the 2 conductors in the cable, but the resistance from A to B is not 0 because the current still has to go from A to P and from P to B through a long cable.

you don't know sigma/A, but it's the same everywhere. If point P is x metres from C then the resistance of the wire CP is (sigma/A)x [itex]\Omega[/tex] . the 2 measurements will give you 2 equations that you kan use to find (sigma/A) and x
 

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