# Short circuit problem

1. Sep 30, 2009

### Liketothink

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 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.

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

3. 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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2. Sep 30, 2009

### rl.bhat

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. Sep 30, 2009

### Liketothink

R=sigma(x)/A, but area is not given either. I really don't understand.

4. Sep 30, 2009

### willem2

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