# Homework Help: Short in Wires with 2 Different Resistances

1. Feb 8, 2010

### skibum143

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.

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2. Feb 8, 2010

### rl.bhat

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.

3. Feb 8, 2010

### skibum143

What is k? The 8.98*10^9 constant?

4. Feb 8, 2010

### skibum143

and did you use 2x because there are two wires?

5. Feb 8, 2010

### rl.bhat

Νο. You know that
R = ρ*L/A. So k = ρ/Α, which is constant for a given wire.

6. Feb 8, 2010

### skibum143

Oh, I knew the resistance = ro*length / pi r^2, but i didn't know what Resistance is ro*length over area?

7. Feb 8, 2010

### skibum143

Sorry, I'm still completely confused. I'm not sure what I'm solving for using the second equation...

8. Feb 8, 2010

### rl.bhat

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.