Please help! 8.[1pt] An underground telephone cable, consisting of a pair of wir

Question

Please help!

8.[1pt] An underground telephone cable, consisting of a pair of wires, has suffered a short somewhere along its length (at point P in the Figure). But, where to dig to fix it? The telephone cable is 6.00 km long, and there is a clever trick which takes advantage of the fact that real wires do have a finite resistivity (so their resistance, while small, is not zero, and depends on length!) In order to determine where the short is, a techician first measures the resistance between terminals AB; then she measures the resistance across the terminals CD. The first measurement yields 110.00 Ohm; the second 10.00 Ohm. Where is the short? Give your answer as a distance from point A. 6.00 km Answer: Incorrect, ONE try left!! Submit All Answers Last Answer: .52 km

Explanation / Answer

Solution;-

First, you must calculate the resistance of the wire perkilometer. Assume the short did not exist, and you placed ashort across terminalscDand measured the resistance at AB. The result would be 120ohms. If we assume the resistance islinear with distance, than the resistance per kilometer is: R/km = (120ohms)/(6 kilometers) = 20 ohms per kilometer. Lets call this .

From the first measurement:

110 ohms = (dCD)()   ===>solve for dAB

dcD= (110ohms)/() = (110)/(20) = 5.5 kilometers

In a similiar manner, solve for daD

dab = (10ohms)/() = (10)/(20) =0.5 kilometer

Therefore the short distance is 5.5 km

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