An underground telephone cable, consisting of a pair of wires, has suffered a sh

Question

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 105.00 Ohm; the second 5.00 Ohm. Where is the short? Give your answer as a distance from point A.

Explanation / Answer

Let us use eqn,

R=L/A

Hence,

R L

So we can write relation,

R(AB)/R(CD = L(AB)/L(CD)

105/5 = L(AB)/[12-L(AB)]

L(AB)=11.45km

Distnce between point A and short = L(AB)/2 = 11.45/2 = 5.725km

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