Because of your physics background, you landed a summer job as an assistant tech

Question

Because of your physics background, you landed a summer job as an assistant technician for a telephone company in California. During a recent earthquake, a 1.0-mile long underground telephone line is crushed at some point. This telephone line is made up of two parallel copper wires of the same diameter and same length, which are normally not connected. At the place where the line is crushed, the two wires make contact. Your boss wants you to find this place so that the wire can be dug up and fixed. You disconnect the line from the telephone system by disconnecting both wires of the line at both ends. You then go to one end of the line and connect one terminal of a 6.0-V battery to one wire, and the other terminal of the battery to one terminal of an ammeter (which has essentially zero resistance). When the other terminal of the ammeter is connected to the other wire, the ammeter shows that the current through the wire is 1 A. You then disconnect everything and travel to the other end of the telephone line, where you repeat the process and find a current of 1/3 A.

Explanation / Answer

Let the wires join at a distance x from the end where current measured to 1A.

Length of the wires which are in series(because they are joined) from the end where current is 1A = 2x

Length of the wires which are in series(because they are joined) from the end where current is 1/3 A = 2-2x, becuase the remaining part of the wires are in series, as observed from other end.

We know Voltage = current*resistance

Therefore, 1*2x = (1/3)*(2-2x)

x=1/4

So, the wires are joined at 0.25 miles from the end where current measures to 1A.

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