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-milelong underground telephone line is crushed at some point. This telephone line is made upof two parallel copper wires of the same diameter and same length, which are normallynot connected. At the place where the line is crushed, the two wires make contact. Yourboss wants you to find this place so that the wire can be dug up and fixed. You disconnectthe 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 onewire, and the other terminal of the battery to one terminal of an ammeter (which hasessentially zero resistance). When the other terminal of the ammeter is connected to theother wire, the ammeter shows that the current through the wire is 1 A. You thendisconnect everything and travel to the other end of the telephone line, where you repeatthe process and find a current of 1/3 A. Where is the short circuit?

Explanation / Answer

Two loops are created at the two attempts.

Suppose the resistance =k*t where t is the length of the wires in a loop.

Let loop1 be that has 1/3 A current and loop2 be that of 1A. Suppose loop1 is L long. Then loop2 is 1-L long. Since the same battery is used, applying ohms law,

I1*t1=I2*t2

1*(1-t)=1/3 *t

t=3/4 miles

Therefore the short circuit is 0.75 miles from the end in which loop2 is connected.

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