11. Experimental Woes You\'ve recently wired up an experiment in the lab. Part o

Question

11. Experimental Woes You've recently wired up an experiment in the lab. Part of the experiment involves having two long wires extended 2 meters below the ground. One day, the experiment stops working. Crap. You suspect there is a short between these two wires somewhere along the length. If you measure the resistance between terminals a and b, your multimeter reads 14 Ohms. Then, when you measure the resistance between c and d, you get 36 Ohms. Based on these measurements, how far from the top do you suspect the short is located? (This would be easier if you had made a note of the resistance per meter of the wire, but you didn't, so you don't have that information.)

Explanation / Answer

Let at x m from top there is short circuit.
When measuring resistance ab, length = 2x
When length is 2x, R = 14 ohm

When measuring resistance cd, length = (2-x) + (2-x) = 4-2x m
When length is (4-2x ), R = 36 ohm

2x/14 = (4-2x)/36
72x = 56 - 28x
x = 0.56 m
Answer: 0.56 m

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