In a telephone line (two conductors) below the ground surface a short circuit occurred. The resistor of the line is measured from both sides of the line (R_1=10,85 Ω and R_2=13,02 Ω). The length of the line is 150 m and the diameter of a single wire is 0,6 mm. The resistivity is ρ=0,0178 (Ω〖mm〗^2)/m.
1)Resistance of the connection at the short circuit position?
2)Distance between one end of the line and the short circuit (where the service team has to dig?)
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The short is obviously not in the center, but is further from R2 side. Just swagging it, I would say approximately 81.8 meters from the R2 end or 68.2 meters from the R1 end. With that you could calculate the value of the short, it may or may not be 0 Ohms, but for the distance part of the problem it could be assumed as 0 ohms. And then use all that wires size and resistivity info and the distance for each wire determine the value of the short.
How did you find 81.8 m and 68.2 and how to use the resistence of wire to find the place of short circuit???
Using the ratio of the two resistance readings (note each reading will include the very low resistance of the short). This ratio is 13.02/10.85 or 1.2. Using this ratio and assuming the short is a real short or close to zero Ohms then you can relate the distances. Letting x equal the distance of R1 and 1.2x the distance of R2 measurement.
1.2x + 1x = 150 meters
2.2x = 150 meters
x= 68.2 meters then the longer distance is 150 - 68.2 = 81.8 meters
or also 1.2 times 68.2 = 81.8
this would assume that the characteristics of the conductor are linear and consistent. and the assumption it is a single point short.
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I believe you have been provided with the info required to find the wire resistance per meter, I just don't want to research the method, but I am sure you are studying the resistance of wire and will be able to quickly determine the resistance. I do remember that it veries directly with distance and resistivity (I thinl) and inversely with cross sectional area. Good luck.