7. You are hired by CDOT as an engineering consultant to tell the power company

Question

7. You are hired by CDOT as an engineering consultant to tell the power company where to dig in order to make a repair to a transmission line that is buried 10 feet under the highway runing east-west. The transmission line consists of two parallel insulated metal cables. Each metal cable has a resistance-per-length of 17 /km. CDOT line. The transmission line has access every 13 km where you can make independent electrical connection to the two wires. claims that they are experiencing excessive power loss in the transmission (a) What should you expect the current to be if you attach a 120-volt source across the two electrical connections at an access point. (b) When you connect a 120-volt source across the connections at station F, a current of 270 mA flows from the source. When this is done at Station G (the next station 13 km east of Station F), a current of 590 mA flows. You conclude that somewhere along the tra insulation is damaged, allowing current to flow through the dirt from one cable to the other. Where should CDOT dig up the highway? n line between Station F and G, the

Explanation / Answer

7. depth of transmission line, d = 10 ft = 3.048 m

direction of transmission line = east-west

transmission line consists of two parallel insulated cables

resistance per unit length r = 17 ohm/km

access every l = 13 km

a. if voltage source V = 120 V is attached to the transmission lines at an access point, current = i

net resistance R = 2*r*l = 2*17*13 = 442 ohm

so from ohms law

V = iR

i = 120/442 = 0.2714 A

b. voltage source applied at station F

i1 = 270 mA

voltage source applied at station G

i2 = 590 mA

let distance of the fault from station F be x km

then

V = i1*(2r*x)

V = i2*(2r*(13 - x))

hence

270*x = 590(13 - x)

x = 8.9186 km

hence the fault in the transmission line is at x = 8.9186 km from station F

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