Question

# An underground cable 10 km long extends east to west and consists of two parallel wires,...

An underground cable 10 km long extends east to west and consists of two parallel wires, each of which has resistance 11 Ω/km. An electrical short develops at distance x from the west end when a conducting path of resistance R connects the wires (see the figure). The resistance of the wires and the short is 160 Ω when measured from the east end and 110 Ω when measured from the west end. What are (a) x and (b) R? (I want the answer exactly by the given decimal numbers)

Given :

underground cable 10 km long, each of which has resistance 11 ohm/km

resistance of west = 110 ohm

resistance from east , r = 160 ohm

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solution:

resistance per unit length = 11 ohm /km

for x

resistance of west = 110 ohm

resistance from west = 2 * x * 11 + R

110 = 22 x + R --------(1)

resistance from east , r = 160 ohm

resistance from east = 2 * (10 -x) * 11 + R

160 = 2 * (10 -x) * 11 + R

- 60 = - 22 x + R --------(2)

from equation (1) and (2)

x = (110 + 60) / (22 + 22) = 3.864 km

R = 110 - (22 * 3.864) = 25 ohm

(a)

x = 3.864 km

(b)

R = 25 ohm

___________________________________________________________________

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