Question

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)

Answer #1

**Answer :**

**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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