Which of the following is the correct interrelation between the variables x1 and x2 used in the expression to calculate the sag in a transmission conductor with different heights, where , variables x1 and x2 represent the horizontal distances of support at lower and higher levels from the lowest point of the conductor, respectively?

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  1. x1 > x2
  2. x1 >> x2
  3. x1 < x2
  4. x1 = x2

Answer (Detailed Solution Below)

Option 3 : x1 < x2
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Detailed Solution

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Concept

The sag in an overhead transmission line is given by:

\(S={WL^2\over 8T}\)

where, S = Sag

W = Weight per unit length of the conductors

L = Length of span

T = Tension of the conductor

Sag for unequal tower length:

qImage657c3e8cee4f91c3e6fe9edf

From the figure: \(L=x_1+x_2\) where, \(x_1<x_2\)

\(h=S_2-S_1\)

\(h={WL_1^2\over 8T}-{WL_2^2\over 8T}\)

\(h={W\over 8T}(L_1^2-L_2^2)\)

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