Question

The effect of increase in temperature on transmission lines:

• A. Sag and tension of conductor decreases
• B. Sag and tension of conductor increases
• C. Sag increases and tension of the conductor decreases
• D. Sag decreases and tension of the conductor increases

Hint:

Remember the inverse relationship: Temperature $\uparrow$ $\rightarrow$ Length $\uparrow$ $\rightarrow$ Tension $\downarrow$ $\rightarrow$ Sag $\uparrow$. Sag and tension always move in opposite directions.

Answer 1

The Correct Option is C

Concept: The physical behavior of an overhead conductor suspended between two mechanical transmission supports is governed by structural catenary mechanics. The conductor sag ($s$) represents the maximum vertical distance between the line connecting the supports and the lowest point of the conductor. It is calculated using the formula: \[ s = \frac{w \cdot l^2}{8 \cdot T} \] where $w$ is the weight per unit length of the conductor, $l$ is the span length, and $T$ is the horizontal tension in the line.

Step 1: Evaluate the thermal expansion of the conductor material.
When the ambient temperature rises (or when internal ohmic losses $I^2R$ heat the line under heavy loading conditions), the conductor material expands physically. The change in length ($\Delta L$) is given by: \[ \Delta L = L_0 \cdot \alpha \cdot \Delta t \] where $\alpha$ is the coefficient of linear thermal expansion and $\Delta t$ is the temperature change. An increase in temperature causes the physical length of the conductor wire to increase.

Step 2: Determine the effect on tension and sag.
1. As the conductor lengthens, it slackens between the fixed tower supports. This elongation relaxes the mechanical line tension ($T$), causing it to decrease. 2. Looking at the sag equation, the sag is inversely proportional to the conductor tension: \[ s \propto \frac{1}{T} \] As the tension $T$ decreases, the sag $s$ increases. Therefore, an increase in temperature causes the conductor sag to increase and its mechanical tension to decrease. This matches Option (C).