T/F: sag absent with supports at different heights

FALSE.

The sag "disappears" when the span is short or when the level difference between supports is large, not small.

For supports at different heights (span $L$, level difference $h$), the lowest point of the conductor lies at a distance

$$x_1 = \frac{L}{2} - \frac{Th}{wL}$$

from the lower support. When $x_1 \le 0$, the lowest point falls at or beyond the lower support. The conductor then rises all the way from the lower support to the higher one, and there is no sag (dip) within the span. The condition is:

$$\frac{L}{2} \le \frac{Th}{wL} \;\Rightarrow\; h \ge \frac{wL^2}{2T}$$

So the sag is absent if:

• the span L is small (the right-hand side $wL^2/2T$ is small), or
• the level difference h is large, or
• the tension is high relative to the conductor weight.

Example: with $L = 300$ m, $w = 1.2$ kg/m and $T = 3000$ kg, $wL^2/(2T) = 18$ m. A level difference of 20 m (more than 18 m) gives no dip. A level difference of 5 m gives a normal dip with the vertex inside the span. A small level difference therefore does not remove the sag; a short span or a large difference does.