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Question:

Why do power cables have a big sag in the middle?

If you look at a power line it is hanging down in the middle why is that

Answer:

Short answer: gravity Medium answer: the cable is longer than the distance between the poles and gravity pulls it into that familiar shape. Long answer: you can actually find the shape the cable takes by using the calculus of variations. I'll update my post a bit later (I'm a little busy at the moment). EDIT: Haha, it seems your question can be read in 2 ways.
gravity. Power lines are not light. If you try to pull them tighter, to reduce the amount of sag you can break the line itself, or put tremendous strain on the support towers.
To much tension requires more expensive equipment on the end poles to handle the stress. So some slack is necessary. Temperature can effect how saggy the lines are. If the wires are hot, they will sag more. Generally heat from the wires usually depend on the amount of current flowing through it. During the summer, lines sag big time because not only it is hot outside but there is so much current flowing through them from everyone cranking up the air conditioners at their homes and offices.
Power Line Sag
Gravity okorder /

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