2
$\begingroup$

I am talking about the wires which get somewhat loose or somewhat like parabolic shaped due to earth's gravity.local electric poles

What I think is due to slackness of wires there is a net increment in resistance which may be responsible for a huge electrical energy wastage.

What can be the solution for this issue?

EDIT

As per the comments I did some exercise to get the magnitude of change in resistance.Imagine a wire hinged between two electric poles.I assume that the wire would be somewhat parabolic.I think that $y=x^2$ would be a good approximation.It is not accurate but is pretty much close to the reality.If the approximation is bad then please inform me.

I set my cartesian coordinate system with the origin as the vertex of the approximated parabola.Let the distance between the poles be $l$,then from symmetry the vertex would be at equal distances from both the poles.The length($R$) of the wire between the poles would be:-(putting limits from $\frac{-l}{2}$ to $\frac{l}{2}$),

$$R=\int\sqrt{1+4x^2}dx$$

$$R=\frac{l\sqrt{1+l^2}}{2}+\frac{\ln\frac{\sqrt{1+l^2}+l}{\sqrt{1+l^2}-l}}{4}$$

Let's assume that the distance between the poles is 1metre, then,$$R=1.1477 m$$ The net increment in length of wire due to slackening is $14 cm$.When distance between the poles is 5 meters then,$$R=13.90 m$$ The net increment in length is $8.90 m$.It is a huge increment.Increasing the distance between the poles results in more increase in effective length which results in increased resistance and large energy wastage.

$\endgroup$
  • 1
    $\begingroup$ It is in fact not responsible for huge energy wastage. Have you done the maths? $\endgroup$ – niels nielsen Aug 20 at 6:57
  • $\begingroup$ Of course a slack wire suspended between two poles is longer than a taut wire. But how much longer? Niels Nielsen suggested that you do the math, but you can also get an intuitive feel for it by doing an experiment at home. Tie one end of a long rope to a tree or a fence post or some other fixed object, and hold the other end tight enough to keep the rope from touching the ground. How much rope do you have to pull in to raise the center by a few feet? $\endgroup$ – Solomon Slow Aug 20 at 13:41
  • $\begingroup$ @Solomon Slow I would post the math of the problem soon. $\endgroup$ – Unique Aug 20 at 15:43
  • $\begingroup$ P.S., Doing the experiment also will give you a good feel for how much extra tension the wires and the poles and the insulators must be able to withstand in order to save that little bit of extra length. $\endgroup$ – Solomon Slow Aug 20 at 15:55
  • 2
    $\begingroup$ Forget that, how about the fact that power lines generally follow streets, instead of performing a straight path? This inefficiency is at least 10x bigger than what you identified, possibly 100x, and nobody cares about it -- so the length of the line can't be all that important. $\endgroup$ – knzhou Aug 20 at 16:51

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.