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There are plenty of references to this claim on the internet that tying knots in power cables will prevent a piece of equipment e.g. television or computer from a power surge.

How can this be debunked (or proven) using mathematics?

I stumbled across this which seems reasonable to me, but is there some way this can be proved?

The surge impedance of any line is the square root of its inductance divided by its capacitance, and electromagnetic waves travel most readily down a line where that surge impedance doesn't change. A point of changing impedance is a discontinuity that causes a partial reflection of the wave back towards its source. As an example, the end of the line is a surge impedance jump to infinity and the whole wave is reflected back (which means the wave voltage at the open end doubles!) This is also the reason why you want to use terminators on the ends of coaxial cables. Open-ended cables will reflect back the signal causing poorer picture quality and ghosting (and similar things happen for poorly made connections that have higher impedances than the surge impedance of the coax).

Knotting the line gives that part of it a higher inductance (think of the knot as a coil with a couple of turns). That means two surge impedance discontinuities (from line to knot, and from knot back to line). It seems to me (too lazy to resort to doing the math) that this is bound to reduce the magnitude (voltage and current) of a surge passing through the knot because some will be reflected back. However, I'd guess that the reduction would be small.

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Similar recent question on Skeptic.SE: Does tying a knot in a power cord provide any protection against lightning?. –  dmckee Aug 26 '11 at 4:12
    
Damned if you do, damned if you don't. Quote: "One just need to coil up the cable a sufficient number of times, or use too much insulation around the cable, or both. Laboratory tests have shown that ignition ... may easily occur in such cases. At one such incident it was sufficient to coil up the cable three times and cover the coil in clothing." Fire or lightning? Take your pick. –  Willie Wong Aug 26 '11 at 14:14
    
@Willie - Thanks for that link. It would have been good if they linked to the 'laboratory tests' they mention. –  xiaohouzi79 Aug 27 '11 at 10:06

3 Answers 3

You can calculate the inductance of such a coil and estimate the capacitance of the wire and try to work it out like a transmission line problem.

This might not be necessary here. According to Wikipedia the duration of a typical lightning event is in the range of 1-100 ms. If we compare this with the line frequency of 50 Hz (20 ms) and can assume that the coil in the wire does not prevent your TV or computer from working how should it protect from lightning? The effects of a 100 ms current pulse of electricity is for most purposes not to different from a DC voltage (disregarding the rise and fall of the pulse) because the frequency dependence of electrical circuits is small if you don't add big capacitors or similar items.

What really helps though are varistors or zener diodes that are used in surge protectors. They have switching times in the microsecond range and can "cut off" the current/voltage pulse long before it reaches it's maximum.

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The inductance of a power cable is nearly independent from "coiling" status! It's just a symmetrical line rolled op. Think of the fact, that it is a bifilar winding, one thread goes in one duirection, the other goes "back". So the inductance is the inductance of a Lecher line. –  Georg Nov 4 '11 at 19:42
    
@Georg: Did I state that it is not a Lecher line? The question was whether coiling it up makes a difference. I said no because it does not make a difference at low frequencies. You wrote "nearly independent", so why is my answer incorrect? –  Alexander Nov 4 '11 at 19:56
    
For low frequencies of about 1 MHz (wich is a typical frequency of a flash) coiling up does not make a difference. Things may differ fore wavelengths about the distance of wires in the cabel or between cable windings. –  Georg Nov 4 '11 at 20:56

I told a friend of mine that I turned off my computer equipment for lightning storms, but left the equipment plugged into the surge strip and the surge strip plugged into the wall. He made a very keen observation: Lightning that extends across miles of open sky would have no problem leaping across the comparatively insignificant gap within the surge strip's switch! Since then, I have been unplugging completely from the wall source.

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Well, by the same argument it could leap across the gap between the wall socket and anything conductive in the room. Actually, electrical grids are grounded so that (the vast majority of) current from lighting strikes flows directly to ground, so this does not happen. –  Nathan Reed Mar 18 '13 at 2:12

A coiled mains cable behaives like a 'common-mode' inductor, Ligtning behaives a little like an impulse - if you could take the FFT of a lightning strike, it would have quite a large bandwidth. A coil in the line may have some impact against the common mode, high-frequency component of the lightning and there may be some benifit in the form of reduced energy avaliable, but knoting the cables won't save your equipment.

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