# Added resistance due to coiled wire

## Main Question or Discussion Point

Hello everyone,

I was wondering how to calculate the added resistance experienced when a cable is coiled rather than layed flat due to the magnetoresistance of the magnetic field created by the solenoid configuration.

I will be running 250A though a cable which will be coiled like a solenoid that has 5 turns and a radius of 40 inches, (although I have not calculated this yet) I can determine the DC and AC resistance of the cable layed flat as well as the length of cable used.

Thanks,
Patrick

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phinds
Gold Member
2019 Award
It's not "resistance" it's "impedance". I can't help you with the formula but I suggest that you look up "coil impedance calculator".

Well the problem we ran into during testing was that the resistance increased when we measured coiled vs uncoiled. We are trying to determine whether or not this was a factor or the fact that the coiled wires are closer together (therefore increasing the heat of the wires) which in turn increases the resistance. As seen in equation R(T) = Ro[1 + a[T-To]].

Thanks for the input. I was able to calculate the impedence given my parameters.

You won't have any magnetoresistance with such figures. But hotter metal possibly, and this increases the resistivity.

Is that 250 amp AC or 250 amp DC.
If it's DC there should not be any increase in resistance except for temperature increase.
If it's AC there will probably be an increase in effective resistance (watt loss) at 250 amp and 60 Hertz.
You might Google skin effct and proximity loss.

phinds
Gold Member
2019 Award
Is that 250 amp AC or 250 amp DC.
If it's DC there should not be any increase in resistance except for temperature increase.
If it's AC there will probably be an increase in effective resistance (watt loss) at 250 amp and 60 Hertz.
You might Google skin effct and proximity loss.
Skin effect at 60Hz? Really?

Yes AC current is being passed through the cable, and skin effect + proximity effect should be taken into consideration since we are using a medium voltage (35kV rated) cable with an aluminum core.

phinds
Gold Member
2019 Award
Yes AC current is being passed through the cable, and skin effect + proximity effect should be taken into consideration since we are using a medium voltage (35kV rated) cable with an aluminum core.
My understanding is that skin effect is a function of frequency and at 60Hz the effect is probably not even measurable, much less significant.

Skin depth in copper at 60 hertz is 0.33 inch. So any copper conductor over say 3/8 inch diameter will have detectable loss due to skin effect. (Yes I know that 3/8 inch diameter could be 1/8 inch or 3/4 inch or anything in-between)

Patrick;
Just curious, but why do you believe that the increase in resistance was caused by magnetoresistance of the magnetic field?
How large was the increase in resistance?
What was the accuracy of the instruments that were used to make these measurements?

I would be inclined to believe that the measured increase in resistance was due to measurement errors.

phinds
Gold Member
2019 Award
Skin depth in copper at 60 hertz is 0.33 inch. So any copper conductor over say 3/8 inch diameter will have detectable loss due to skin effect. (Yes I know that 3/8 inch diameter could be 1/8 inch or 3/4 inch or anything in-between)
Having now done some research, I now see that my "knowledge" of skin effect was completely wrong, colored as it was by recollections of calculations regarding very high frequency wave guides some 40+ years ago. Thank's for the correction.

sophiecentaur
Gold Member
Could you, perhaps, measure the temperature in the coil? The thermal coefficient for Aluminium is about 0.4% per degree C so a 10 degree rise could account for a 4% increase in R. See here
Does that square with what you have been getting?

Well we were only testing this to measure the temperature differential between the coiled and uncoiled wire. We were told that the magnetic field induced by the coiled wire would increase the temperature of the conductor therefore increasing the resistance. Before testing, we wanted to get a ballpark estimate for this increase in resistance.

We measured a 14% temperature increase between the coiled and uncoiled configuration using the same cable and meter to measure the DC resistance (we do not have a meter to measure the AC resistance).

I'm sure most of the temperature increase is due to the proximity of the cable to itself in its wound formation and the fact that its in an enclosure with insufficient ventilation.

sophiecentaur
Gold Member
I think you probably don't mean 14 "percent" because the only way that would mean anything would be if you use the absolute (Kelvin) scale?
So 14oC of temperature increase would be expected to increase the resistance by about 5.6% due to the positive temperature coefficient of resistivity of Aluminium. Afaik, any other effects are at a much lower level and 'only just detectable'.
The Inductance is an entirely different thing but it is easy to estimate this using the formula for inductance of a coil. There are 'calculators' for this, which you can easily find with a Google search - you put the dimensions in and you get the value of L. The inductance would not be much for the coil size you quoted unless you added an iron core.

I can't find any mention of the actual resistance values you got (hot and cold)?? If they differ by about 5%, then we've explained it.