Resistivity anti-helmholtz configuration

[Void123]

If I have a pair of coils connected in an anti-helmholtz configuration, with current flowing oppositely in both, and I wanted to calculate the resistivity- wouldn't the length of both coils just be summed up? I tried this but I am not getting the answer I want.

 

[UltrafastPED]

The resistance of a coil changes with the temperature of the wire - other than that you can simply look up the resistance per unit length for copper wire of your gauge, and multiply by the length.

If the wire is long enough, as it is in a typical coil, then you should be able to measure the total resistance of each coil with an ohm meter.

 

[sophiecentaur]

If I have a pair of coils connected in an anti-helmholtz configuration, with current flowing oppositely in both, and I wanted to calculate the resistivity- wouldn't the length of both coils just be summed up? I tried this but I am not getting the answer I want.

How badly 'out' is your answer?

 

[Void123]

The resistance of a coil changes with the temperature of the wire - other than that you can simply look up the resistance per unit length for copper wire of your gauge, and multiply by the length.

If the wire is long enough, as it is in a typical coil, then you should be able to measure the total resistance of each coil with an ohm meter.

Thanks I am just calculating at room temperature. Based on the thickness and width (it's more like tape) and the length calculated:

Resistivity=(resistance*thickness*width)/total length of both coils in connection

 

[Void123]

How badly 'out' is your answer?

We'll I'm within the right factor of 10^-8 but my answer is about 2-3 times too high compared to the index value.

 

[sophiecentaur]

The formula involves Cross Sectional Area and not "width". That could be your problem. Look it up again and you'll see what I mean.

 

[Void123]

Yes but isn't the cross sectional area the width of the strip (if you're looking at a slice of it from the yz plane) multiplied by its thickness?

 

[sophiecentaur]

Oh yes. I missed the bit about "tape".
So, if you just measure the DC resistance with a DMM, do you get the same answer as your AC (?) method?
Could there be a contact resistance problem or could there be shorted turns of the coil?

 

[Void123]

The coils are a bit worn out and rusted...could that affect the resistance? Unless of course the material is not pure either, I don't know.

 

[sophiecentaur]

Are you measuring resistance with a DMM?

 

[sophiecentaur]

Have you measured the wire length right? It would help if you posted a photo or sketch perhaps.

 

[Void123]

Yes, I've measured the total resistance.

Please see attached file for rough schematic representation of the coils. The lines indicate the connection between coils and the four aligned black segments are the coils as they would appear looking from the top down. So basically, current in, current out. In my calculation i summed up the length of all four coils.

 

[sophiecentaur]

You still don't mention the dimensions or the measurements. This is not helping and doesn't encourage people to contribute. This is a practical problem and the details are crucial.

 

[Void123]

Sorry, I haven't mentioned the details because I have been thinking of it as a conceptual problem. But here are the numbers:

Tape thickness: 0.276 mm
Tape width: 3 cm
Outer diameter of coil: 43.5 cm
Inner diameter of coil: 31.7 cm
Coil separation distance (center to center): 33.3 cm
Total resistance of whole coil set: 5.4 ohms

 

[Void123]

I calculated the wire length based on the inner and out diameters, plugging them into an automatic formula I had.

 

[sophiecentaur]

Sorry, I haven't mentioned the details because I have been thinking of it as a conceptual problem. But here are the numbers:

Tape thickness: 0.276 mm
Tape width: 3 cm
Outer diameter of coil: 43.5 cm
Inner diameter of coil: 31.7 cm
Coil separation distance (center to center): 33.3 cm
Total resistance of whole coil set: 5.4 ohms

This really must be a secret project lol. And how are you measuring the resistance? What is the state of the contacts? How much current is passing. Have you a reliable resistance to use for calibration? Are you sure of the metal used in the coils? Is there one in a table of resistivities that would fit? I would suggest this is not "conceptual" at all but real nuts and bolts stuff.

 

[UltrafastPED]

With such a thin tape I would suspect variations in the thickness ... and the thinnest spot would determine the effective cross section for the entire length.

Also I don't trust your "OD-ID" geometric formula for the length of the tape. For these to work your tape must be wound uniformly, under tension. And the thickness of the conductor is not the relevant figure here ... you must use the thickness of the tape, including the insulation layer.

Unfortunately, the thickness of the insulation layer will be even less uniform than the thickness of the tape.

So I vote that you just measure the resistance with a meter. When you run a current through the coil, it will heat up - all coils heat up! - and the resistance will change. If you have convenient contacts you can measure the resistance while the coil is running, and calculate the temperature from the changes in the resistance.

I used to do this for a magnetic steering coil in a vacuum chamber - worked great! I had to keep the temperature below a certain level so that the insulation didn't give off vapors into the vacuum chamber. In my case it limited the current to 3 amps, which was a problem ... so I had to re-do the design.