What is the correct designation for resistivity and its unit for a copper wire?

[gsairus]

Hello to everyone. I am a little confused regarding what stands for the designation of [Ohm/m]. Before I used to [Ohm*m] for designation of resistivity (it calls sometimes resistance per unit length). For example I have a wire (copper). The resistivity could be found from the table (17.2 [nOhm*m]). What means Ohm/m for the same wire and how I can unite it at one (by equation)? I suppose that it should be done in this way: [Ohm/m]=R/L (R - usual resistance, L - length of the wire)={ro*L/S}/L = ro/S, where ro is actually resistivity [Ohm*m]; S - cross-section of wire. - Is that correct?

And, by the way, how can I call the unit [Ohm/m]? Is that also called resistance per unit length??

I Will be thankful for the explanation.

 

[sophiecentaur]

The units for resistivity are Ohm metres and not Ohms per metre.
If you look at the formula for working it out:
ρ = R A/ L
it is obvious. (units =Ω m²/m = Ωm)

Ohms per metre could be a useful description of a particular piece of wire, of course, but it shouldn't be called the resistivity.

 

[gsairus]

Thank you. I'm just meeting often Ohm/m and I am trying to understand the connection between well known conductivity and...it!

 

[sophiecentaur]

Conductivity is just 1/ρ.
Units are Siemens per metre.

 

[gsairus]

Exactly! But why people are using S*m!? I met it before only in transmission lines, TL. This unit [Ohm/m or S*m] was called as resistance/conductivity per unit length and is used for description of TL. And I wonder if my idea is correct for transferring unit from [Ohm/m] to Ohm*m?

 

[sophiecentaur]

There must be some confusion in terminology. What I have written is strictly true. Have you read, specifically that Conductivity is in Sm or are you making assumptions from what they have written.
For a start, you can't have "conductivity per unit length" because that's a meaningless concept (Like saying density per unit length) because conductivity is an intrinsic quantity. You can have conductance divided by length, which would tell you the conductance of a certain length of wire (The conductance would get less as the length got greater - so it makes sense).

Is this the sort of thing you're after?

 

[gsairus]

oh, I am sorry, of course, conductance, not conductivity. Thank you for caching me. I have an exotic material (isolation) in my project and in the documentation it was described by "parameter" {Ohm/m}. Before I could start any estimation/calculation with it I should figure out the resistivity of the material...

 

[Studiot]

Pretty obvious really.

Sophie Centaur is absolutely correct

resistivity is measured in Ohm-metres.

This comes about because resistance of a given piece of material is proportional to its length and inversely proportional to its cross sectional area.

The constant of proportionality is called the resistivity, so

$${\rm{resistance(ohms) = constant*}}\frac{{{\rm{length}}}}{{{\rm{area}}}}{{ = constant*}}\frac{{\rm{L}}}{{{{\rm{L}}^{\rm{2}}}}}$$

You should be able to see that to maintain the correct dimensions (units) this constant must have units of ohm-metres.

Normally lengths of wire have constant cross sections so in order to save having to work out the cross section of a wire every time, manufacturers often specify the resistance in ohms per metre so to obtain the resistance of say 100 metres of 1mm² copper wire you just multiply by the manufacturer's figure. (note the wire itself is specified in cross sectional area not diameter).This is especially important when you come to stranded wire as you may not know the physical cross section and the manufacturer provides and 'equivalent figure'.

Transmission line are different in that they are meant for ac and the impedance or conductance works slightly differently.
That explanation is for when you have understood the basics of resistivity.

go well

 

[sophiecentaur]

Perhaps they should use a term like 'specific resistance', rather than conductivity??

Transmission lines are definitely for the 'more advanced' student. They can give you just about any answer you want!

@ studiot
Impedance or Admittance, I think!

 

[Studiot]

Admittance is right, and usually represented by the symbol Y.

Thanks for the correction.

 

[gsairus]

Thank you for your explanation! So [Ohm/m] - this is a so called "specific resistance (R$_{sr}$)". And if I simply multiply it by cross-section of the material I will obtain the resistivity, expressed by Ohm*m?

R$_{sr}$=$\frac{Ohm}{m}$=R/L=$\rho$$\frac{L}{S}$/L=$\rho$/S -> $\rho$=R$_{sr}$*S

R - resistance; L - length of the wire; $\rho$ - resestivity, $\Omega$*m

 

[Studiot]

Edit.

Sorry to revise my original thoughts.

My text defines specific resistance as another little used name for resistivity.

So no specific resistance is not ohms per metre.
If someone has chosen to redifine it this way I would avoid using it because of the confusion.


if you know the effective cross section of your sample.

But remember that this may not be the actual cross section as with my stranded wire example. It depends upon the physical condition of the material.

 

[gsairus]

Thank you. Yes, I know my cross-section value exactly. It is not a stranded wire). I think also the method I mentioned before is correct.

 

[Studiot]

Can't find any reference that suggests specific resistance is other than resistivity.

You may be confused witt the units some sources specifiy.

Look here.

http://www.allaboutcircuits.com/vol_1/chpt_12/5.html

 

[sophiecentaur]

OK, let's call it resistance constant. Or banna? As long as we don't call it resistivity.