# Does Resistance change wrt temperature include effect of size change

Summary:
Changing the temperature of a metal changes the resistivity. It also changes the size of a sample under test. Does the change in size have an additional effect or is that already factored in ?
Changing the temperature of a metal changes the resistivity. But It also changes the size of a sample under test. Does the change in size have an additional effect on the resistance or is that already factored in ?

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berkeman
Mentor
That's a good question. Given that the resistance is ##R = \frac{\rho L}{A}## the resistance is dependent on both the resistivity and the physical expansion of the sample. I would guess that any measurement of resistivity would have to take that into account, but I don't know what the standard resistivity measurements entail.

Off to Wikipedia to find some references... (BTW, did you try looking this up first?)

synch
berkeman
Mentor
Okay, nothing definitive yet in my searching, but it definitely looks like anybody measuring resistivity to any fine accuracy would want to be sure to use the dimensions of the sample at the temperature measured during the test. And since you don't need to use a large current to measure the resistance of the sample, the temperature increase of the sample due to the test current may be very small...

https://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

synch
DaveE
Gold Member
Of course resistivity of an object isn't defined to be dependent on the objects dimensions. It is often called "bulk resistivity" and assumes essentially infinite dimensions. Otherwise you would speak of resistance.

So, your question must relate to the atomic level then. How much does the expansion between atoms affect the resistivity of the bulk material, I guess. This question is a bit above my pay grade, but I'll give you my guess. Since in good conductors (metals) the conduction band electrons are able to move easily from atom to atom, I would assume the effect is insignificant. Short of vaporizing the metal, I don't think it matters how far apart the nuclei are, they still share those electrons. As I understand it, the increase in resistivity of metals is the result of the reduction of the mean free path of the electrons due to thermal energy. I doubt that a small change in atomic spacing would have any significant effect on how thermal electrons are moving, particularly at high temperatures.

BTW, for soft Cu:
electrical conductivity = 59.6×106 S/m
temp. coefficient of resistivity = 0.004 Ω/K
T.C.E. = 16.7 x 10-6/K
density = 8940 kg/m3

Ballpark numbers if you want to do some calculations (which I'm too lazy to do myself)

synch
Baluncore
The coefficient of linear expansion is not significant when compared to the coefficient of resistance or the material variation.
Length = 0.000016 / K.
Resistance = 1/293 = 0.0034 / K.
Ratio is 1 : 210 so linear expansion is only 0.5% of the change in resistance.

The variation in composition of the metal, and the mechanical treatment, will change the resistivity by several percent, which is equivalent to a temperature change of maybe ±5 K.

synch
Thanks for your replies, and sorry about my delay in getting back.

It is a good point, that the measurements of resistivity would accurately measure the linear size at the temperature involved.

My interest was in measuring temperature eg with a platinum resistance, and follows on from an old memory of an experimental calorimeter, which required accurate temperature measurements in a small glass helical tube coated in a thin film of gold. There was a suggestion that the gold film would have a certain resistance which could be measured and used to ascertain the temperature, I never found out if it was tried or not.

But it made me wonder if the metal involved eg in a platinum resistor was dimensionally restrained or was free to expand and so on. Of course the way to use it is to practically calibrate it insitu which bypasses the theory !!

Guessing that a (say) standard cube of material will expand cross-section area more than length, the resistance should at first thought decrease more than increase, but then strain (and Poissons ratio ??) will affect the dimensions further..quite a rabbit burrow.