copper resistance vs temperature

[Roy McCammon]

can anyone point me to a web site that gives resistivity of any typical
copper wire from about -40C to + 60C?

 

[Spehro Pefhany]

can anyone point me to a web site that gives resistivity of any typical
copper wire from about -40C to + 60C?

The tempco of resistance of copper is approximately +3930ppm/K at room
temperature, depending on how pure it is and upon annealing.

So R(T) ~= Ro * (1.00393)^(T-To)

From another source, relative resistance of wire:

-40°C 0.7490
-20°C 0.8263
0°C 0.9035
20°C 0.9807
25°C 1.0000
40°C 1.0580
60°C 1.1352

Best regards,
Spehro Pefhany

 

[Robert Strand]

can anyone point me to a web site that gives resistivity of any typical
copper wire from about -40C to + 60C?

Off hand,

Resistivity @ 20C (<--I think)

rho = 1.724e-8 [ohm m]

Temperature:

R(T2)/R(T1) = (234.5 + T2) / (234.5 + T1)

where T's are in Celsius.

I believe this for annealed copper. The different forms of copper have
slightly different rho and temperature dependency constant.

Rob

 

[Tom Bruhns]

can anyone point me to a web site that gives resistivity of any typical
copper wire from about -40C to + 60C?

You can get the variation with temperature from
http://www.cda.org.uk/Megab2/ElecApps/pub122/sec11b.htm. That's from
a google search, and it's interesting to note that it shows a
relationship between Spehro's first method and Robert's. You can get
the resistance per 1000 feet of annealed copper wire at 20degrees C
for AWG gauge numbers amazingly closely from the very simple formula,
10^(0.1*AWG-1), so for 10 gauge wire, it predicts 1 ohm, and my wire
table says 0.9989 ohms and for 30 gauge it predicts 100 ohms, while
the table says 103.2.

Cheers,
Tom

 

[Roy McCammon]

can anyone point me to a web site that gives resistivity of any
typical copper wire from about -40C to + 60C?

Off hand,

Resistivity @ 20C (<--I think)

rho = 1.724e-8 [ohm m]

Temperature:

R(T2)/R(T1) = (234.5 + T2) / (234.5 + T1)

where T's are in Celsius.

I believe this for annealed copper. The different forms of copper have
slightly different rho and temperature dependency constant.

thanks Robert

 

[Roy McCammon]

You can get the variation with temperature from
http://www.cda.org.uk/Megab2/ElecApps/pub122/sec11b.htm. That's from
a google search, and it's interesting to note that it shows a
relationship between Spehro's first method and Robert's. You can get
the resistance per 1000 feet of annealed copper wire at 20degrees C
for AWG gauge numbers amazingly closely from the very simple formula,
10^(0.1*AWG-1), so for 10 gauge wire, it predicts 1 ohm, and my wire
table says 0.9989 ohms and for 30 gauge it predicts 100 ohms, while
the table says 103.2.

Cheers,
Tom

thanks Tom

 

[Roy McCammon]

The 1922 Standard Handbook for Electrical Engineers provides a table of
values depending on where the copper is from and who measured it. Their
values, at 25C, are 0.380%/C to 0.386%/C.

By 1943, the Bureau of Standards had weighed in with 0.393%/C for annealed
copper and 0.382%/C for hard drawn copper at 20C.

-- Mike --

thanks a lot

 

[Roy McCammon]

The tempco of resistance of copper is approximately +3930ppm/K at room
temperature, depending on how pure it is and upon annealing.

So R(T) ~= Ro * (1.00393)^(T-To)

Thanks Spehro. Any idea how accurate that that formula is
over -40 to +60?

 

[Roy McCammon]

No, compare to the values I gave below, I think you'll find at least a
couple percent difference. What are you up to? Copper RTDs are not a
"precision" way of temperature measurement, but they are used.

I'm just trying to use a thermister to compensate
for the copper resistance in a coil. No doubt but
that your formula is good enough, but I'd still like
to see the "official" data.

 

[Tony Williams]

I'm just trying to use a thermister to compensate
for the copper resistance in a coil. No doubt but
that your formula is good enough, but I'd still like
to see the "official" data.

The official (IEC) spec for copper is a resistivity of 1.7241
microhm-cm at 20C, but is qualified by a variation of up to 3%,
depending on the annealed/worked state. The tempco is given as
the single figure of 0.00393 ohms per ohm at 20C.
2
The usual sum is, R(T) = R(0)*(1 + AT + BT + etc)

A and B are constants defined at 0C, but B is very small for
copper and we can rejig the sum for use with the value of A=
0.00393 that the IEC has specified at 20C.

R(T) = R(20)*(1 + 0.00393*(T-20) )

Where R(20) is the value of the copper resistor at 20C.

If I compare a calc'd R(T) with those on Speff's table,
using his 20C value of 0.9807 ohms for the R(20).

Speff's R(T) calc. % difference
~~~~~~~ ~~~~~~~~~~ ~~~~~~~~~~~~
-40°C 0.7490 0.7495 +0.067 (= 0.12C equiv)
-20°C 0.8263 0.8265 +0.024
0° 0.9035 0.9036 +0.011
20°C 0.9807 0.9807 ------ Rref
25°C 1.0000 1.0000 ~0
40°C 1.0580 1.0578 -0.019
60°C 1.1352 1.1349 -0.026

If Speff's table is authoritive we could use it to generate
values for A and B which would pull the R(T) sum in tighter.

 

[Mike]

Thanks Spehro. Any idea how accurate that that formula is
over -40 to +60?

Sounds like you're getting pretty serious.

My 1922 Standard Handbook for Electrical Engineers lists a table of 8
different researchers/organizations that had measured copper resistivity,
along with their results (more on that in a moment). My 1913 Electrical
Engineer's Handbook lists this result from Matthiessen:

R = Ro(1 + 0.00387t + 0.00000597t^2)

However, they also point out that, "The wire used by Matthiessen was as
pure as could be obtained at the time (1860), but in reality contained
considerable impurities; the above formula, therefore, is not generally
applicable."

The 1922 Standard Handbook attributes a different formula to Matthiessen:

S = So(1 - 0.0038701t + 0.000009009t^2), where S is the conductivity and So
is at 0 degrees C.

Back to the table of results. The last two colums of data were the most
recent standards adopted at the time. The Bureau of Standards and AIEE
adopted a set of values in 1911, and there was also an "International
Annealed Copper Standard." Both list values at 0, 15, 20, and 25C:

Bureau of International
Standards Annealed
/ AIEE Copper Standard

------- Resistivity ---------

0 0.14106 0.14133
15 0.15003 0.15029
20 0.15302 0.15328
25 0.15601 0.15626

--- Temperature Coefficient ---

0 0.00427 0.00427
15 0.00401 0.00401
20 0.00394 0.00393
25 0.00386 0.00385

As is clear, resistivity is itself a function of temperature. Over this
temperature range, it's a fairly linear function of temperature; assuming
that linearity holds up over a wider range, you could estimate the
temperature coefficient by linear interpolation/extrapolation.

-- Mike --