Electrical Resistance Temperature Calibration

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Last update: 15-11-2023

Temperature Variation of Resistance[1]

The resistivity of all materials depends on temperature. Some even become superconductors (zero resistivity) at very low temperatures. Conversely, the resistivity of conductors increases with increasing temperature. Since the atoms vibrate more rapidly and over larger distances at higher temperatures, the electrons moving through a metal make more collisions, effectively making the resistivity higher. Over relatively small temperature changes (about 100ºC or less), resistivity ρ varies with temperature change ΔT as expressed in the following equation

ρ=ρ0(1+αΔT)

, where ρ0 is the original resistivity and α is the temperature coefficient of resistivity. (See the values of α in Table 2 below.) For larger temperature changes, α may vary or a nonlinear equation may be needed to find ρ. Note that α is positive for metals, meaning their resistivity increases with temperature. Some alloys have been developed specifically to have a small temperature dependence. Manganin (which is made of copper, manganese and nickel), for example, has α close to zero (to three digits on the scale in Table 2, and so its resistivity varies only slightly with temperature. This is useful for making a temperature-independent resistance standard, for example.

Table 2: Temperature Coefficients of Resistivity α

Material	Coefficient α (1/°C)2
Conductors
Silver	3.8×10−33.8×10−3
Copper	3.9×10−33.9×10−3
Gold	3.4×10−33.4×10−3
Aluminum	3.9×10−33.9×10−3
Tungsten	4.5×10−34.5×10−3
Iron	5.0×10−35.0×10−3
Platinum	3.93×10−33.93×10−3
Lead	3.9×10−33.9×10−3
Manganin (Cu, Mn, Ni alloy)	0.000×10−30.000×10−3
Constantan (Cu, Ni alloy)	0.002×10−30.002×10−3
Mercury	0.89×10−30.89×10−3
Nichrome (Ni, Fe, Cr alloy)	0.4×10−30.4×10−3
Semiconductors
Carbon (pure)	−0.5×10−3−0.5×10−3
Germanium (pure)	−50×10−3−50×10−3
Silicon (pure)	−70×10−3−70×10−3

Note also that α is negative for the semiconductors listed in Table 2, meaning that their resistivity decreases with increasing temperature. They become better conductors at a higher temperature because increased thermal agitation increases the number of free charges available to carry current. This property of decreasing ρ with temperature is also related to the type and amount of impurities present in the semiconductors. The resistance of an object also depends on temperature, since R0 is directly proportional to ρ. For a cylinder, we know

R=ρL/A

, and so, if L and A do not change greatly with temperature, R will have the same temperature dependence as ρ. (Examination of the coefficients of linear expansion shows them to be about two orders of magnitude less than typical temperature coefficients of resistivity, and so the effect of temperature on L and A is about two orders of magnitude less than on ρ.) Thus,

R=R0(1+αΔT)

is the temperature dependence of the resistance of an object, where R0 is the original resistance and R is the resistance after a temperature change ΔT. Numerous thermometers are based on the effect of temperature on resistance.

Reference

[1] British Columbia/Yukon Open Authoring Platform