Temperature
coefficient of resistance
You might have noticed on the table for
specific resistances that all figures were specified at a
temperature of 20^{o} Celsius. If you suspected that
this meant specific resistance of a material may change with
temperature, you were right!
Resistance values for conductors at any
temperature other than the standard temperature (usually
specified at 20 Celsius) on the specific resistance table
must be determined through yet another formula:
The "alpha" (α) constant is known as the
temperature coefficient of resistance, and symbolizes
the resistance change factor per degree of temperature
change. Just as all materials have a certain specific
resistance (at 20^{o} C), they also change
resistance according to temperature by certain amounts. For
pure metals, this coefficient is a positive number, meaning
that resistance increases with increasing
temperature. For the elements carbon, silicon, and
germanium, this coefficient is a negative number, meaning
that resistance decreases with increasing
temperature. For some metal alloys, the temperature
coefficient of resistance is very close to zero, meaning
that the resistance hardly changes at all with variations in
temperature (a good property if you want to build a
precision resistor out of metal wire!). The following table
gives the temperature coefficients of resistance for several
common metals, both pure and alloy:
TEMPERATURE COEFFICIENTS OF RESISTANCE, AT 20 DEGREES C
Material Element/Alloy "alpha" per degree Celsius
==========================================================
Nickel  Element  0.005866
Iron  Element  0.005671
Molybdenum  Element  0.004579
Tungsten  Element  0.004403
Aluminum  Element  0.004308
Copper  Element  0.004041
Silver  Element  0.003819
Platinum  Element  0.003729
Gold  Element  0.003715
Zinc  Element  0.003847
Steel*  Alloy  0.003
Nichrome  Alloy  0.00017
Nichrome V  Alloy  0.00013
Manganin  Alloy  +/ 0.000015
Constantan  Alloy  0.000074
* = Steel alloy at 99.5 percent iron, 0.5 percent carbon
Let's take a look at an example circuit to
see how temperature can affect wire resistance, and
consequently circuit performance:
This circuit has a total wire resistance
(wire 1 + wire 2) of 30 Ω at standard temperature. Setting
up a table of voltage, current, and resistance values we
get:
At 20^{o} Celsius, we get 12.5 volts
across the load and a total of 1.5 volts (0.75 + 0.75)
dropped across the wire resistance. If the temperature were
to rise to 35^{o} Celsius, we could easily determine
the change of resistance for each piece of wire. Assuming
the use of copper wire (α = 0.004041) we get:
Recalculating our circuit values, we see
what changes this increase in temperature will bring:
As you can see, voltage across the load went
down (from 12.5 volts to 12.42 volts) and voltage drop
across the wires went up (from 0.75 volts to 0.79 volts) as
a result of the temperature increasing. Though the changes
may seem small, they can be significant for power lines
stretching miles between power plants and substations,
substations and loads. In fact, power utility companies
often have to take line resistance changes resulting from
seasonal temperature variations into effect when calculating
allowable system loading.

REVIEW:

Most conductive materials change specific
resistance with changes in temperature. This is why
figures of specific resistance are always specified at a
standard temperature (usually 20^{o} or 25^{o}
Celsius).

The resistancechange factor per degree
Celsius of temperature change is called the temperature
coefficient of resistance. This factor is represented
by the Greek lowercase letter "alpha" (α).

A positive coefficient for a material
means that its resistance increases with an increase in
temperature. Pure metals typically have positive
temperature coefficients of resistance. Coefficients
approaching zero can be obtained by alloying certain
metals.

A negative coefficient for a material
means that its resistance decreases with an increase in
temperature. Semiconductor materials (carbon, silicon,
germanium) typically have negative temperature
coefficients of resistance.

The formula used to determine the
resistance of a conductor at some temperature other than
what is specified in a resistance table is as follows:

