Temperature coefficient of resistance
You might have noticed on the table for specific resistances that
all figures were specified at a temperature of 20o
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 20o 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 20o 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 35o
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 20o
or 25o Celsius).
- The resistance-change factor per degree Celsius of temperature
change is called the temperature coefficient of resistance.
This factor is represented by the Greek lower-case 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:
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