NE6 DETERMINATION OF TEMPERATURE COEFFICIENT OF RESISTANCE
Electrical resistance of a metal conductor depends not only on the shape of the conductor but also on its
temperature. Dependence of resistance on temperature can be explained by classical electron theory that
says that the increase of temperature results in the increase of amplitude of thermal oscillations of atoms in
crystal lattice and then also the probability of collisions among electrons and lattice ions increases. Decrease
of the mean free path of electrons with temperature results from macroscopic point of view in the increase of
electrical resistance. The increase of resistance dR at the increase of temperature dt is proportional to the
resistance R and the temperature increase dt :
dR = α R dt ,
(1)
where the coefficient of proportionality α characterizes temperature dependence of a specific material and it is
called temperature coefficient of resistance. For metal conductors coefficient α depends on the temperature
only slightly and it can be considered constant for a not very wide temperature interval. Integrating equation (1)
from the reference temperature t0 to the temperature t (on assumption that α (t – t0) <<1 ) we get the following
formula for electrical resistance at temperature t:
R = R0 [ 1 + α (t − t 0 )] ,
(2)
where R0 is the resistance at temperature t0 (this temperature is chosen to be t0 = 0°C in the following text).
Dependence of electrical resistance on temperature can be experimentally obtained by simultaneous
measurements of resistance and temperature of conductor. In our experimental set-up the coil of wire is
immersed in oil in the glass vessel. The temperature of oil, that is in equilibrium state the same as the
temperature of conductor, is controlled by the thermostated water bath.
The resistance of conductor is measured by the so called resistance comparison method whose scheme can
be seen in the figure. Electric current flows through unknown resistance R that is connected in series with
normal resistance Rn .
The following formula for unknown resistance R can be derived :
R=
Ux
⋅ Rn
Un
(3)
where Ux and Un are the voltages on unknown resistance and normal resistance, respectively, and Rn is
the normal resistance.
Since in our experimental set-up voltages Ux and U0 are measured, the formula (3) can be rewritten in the
following way:
R=
Ux
⋅ Rn
U0 − U x
Scheme:
(4)
Laboratory Tasks
1.
2.
3.
4.
5.
To measure simultaneously the resistance of copper conductor and its temperature and draw the graph of
the dependence of resistance on temperature.
To analyze this dependence, i.e., to determine the parameters of regression straight line.
Using parameters of regression straight line to calculate the value of temperature coefficient of resistance
α of studied conductor.
To calculate the uncertainty of the quantity α using statistical processing of experimental data.
To compare calculated value α with the table value and to calculate relative error of experimental value
in percents.
Experimental Procedure
Glass vessel with oil (B), in which the coil of copper wire (R) is immersed is put in the thermostated water bath
(VT), filled with cold water. It is necessary to wait for cca 5 min to achieve temperature equilibrium between
water bath and glass vessel with oil (B). Resistance R and normal resistance Rn are connected as it is shown
in the scheme. Water thermostat is set to the highest required temperature (≈ 80°C) and switched on. While
stirring the oil manually, the temperature measured by the temperature probe is permanently displayed in one
of the CoachLab windows. The experiment is started at the closest higher temperature rounded off to 5°C (e,g,
15°C, 20°C, or 25°C) when Ux, U0, and temperature t are measured by clicking on green “measurement
button” and resistance R is automatically calculated. The other measurements are done at temperatures
higher by equidistant step of 5°C under continuous stirring of the oil bath. The experiment is finished at the
temperature of 80°C.