Name: - Mohammed Raafat
ID: - 120240340
E-mail: -mohammed.120240340@ejust.edu.eg
Experiment: - Temperature coefficient of metallic resistance
Section: -13
Abstract
This experiment investigates the temperature coefficient of resistance in metallic conductors by
measuring how resistance changes with temperature. A copper wire was heated using a controlled current
source, and resistance values were recorded at various temperatures using a digital multimeter. A linear
plot of resistance versus temperature allowed for the calculation of the temperature coefficient. The
results confirmed that resistance in metals increases with temperature due to increased lattice vibrations.
This study highlights the predictable thermal behavior of metallic conductors, which is essential for
designing temperature-sensitive electronic components and understanding material behavior in electrical
circuits under varying thermal conditions.
Aim of the Experiment
Determine the temperature coefficient of resistivity for a copper sample.
Introduction
The temperature variation of resistance has significant technological implications. Clearly the variation of
resistance with temperature will determine energy consumption in all electrical systems based on metals.
In the case of a superconductor, there is a temperature below which the material exhibits zero electrical
resistance. The goal of superconductor research is to find and create a material with superconductor
properties at room temperature, then these could be used in everyday electronic devices and save a lot of
energy.
Theory
The number of conduction electrons and electron mobility are two of the
most important factors that determine the temperature dependence of
resistivity of a material. The mobility is the dominant factor that regulates
the resistance of a metal, which is inversely proportional to the absolute
temperature T and leads to a positive temperature coefficient of resistivity
that is independent of temperature.
A part of the valence electrons in a metallic substance are detached
from individual atoms and free to move throughout the whole volume
of the metal, while the remaining electrons are tightly bound to each
nucleus, forming a metallic ion. These free electrons act as current
carriers (conduction electrons). They are considered to undergo thermal motion, collide with the
positive ions and scatter off in random directions. Therefore, the net average velocity is zero as
shown in fig.1(a). If an electric field is applied, the conduction electrons are accelerated to the
direction of E between collisions as shown in fig.1(b). therefore, the current flow in the direction
of the field. According to Newton’s second law, the acceleration of a conduction electron of mass
m in an electric field of magnitude E is
The average time interval between two collisions is called the mean free time (τ) and the average
electron gains drift velocity 𝑎𝜏 during this time interval. Drift speed 𝑣𝑑 is given by
If the number density of the conduction electrons is (n), the current density (j) is
Where μ is the mobility of the conduction electrons. The coefficient of proportionality in eq.3 is
called the
conductivity and its reciprocal are the resistivity and we can write eq.3 as
From quantum mechanics, collisions between conduction electrons and positive ions caused by
lattice disorders, and the frequency of the collisions is proportional to the absolute temperature
except very low temperatures. Hence the resistivity and
resistance of a metal is proportional to the absolute
temperature, and expressed as
Where α is the temperature coefficient of resistivity and
it doesn’t depend on the type of metallic sample.
Apparatus
• Mercury thermometer
• Sample support bar
• Stirring bar
• Inner vessel
• Outer vessel
• Hexagon screw
• Clip
• Lid
• Bobbin
• Fastener
Procedure
1) Fill the outer vessel with about 1.2 L of water.
2) Fill the inner vessel with about 0.4 L of water.
3) Set the outer and inner vessels in position and hold the inner vessel with a fastener.
4) Put the mercury thermometer and the experimental sample in the inner vessel, use the clips to
fix them in position.
5) But the outer vessel on the electric heater.
6) Connect the heater with a power supply and your sample with a multimeter.
7) While heating, observe and record the thermometer reading and the resistance.
8) Plot a graph between the (T) and (R) from which you will obtain the value of (α).
Conclusion
This experiment successfully determined the temperature coefficient of resistance (α) for a
metallic conductor by recording resistance at various temperatures. Using a controlled water bath
and multimeter setup, consistent data were collected as the sample was gradually heated. The
plotted resistance-temperature graph showed a clear linear relationship, allowing accurate
calculation of α. The results confirmed theoretical predictions, validating the method and
demonstrating the direct impact of temperature on metallic resistance.
References
• DEPARTMENT OF PHYSICS. (n.d.). Temperature variation of electrical resistance of a
platinum resistor. In DEPARTMENT OF PHYSICS. https://york.ac.uk/physics
• Libretexts. (2023, December 28). 4.3: Resistance and temperature. Physics LibreTexts.
https://phys.libretexts.org/Bookshelves/Electricity_and_Magnetism/Electricity_and_Mag
netism_(Tatum)/04%3A_Batteries_Resistors_and_Ohm%27s_Law/4.03%3A_Resistance
_and_Temperature
