Physics Lab Report: Determining Wire Resistivity Using Ohm's Law

This physics lab report details an experiment to determine the resistivity of a wire using Ohm's Law. The introduction provides a theoretical background on resistivity and its relationship to resistance, length, and cross-sectional area of a conductor. The aims of the experiment were to differentiate between resistivity and resistance, examine how resistance varies with length while keeping the area constant, and calculate the resistivity of the conductor. The methodology involved using an online simulator to record current values at different lengths of the wire while keeping the voltage constant. Resistance was then calculated using Ohm's Law, and a graph of resistance against length was plotted. The results section presents the collected data and calculations, while the discussion analyzes the linear relationship between resistance and length, the gradient of the graph, and potential sources of error, such as parallax error in the simulator. The experiment concluded that the resistivity of the conductor was 3.375 Ωm, and that resistance varies linearly with length. The report includes references to relevant physics literature.

DETERMINATION OF
RESISTIVITY OF A WIRE
FROM OHM’S LAW

INTRODUCTION
Summary of the Physics how it was applied to the project.
Resistivity refers to the tendency of a material to behave like a resistor. It is a fundamental property of
conductors (Surhone, Timpledon, & Marseken, 2010). Resistance of a conductor is known to depend on
geometry, nature of the material and temperature (Millikan & Bishop, 2017). This relationship is
mathematically modelled as
is the resistivity of a given conductor Ωm, A is the area m2, L is the length in m, R is the resistance in Ω.
From the above relations, if resistance and geometrical properties are known resistivity can be found.
In this experiment, resistivity of a conductor is found based on Ohm’s law. Given a circuit with a varying
length of the conductor, the voltage supply is fived, from Ohm’s law, resistance will vary. By measuring
current at different lengths, the varying resistance can be found. Once evaluated from Ohm’s law a
linear relationship between resistance and length can be graphically obtained (Harris, 2011). The
gradient of the line m= and since areas of the wire can be evaluated, resistivity can be evaluated.
Resistivity refers to a conductor’s resistance of a given material per unit length and a unit cross-
sectional areas. It depends on material nature and temperature while resistance is an obstruction a
conductor offers to the flow of current in it (Maxwell, 2014). It depends on temperature, length and
cross-sectional area.

AIMS OF THE EXPERIMENT
• To distinguish between resistivity and resistance
• To apply Ohm’s law in examining how resistance of a conductor varies
with length when the area is held constant.
• To evaluate the resistivity of conductor by varying the length of a wire
and recording the corresponding current at a fived voltage.

METHODOLOGY
• Materials
• A computer
• Access to the internet
• Using an experimental simulator (
https://www.thephysicsaviary.com/Physics/Programs/Labs/Resistance
OfWireChallengeLab/index.html
), at a fixed voltage of 9, 5 sets of current values and length and the
corresponding length of the wire were recorded in table 1. The
resistance was then calculated from Ohm’s law R=V/I. Using the
obtained values of R, a graph of R against length was drawn. From a
line of best fit, the gradient was evaluated to obtain resistivity

RESULTS
length (m) Current (A) Voltage (V) Resistance(Ω)
1.1 0.68 9 13.23529412
2.5 0.29 9 31.03448276
3.1 0.23 9 39.13043478
4.6 0.16 9 56.25
5.5 0.12 9 75

DISCUSSION
0 1 2 3 4 5 6
0
10
20
30
40
50
60
70
80
A garph of length (m) Against Resistance (Ω)
Length (m)
Resistance(Ω)

Continuation
• A graph of resistance against length is a linear graph with a positive gradient. The positive gradient shows that as the length increases the resistance
increases too. This support the fact that the greater the length of a wire the lesser the number of collisions. These collisions determine the resistance of
a conductor. From the graph, the greater the length, the greater the resistance. Theoretically, the graph should have a y intercept of zero. This is
because a conductor of zero length has no resistance. This is however not the case. From least square regression, this intercept is at -2.7211. This
discrepancy is attributed to the sources of errors in the experiment.
• From the above graph, it can be seen that a graph of R() against L(m) is linear.
• The gradient of the line of best fit
• Evaluation of the cross-sectional area of the conductor.
• Areas of each block=0.10.1=0.01m
• Number of complete blocks=16
• Number of incomplete blocks=18
• Total area=(16+18/2)0.01=0.25 m= 0.00000025
• Since the gradient m=
• Hence 13.5=
• Hence 0.00000025=3.375Ωm
• Possible sources of errors in the experiment.
• Because the entire procedure was carried out in simulator, only source of experimental error was miss-reading due to parallax error. The was a
possibility of misreading either the ammeter reading or the length of the conductor or both as result of parallax error.

CONCLUSION
Resistivity of a conductor can be evaluated if a set of voltages,
corresponding currents and length of the conductor at that particular
point is known. The procedure involves the use of Ohm’s law which
relates voltage and current. The gradient of resistance VS length plot
provides information that is used in computing resistivity if the area of
the conductor is fixed. In this exercise, the resistivity was found to be
3.375Ωm. The experiment has also shown that resistance varies linearly
with length. As the length increases, resistance of a conductor
increases too.

REFERENCE
• Harris, S. W. (2011). Rudimentary Electricity: being a concise exposition of the
general principles of Electrical Science, and the purposes to which it has been
applied.
• Maxwell, J. C. (n.d.). CONDUCTION AND RESISTANCE. A Treatise on Electricity and
Magnetism, 295-298.
• Millikan, R. A., & Bishop, E. S. (2017). Elements of Electricity: A Practical Discussion
of the Fundamental Laws and Phenomena of Electricity and Their Practical
Applications in the Business and Industrial World.
• Surhone, L. M., Timpledon, M. T., & Marseken, S. F. (2010). Ohm's Law: Ohm's
Acoustic Law, Electrical Network, Electric Current, Voltage, Electrical Resistance,
Ampere, Ohm, Current Density, Drude Model, Classical and Quantum Conductivity.