University Physics Lab: Measuring the Resistivity of a Wire

This assignment details a physics experiment designed to measure the resistivity of a wire and its relationship to wire length and material. The experiment used constantan and nichrome wires of varying lengths and diameters. Measurements of voltage and current were taken, and resistance was calculated using Ohm's law. The results demonstrated a direct relationship between wire length and resistance, confirming that longer wires exhibit higher resistance. The experiment also highlighted the inverse relationship between wire diameter and resistance, as thinner wires offered greater resistance. The analysis included calculations of resistivity and a comparison of experimental and theoretical values, with a discussion of potential sources of error. The conclusion emphasized the validity of the experiment's findings and its successful attainment of the objective.

MEASURING THE RESISITIVITY OF A WIRE
AIM
The purpose of the experiment is to measure the amount of resistivity experienced in a wire
when the length changes. The experiment was meant to investigate the changes in electrical
resistance on a wire when the length of the wire is increased for different materials. The current
is wired through the wire and key factors such as the voltage used, the diameter of the wire and
the current used are measured. These values are then used to determine the amount the electrical
resistance in the wire.
Introduction
Resistance is used to determine the condition of the circuit component or even or a component.
Resistance is a force which opposes the movement of the current. The higher the resistance of
the wire the lower the current of the within the wire (Henry, 2017). The resistance in wires are
used to control circuits from damages. On applying the voltages on a material such as wires, the
current flows. The amount of the current in the materials is based on the amount of resistance.
According to Ohms law, “resistance on a material is the capacity of a circuit to oppose the flow
of current in it” (Gómez-Ferrer, 2016). This is responded as the ratio of electromagnetic force
and the current through the material (R=E/I) (Chin, 2017 and Gómez-Ferrer, 2016). Resistivity
on the other hand is the measure of the quantity of resistance experienced in a material. The
resistivity of the materials is depended on factors such as resistivity. The resistivity on a wire is
majorly depended on the size and the thickness of the wire. Additionally, there other factors such
as the temperature, humidity and electrification time which also affect the resistivity in a wire.
Nevertheless, these factors are not major and therefore this experiment majorly focused on the

size and thickness factors to measure resistivity (Schlumberger Limited, 2016). The experiment
was carried out to determine the resistance from the wire to electricity and then deriving the
resistivity of the wire. The changes in length was the main determinant used on this experiment
was the change in the length of the wire for different materials.
A. Materials
The following materials were used in the experiment in order to measure the electrical resistance
to the wire;
 constantan wire -1m of diameters 0.28 and 0.45mm
 nichrome wire- 1m of diameters 0.28 and 0.45mm
 12V Voltage Supply
 2 multi-meters
 Micrometer screw gauges
 Ammeter
 Voltemer
Methods / Procedure
i. First, measurement of one piece of the constantan wire was taken
ii. The diameter of the wire was measured and recorded in three places
iii. The average of the three diameters was done
iv. The set-up of the experiment was done as on the following diagram

v. Setting up of the power supply up to IV was done. (the power setting is able to provide a
limiting factor to the current which is passing through the wire. This is meant to reduce
the heating effect which is likely affect the resistivity and resistance to the electricity)
vi. The switch was connected and the different reading on the ammeter and voltmeter
devices were taken for 8 different lengths of the wire
vii. The results were recorded in a table containing the values of length, voltage, current and
resistance
viii. Procedure i to vii was repeated for the other constantan wire and the 2 No. nichrome
wires.
Results
Recording of the constantan wire results
Length (m) Voltages (V) Current (A) Resistance
0.10m 1.01 1.50 0.67
0.20m 0.98 0.79 1.24
0.30m 1.01 0.62 1.62
0.40m 0.99 0.48 2.15
0.50m 1.00 0.38 2.63
0.60m 0.99 0.33 3.00
0.70m 0.99 0.27 3.67
0.80m 1.00 0.25 4.00
Recording of the constantan wire results
Length (m) Voltages (V) Current (A) Resistance
0.10m 0.96 1.13 0.84
0.20m 0.98 0.64 1.53
0.30m 1.00 0.40 2.50
0.40m 1.00 0.33 3.03
0.50m 0.99 0.26 3.81
0.60m 0.98 0.22 4.45
0.70m 0.99 0.19 5.21
0.80m 0.99 0.16 6.18
Graphs
The graph representing the resistance against the length of constantan wire

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
1
2
3
4
5
6
7
Graph of Reistance Vs Lenth
Series1
Length
Resistance
The graph representing the resistance against the length of constantan wire
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
1
2
3
4
5
6
7
Graph of Reistance Vs Lenth
Series1
Length
Resistance
Discussion / Analysis
From the results, it was clear that the amount of resistance experience is related to the length of
the wires. Increasing the wire length was found to increase the resistivity to the current. The
current is meant to travel a longer distance and this is seen to increase the resistance which the
current faces as it moves through the distance (Dyos, & Farrell, 2016). Increase in both the wire

length and the thickness of the wire are found to increase the amount of resistance experienced.
Since resistance is found after the collision of the electrons with the ions in a wire, increasing the
length increases the ions and the electrons have more resistances. The electrons in a longer wire
is able to meet more ions on the longer distances and this increases the resistance. This is the
main reason why the distance is seen to increase in longer wires from the results than the amount
recorded from shorter wires (Van, Cook, & Geological Survey (U.S.), 2015). Therefore, it was
found to be clear that the correlation which exist between the wire length and the resistance is
inverse proportional. Changing the diameters is able to affect the resistance which is
experienced. Thin wires offer greater resistance than wider wires. The thin wires are able to
accommodate fewer electrons to carry the current than wider wires (Grace, & Commonwealth
Scientific and Industrial Research Organization (Australia), 2017). Therefore, increasing the
thickness is able to increase the ions and therefore offering more less to the current flow through
the electrons.
The electrical resistance in the wire as assumed was found to be higher in the longer wire and
lesser in the wire with large cross-section. From the formula, resistance is equal to
Resistivity will be equal to RA/L
Keeping the area constant and increasing the length will lead to the reduction of resistivity of the
wire. This is the same case of the results achieved during the experiment (Turner, &
Aeronautical Research Laboratories (Australia), 2014). In our experiment, we were able to keep

the temperature constant and thus it is not in any way attributed to the increased level of
resistance achieved. In addition, the gradient of the graph is able to represent the quantity of
resistance divided by the area. Performing the multiplication between the gradient and the cross-
sectional area leads to the result of the resistivity of the wire.
For the first round,
Diameter average = (0.4+0.5+0.4)/3 = 0.217
Area of the wire = 22/7* (0.217)2 = 0.148m2
Gradient = Change in y/ change in x
= (3.03-0.84)/ (0.40-0.10) = 2.19/0.3 = 7.3
Area x gradient = 7.3 x 0.148 = 1.0804
For the second round,
Diameter average = (0.3+0.4+0.3)/3 = 0.167
Area of the wire = 22/7* (0.167)2 = 0.087m2
Gradient = Change in y/ change in x
= (3.0-0.67)/ (0.60-0.10) = 2.33/0.5 = 4.66
Area x gradient = 4.66 x 0.087 = 0.40542
The values of the resistances calculated values are nearing the values experienced. Nevertheless,
there are little discrepancies between the calculated figure and the read figure (Casualties, 2012).
This can be attributed to the other factors which are able to affect the resistance in the wire such
as the temperature (Schenkel, 2012). In addition, the materials types are able to affect the amount

of the resistivity between the calculated figure and the figure from the results (Chui, & Zhou,
2013). The calculated figure on the other hand is unable to be affected by these factors.
Therefore, the results achieved during the results can be relied on since the difference is little.
Conclusions
In conclusion, the experiment was able to prove the relationship between the length of the wires
and the resistivity. It was found clear the longer the length of the wire the higher the resistance.
As explained earlier, the longer lengths are able to offer higher resistances due to the presence of
high number of ions going against the electrons. The electrical resistance is therefore inversely
proportional to the length of the wire. Additionally, both the calculated figure and the results of
the experiments were able to agree to this fact that they resistance increases with increase in wire
length. The experiment was able to attain the objective which was achieved.

References
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Chui, S. T., & Zhou, L. (2013). Electromagnetic Behaviour of Metallic Wire Structures. London:
Springer London.
Dyos, G. T., & Farrell, T. (2016). Electrical resistivity handbook. London, U.K: Peter Peregrinus
on behalf of the Institution of Electrical Engineers.
Gómez-Ferrer, B. (2016). Resistivity Recovery in Fe and FeCr alloys. Cham: Springer
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Schlumberger.
Turner, P. E., & Aeronautical Research Laboratories (Australia). (2014). Resistance coefficients
of wire gauzes. Melbourne: Aeronautical Research Laboratories
Van, N. R., Cook, K. L., & Geological Survey (U.S.),. (2015). Interpretation of resistivity data.
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