Quantitative Investigation of Resistivity and Ohm’s Law
Autor: Sara17 • December 22, 2017 • 2,344 Words (10 Pages) • 826 Views
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Table 1 presents the data gathered by measuring the resistance of wire spools.
Table 1. Properties of unknown resistance wires on the spools
Spool No.
Material
Length, L. (m)
Wire Size #
(E & S)
Diameter(D)
(m)
Area
A=πD2/4
(m2)
Resistance, R
Ω
Resistivity([pic 14]
(Ω-m)
1
Cu
10
22
0.000644
3.26x10-7
3.09
1.01x10-7
2
Cu
10
28
0.000321
8.09x10-8
4.02
3.24x10-8
3
Cu
20
22
0.000644
3.26x10-7
3.32
5.14x10-8
4
Cu
20
28
0.000321
8.09x10-8
6.48
2.62x10-8
5
Cu-Ni
10
22
0.000644
3.26x10-7
18.48
6.02x10-7
Analyzing the obtained data, specifically for spools 1 and 2, which are of the same length(10m) and made up of Cu, we can see that as the area decreases (3.26x10-7m2for spool 1 and 8.09x10-8m2for spool 2), resistance increases (3.09Ω for spool 1 and 4.02Ω for spool 2). The result is consistent with equation 6 that resistance of a given material is inversely proportional to their cross-sectional area.
For spools 1 and 3, which are of the same cross sectional area (3.26x10-7m2) and made up of Cu, we can see that as the length increases(10m for spool 1 and 20m for spool 3), resistance also increases(3.09Ω for spool 1 and 3.32 Ω for spool 3). The result is consistent with equation 6 that resistance of a given material is directly proportional to their given length. The same observations can be formulated from the resistance of spools 2 and 4.
The results of our experiment were compared to the theoretical values of resistivity of Cu and Cu-Ni spools, which was given prior to the experiment. Table 2 shows the percent errors.
Table 2. Percent error of Cu and Cu-Ni resistivity.
Material
Theoretical ValueΩm
Experimental Value Ωm
Percent Error
Cu
1.72x10-8
5.28x10-8
210.62%
Cu-Ni
4.9x10-7
6.02x10-7
22.93%
Theoretically, the resistivity of spools 1, 2, 3 and 4 must be of the same value all of them are made from copper. Spool 5, an alloy, should have a different resisitivity with the 4 cooper spools.
The results of the first part of the experiment yielded to a great value of experimental error. This may be attributed to the quality of the materials used, including the alloys and the ohmmeter. The wires heating up as a result of the current can also introduce experimental error.
Based on the Table 2, Cu is a better conductor of electricity since it has lower resistivity than Cu-Ni. The lower the resistivity of a given material, the better conductor it is. The greater the resistivity, the greater is the field needed to cause a given current density, or the smaller is the current density caused by a given field [2].
The second part of the exercise dealt with the relationship of voltage with current when resistance is held constant, as described in Ohm’s Law. It states that the electric potential difference between two points on a circuit (ΔV) is equivalent to the product of the current between those two points (I) and the total resistance of all electrical devices present between those two points (R) [3]. The mathematical representation is given in equation 1 as:
∆V = IR
Voltage is a measure of potential energy that is always relative between two points. As energy is the ability to do work, this potential energy can be described as the work required to move electrons in the form of an electrical current around a circuit from one point to another [2].
Resistance is the hindrance to the flow of charge.While the electric potential difference established between the two terminals promotes the movement of charge, it is resistance that impedes it [2].
The resistance of the resistor was measured using a multimeter set to Ohmmeter. The value obtained was 148.5Ω. This value was assumed constant all throughout the experiment. Using the equation for Ohm’s law, the expected current
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