Investigating the Resistance of Wire
Investigating the resistance of wire
Aim: To find out what affects the resistance of a piece of wire
Planning
I am going to find out what affects the resistance of a piece of wire, and there are a few variables:
* The Temperature: If the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance.
* Material: The type of material will affect the amount of free electrons, which are able to flow through the wire. The number of electrons depends on the amount of electrons in the outer energy shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high number of electrons causing a lower resistance because of the increase in the number of electrons. Also if the atoms in the material are closely packed then the electrons will have more frequent collisions and the resistance will increase.
* Wire length: If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this the length increase should be proportional to the resistance increase. This can be proved by this equation:
Resistance = Resistivity of wire x Length of wire / Cross-sectional area of wire
* Wire width (SWG): If the wires width is increased the resistance will decrease. This is because of the increase in the space for the electrons to travel through. Due to this increased space between the atoms there should be less collisions.
It is also relevant to know of Ohm's Law, which states that the current through a metallic conductor (e.g. wire) at a constant temperature is proportional to the potential difference (voltage). This means that the resistance of a metallic conductor is constant providing the temperature also remains constant. Furthermore, the resistance of a metal increases as its temperature increases. This is because at higher temperatures, the particles of the conductor are moving around more quickly, thus increasing the likelihood of collisions with the free electrons.
Preliminary experiment
I have carried out a trial experiment to find out the range of the experiment, and what variables I would use. There are 4 variables, the material of the wire, the temperature of the wire, the length of the wire and the width of the wire (SWG). First of all, I cannot use the temperature and the material variable, because there is only one type of wire and the temperature is very difficult to control, this leaves with 2 variables, the length and the width of the wire. I have carried out tests with both ...
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Preliminary experiment
I have carried out a trial experiment to find out the range of the experiment, and what variables I would use. There are 4 variables, the material of the wire, the temperature of the wire, the length of the wire and the width of the wire (SWG). First of all, I cannot use the temperature and the material variable, because there is only one type of wire and the temperature is very difficult to control, this leaves with 2 variables, the length and the width of the wire. I have carried out tests with both variables, the SWGs did not work very well, I used two very different SWGs and the difference is not as significant as the length variable.
In the preliminary test, I only used 2 lengths. To find out more about the resistance, I need more variables, so I need to extend the experiment further, i.e. use more lengths. In the preliminary test, I used 50 cm wire and 1 metre wire, to make the experiment more accurate, I would use the lengths of 40cm, 50cm, 60cm, 70cm, 80cm and 90cm. I will also be using different voltages as repeats, e.g. 2V, 4V etc.
Prediction
I predict the longer the wire the bigger the resistance, because the longer the wire, there more electrons the electricity has to pass, meaning there are more collisions, which means more energy are lost. So if the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. My graph should show that the length is proportional to the resistance, this can be proven by the equation:
Resistance = Resistivity of wire x Length of wire / Cross-sectional area of wire
I also predict that the line on my graph would be straight, because the resistance is proportional to the length.
Apparatus
m Constantine (SWG 36) attached to a metre stick
Power Pack
Crocodile clips
Ammeter
Voltmeter
Method
Due to the results of the preliminary experiment, I have decided a reasonable variable with a wide range of lengths. I will also be using different voltages as repeats to get a fair result. Here is the detailed method of the experiment:
. Set up the equipment as shown above, the wire is connected by a crocodile clip. It is set up as a variable resistor. The clip can be slid along the wire to change the length of the wire in the circuit.
2. Put the power pack on 2V and measure the Amps and Voltages when the wire is placed on 40cm from the start of the metre stick.
3. Increase the length in 10cm intervals by sliding the clips until you have readings up to 90cm.
4. Switch the power pack up to 4V, 6V and 8V as repeats.
Fair test
There are a few different types of variables to the experiment, to make it fair, I decided to only change one variable and keep all the other variables the same. I am only going to change the length of the wire and nothing else. There are some other precautions that I will take:
* Use the same wire instead of cutting separate pieces into required lengths, because the cuttings might not be accurate and affect the results. Instead, I would use one 1 metre wire, and use a crocodile to slide on the wire to change the lengths of the wire that is connected to the circuit.
* Use the same wire throughout the experiment, to keep SWG exactly the same.
* Use an ammeter and a voltmeter to measure the figures accurately and to 2 decimal places.
* I would do the experiment in the same environment every time, so the temperature would be the same, so the resistance of the wire is not changed.
* Use different voltages (2V, 4V, 6V and 8V) as repeats to avoid anomalous results.
Safety
This is a experiment with very low risks, but precautions must still be taken:
* The lengths of the wire in the circuit must not be lower than 40 cm to prevent over heating.
* Make sure the surrounding environment is free of liquids, to prevent leak of electricity from circuit and forming a short circuit.
Results
2V
Length (m)
Current (A)
Voltage (V)
0.40
0.17
.15
0.50
0.14
.18
0.60
0.12
.20
0.70
0.10
.23
0.80
0.09
.25
0.90
0.08
.27
4V
Length (m)
Current (A)
Voltage (V)
0.40
0.42
2.85
0.50
0.35
2.92
0.60
0.25
2.96
0.70
0.22
3.01
0.80
0.20
3.05
0.90
0.17
3.08
6V
Length (m)
Current (A)
Voltage (V)
0.40
0.72
4.79
0.50
0.58
4.90
0.60
0.48
4.98
0.70
0.42
5.03
0.80
0.37
5.08
0.90
0.33
5.10
8V
Length (m)
Current (A)
Voltage (V)
0.40
.03
7.00
0.50
0.85
7.10
0.60
0.71
7.30
0.70
0.61
7.36
0.80
0.54
7.40
0.90
0.48
7.50
With the results above the resistance could be worked out by dividing the voltage by the amps, e.g. for the resistance of the 40cm wire at 8 volts:
7
.03
=6.796 ?
Table of resistance (Ohms ?)
Length (m)
2V
4V
6V
8V
Average resistance
0.40
6.765
6.786
6.690
6.796
6.759
0.50
8.429
8.343
8.448
8.353
8.393
0.60
0.000
0.207
0.375
0.282
0.216
0.70
2.300
2.040
1.976
2.066
2.095
0.80
3.999
3.834
3.730
3.704
3.816
0.90
5.875
5.400
5.455
5.625
5.589
Conclusion
From my results, I have found out that the longer the wire, the higher the resistance. All the wires show a strong trend of a straight line, i.e. the length of the wire is shown to be directly proportional to the resistance - double the length and the resistance doubles. This can be proven with my results. The resistance at 40cm at 2 volts was 6.765 ohms, and when the length is doubled at 80cm at the same voltage, the resistance doubles roughly (13.999 ?). This obeys ohms law: "The amount of current flowing in a circuit made up of pure resistances is directly proportional to the electromotive forces impressed on the circuit and inversely proportional to the total resistance of the circuit."
From my graph I have shown that my prediction was correct, as the Line of Best Fit is a straight line proving that the resistance of the wire is proportional to the length of the wire. The length of the wire affects the resistance of the wire because the number of atoms in the wire increases or decreases as the length of the wire increases or decreases in proportion. If the wire is longer, the electrons carrying the current would have to collide with more atoms, during the process, which is losses energy.
Evaluation
I think the test was very successful, it proved the ohms law, and showed that the resistance is proportional to the length of the wire. So when the length doubled, the resistance doubled. The results were quite accurate to support my prediction.
To test the accuracy further, I could work out the gradient of each graph, which would show the resistance per cm. The gradient could be worked out like this:
The highest value in the graph - the lowest value in the graph
Length of the wire (50cm)
Table of gradients
Voltages
Gradient (resistance per cm)
2V
0.1822 ?/cm
4V
0.1723 ?/cm
6V
0.1753 ?/cm
8V
0.1764 ?/cm
The 'book of constants' shows that the resistance for the metal Constantine is 16.7 ?/m, which is 0.16 ?/cm. My results were very close to 16.7 ?/m. The reason that the resistance were slightly higher in my results was because the were resistance in the rest of the circuit, e.g. the crocodile clips and wires, the ammeter and the voltmeters. There were not many anomalous results, however, the resistance per cm were over the figure in the 'book of constants', and the extra resistance were caused by the rest of the circuit. To make the experiment more reliable, less resistant crocodile clips ammeters and voltmeters must be used to measure the resistance more accurately. Overall, my results were accurate, and are reliable enough to support my predictions.
Shan Jiang
