Furthermore, the cross-sectional area affects the resistance because if the wire is thick, more free electrons will be able to flow. This is the same with water flowing through a big pipe.
The other factor that is known to affect the resistance is the material that a wire is made of. Not all materials are created equal in terms of their conductive ability. Some materials are better conductors than others and offer less resistance to the flow of electrons.
If a wire is at a constant temperature, its resistance depends on its dimensions and the material from which it is made. There is a property called resistivity for every material and it is measured in ohm meters (Ω m).
If the resistivity, cross sectional area and length of a piece of wire is known, the resistance can be calculated by using the formula:
Resistance, R = resistivity, p (ohm meters) × length, l (meters)
Cross-sectional area, A (square meters)
This shows that the resistance of a wire is proportional to its length and inversely proportional to its cross-sectional area.
Current-Voltage Characteristics:
If a resistor is in the circuit, the graph will be a straight line passing through the origin. This shows that: I is directly proportional to V. if the voltage was doubled, the current will also be doubled so the value of V and I are always the same and the wire has a constant resistance.
If a filament lamp is in the circuit, the graph will be a curve. If the voltage is doubled, it will produce less than double the current. This means that the resistance increases as the current increases because the metal filament gets hotter.
If a diode is in the circuit in the forward direction, the current increases very rapidly when the voltage rises above a certain point. It has a very low resistance when it is forward. However, when the diode is in reverse, there is almost no current when voltage is applied. It has a very high resistance when it is in reverse.
Insulators and semiconductors:
There are very few free electrons for conduction in insulators at room temperature. When the temperature is high, some electrons ‘escape’ from their atoms and the insulator is able to conduct. So the resistance decreases as the temperature increases for insulators. This is called a semi conductor and silicon is an example.
Superconductors:
When metals are cooled to very low temperatures, it loses all of its resistance and becomes a superconductor. Superconducting wires don’t become hot because electrons flow through them without transfer of energy. Materials that can become superconductors must be cooled to below its transition temperature.
Plan:
For this investigation, I will change thickness of the wire. I will record the current and voltage and use it to calculate the resistance.
To make this investigation fair, I will have to keep the other factors the same. Because of the factors that affect the resistance above, I will have to keep the temperature the same and the type of wire the same. I will keep the temperature the same by leaving all the wire in the lab for a day before I use them. This will ensure that all the pieces of wire will be at room temperature. Furthermore, I will have to use the same type of wire because different materials have different resistances. Also, I will have to keep the length the same by measuring the amount I use.
Prediction:
Because I am testing the thickness, I predict that as the thickness increases, the resistance decreases. This is due to the fact that the free electrons will have more room to move so it will travel faster. Also, there are more free electrons because the wire is thicker.
Preliminary experiment:
For me to decide what the best length of wire and material of wire is, I conducted a pilot experiment. I decided that copper wire is the best to use because it is very conductive. I also decided using 97cm of wire is best to use. Furthermore, I found out that the whole wire doesn’t have the same cross sectional area so I realised that taking 5 measurements in different places of the wire is best. I will use 0 to 6 volts because anything higher than that will result in over heating and the wire breaking. By using that range of voltage, I found that the wire stayed intact and gave good readings.
Equipment:
- Digital Voltmeter
- Digital Ammeter
- Power pack
- Copper wire of different thicknesses
- Crocodile clips
- Leads
- Callipers
- Sand paper
Safety:
I must be careful with the wire because it could get very hot and I could get burnt.
Method:
I am going to assemble the equipment I need into a circuit with the voltmeter parallel to the wire. After that, I will sand the wire to get rid of any wax coated on it. Then I will use the callipers to measure the thickness of the wire. I will take 5 measurements so I can calculate the average which will make my results more reliable. I am going to use callipers because they are accurate to 2 decimal places which make it more accurate. I will then switch on the power pack and start from a low voltage and then record the readings on the ammeter and voltmeter. After that, I will slowly increase the voltage and continue to record the readings.
Once I’ve got at least 6 readings for one wire, I will repeat this with a different piece of wire that has a different thickness until I have 5 different sets of data.
Obtaining:
Analysing:
I plotted my results onto graphs with averaged thicknesses to easily see the trend in the results and to work out the equation of the line.
The graph of my results shows that the thinner the wire is, the steeper the gradient of the line is. Also, the steeper the lines are means the higher the resistance. This means that for the thinner pieces of wire, less current flows. This is because more free electrons will be able to flow in the thicker wires. My prediction is correct and my results support the theory because the theory is: the thicker the wire, the more free electrons will be able to flow. However, one of the trend lines does not support the theory and my prediction. That is the 0.704mm trend line marked in red. This is because it should be steeper than the 0.866mm line but not as steep as the 0.644mm line. It should be in between these two lines because the thickness is in between them.
I made a graph of resistance and cross-sectional area to show the correlation between them. I made it by using the formula above. I calculated the resistance by using the resistivity of copper wire, the length of copper wire I’m using and the cross sectional area. The graph shows that as the cross-sectional area increases, the resistance decreases. This means that resistance is inversely proportional to its cross-sectional area. The graph of my results should look similar to this.
I made this graph of resistance and cross-sectional area to show the correlation between them. I made this graph using my results. This graph is quite similar to the graph above. The only thing is that it doesn’t curve as much as the one above. This could be because of the heating in the wire which increases the resistance. Also, the anomaly clearly sticks out and doesn’t go with the trend line. With the exception of the anomaly, my graph also shows that as the cross-sectional area increases, the resistance decreases.
Evaluating:
My results seem quite consistent and reliable and generally fit the trend line. The method I used is good because I am confirming V=IR with a lot of results so it is more accurate. I also used a digital ammeter and voltmeter to get more accurate results. They’re more accurate because the values are given to 2 decimal places. The callipers also give readings accurate to 2 decimal places which make my results more accurate. This makes the results I get more reliable. However, I had a hard time getting a decent set of results and the 0.704mm thickness does not fit pattern and theory.
I think the 0.704mm thickness is an anomalous result and can be excluded from my conclusion because all of the other results support the theory. The problem could be that I didn’t measure the thickness correctly and didn’t set the callipers to 0 before I measured the copper wire. The wire also could’ve been waxed which made it thicker than it actually is and I didn’t sand it properly.
My method could be improved by using better crocodile clips and better leads because the results were fluctuating. I had to hold down the leads and crocodile clips until I got reasonable results to record. Also, using copper wire that isn’t waxed could help because I wouldn’t need to sand it. Sanding it takes off the wax but I could also sand off the copper, making it thinner. Furthermore, after recording a reading, I could turn the power pack off to allow the copper wire to cool down. This would make my results more reliable because there wouldn’t be any heat left in the wire to increase resistance. I will be keeping the temperature of the wire fairly the same for each of my readings. This should make my graph of cross-sectional area and resistance more similar to the graph made using the formula.
For further work, I could use a different type of wire to be able to compare the resistance difference. From this, I will be able to tell if different wires have different resistances and by how much.