Factors Affecting the Resistance of a Wire
There are four main factors which affect the resistance of a wire. These four factors are as follows:
- Temperature
- Length
- Cross sectional area
- Material
Temperature
Temperature is a factor that has the least observable affect on the resistance of a wire. However, even still as the temperature increases, so does the resistance of a wire, i.e. it becomes harder for the electrons to make their way around the circuit. Increasing the temperature applied to the conductor, means increasing the vibrations of the atoms and molecules of the conductor. Higher temperature means more vibrations. When the wire is cold the atoms are not vibrating as much, hence it becomes easier for the electrons to pass through the atoms and the flow of the electrons becomes more rapid. However, as the conductor is heated up, the motion of the atoms becomes more impulsive and thus the atoms have a more likely chance of colliding with the electrons and getting in the way. Hence the flow of the electrons is interrupted and delayed. Conclusively, higher temperature means higher resistance.
Length
Another factor that affects the resistance of the wire is the length of the wire. As the length of the wire increases, the resistance of the wire also increases. This is because as the length of the conductor increases, the distance required to be travelled by the electrons also increases, the electrons have further to travel. Hence, the electrons are more likely to collide with the atoms in the conductor. Electrons, passing through the shorter wire, will only feel resistance for a shorter period of time compared to the longer wire. Thus, if the wire is shorter, then the resistance is less. However, if the wire is longer then the resistance is high. Resistance is directly proportional to the length of the wire. If the length of the wire doubles, then the resistance also doubles. If the length of the wire is halved then the resistance also halves. R=L
Cross - Sectional Area
The cross – sectional area is basically the thickness of the wire. An increase in the cross- sectional area of the wire results in a decrease of resistance. I say this because, if the wire is thicker then is much more room for the electrons to pass through and they won’t have much trouble in passing through. However, electrons would have much less room to pass through a wire with a smaller cross – sectional area, simply because there is much less room for the electrons to pass through. Hence from this it can be extracted that, a larger cross – sectional area results in a decrease of resistance and a wire with a smaller cross – sectional area results in an increase of resistance. Thus it can be said that resistance is inversely proportional to the cross – sectional area of the wire. R=L/A
Material
The material of the wire also affects the resistance of the wire. Electrons find it easier to travel through some materials more than others. This is because not all materials are equal in concerns to their conductive ability. Some materials are better conductors than others and hence they offer much less resistance to the flow of electrons than other materials would do. Electrons find it especially easy to travel through materials such as silver, due to its high conductive ability. The conducting ability of a material is specified to as it resisitivity. The resistivity of a material is highly dependable on its electronic structure and temperature.
Prediction
My prediction is that as the length of the wire is increased, the resistance of the wire will also increase because as I have already mentioned that increasing the length of the wire increases the distance required to be travelled by the electrons, they have to travel further. Thus, the electrons have now got a much higher probability of colliding with the atoms of the conductor, resulting in more collisions and an increase of resistance. Also the length of the wire is directly proportional to the resistance. So by doubling the length of the wire we are also doubling the resistance. I also predict that having obtained the results, the graph extracted from them results will look similar to the one below:
I am basing my above prediction on the basis of ohm’s law. As I have stated that length is directly proportional to resistance so the hence the graph should look very much like this. The above graph represents ohmic correlation
Apparatus
To carry out this experiment, I will need the following pieces of equipment:
- Nichrome Wire
- Ammeter
- Voltmeter
- Wire connecting crocodile clips
- Power pack
Variables
The independent variable of my experiment will be the change in the length of the wire. The dependant variable of the experiment will be the readings of the voltmeter and ammeter which I will use to determine the resistance of the wire. Apart from this, there will also be certain variables that will be kept constant throughout the course of the experiment, in order to carry out a fair test. These variables are as follows:
- Voltage give out by power pack
- Material of the wire
- Thickness of the wire
- Temperature of the wire
I will keep these above variable constant and same in order to keep the experiment fair throughout. If I was to change any one of these at a given point, then the readings could alter, and the wrong resistance would be recorded.
Preliminary
Before the start of the experiment we had to decide what material of wire we were to use. We were given a choice of wires, ranging from copper, nickel and nichrome. Having done a bit of research, I realised that nichrome would be the best material of wire to select compared to the other two. Thus we chose nichrome and selected it for further work.
Having chosen the wire material, we now had to decide at what voltage setting we were to keep the power pack at, i.e. we had to decide how much voltage would be given out to the electrons. Thus we tested the power pack with a voltage setting of 5V with a 10cm wire sample. This took quicker than expected and the wire melted too quickly. Hence, this meant that the overall experiment would be too quick and short. Thus, we decreased the voltage, in order to increase resistance and lengthen the experiment. We then decreased the voltage to 3V and once again tested it with a 10cm wire sample. The wire did not melt this time round, and so we decided that 3V was a good voltage to keep the power pack at and we kept it the same throughout the course of the experiment.
We now knew what voltage we were to use and now moved on to choosing the various lengths of wire. We decided that we would keep 10cm as the shortest length for the wire and decided to go up in 10cm’s each time. We decided that we would keep 1 metre as the highest length for the wire.
We also decided that we would repeat the experiment for each length of wire, three times in order to obtain an average. We did this to improve the reliability of the results. However, we also found that when re-using the same length of wire in order to obtain an average, we realised that the wire was too hot after the first experiment, and knew that the high temperature would affect the readings. Thus, we repeated the experiments after having done all the different lengths of wire for the first take, then did the second take, and then finally did the last take.
Method
Having everything ready and decided, we now went on to doing the actual experiment. We kept the ammeter in series throughout the experiment because ammeters must always be placed in series…….we also kept voltmeter in parallel throughout the experiment because voltmeters must always be placed in parallel…….We then set the power pack to 3V, and connected the crocodile clips to it. We then placed a 10cm wire between the crocodile clips in order to complete the circuit. Having set the circuit up, we turned the power on the power pack, and recorded the readings off the voltmeter and ammeter and then using ohm’s law, we worked out the resistance. We repeated the experiment for each length of wire three times, in order to obtain an average. By doing this the results became more reliable and helped us to rule out any anomalies. At certain times we did have a few freak and odd results that did not compare well with the others. We discarded these and repeated them. We also made sure that the wire didn’t burn, because sometimes the wire can be seen to melt at the ends and the results could become inaccurate. We repeated the above for all the different lengths of wires.
Safety
When doing the experiment there were certain safety issues to be taken into account. We took into account any overheating aspects in case of any possible burns. Thus, to avoid any burns we used the power pack at a very low voltage to minimise heating. Another fairly obvious and important aspect was making sure that the electricity was turned off when connecting the wires and setting up the circuit. At the same time we made sure that the voltage of the power pack was never too high. At any given points if we smelt burning we would have definitely made sure that the power pack was promptly turned off. Fortunately we did not smell any burnings or have any other accident of any kind during the course of the experiment.
Results
Having obtained the results, I plotted a graph of Resistance Vs Length. Below are my results in a recorded table:
Below is a graph with my above results plotted upon:
Analysis
As can be seen from above there is clearly an anomaly to be spotted. I have circled the anomaly on the graph as can be seen. The circled anomaly does not fit in with the line of best fit. All the other results fit in with the line of best fit, however the result for when the length of the wire is at 90cm does not fit in with the line of best fit, hence it is classified as an anomaly. I believe that this anomaly was obtained due to a mistake made by the scientist when testing the resistance of the wire in the first take when the length was at 90cm. In other words we made a mistake, for the first take when the length of the wire was at 90cm. this is proven in the results table;
From the above section taken from the results table, it can be seen that ‘V (2)’ does not compare well with ‘V (1)’ and ‘V (3)’. There is a substantial amount of difference between ‘V (2)’and the other voltage readings for 90 cm length of wire. The difference between ‘V (1)’ and ‘V (3)’ is only 0.01. Whereas, the difference between V (1)’ and ‘V (2)’ is actually far greater; 0.08. It is the same case for the ammeter readings for 90 cm length of wire. The difference between ‘I (1)’ and ‘I (3)’ is nil. However the difference between ‘I (1)’ and ‘I (2)’ is way bigger; 0.07. From this it can be proven that the second take for 90 cm length of the wire is where the mistake took place.
The only logical reason that I can think of as to why the anomaly took place is because; we might have reused the wire too quickly and did not allow it enough time to cool down before reusing it for the second take. By not allowing the wire enough time to cool down, we unknowingly made it more difficult for the electrons to pass through the wire. This is due to the increase in kinetic energy gained by the atoms of the wire. Increasing the temperature applied to the wire, means an increase in vibrations of the atoms of the wire, this results in a larger resistance which is visible on the results table and on the graph.
From the graph it can also be seen that apart from the anomaly the graph shows a line of best of fit and supports my earlier prediction. I had predicted that when plotting the length of the wire against resistance, a straight line crossing through the gradient would be visible and this is visible in the graph.
I had also predicted that the length of the wire is directly proportional to the resistance; this is also visible from the graph and results. The graph and the results show that the resistance of the wire when it is at 10 cm is 0.49 ohms. So using the theory that the resistance is directly proportional to the length, the resistance should be double the resistance of the 10cm wire when the length of the wire is 20cm. Because doubling the wire means doubling the resistance and this proven in the graph and results because the resistance for the 20cm wire is in fact exactly double the resistance of the 10cm wire; 0.98 ohms.
Conclusion
I believe that my experiment was quite successful and good overall. However, the method used was not totally precise as the anomaly clearly proves this. The method had numerous bad points, one of the fundamental ones being the fact that we had to allow the wire to cool down before we could use it in order to keep the experiment fair. I think that if we were given a second chance to repeat the experiment from scratch, I would almost certainly use a different and more reliable method. For example, I could use……………………………
Apart from changing the method, we could alternatively also improve on the existing method used. The method could be improved by using a new wire for each and every experiment rather than reusing the wire three times for each different length. By doing this the need to allow the wire to cool down in order to keep the test fair would be erased.
I also believe that I have been successful because my graph shows some very accurate results (excluding one), because all the points apart from the anomaly sit on the line of best fit. The only point on the graph that does not sit on the line of best fit, is when the length of the wire is at 90 cm. And a s I have already stated, that I believe this anomaly was obtained due to the fact that we did allow the wire enough time to cool down before reusing it for the second take.
Apart from the anomaly my points were very accurate because the straight line of best fit proves that the length of the wire is directly proportional to the resistance. Furthermore, the graph also proves that an increase in the length of the wire results in an increase in the resistance.
If I was to repeat the experiment, we could use a different factor to test against resistance, rather than using the length of the wire as the factor. For example, we could test the cross-sectional area of the wire as a factor. If this was the factor we would test against resistance, my prediction would be that an increase in the cross-sectional of the wire would result in lower resistance and vice-versa. In other words, using a thicker would mean less resistance and using a thinner wire would mean a higher resistance. I say this because if there is a thinner wire used, then there would be less space for the flowing electrons to flow through causing more difficulty and this would consequently mean higher resistance. Furthermore, using a thicker wire would create more space for the flowing electrons to flow through; this would mean less difficulty for the flowing electrons and would consequently mean less resistance.
Additionally, I believe that the anomaly was not all bad news. I say this because the anomaly proves that higher temperature does mean higher resisitance.
I believe that we carried out the investigation very well and safely. We used all the right equipment and used it professionally. We took into account all the safety procedures before starting the investigation and practiced them throughout. There were no mishaps to report of, no accidents or anything like that.
