From these results I decided to use 8H, as it showed the greatest range. I will also measure the resistance starting at 1cm, ending at 10cm, with increments of 1cm Results will be repeated twice, and all anomalies will be repeated until a satisfactory result is obtained. However, for analysis purposes I will use the average of these resistances in order to produce more accurate results.
The maximum current I am likely to obtain from 8H is:
Imax = Vmax = 6V
Rmin 11.0
My Imax is 0.55 A, therefore I will need an ammeter with a range of 0-1A.
Method
First I will take my pencil lead, which has been glued to a piece of M.D.F., which is particularly non-conductive and will stop the lead being damaged during the process of the experiment, or coming into contact with something conductive, and thus altering the results. I will plug a lead into the + end of the battery pack, and then fasten a crocodile clip to the other end of the wire. This will then be clamped as close to the end of the pencil lead as possible, without actually going off the end, and ensuring the jaws make full contact with the pencil lead. The other lead will be fastened to the – end of the battery pack, and the other end will have a crocodile clip placed over it. The end of this lead in the battery pack will be placed in the second plug to give a potential difference of 3V (2 batteries). This clip will be attached to varying lengths of the lead, starting with 1cm. This distance will be measured by placing a ruler next to the lead and carefully placing the crocodile clip, and once the reading on the ammeter and voltmeter has settled it will be recorded on paper. I will then wait 10 seconds in order to let the pencil lead cool down; otherwise my results will be affected.
This length is then increased to 2cm, the results are recorded, a 10 second break, distance increased to 3cm, and so on until measurements every cm up to 10 cms has been recorded. I will then repeat this process, using 3 batteries (4.5V) and 4 batteries (6V).
I will keep this experiment a fair test by ensuring that several areas are kept constant:
- The area of the pencil lead will be kept the same throughout by taking extra care that the lead doesn’t lose any area by being chipped from the crocodile clip’s sharp teeth.
- I will keep the type of pencil the same, and not change it during the experiment.
- The temperature is more difficult to control, but I will keep it constant by letting it cool off by disconnecting the circuit between measurements for 10 seconds, which should ensure that any heat gained from the current has dissipated by the time I take the next reading.
- I will use the same degree of accuracy (0 D.P.) when measuring throughout, and I will also use the same ruler for consistency.
Prediction
I predict that as the length of the pencil lead increases the resistance will increase accordingly.
Scientific knowledge
My reasons for my prediction are:
As the length increases, the electrons that form the current will have to travel a greater distance along the pencil lead. This means that the number of collisions between the electrons and the graphite atoms will increase, causing the electrons losing kinetic energy to the atoms. This kinetic energy causes the atoms in the pencil lead to vibrate more, and some of this is given off as thermal energy. However, I want to avoid this, as it alters results by reducing the resistance as the temperature increases. I should also expect to see the resistance roughly double as the distance doubles, as there is double the number of graphite atoms, so increasing the possibility of collisions.
An analogy to illustrate this would be a man walking along a corridor. As it is packed with people, he is more likely to bump into them. This takes up more movement (kinetic) energy, and means that he becomes more tired than if the corridor was empty and he didn’t hit anyone. It also means that he moves more slowly as well. In a relatively empty corridor, because there are fewer people, he is less likely to hit them, and the net loss of kinetic energy is lower than that of the man in the packed corridor. Therefore the length (cm) is proportional to the resistance (Ω).
Safety is important, and I should keep well away from water and wet areas to prevent the risk of electric shock, and normal lab. rules will apply as usual.
Results
Analysis
In my analysis I have found that as the length increases, so does the resistance, and that the relationship between the two is as the length doubles, so does the resistance i.e. they are proportional. For example:
We can see from this that as the length doubles (2 → 4, and 3 → 6) so does the resistance (14.76 → 22.74, and 18.56 → 30.42). Although these results are not 100% accurate, they are close enough to show that the proportional relationship works in a ratio of roughly 1:1. The graph shows me that that the trend is a linear one, this means as the length increases at a steady rate so does the resistance, in the ratio 1:1, so as the length doubles from say, 4 to 8, the resistance increases from 22.74Ω to 37.49Ω.
I decided upon this from the information in the table, where it was possible to quantify the information by dividing the resistances by 2, in order to find the theoretical values for half the length, so half the resistance at 6cm was 15.21Ω, and the resistance at half that length (3cm) was 15.49Ω. I also looked at the graph, and using the least squares regression line, I found that the gradient was 1.2, so for every x square, there were 1.2 y squares, lending evidence to my theory that as the length doubles, so does the resistance. This therefore means that for every 1cm of pencil lead there were 1.2Ω of resistance. The actual shape of the graph was a straight line.
My initial prediction was accurate, I predicted that the resistance length would increase in the ratio of 1:1, and they have, with the resistance increasing as the length increased. My evidence for this has been stated above.
This can be explained by the collision theory – as the length increases, so does the number of graphite atoms, and therefore the likelihood of collisions between the electrons flowing through and the graphite atoms in the pencil lead. The electrons are slowed because when they collide the electrons lose kinetic energy to the graphite atoms, causing the atoms to vibrate more and therefore heat up.
Going back to my man walking down a corridor analogy, if the man has to walk along the corridor and back again, he will be twice as likely to hit someone, as he has to pass the same people all over again. Effectively this means that he would have to pass 40 people instead of 20, or 100 instead of 50 and so on. He will therefore me likely to lose more kinetic energy colliding with the people in the corridor, and therefore moves more slowly.
Finally, the overall resistance from the wires, crocodile clips, voltmeter and ammeter came to 7.55 Ω, obtaining the result from the y-intercept value displayed on my graph. This would be due to the factors mentioned above, i.e. the rust on the crocodile clips, human error making the apparatus error seem worse e.t.c.
Evaluation
My data was relatively accurate, however there were some inaccuracies. My equipment had a degree of inaccuracy, the ruler to ±1mm, the voltmeter to ±0.1V, and the ammeter to ±0.005A. An area of error is likely to be the ammeter, as it was analogue. This meant a degree of human error would have become apparent, as the scale was difficult to read from. The voltmeter was digital, so in this case there would only have been apparatus error to be concerned with. The ruler was a standard classroom ruler, and was therefore fairly battered, with the markings being slightly blurred. However, this didn’t matter much as getting the crocodile clips to be relatively in line was difficult, and made accurate equipment set up very difficult. The crocodile clips were also slightly rusty, which would have increased the resistance, but this would have been unlikely to affect the results. This was therefore reliable enough to use to draw a conclusion.
There was also a small source of error in the use of the pencil lead, as the teeth of the crocodile clips chipped the lead, and this would have affected the results by increasing the resistance. However, this error was also minimal, and would not have affected the results enough to stop me from drawing a conclusion.
However the greatest source of error is most likely to be from the pencil lead heating up. This was caused by the transference of kinetic energy from the electrons in the current to the graphite atoms in the lead. This caused them to vibrate more, giving off thermal energy. This meant that the resistance was decreased, biasing the readings. This effect would have been most apparent with the greater voltages, as the current was greater, so the electrons hit the graphite atoms with more force, and lost more kinetic energy to the atoms, causing them to vibrate more, giving off more thermal energy. However, this was kept minimal by having a 10-second break in between taking measurements, in order to let the apparatus cool off. This means that this information was also good enough to use to draw a conclusion, as the inaccuracies were too small to interfere with an overall conclusion.
The overall resistance from the wires, crocodile clips, voltmeter and ammeter came to 7.55 Ω, obtaining the result from the y-intercept value displayed on my graph. This would be due to the factors mentioned above, i.e. the rust on the crocodile clips, human error making the apparatus error seem worse e.t.c.
The agreements between the repeated readings was good, but they were unsatisfactory as to drawing conclusions, so I decided to take a mean average for each set of results for a length. When I took the mean averages the slight anomalies balanced out, giving me a good overall average, which closely followed a trend with a good R2 value. There was little variance from the trend line, as any slightly anomalous results above and below the line cancelled each other out when I took the mean average.
I found that I didn’t have any anomalies as such, as the averages followed the trend so closely that there was little variation from the trend line.
I feel that my procedure was efficient and organised, and gave rise to accurate and therefore useful results. I believe this is true because I was able to take results quickly, and I didn’t have any anomalies whatsoever, and any minor inaccuracies were balanced out by taking averages for all of the lengths.
I could improve the reliability of my data by firstly ensuring that all of the equipment that I used was brand new, so that there wouldn’t be any wear on the pencil lead, or rust on the crocodile clips e.t.c. This would minimise the apparatus error. I would also make sure that I had a digital ammeter, which would keep the level of human error when reading from it to a minimum. I would also allow myself more time to be able to let the pencil lead cool off between measurements, as this was the greatest source of error during my experiment. I could also take more readings, as this would allow me to produce a more accurate set of results, as the greater the sample, the more accurate a mean average would be. I would also use a more accurate system of measurement, with markings on the pencil lead so that I could place the crocodile clips more accurately. Shorter wires would also be useful, to decrease the apparatus error a little more.
I would extend my enquiry by using different types of pencil lead, to explore how affecting the concentration of graphite particles in space would affect the resistance. This would mean repeating my experiment, but with different pencil leads each time, and without the distance adjustments. Another idea would be to try and vary the temperature, this would be difficult, but it could be done with some kind of constant heating system like a radiator close by, and leaving ample time between temperature adjustments to allow the pencil lead to warm up or cool down. This would be in order to look a how temperature causes the resistance to decrease. I could also explore the use of other conductive materials, in order to see how materials composed of different elements other than carbon would affect the amount of collisions between the electrons on the current and the atoms in the element. I would repeat the experiment, but without distance adjustments, and I would put the different materials between the crocodile clips.