Hypothesis: I think that the resistance of a length of carbon track will increase in proportion to its length for the reasons explained on my theory section.
I think that the resistance of a carbon track will be inversely proportional to the width for the reasons explained in my theory.
Fair Test: To make it a fair test I will only have one independent variable and one dependant variable for each series of results. I am testing the carbon track to see how length and width affect its resistance but I will only do one at a time. EG. When investigating how length affects the resistance the width will be kept constant. This is because otherwise I will not be able to tell whether a change in resistance is caused by a change in length or width. It is also important that the thickness or height of the carbon track remains the same. This depends on how hard you press down on the pencil and so is very hard to keep constant as it depends on opinion. To remedy this I will be the only one to draw the track as if one person does it they can keep it constant more easily and I will make it as thick as possible.
The amount of current passing through the track should also be kept constant as the change in temperature, a change in current causes will affect the resistance (as explained in the theory). The connecting wires used should be kept constant as well as individual wires may have different resistances and so this could affect your results. The resistances of the wires used should be found before the investigation, this is done by taking out the carbon track from the circuit and joining up the wires. The resistance of the wires will then appear on the ohmmeter, this is known as the zero-error.
These are all known as control variables meaning they must stay the same throughout the investigation.
The Measurements: I will be investigating one dependent variable, which will be the resistance of the carbon track and two independent variables, which will be the length and the width of the carbon track.
I now have to decide what equipment will be most suitable for this experiment and so which one I will use:
Equipment: Using an Ammeter and voltmeter and then calculating resistance.
Advantage: Very accurately measures resistance when it is small.
Disadvantage: Its very time consuming having to set up the circuit, take both of the readings and then calculate the resistance. Having two measuring devices not only causes confusion with zero error but increases the possible percentage error as you have to add together both of their possible percentage errors. Having to calculate the resistance offers more possibilities of mistakes and so the possible percentage error increases even more. This means that you can’t really be fully sure of any of your results.
EG.
Equipment: Using a digital multimeter in the ohm-meter mode.
Advantage: Simple and quick to use and has different ranges to measure both large and small resistances accurately. It’s very safe to use as it only puts a small current through the example.
Disadvantage: Accuracy not that good for small resistances and the resistance of the connecting wires has to be taken into consideration.
Best choice: Digital multimeter in the ohmmeter mode.
Reasons: I have chosen this because it is far quicker to use meaning that I can repeat readings to get more reliable results and the results also have a smaller percentage error. Although it is not particularly good at measuring small resistances, I expect that carbon being a semi-conductor will have quite high resistances.
The smallest value of length I will measure will be 2cm and the largest will be 20cm. I will take a reading every 2cm and so this will give me a total of 10 readings.
The smallest value of width I will measure will be 0.5cm and the largest will be 5cm. I will take a reading every 0.5cm and so this will give me a total of 10 readings.
To make sure the readings are reliable I will repeat this at least two times and more if time permits. To make sure the readings are as precise as possible I will measure both the length and the width to the nearest ½mm.
Precautions and special techniques: When I connect the carbon track to the ohmmeter, I have to decide between these two connection ideas.
Idea: A sharp pointed connector
Advantage: Can easily measure accurately and confidently between the two connectors because the connector is very thin.
Disadvantage: May not provide a large enough contact area for it to be effective and because it is pointed may cause particles of carbon to lift and so cause fluctuating results.
Idea: A smooth blunt connector
Advantage: Will make a larger contact with the carbon track and will not cause carbon particles to lift off and so less fluctuating results
Disadvantage: Will be harder to accurately and confidently measure the distance between the two contacts.
Best Choice: Smooth blunt connector
Reason: This is because having a good connection is very important for obtaining the results required and we can overcome the measuring between the two connectors problem by measuring between the two closest points of the connectors.
To make different lengths of the carbon track I am going to use a ruler to draw two parallel lines with a 1cm gap in between, the two lines will be 22cm long. As shown below:
When taking the other measurement I will just move one of the connectors closer to the other using the same carbon track to obtain the smaller measurements. I will do the same for investigating the width. Drawing a line 10cm long and 7cm wide and then moving the connectors closer to obtain smaller measurements. I have added 2cm onto the largest measurements for both the length and width to account to the size of the connector (as shown in the diagram above). I will also use a pencil with as soft graphite as is available and make the line as thick as possible to make the carbon tracks thickness constant.
In this experiment it is very important to consider zero error (found as in the measurements section), you may need to subtract the zero error from your final results to obtain correct results. Although if the zero error is very small in proportion the result value then it is unnecessary to subtract it because it will make very little difference and may cause you to make errors in the calculation and so get fluctuating results.
Safety: This is quite a safe experiment to undertake although you must always be careful when undergoing an experiment as careless mistakes can cause accidents and something dangerous you may not have foreseen could happen.
There is an electrical current being used in this experiment although it is very small and cannot harm you. Carbon is also being used in this experiment and according to its hazchem it can cause irritation of the respiratory tract if inhaled, mild irritation and redness on contact with skin and most seriously chronic exposure is known to cause disease and cancer of the lungs. This means you must be sensible when handling carbon and wash it of quickly is gets on your skin.
What I will do to verify my Hypothesis:
I am going to plot a graph of Length against resistance and Width against resistance. This what I expect them to look like: -
Graph expected for Length against resistance:
Graph expected for Width against resistance:
Graph of Resistance against reciprocal of Width:
If the graphs I produce with my results look like this then I will have verified that length is proportional to resistance and width is inversely proportional to resistance. To prove that the width and resistance have a proportional relationship I have to draw a graph of width against the reciprocal of the resistance. This should then produce a straight line, which passes through zero proving proportionality. I will then look to see if one variable seems to have more effect on the resistance than the other and I think that length will have more effect.
If there are any strange looking results on my graph then I will repeat them and see of I can obtain a more consistent value and re-plot the corrected ones. I will then draw a line on the curve which seems most suitable for the results it will be either be a best fit straight line or a best fit curve.
Conclusion: Length against resistance
The graph I produced when investigating the effect of length on the resistance of a carbon track very nearly produced the shape I had expected, which was a straight line that passed through zero. It seems to follow the shape I had expected exactly up to the carbon track length of 12cm where afterwards the readings are always slightly below what would have been expected. This may be down the inconsistency of the carbon track, which may have had thicker carbon in the track over 12cm, and the resistance would be slightly lower than the rest of the readings because of this. Although when a best-fit line was drawn onto the graph that dissected all of the readings in half it did produce a straight line but this did not quite pass through zero but as shown on the graph it came very close. This means that my hypothesis was approximately true and the small error can be explained by the degree of experimental error in this experiment, which I will look into in the evaluation.
The shape of the graph suggests to me that length and resistance have a proportional relationship and this means that my idea was also correct. I know that they are proportional because the graph shows a straight line that approximately passes through zero, which indicates proportionality.
If two variables are proportional it means that the ratio between them always remains the same. Eg. 1 : 3 or 3 : 9 or 10 : 30.
The shape of the graph also tells me that resistance of the carbon track increases as the length increases, I know this because the line is sloping upwards.
Conclusion: Width against Resistance
The width against resistance graph I produced was only roughly the shape I had expected as there were a few anomalous readings, which threw of the general pattern slightly. Although when I plotted best-fit line it made the pattern much clearer and it was almost exactly how I expected it to be. Although with this line I could not prove that width and resistance of a carbon track have an inversely proportional relationship, this means that as one increases the other decreases in proportion. Although to show that this relationship applies in this case I have to plot in a graph resistance against the reciprocal of the width (which is 1 divided by the width).
When I did this the graph produced a set of results which when a line of best fit was drawn it produced a straight line which passed through zero. This means that my prediction that width and resistance would be inversely proportional was true.
The shape of the initial graph of width against resistance also shows simply that as the width increases the resistance decreases. The resistance also decreases far quicker for the smaller widths and as the width gets to about 5cm although it is still decreasing it is much more gradual.
Evaluation:
I believe that using my results I can draw useful and correct observations this is because I repeated every reading I took three times and then averaged them. I then plotted the graphs with the averaged results meaning that they are fairly reliable. Although, there are some results I feel especially on the width and resistance graphs that appear anomalous and I would have liked to repeat these readings again but due to time restraints I couldn’t. In particular the resistances of the widths above 4cm appear incongruent. This may be because on the larger widths the contact did not span the entire width of the carbon track (as shown in the diagram below) although on the smaller widths, which produced the results, I had expected it did span the entire width.
The results may have also been affected by the fact that the contacts remained in the same place for every reading, meaning that towards the end as the contact had a fairly sharp edge the carbon where the readings were being taken may have been rubbed off. This would mean that the resistance would be greater than expected which is the case in the later results. Therefore if was to do the experiment again and had unlimited time I would have redrawn the width line every time so that the effect of the contacts rubbing off carbon would not have an effect. This is because the contact would not have been removed from the track and so no carbon could be removed from the track.
Another improvement to the experiment I would make would be improving the accuracy of the carbon track. This would mean that the carbon would be uniformly thick throughout the line and would go exactly up to the line and not pass it. This is so that we could know that the resistance was of exactly 5cm was not the resistance of between 4.5cm and 5.5cm. To do this I would make a template for the carbon track, which, could be coloured in ensuring that the carbon would no go past where it is, desired which happens no matter how hard you try to stay within the lines. An example of this is in the carbon track I drew, which appears to be quite good in that no carbon went over the lines but on closer inspection it in place is over a millimetre past the line.
My carbon line in normal view:
As you can see the line appears perfect.
Magnified view of Carbon track:
This closer view shows that the carbon track is by no means perfect and this degree inaccuracy means that the results may not be what they should.
The patterns in my graphs were fairly obvious to find and I believe that when I did use a straight fit best line instead of a curve it was acceptable because it was more fitting for the readings.
