Planning the Method
I am going to set my circuit up as shown in my diagram. I am going to first of all stretch the wire out along the metre rule, up to past 50cm. I will then place one of the crocodile clips on the wire adjacent to 0cm on the ruler and the other crocodile clip adjacent to 10cm on the ruler. After that I will use the variable resistor to obtain a voltage of 0.30 volts, then subsequently read off the current using the ammeter and record it in a results table. I will then do this for my other lengths then repeat the experiment all over again to prevent rogues and to confirm my results. I will later use Ohm’s law to find the resistance of the wire.
Diagram
Apparatus
Variable resistor, Circuit board,
Ammeter,
Voltmeter,
Just over 50cm of constantan wire,
Metre Rule,
Two Crocodile Clips,
Connecting Wires.
Fair test
In this experiment we are only changing one factor – the length of the wire, the factors that we are going to keep the same are as follows:
We must keep the surrounding room temperature the same or the particles in the wire will move faster (if the temperature is increased) and this will therefore have an effect on the resistance.
The cross sectional area of the wire must be kept constant throughout as well. The material of the wire must also be kept the same as different materials have different conductivity. These two factors will be kept the same by using the same wire all of the way through the experiment.
The voltage that we have across the wire is to be kept the same.
Measurements and Accuracy
I will use the metre ruler to measure five different lengths of wire: 10cm, 20cm, 30cm, 40cm and 50cm. I am doing the experiment at five different lengths to make sure I get a big enough range to be able to comment on. I will then repeat these five results for reliability and so I can average my results also so I can spot and discard any anomalous. To keep this experiment as accurate as possible we need to make sure that the length of the wire is measured precisely from the inside edge of the crocodile clips, making sure that the wire is straight when we do this. We must also make sure that the wire is straight when we conduct the experiment. If it is not, short circuits may occur and bends and kinks in the wire may affect the resistance. The voltage will be measured using a voltmeter and current will be measured using an ammeter. I will also use a variable resistor to acquire my required voltage. To maintain accuracy the reading of the voltage, adjusting of the voltage and reading of the current should be done fairly promptly after the circuit is connected. This is because as soon as a current is put through the wire it will get hotter and we want to test it when heat is affecting it the least, i.e. at the beginning.
What will I do with the results?
I will put my results into a table. I will work out resistance later by dividing the voltage by the current, shown in the formula: R = V
I will then plot 2 graphs, one of current against length and another one for resistance against length to see how length affects the current and resistance of a wire.
Preliminary Experiment
After doing a preliminary experiment to determine if my intended method, measurements and apparatus was suitable. Here are my results:
Actual Method
After completing my practical I had found that during the experiment the wire was dangerously hot due to large currents being passed through it. This was not only causing a safety hazard but this may also have affected my results. This prompted me to use lengths from 40cm-80 thus decreasing the amount of current. I kept the measuring every 10cm the same as it had given a good spread of results. I did not make any other changes other than being more careful that the wire was straight.
Analysis
Trends
From graph 3, which is the graph of average current against length of wire, we can see one very clear trend, which is, as the length of the wire increases the current decreases. The line of best fit is straight and highlights the fact that unlike my predicted graph, the current is inversely proportional to the length of wire.
By looking at graph 4, which shows the average resistance against length of wire, we can see that as the length of the wire increases so does the resistance of it. Another, more significant thing is that it the increase is constant. This is indicating by the fact that the line drawn is a straight one. This means that the resistance of a wire is directly proportional to the length.
Conclusion
I think that from my results table and graphs I can safely say that my prediction was right. ‘…As the length of the wire increases the current’ does decrease and ‘thus resistance’ does increase. I was slightly out on my first predicted graph of current against length as it showed a curve, however my results form a straight line of best fit. This illustrates that unlike my predicted graph the current is inversely proportional to the length of wire. The reason for the resistance increasing as the length of wire increases is because as the length of the wire increases the number of atoms in the wire increases in proportion. The resistance of a wire depends on the number of collisions the electrons have with the atoms of the material, so if there is a larger number of atoms there will be a larger number of collisions, which will increase the resistance of the wire. As I sated in my prediction ‘…the resistance of the wire’ was directly proportional to the length. I can conclude this by studying graph 4, which like my predicted graph has a directly proportional and straight line of best fit. The reason for this direct proportionality is that as the length of the wire increased the electrons that made up the current, had to travel through more of the fixed particles in the wire causing more collisions and therefore a higher resistance. For this reason we can also prove the fact that as ‘…the length is doubled the resistance’ does also double. This can be confirmed by analysing my average set of results and noting that when the length of wire is 40.0 cm, the resistance is 0.13 ohms. Using my prediction I would calculate that when the length is doubled to 80.0 cm, the resistance should be doubled, (2 x 0.13 = 0.26) therefore the resistance should be 0.26 ohms. My actual resistance for 80.0 cm length was 0.25 ohms which is just 0.01 ohm less than the perfect answer so my prediction was correct: ‘…as the length is doubled the resistance’ does also double. Using more calculations I would estimate that if the length of wire was tripled to 120.0 cm the resistance would be (3 x 0.39) 1.17 ohms.
Evaluation
I feel that overall my results were quite reliable. This can be seen when we look at graph 3 and 4, which both show straight lines with all of the points being very close to or on that line. The one point that was not that close to the line was a slight anomaly was the point on graph 3 were length equals 50.0 cm and resistance equals 2.00. This did not affect my overall results though. The reason for this slight blip could have been due to a number of different factors. Firstly the temperature of the wire was not fixed when we conducted the experiment and the material of wire may not be as pure as it should have been. Most errors in our experiment were encountered in the measuring of the wire. This is because it simply was not very practical to hold a piece of wire straight, whilst holding it next to a ruler and then trying to accurately fix crocodile clips to the right part on the wire. The wire not being straight could result in extra length, which would affect results by increasing the number of collisions thus increasing the resistance. Human error could have also been the cause of this slight anomaly, the mis-reading of the ruler, ammeter and voltmeter all could have caused this.
I do not think that doing any more results in our experiment would have made it any more reliable as the range was sufficient. I feel that the only way to make it more accurate would be to use a different method – perhaps were we had a bar that did not bend in place of the wire. We could even use a rheostat in place of the wire, because it is essentially a long coiled wire that is connected at different lengths to change the resistance of the circuit. To also improve on my results I would use a digital voltmeter and ammeter instead of an analogue version. I would do this because a digital voltmeter is a lot more accurate than an analogue because if the needle in the analogue voltmeter is bent then the readings given off will be false whereas a digital voltmeter does not rely on a needle or any other manual movements and would also prevent human error.
The next modification I would make would be to use pointers instead of crocodile clips; I would do this because pointers would be more accurate. The pointers would be more accurate because the tips have a much smaller area than the crocodile clips giving a more accurate measurement of the length of wire.
As well as making these modifications I would also improve my Investigation by expanding on it, investigating another factor long side i.e. the width, and working out the cross-sectional area.
