For my preliminary experiment, I was experimenting on how I should set up for my real investigation. I adjusted different volts on the power pack. I initially used 1.5V, which gave me the results in the first table. It showed a clear trend, and there was no overflow of current, as my ammeter had no trouble displaying any readings. There was no problem with the readings on the voltmeter either, which stayed the same throughout. (Because of the low readings I only had to connect the wire to the 3V on the voltmeter)
A power of 3V went fine as well, although the wire did become quite hot when I used a power of 3V, and had even smoked a little when I used a wire length of 5 cm – my shortest length chosen. There must have been a big flow of current there. The readings for the voltmeter however were fine.
I figured that I could not use a power of 4.5 V as the wire immediately began to smoke a lot, and was very hot when I turned the switch of the power pack on. I knew there was an overflow of current as my ammeter’s pointer went over the limit to a point where I could not obtain a reading. Therefore, I knew I must not use a voltage of 4.5 V or anything above.
To prevent difficulty like burning myself in my real experiment, I decided to then settle on a power supply voltage of 1.5 V, as the trend in the results is not significantly different to the one for 3V. With using a power supply of 3.0 V I would have to take my readings really fast to prevent the wire from over heating and smoke, so using a power supply voltage of 3V is not a good idea. I therefore will settle on using a power supply voltage of 1.5 V.
When deciding on the range of lengths I should use, I initially measured the resistance in 10 centimetres each time. Although it was enough for me to see a trend, I felt that I needed more readings for my graph so that I can spot any anomalies more easily. I then measured the resistance in every 5 centimetre, which would allow me to have a more reliable, as I have more data to plot more points. More points would give me a more obvious pattern and correlation, if any.
Therefore, from my preliminary experiment, I know I will use 1.5 V as the power supply voltage used, and measure the resistance in every 5 centimetres to obtain a more reliable result as well as a clear pattern on my graph.
Apparatus: (As shown in photo below)
An ammeter
A voltmeter
A metre ruler with a piece of wire (nichrome) spread across it (readings in centimetres)
A power supply voltage of 1.5. V
Crocodile clips
Variables:
Independent Variables: The length of the wire
The lengths will be 5cm, 10cm, 15cm, 20cm, 25cm, 30cm, 35cm, 40cm, 45cm and 50cm
Dependent variable: The resistance of the wire, measured in ohms and calculated by dividing current (amps) by the voltage (volts). I will set them to two decimal points.
Controls to keep a fair test:
I will not change the width of the wire, as the thicker the wire, the less the resistance. A thicker wire means there will be more room available for the electrons to flow through without causing catastrophe by bumping into each other a lot or into the atoms, causing blockage. (Imagine a small room with 10 people in it compared to a huge room with 10 people in it, the people in the big room would be able to run across the room from one end to the other more easily.)
I will keep the material of wire the same as each material have different resistances and I don’t want it to affect my readings, as I am only investigating on how the length affects the resistance. Some materials are better conductors, meaning they have more free electrons, hence it has less resistance. Furthermore, some materials will heat up more than others after use. Therefore, I am keeping the material of wire as nichrome for my entire investigation.
Temperature will be kept at room temperature throughout the entire experiment because I don’t want temperature to affect resistance. The higher the temperature, the more the resistance as the electrons move more faster, and the atoms in the conductor will vibrate (the wire) causing the electrons to collide with them more easily, hence a difficult flow. That means I will also avoid using any light to shine on it, such as a torch as it brings heat as well.
I will keep the power supply voltage used the same, at 1.5 V as the voltage and current would change depending on the voltage I adjusted on the power pack. The more power supply voltage, the bigger the current and voltage. I don’t want it to affect my calculation resistance by doing the calculation V/I. My voltage needs to be the same (only increasing a little as the length of wire increases), and my current is the one that is changing. (Increasing)
Diagram:
Method:
- Set up the circuit as shown above, use a power supply voltage of 1.5V throughout the experiment.
- Connect the wire on your left side (positive) to the end of the ruler with a crocodile clip, at the reading of 0cm, and keep it fixed as shown in on the diagram. You do not move this wire.
- Move the wire at your right and use the crocodile clip to clip onto the wire at the length you want, beginning at 5cm from 0. This wire is variable.
- Turn on the power supply’s switch.
- Record ammeter reading
- Record voltmeter reading
- Calculate resistance by dividing the ammeter reading (in amps) by the voltmeter reading (in volts.)
- Repeat experiment at least 3 times, moving the variable wire 5 cm more on the wire each time until you get to 50cm. This means you clip onto the reading 10cm from 0 on the ruler when doing the second reading for the experiment.
Results
Graph:
Graph to show how the length of a wire affects the resistance
Analysis:
My graph shows that as the length of the wire increases, the more the resistance measured in the wire. When the length of wire was 50cm (the longest length I used), the resistance was highest, at around 7 ohms. As the length decreased, the resistance decreased as well. I drew a trend line to determine this relationship. The line is an upward slope, which means that the relationship between the length and resistance is direct.
This proves my hypothesis to be true, as I had predicted that the longer the length of the wire, the higher the resistance. My shortest length chosen for the wire at 5cm showed a result of 0.56 ohms. The longest length chosen for the wire at 50cm showed a result of 7.08ohms. As the points on my graph shows a strong, positive, correlation, I can ensure that the theory of wire length and resistance being directly proportional is true.
This is because increasing the length of a wire means that the electrons have a longer distance to move through, which increases the frequency of collisions with the atoms within, as well as with each other (the neighbouring electrons). In a longer wire of the same material, there will be more atoms within. Because of this, electrons have more difficulty to flow through, as there is less free space. Electrons do not flow in a straight line through a conductor. Their movement is random. Therefore, as the free space is being taken by the atoms, the electrons will move around to where there is free space (even if it means they move backwards) in order to get to the other end of the wire. Thus, the flow has decreased as the electrons are moving slower and so the resistance increases. The more atoms, the more frequent the collisions between the atoms and electrons, and so the more obstruction there will be. In a longer distance, it also means that there is more chance of the neighbouring electrons to collide with each other on the way, thus slowing their pace down. It is like a person running down an alleyway. In a long alleyway, (with width kept the same), a person will have higher chances of bumping into other people as well as each other rather than in a very short alleway. This means the person will move through slower. In terms of current, the electrons would move across more slowly so there is less flow resulting to a higher resistance.
The opposite, the shorter the length of wire means that the lower the resistance. This is because there are fewer atoms in the wire and so when the electrons flow through it, there is less chance of colliding with the atoms. (An alleyway with less people to bump into) A shorter length of wire also means there are less chance that the neighbouring electrons collide with each other and slowing each other down. Fewer collisions mean less resistance as it is easier for the electrons to get across and they move faster as well.
In terms of my data collected, looking at my graph, there is an anomaly. I can see this as tall the points are very close to the trend line except for one. When the length of wire was at 50cm, the point is far off the trend line I drew than any of the other points. I cannot explain a reason for this anomaly as I did the experiment three times, and the resistance I calculated out was 7.08 ohms. Even the readings for all three trials were fairly close together: 7.26 ohms, 7.00 ohms and 7.00 ohms again, so inaccuracy was not caused by one extreme value of reading. It could however, be because of some flaws within the setting up of my experiment, which I will explain in the evaluation.
Therefore, my graph proves that increasing the wire length increases the resistance. At 5cm the resistance is around 0.6 ohms, whereas at 25 cm the resistance is around 3.4 ohms, and at 45 cm the resistance is around 5.6 ohms. These points all show a clear pattern of a positive correlation. This means that the relationship between wire length and resistance have a direct relationship. This is because the longer the length of wire, the more atoms within it, thus there is more chance of the moving electrons colliding with them on the way, (as well as increasing the chance of electrons colliding with each other) causing obstruction in the flow.
My quantitative prediction is also proven correct. Following the trend line I drew on my graph, it shows that the resistance doubles more or less as the length doubles. My trend line is not drawn perfectly, but following the points plotted, it is very close to my prediction. On the graph, at 5 centimetres the resistance is around 0.6 ohms, and when the wire is 10 centimetres, it is around 1.2~1.3 ohms. And at 20 centimetres, the resistance is around 2.5-2.6 ohms. As the length doubles (40 centimetres), the resistance on my graph is 4.8-4.9 ohms, which is about 5.0ohms. (Double of 2.5 ohms) Therefore, my graph proves my quantitative prediction to be correct. Doubling the length of the wire means the resistance also doubles; they are directly proportional. This is because twice the length of a wire means twice the amount of atoms within, which doubles the chance of the moving electrons to collide with them, and become slower to move through the wire due to obstruction. Twice the length of the wire also means double the distance the electrons have to travel, so double the chance of them colliding with each other, (as their movements are random) making the flow more difficult, and thus, higher resistance.
My readings aren’t exact only because the ammeter and voltmeter I used must have been slightly inaccurate.
In conclusion, both of my predictions are proven to be correct as my graph shows a strong, positive correlation, meaning that resistance increases as the wire length increases.
Evaluation:
I generally took enough readings for my graph to give me an obvious trend in the experiment. I felt that after averaging the result from 3 trials, my readings were fairly accurate. Nearly all the points on my graph are fairly close to the trend line, or lying right on it. Only a few are slightly out. However, there is still room for improvement. Although my graph had showed a clear trend, there are still quite a few flaws in this experiment, which is why my results had an anomaly.
Looking at the graph of my line of best fit, there seems to be a point that is further way from the line than others. When the length of wire is 50 cm (the longest length I used), the resistance was 7.08. Looking at my trend line, the point at 50cm should have been a bit less than 6.5 ohms instead. The existence of this anomaly that is around 0.7 ohms more than expected as well as the points that are a bit far away from the line could be for several reasons:
The ammeter and voltmeter I used was different every time, therefore this may have lead to inaccuracy in my results, as electrical equipments scarcely ever show the same, exact readings. They are all slightly inaccurate.
Furthermore, the wire attached to the metre ruler could also have caused slight inaccuracy. The wire is not perfectly straight, and is rather irregularly bent, meaning that I may not have the exact length I wanted. As the length clearly affects the resistance, I feel that this could be something that affected my results, though it is not a very serious problem that would have affected my anomaly severely.
Moreover, I did not use a thermometer to measure the room temperature. I had only assumed the temperature was same, but the room temperature could have changed throughout the experiment. As temperature is one of the factors that could change the resistance, my experiment could have been interfered with the changing temperature; when the temperature the resistance would be higher due to the mobile electrons moving faster and creating difficulty for each other to move through. Therefore, next time I will ensure that the temperature is the same by actually using a thermometer.
Furthermore, I didn’t think about the temperature rising after current flowed through the wire when I did the experiment. I didn’t allow the wire to cool down for a certain amount of time. Sometimes I left the wire after I took the readings for a few minutes, whilst sometimes I carried on the experiment immediately after taking my readings. The temperature rises once current passes through it, which causes the atoms within the wire to vibrate. This increases the chance of electrons colliding with them, leading to a higher resistance. This would have caused inaccuracy in my results. Therefore, to prevent this if I do this investigation next time, I can time how long I leave the wire to cool by using a timer. This will make every trial I do have the same amount of time to cool down, meaning that the temperature of the wire would be more or less the same, thus making it a fair test.
Finally, although I feel that I chose a decent range of readings to provide a clear pattern for me, I could try to use more readings in between the range I chose, for example, take a reading for every one centimetre, or increase the range I used, like 0cm to 100cm instead of just 0 to 50cm. More readings recorded means more points on the graph when I plot it, so the trend line drawn would be more accurate and reliable, and I will be able to spot any anomalies more easily. I could also do even more trials in the future to increase reliability of my results.
To take this investigation to a higher level, I could also try with different materials of wire to see if increasing the length of the wire does increase the resistance. For this experiment, I had only used nichrome.
Thank you for reading this piece of coursework