Prediction:
The free electron model is the representation of a metallic solid as a container filled with a gas composed of free electrons (i.e. those responsible for high electrical and thermal conductivity) and fixed metal ion particles. I predict that the length of the constantan wire and the resistance of the wire will be directly proportional, so that when I increase the length of the wire the resistance will also increase. And I also predict that the resulting graph from the investigation will be a straight line, this means that if I double the length of the wire then the resistance of the wire will also double. This is because of the free electron model. It shows that when I make the wire twice as long I am doubling the number of fixed metal ions in the circuit:
Therefore I am doubling the number of particles in the way of the free flowing electrons, this results in twice as many collisions and that means the resistance has doubled.
Method:
I plan to take two results at each of the 10 lengths of constantan wire I will be using. These 10 lengths will be as following:
10cm, 20cm, 30cm, 40cm, 50cm, 60cm, 70cm, 80cm, 90cm and 100cm.
If both of my results for each length agree then I will take that average as accurate. However if they do not agree then I will continue to get results for that length until my results are sufficiently reliable. For a list of equipment see figure 1. Here is the method I am going to use to acquire my results:
- Set up the apparatus as shown in the circuit diagram (figure 2).
- Make sure the wire is straightened out and taped down.
- Attach the end crocodile clip making sure it is securely connected.
- Measure 10cm from the end crocodile clip and attach the other crocodile clip.
- Read the voltmeter and ammeter.
- Record the results.
- Repeat for each further length.
- Repeat once more for all 10 lengths, until you have 2 reliable results for each length.
To record my results I plan to use a simple table, gaining the resistance using Ohm’s Law as R = V ÷ I. I will get the mean average for each length by finding the midway point between each pair of readings. I will do this by adding the two results then dividing that number by two to get the mean average.
Accuracy and Reliability:
One possible problem concerning the accuracy and therefore the reliability of the results is parallax error. This occurs when reading an instrument when it is not inline horizontally or vertically with the piece of equipment you are reading from. It means that your results will be inaccurate. To solve this I will simply make sure I read my results with my eye directly inline with the piece of equipment, this makes sure I read all the meters as accurately as possible.
Other points of accuracy are the equipment I will be using. I plan to use a 100cm ruler for measuring the length of the wire, as using a more accurate ruler (i.e. a 30cm ruler) would involve moving it and making different points of 30cm. This would infact be less accurate than using the 100cm ruler. Also I will make sure that the meters are set exactly to 0 before starting to get the most accurate results. The crocodile clips used in the investigation are also very important, as the connection must be secure to allow full flow. To ensure this I will use the best crocodile clips I can and I will check they are attached securely.
For the reliability of my mean results, as I said earlier, I will get two similar results to ensure an accurate average. Another point on making my results reliable is linked to the variable of temperature. To try and maintain a consistent temperature I will of course take into account the room temperature, but this is unlikely to change. However, if a current is flowing through the wire for a long period of time, it will heat up and the resistance will increase due to more collisions between the electrons and metal ions. To solve this, whenever I am not taking readings I will disconnect the battery from the circuit to stop the current flowing. This stops the temperature (and the resistance therefore) from increasing. An important factor of the constantan alloy wire that we will be using is however the fact that its resistance changes little when heated, giving even more accurate results.
Also the battery’s longevity must be considered incase the voltage drops. But, if the voltage were to drop, assuming the resistance is constant, then the current will also drop so my results will not be affected.
Also a point of accuracy is the wire itself. The constantan alloy we are using has a naturally high resistance for electrical wire; this is to give us results the equipment will read and therefore a good, wide range of results. Also the wires we will be given will be wound up. Therefore to gain accurate measurements of length it is necessary to lay the wires out perfectly straight. To do this I will bend out any kinks or bends in the wire and use tape to stick down the wire next to the ruler. This will give the straightest possible wire and the most accurate reading of length. All this makes my results much more reliable and accurate.
Safety:
There are no major safety points for my investigation, especially as I am investigating electricity using a very small current. Also, I am not investigating temperature so no bunsen burner will be needed. However, if I was using a bunsen burner then I would make sure all hair and ties were out of the flame at all times, and when not heating I would ensure I kept it on a visible flame. A safety issue that is applicable is burns from the wire. If the wire heats up a lot, especially if it has a thin diameter (and therefore a higher resistance, resulting in faster heating) it could result in burns. Therefore I will break the circuit by disconnecting the battery after each taking each reading. This means the circuit will only be connected for each reading for a short period of time. The result is to stop increases in the temperature of the wire and allow it to cool down after each use. I will be careful as well when handling some of the equipment as it could be sharp, for example the ends of the wire could be dangerous.
Preliminary results:
The results below show what I found from my preliminary work done as put forward earlier in the plan. The preliminary work I have done investigates the variable of the diameter of the wire. It has helped me to plan my experiment, by showing me which diameter it is best to use. I did this because the diameter of the wire is a variable that I need to keep the same, so I had to find out which diameter gave the widest range of results. For the investigation we are given wires 1-5, these have diameters of:
Wire 1: 0.193
Wire 2: 0.234
Wire 3: 0.274
Wire 4: 0.315
Wire 5: 0.376
Here are the results of my preliminary work:
This work clearly shows that wire 1, with the thinnest diameter and therefore the highest resistance, has the widest range of results. Therefore I am going to use wire 1 for my investigation as it will give me the best results. Interestingly, wires 3-5 did not even give results for 10cm within the range of the ammeter as their resistance was to low, and therefore the current to high to give a readable current. It is possible that infact the thicker wires would have given a wider range of results, which is a problem, but the ammeter provided couldn’t read their results so this is unimportant. As wire 1 gave the best results it agrees with my earlier prediction that the wire with the highest resistance would give the best results. So, wire 1 is used to gain all my results.
Results:
Analysis:
The free electron model is the representation of a metallic solid as a container filled with a gas composed of free electrons (i.e. those responsible for high electrical and thermal conductivity) and fixed metal ion particles. The graph, which can definitely be seen as a straight line, clearly shows that the length of the constantan wire and the resistance of the wire are directly proportion, so that when I increase the length of the wire the resistance will also increase. As the resulting graph from the investigation is a straight line, this means that if I double the length then the resistance will double, which is seen when looking at the line of best fit on the graph. This can be clearly explained with the free electron model. The table and graph help in proving that when I double the length of constantan alloy wire I am doubling the number of fixed metal ions:
Therefore there are twice as many fixed particles in the wire to obstruct the flow of the free electrons. The result is twice as many collisions and therefore the resistance has obviously doubled. This is therefore also proving that the length of constantan alloy wire and the resistance of the wire are directly proportional. An example of this using my results can be seen using the 10cm and 20cm results, and using the 50cm and 100cm results. The mean rates for 10cm and 20cm results were 1.735 ohms and 3.360 ohms. 1.735 ohms doubled would be 3.470 ohms, so my results are very close indeed, and are almost exactly directly proportional as 3.360 ohms is very near to 3.470 ohms. This helps by agreeing with my earlier analysis. The mean rates for the 50cm and 100cm results were 8.605 ohms and 17.440 ohms. 8.605 ohms doubled would be 17.210 ohms, so again my results are almost exactly directly proportional. These results obviously justify my above analysis as they and the graph show that my results are all accurate and reliable due to the straight line of best fit and their closeness to it, and therefore the analysis is true.
All this analysis is based on scientific knowledge as the free electron model clearly shows, which is why my prediction of ‘I predict that the length of the constantan wire and the resistance of the wire will be directly proportional, so that when I increase the length of the wire the resistance will also increase. And I also predict that the resulting graph from the investigation will be a straight line, this means that if I double the length of the wire then the resistance of the wire will also double’, was extremely accurate as it was based on the same scientific knowledge and used the same ideas as my analysis. I therefore think that my prediction was very accurate, and because of this my conclusion and prediction definitely support each other strongly.
Evaluation:
When looking at my results I do not think there are any obvious anomalies.
Even though there are no anomalies, my results could still have been slightly inaccurate. Also though I did not have any anomalous results, if I had repeated the experiment it is possible I would have done so later. These inaccuracies could have been due to many different things. One problem would be the parallax error. It is one possible thing concerning the accuracy and therefore the reliability of the results. Parallax error occurs when reading an instrument when it is not inline horizontally or vertically with the piece of equipment you are reading from. It means that your results will be inaccurate. I solved this by make sure I read my results with my eye directly inline with the piece of equipment, therefore making sure I read all the meters as accurately as possible.
Also I considered the battery’s longevity incase the voltage dropped. But, if the voltage were to of dropped, assuming the resistance were constant, then the current would also drop so my results will not be affected. Also the wires I was given were wound up. Therefore to gain accurate measurements of length I needed to lay the wires out perfectly straight. To do this I bent out any kinks or bends in the wire and used tape to stick down the wire next to the ruler. This will give the straightest possible wire and the most accurate reading of length.
The results could also have been inaccurate due to other points of inaccuracy such as the equipment I used. I used a 100cm ruler for measuring the length of the wire, as using a more accurate and shorter ruler (i.e. a 30cm ruler) would have involved moving it and making different points of 30cm. This would infact be less accurate than using the 100cm ruler. Also I made sure that the meters were set exactly to 0 before starting to get the most accurate results. The crocodile clips I used in the investigation were also very important, as connections must be secure to allow full flow. To ensure this I used the best crocodile clips I could find and I checked they were attached securely as in my method.
But overall, I believe my results are as reliable and accurate as possible. My least accurate result was the mean average for my 60cm results, but this is clearly not an anomaly as it is still near to the line of best fit and both results for this length support each other. However it is the least accurate result, due to the reasons given above. I have no anomalies because my results are all near the line of best fit, and there are a roughly even number on, above and below the line. Also all my sets of results are reliable as they support each other by being similar. My results are accurate and the second results support the first. All in all due to the sufficiency of the evidence there are no anomalies in my results. The constantan alloy I used has a naturally high resistance for electrical wire; this gave results the equipment read well and therefore a good, wide range of results. All this makes my results much more reliable and accurate.
To try and maintain a consistent temperature I of course took into account the room temperature, but that did not change. However, if a current were flowing through the wire for a long period of time, it would have heated up and the resistance would increase due to more collisions between the free electrons and fixed metal ions. To solve this, whenever I wasn’t taking readings I disconnected the battery from the circuit to stop the current flowing. This stopped the temperature (and the resistance therefore) from increasing. An important factor of the constantan alloy wire that I used was the fact that its resistance changes little when heated, giving even more accurate results. Overall therefore, I did many things that ensured good results and therefore I have no anomalies as the sufficiency of the evidence shows. From this all the evidence is there to support my analysis.
If I were to do my investigation again I would be more exact with my readings and take a third set of results. That way I get even more reliable results and it would provide further support for my original readings. However as mentioned above, I used alot of precision, gaining accurate results and my investigation was well planned so I would not change anything else in my method.
For further work I would like to investigate the variable of the diameter of the constantan alloy wire. I would investigate whether the diameter of the constantan wire and the resistance of the wire were directly proportional. I would do this by using the same method as my original investigation, but doing so on each of the five wires. This would have given a much more detailed investigation and would also have shown whether the fact that length and resistance are directly proportional is true for every diameter of wire, and if so to what extent. It would also show clearly the relationship between diameter of the wire and resistance. Problems with this would be that doing so many experiments would mean a much higher likelihood of anomalies. It would also be very time consuming to get so many results, so a way of needing to take fewer results for the same conclusion would also be helpful. Problems with equipment and wires heating up and changing resistance would also be more prominent in this further investigation, so these problems would be analyzed more in my further work. I predict that this further work would show that infact the diameter of the constantan alloy wire and the resistance of the wire is indirectly proportional. Therefore if I increased the diameter of the wire the resistance would decrease. This can be shown from the use of the free electron model:
This shows that for the same distance of wire if the diameter doubles then the number of free electrons doubles with the same probability of collisions occurring. Therefore there are twice as many free electrons to flow around the circuit resulting in half the resistance. This means that as they are indirectly proportional then doubling the diameter of the wire would half the resistance. This is what my further work would show, in investigating the variable of the diameter of the constantan alloy wire.
