I will then draw graphs for both of my experiments
Method
- I will get my apparatus ready and set up my circuit
- I will place my wire in between the crocodile clips in my circuit and take readings of the voltage and current. This will be repeated three times for the most accurate results
- I will turn off the power after I have taken my readings and wait a minute for the wire to cool down before taking other readings with the same wire.
- I will then work out the resistance using ohms law R=V/I
- Steps 1-4 will be repeated with other wires of different lengths and thicknesses. The voltage will be the same and so will the temperature.
Fair Test
In this experiment my independent variables are the voltage from the power pack, the lay out of the circuit, temperature and the material of the wire that I am going to use.
The temperature of the circuit is quite hard to control so the best way I can do this would be to take my readings as fast as possible and then switching off the power pack and leave time for the wire to cool down so the temperature doesn’t change too much and affect my results.
In order to make my results as accurate as possible I will use a low voltage from the power pack to prevent over heating of the wire. If the voltage is too high and my wire is short the wire could heat up so much that it will melt.
I will also straighten out the wire when measuring it so that the length of wire I have used is accurate.
I will also repeat each experiment 3 times in my practical and average the results to get the most accurate result in the end.
Safety Precautions
In order to prevent accidents during my experiments I will follow the following safety precautions:
- I will tuck all bags, coats and stools under my table so that people don’t trip on them when walking past
- I will take precaution when cutting the wire with the scissors as they are sharp objects
- The voltage used is 3Volts so the wire does not overheat too much and cause a fire.
- When I am conducting my experiment I will also tie my hair up in case the wire does cause a fire so that my hair does not get burnt
- The table I am conducting my experiment on must be clear and have enough space to hold my apparatus so that it doesn’t accidentally get knocked off my table.
- The wire I am going to use in my experiment should be all straight as curly wires may touch each other and cause a short circuit.
I have done three preliminary experiments to help me with my practical experiment.
The first experiment was to help me decide which length of wire to use for my experiments when I am testing the thickness of a wire.
The second experiment was to give me a rough idea of what the pattern in resistance was when the thickness of the wire was increased
And the third experiment was to help me decide which material I am going to use in my practical experiment that will give me the most accurate results.
The results from my preliminary experiment are as follows:
Experiment 1:
I have used the material Nichrome to conduct this experiment and when how the thickness affects the resistance of a wire the length for the wire I am going to use would be 50cm as this shows medium resistance.
Experiment 2:
I have also used the material Nichrome to conduct this experiment as it would be a fair test and I can also compare the results with those of experiment 1. This would also give me a rough idea of what the results should be like for my practical experiments.
Experiment 3 :
From this experiment I have come to a conclusion about which material I am going to use for my practical experiment. I am going to use constantan for my practical experiment as the resistance is not too high but not too low, copper would be a bad material to use as its resistance is very low and therefore it is hard to control it heating up. I am going to use constantan for my experiment as it has medium resistance so it doesn’t heat up quickly and the results are not affected as much because the wires resistance isn’t very high unlike Nichrome.
All three experiments were carried out with the same voltage.
In order to make my results as accurate as possible I will straighten out the wire when I cut it so the length will be accurate. I will also take readings from my practical experiment three times and average out the average resistance of the wire so that it reflects on the most accurate result.
I will also wait for a minute after taking each reading so that the wire will have enough time to cool down and not affect the results as temperature affects the resistance of a wire.
Prediction
The factors that I have chosen to investigate are how the thickness and length affect the resistance of a wire.
As the length of a wire increases so does the resistance of the wire in the same proportion. Example, if the wire was doubled the resistance would be doubled. This is because wire has naturally some impurities within it so as the length of the wire increases so does the amount of impurities within the wire. Therefore if there are more impurities in the wire then the electrons will need more energy to push across the impurities that oppose the flow of electrons.
I predict that the resistance will double as the length of the wire doubles, this will be in a linear relationship and the graph will be a straight line x = y providing that the wire doesn’t heat up.
I predict that as the diameter of a wire is doubled the resistance is decreased by a quarter. This is because resistance is inversely proportional to the cross sectional area, in my experiment this would be the area of the wire. The area is proportional to the diameter squared. So if you double the diameter the area increases by a factor of four and the resistance decreases by a factor of four as the two relationships are inversely proportional to each other. This means that as one increases the other decreases by a constant (k). I predict that the graph will be curved but never touching the X axis as the equation of the line will be y=1/x
I will draw a diagram to illustrate this.
From the diagram I can see that as the radius is doubled the cross sectional area of the wire quadruples. This shows that as the resistance of a wire is inversely proportional to the cross sectional area of a wire the resistance would decrease by a quarter of the original resistance.
A thick wire also lets a higher current through it than a thin wire due to its restriction on a high rate of flow. There are more electrons in a thicker wire because it has a larger area. This results in a larger current which shows that the resistance is less in a wire with a larger cross sectional area. A larger cross sectional area reduces the resistance because it is easier for the electrons to move through it.
Observations
For investigating how length affects the resistance of a wire I have changed the length of the wire. The values I have recorded are that of the voltage and current. I have used the formula R = V/I to calculate the resistance of the wire.
The voltage is measured in volts, current in amps and the resistance in ohms.
For investigating how the thickness of a wire affects the resistance of a wire I have changed the thickness of the wires. The values I have recorded are of voltage and current the voltage is also measured in volts, and current amps. I have used the same formula to calculate the resistance of the wire which is also measured in ohms.
Results:
Here are the results from my experiment for how resistance affects the length of the wire.
I have repeated my experiment 3 times to ensure the most accurate result.
I have worked out the average resistance for all three experiments so that my results are a better reflection on the resistance of the wire.
My results do seem to follow a trend. I have noticed from the table that as the length of the wire increases the resistance increases as well. This seems to match my prediction as the table shows that as the length of the wire is doubled the resistance is roughly doubled.
I had trouble measuring the current for this experiment as it alternated a lot. This is due to the changes in temperature as the wire heated up. So to avoid this I took my reading as fast as possible and then switched off the power from the power pack.
These are the results from my experiments on how the thickness of a wire affects the resistance of a wire.
I have calculated the cross sectional area of the wires using the formula πr².
From this table I can see a pattern emerging as the cross sectional area of the wire gets bitter the resistance decreases considerably.
I am going to draw graphs for both of my results and see if my predictions are right. I will show on the graphs if my predictions are right.
I n order to see if my prediction “the resistance will double as the length of a wire doubles” is right or not I will show on my graph how the resistance changes as the length of a wire changes.
I will also do this on my graph to show how the cross sectional area of a wire affects the resistance of a wire.
I am hoping to see a negative curve going down that will not touch the X axis as this will prove my prediction as right. This will also show an inversely proportional relationship between the cross sectional area of a wire and its resistance as the area of cross section is increased.
I am also hoping that the points on my graph will be a nice smooth curve and fit my line of best fit as this will show that my results are also very accurate and this will verify my prediction more.
For my investigation on how the length of a wire affects the resistance of a wire I am going to draw a table showing how resistance changes as the length of the wire is doubled.
I had to predict the results for the resistance of a 30cm and 50cm wire using my line of best fit but my results were very accurate so I think that they are reliable. From the graph I can see that my results were very accurate as they all fitted the line of best fit very well and there seems to be no anomalies.
For my investigation on how the diameter of a wire affects the resistance of a wire I am going to draw a table showing how resistance changes as the diameter of the wire is doubled.
I had to predict the result for the resistance of a wire with a diameter of 0.54 mm using my graph but it should be accurate as the line of best fit fitted my graph very well and there seems to be no anomalies.
I have drawn lines of best fits for both of my graphs to see if my results are accurate and see if a pattern emerges.
Conclusion: Explaining results
From my results I can see that my prediction “as the length of the wire doubles the resistance doubles” this is proved right from my results. My graph shows as the length doubles the resistance also doubles although my results were not as accurate as I would like them to be.
I have also found the gradient of my graph, since it is a linear equation it will conform to the general equation y = mx + c where m is the gradient and c is the point of intercept on the y axis. I will work out the gradient using the formula m = y/x
My gradient is 0.9 as 3.2/4 is equal to 0.9
Therefore the equation of my line is y = 0.9x - 0.15
This proves that my prediction was right, the relationship between the length of a wire and the resistance is that of a liner relationship however it is not quite y=x as its gradient is a bit steeper.
My graph shows strong correlation as the line of best fit goes through nearly all the points of my graph and is very close to the line of best fit. This therefore fits my prediction although my results from my table above are not as accurate as I hoped. From the table I can see that when the length of the wire is doubled the resistance is roughly doubled but my results were not exact, my results were an average taken from three repeats of my experiments so there may have been some heating up of the wire that caused a change in resistance. My results do show that the resistance doubles roughly when the length is doubled, this is a trend that occurs in all of my results in the table above. However my results do show a trend that the resistance increases as the length of the wire increases.
From my results I can also see that as the thickness of a wire increases the resistance decreases which supports my prediction. I also predicted that the graph would show an inversely proportional curve (which slopes off but doesn’t touch the x axis). I have also predicted that as the cross sectional area of the wire is doubled the resistance decreases by a quarter. This is also proved correct in my results as you can see from the table that they all follow a pattern.
The resistance decreased by about a quarter when the thickness of the wire is doubled. This shows that my prediction is right. As the cross sectional area of the wire is doubled the resistance decreased by a quarter is because as the diameter of the wire is doubled so the cross sectional area of the wire increases by a factor of four.
This means that there is four times as much more space for the electrons to move through, this means that the electrons move through the thicker wire much faster as there is more volume and therefore the resistance is decreased by a quarter as there is now four times as much more space for the electrons to flow through.
The results from my table all show this, especially the resistance for the wire with a 0.27mm diameter. The results from my experiment for the resistance of a 0.27mm thick wire is 4.22 ohms, when the diameter of this was doubled the resistance was 1.05 ohms which is exactly a quarter which proves my hypothesis. My results were also quite accurate as they all fitted the line of best fit quite closely and were all with in + or – 10% accuracy.
I am also going to draw a straight line graph with the reciprocal of resistance because if resistance gives a inverse proportion then my graph should show direct proportion and this is to back my prediction and see if my results are accurate. I will also draw a line of best fit on to my graph.
I am hoping to see that the resistance of four times the cross sectional area of a circuit as this would show inverse proportion when R is divided by one.
Table of results:
After plotting a graph to show how the reciprocal of resistance changes when the cross sectional area increases in a wire I can now see that my results were fairly accurate as the graph shows a definite direct proportion. The points on my graph also fits my line of best fit very well and shows the relationship between X and Y clearly. It is easier to see the relationship between X and Y in this graph.
The equation of this line is y = 4x
From this graph I have also noticed that as the cross sectional area of the wire is doubled the resistance is also doubled, such as the resistance of the wires with a 0.03 and 0.06 cross sectional area.
From this graph I can tell that the resistance is roughly four times larger than the cross sectional area of the wire.
Evaluation
I am quite pleased with my results as they were all fairly accurate. They all followed a trend that verifies my prediction. My graphs also show very strong correlation between all my points and my line of best fit. This shows that my results are fairly accurate.
There were no anomalies for my graph to show how resistances changes when length of a wire changes. My results also verified my prediction and were very accurate as they were all very close to my line of best fit which shows very strong correlation.
Although there were some anomalies in my graph to show how the reciprocal of resistance changes as cross sectional area increases in a wire. This is much easier to spot as it is not in inverse proportion and it is a linear equation. The anomaly in my graph is the resistance for the wires with a cross sectional area of 0.17mm.
The resistance is more than four times the cross sectional area. I have taken the average for my results from three repeated experiments; the anomaly was in the original repeats for my experiment. For all of my experiments I have achieved different results; 1.51 ohms, 1.53 ohms and 1.49 ohms. This would have had quite a big impact on my over all result as all three results are different so there seems to be no exact reflection of what the resistance for the wire should be. As you can see on the graph the point plotted for this anomaly is quite far away from the line of best fit compared to the rest of my points that are all very close to my line of best fit.
This anomaly may have occurred due to the following factors:
- The wire may not have been measured properly when cut as I found it quite hard to straighten out the wires and cut it to the correct length.
- The wire may not have cooled down properly from the previous experiments therefore causing a higher resistance.
Although I think that there factors may not have affected the resistance of the wire a great deal as the result is still accurate to + or – 10% compared to the ideal result predicted by my line of best fit.
However it was hard to tell if I had any anomalies in my graph to show how cross sectional area of a wire affects resistance of a wire as the graph is a curve and shows inverse proportion. It is a lot harder to tell by eye if I have any anomalies on that graph as the points I have plotted all fitted a smooth curve but when I turned this graphs resistance into the resistances reciprocal it was a lot easier to see the anomalies as this was a line graph and has a direct proportion relationship.
In order to extend my experiment for more accurate results and a general reflection of how the resistance changes as the cross sectional area of a wire changes I could repeat my experiment with different wires that have different resistances and see if a common pattern emerges for all the different wires.
I could also repeat with experiment with a wider range of thicknesses for the wires to get a better impression of the shape of the graph.
The wires for the experiment would also have to be straightened out properly before cutting to ensure that it is cut correctly and that the length if right.
Temperature is a very hard factor to control that affects the outcome of my results but the wire could be put in a water bath as this keeps the temperature constant and the results would be more accurate.
In conclusion both of my predictions are right, as the length of the wire doubles so does the resistance. This is due to the fact that the electrons have to push past twice the amount of force that opposes their flow therefore the resistance is doubled.
My prediction as the diameter of the wire is doubled the resistance decreases by a quarter is true. The relationship between them is inversely proportional and this is proved by my graph. This is due to the fact that as the diameter is doubled the surface area increases by a factor of four, this means that the electrons within the wire has four times as much more space to move through the wire therefore there is less obstruction to their flow.
