I will use various calculations to find the resistance of the wire (in Ohms), as different lengths of nickel-chrome are used. These include: V÷I = R which can be manipulated into V= I×R. The drawing (figure 1) shows the circuit diagram.
In my prediction I stated my opinion that resistance should increase as the length of the wire increases. After conducting the test, I found that my prediction was indeed correct and there was a clear trend which showed an increase in resistance at a steady rate. The graph shows this trend.
Analysis of Experiment 1
This table shows the potential difference of various lengths of nichrome wire when included in the 10v circuit:
To show how the resistance was calculated, here is an example of the process of calculating resistance. This calculation was for the first recording of the mean of 10cm of wire. I used the formula, V÷I=R. (1.00+0.97+0.93) ÷ 3 = 0.97 (mean). 0.97(voltage) ÷ 0.56 (amps) = 1.7(ohms).
These tests were done using a 1m length of wire with a diameter of 34mm. I chose to use 10v of voltage because it gave the clearer results than a lower voltage because the numbers where higher. I made certain that this voltage did not heat up the wire. I felt the wire and found no heating effect. Therefore there was little additional resistance caused by the temperature of the wire.
I originally chose to record the results for this experiment using 3 decimal places (3d.p.) however due to an error in the recording of current in this experiment; the only data available is resistance to 1d.p. The error in this experiment was a small and single mistake but one which had a huge affect on the results. When I was recording the current for this experiment, it is most likely that I either misread the ammeter when recording current (56amps instead of 0.56amps), or it could have been a typing error. I may have entered 56amps into the table instead of 0.56amps. I chose to use the results to 3d.p. because I realized the mistake, the results for resistances were all in decimal places, and therefore the significant figures were all below the decimal point. Therefore by having 3d.p, plotting an accurate graph is easier and the results are clearer to analyze and evaluate.
These results support the claim that the results are very accurate. There is also a definite trend or pattern which the results follow. This also supports the fact that the data is accurate because it there are no stray results and each reading fits nicely into a pattern when drawn on the graph.
See Graph on the next page
The graph shows the relationship between the length of nichrome wire, and its resistance. Length (cm) is plotted on the 'X' axis as the independent variable and on the 'Y' axis is the resistance (ohms) being the dependent variable.
The results from the graph indicate a steady increase in resistance as the length of wire increases, shows by the positive correlation of the graph. The relationship between the length and resistance of the wires is shown by the graph to be a proportional relationship. The resistance of the wire is proportional to the length of the wire. The graph clearly shows that the longer the wire, the higher the resistance. As the wire gets longer, the resistance is increased.
E.g. At 20cm there is a mean of 3.3ohms of resistance. At 80cm of wire, the mean resistance is 12.4ohms.
This is evidence to suggest that the longer a piece of wire, the more resistance it has. This increase of resistance is at a steady and constant rate of increase. This is shows because the ‘line of best fit’, goes through the center of each mean recording. This is also shown as the increase of resistance every 10cm is the same. The graph indicates an increase of 1.5ohms every 10cm. So for every 10cm of nickel-chrome wire with a diameter of 34mm, 1.5ohms of resistance is added on.
The range bars, shown on the graph show how accurate the results are. A smaller range bar indicates a very high degree of accuracy; however a larger range bar indicates a low degree of accuracy. As shown on the key, on the graph, the highest line on the range bar represents the value of the highest recording taken from the experiment, and the lower line represents the lowest value. The cross in between the two lines represents the mean result. This is the most accurate result, calculated by dividing the sum of each recording by the number of recordings. The graph is indicated additionally accurate due to the fact that the ‘line of best fit’, goes through each mean recording. In this test there are no anomalies, shown because each recording fits into the general trend. In other words there is a narrow channel in the spread of data, shown in the range bars and ‘line of best fit’.
The graph shows a trend in the results that goes up, as length is increased. This shows that the relationship between length of the nichrome with and resistance is that the more length that the wire has, the more resistance the wire has.
This graph could be described using the equation y=nx. For example if n was 3 and x=2 then y would equal 6. This can be found by dividing the mean resistance by the length of wire. So for the first test for 10cm, 10÷1.7=5.88(2d.p.). So in this case y=nx, if n=5.88(2d.p.) and x=1.7. For the second result for 20cm, 20÷3.3=6.06(2d.p.). So for the second result, y=nx, if n=6.06(2d.p) and x=3.3. This graph showed what ‘n’ is for each length of wire.
This graph tells us what ‘n’ would be to enable the formula y=nx, to work for each result. This is useful to us in that it enables us to see in detail, the accuracy of our results. This is because the results appear to be in exact proportion between their length and resistance. This calculation tells us that that is in fact not completely true for this experiment. As shown in the table, the results do tend to increase. This should not be the case if the two variables are in direct proportion to each other. This increase in the value of ‘n’, can however be explained. My explanation for this is similar to the reason for the range bars increasing in size of scatter as length is increased. I assume that it is due to the fact that I conducted the tests chronologically from the shorter length of wires, to the longer lengths. Due to the fact that I used the same wire each time, the temperature could have increased marginally despite the fact that I momentarily turned the power off between each recording. This amount of time when the power pack was off, may not have been long enough. The heat could be building up in the test wire, causing an increase in resistance and shown on the diagrams on page 3b in the introduction section. If drawn on a graph, and if the results had been more accurate by me waiting for the wire to cool down for longer, the results for ‘n’, in the equation y=nx, would have shown an exactly straight line because the relationship between length and resistance is directly and exactly proportional as calculated below.
I calculated the mean value of ‘n’ by using the values of ‘n’ for the various lengths. I calculated the value of the mean by adding up all the 10 values for ‘n’, and dividing that sum by the amount of results which was 10. This gave me 6.31. This mean is not however accurate due to the results not being completely accurate as mentioned above. A much more accurate way of calculating a value of ‘n’ that should would work in the equation y=nx would be to use the value of ‘n’ for the result taken first in chronological order because here there is no unfairness in the result caused by heat because the wire could not have been heated. This value is 5.88. Obviously this value is not 100% accurate, partly due the fact that the calculations of ‘n’ were only taken to 2d.p, but it is the most accurate reading of ‘n’ that I can conclude with. This value of ‘n’ can be used for any length due to the fact that the relationship between length (y) and resistance (x) is always directly proportional.
Therefore this value of ‘n’ can be used to calculate the resistance of any length of wire. For example if ‘n’ is always 5.88, then y=5.88×x. So 5.88×x will always give the length of wire that has that specific resistance. And y/5.88 will always give the amount of resistance that that length of wire has. This value of ‘n’ only is relevant to wires with the same diameter as that of which ‘n’ was calculated (34mm). For example, if I were to find the value of the resistance of a wire with a length of 250cm I would use the calculation 250/5.88. This would give me an answer of 42.5ohms. Or if I were to calculate the length of wire with a diameter of 34mm when the resistance was 5ohms, I would use the calculation 5.88×5. This would give me an answer of 29.4cm. This can be proved to be reasonably accurate when plotted on the graph. I have done this as shown on the graph. The reading given by the graph is 31cm, which considering the possibly inaccuracy of the value of ‘n’, is evident to support the reliability of the equation and the accuracy of the recorded results.
It is possible to calculate the amount of resistance 10cm of wire has by reading the graph to measure how much resistance increases every 10cm along the wire. To calculate the amount of resistance that 10cm of wire has, I simply read across the graph from the mean point of 10cm to the ‘y’ axis and found the resistance to be 1.8ohms. Then I did the same for the recording of 20cm, and found a measurement for 3.3ohms. To calculate the resistance change I deducted 1.8 from 3.3 which revealed a change in resistance of 1.5ohms. This is therefore shown to be the amount of resistance that 10cm of the wire has because the different in resistance between 10cm and 20cm (10cm difference in length) is 1.5ohms.
I calculated the resistance of 15cm of the wire, by reading the resistance in ohms when the length of wire is at 25cm. The graph shows how I read the recording. The graph showed that at 25cm, there was a resistance of 4.0ohms. By deducting the previous recording for 10cm of 1.8 from 4.0, 2.2ohms remains. ). 2.2ohms is therefore the amount of resistance that 15cm of wire has because the difference between 10cm and 25cm is 15cm. This method can be used to find the amount of resistance for any length of wire, providing it is nickel-chrome wire with a diameter of 0.34mm. This method will only be accurate with a wire with these properties because the wire used to record this data did have these properties. Any change in these properties would resistance to be different and therefore each length of wire would have a different resistance.
As briefly mentioned before, these results, on the whole are very accurate due to the fact that careful consideration was taken in planning to produce results with very small parameters, shown by the narrow range bars. Accuracy is also shown as each mean results is almost an exact fit into the ‘line of best fit’ of the graph.
Despite this accuracy, the results from higher lengths of wire are shown to have a wider parameter in the range bars. This indicates slight inaccuracy in the recordings. A possible reason for this could be that despite me turning off the equipment in between each recording, the wire could have heated up, and retained some of the heat from the previous recording. This theory fits the pattern because the range bars become wider as the length of wire is increased. Due to the fact that the shorter amount of wire was measured first, an increase in heat over time could have caused a gradual increase in resistance, which produced the increase in the size of the range bars. This is not a certain reason, however it is probable. Assuming that this idea is correct, the lower parameters would have been recorded first at a lower temperature, and the higher parameters of the range bars would have been recorded later on when the wire was hotter.
If I were to conduct this experiment a second time, I would increase the amount of time that the power was turned off, to ensure a sufficient amount of time to allow the wire to fully cool down. This would mean that each range bar would be of a more similar size and they would not increase as length was increased.
As shown on the graph, the line of best fit if kept straight would not go through the point (0, 0) on the graph. It is assumed that the graph may go through this point; however this is not indicated by the graph. This could either be due to a recording error or a lack of detail in the recordings. The idea of a recording error can be tested by re-conducting the experiment. A much more likely explanation is that the measurements were not detailed enough to show a slight curve in the beginning of the ‘line of best fit’. Assuming that the results are in the correct positions, the remaining explanation would be that if the gaps between the independent variables were smaller, e.g. every 1cm, results could have revealed a slight curve in the trend of results. This would answer this question.
It is possible that as shown with the current data, the results, despite a lack of detail, do not appear to curve towards (0, 0), but instead continue to around (0, 0.004).This could be possible because at the instant that the length reaches the ‘Y’ axis, the resistance could drop to 0 ohms. This is surely the case because no wire, has no resistance, however the minutest amount of wire could begin at a certain amount of resistance, without following a proportional ‘line of best fit’ from (0, 0), at a rate of increase of 2.6ohms per 10cm. The presence of a small amount of wire could result in a disproportional amount of initial resistance.
Conclusion
In conclusion of this experiment, the results show that as the length of the nichrome wire is increased, the resistance of it increases. The amount of resistance caused by a certain length of wire being added on can be calculated by measuring the difference in resistance between two values of length with a difference of the amount of wire that is being measured for resistance. For example to find the resistance of 10cm of the 34mm nichrome wire the calculation would subtract the resistance of 20cm of wire with the resistance of 10cm to reveal the resistance of 10cm of wire. As shown above, this difference in resistance is 1.5ohms. Therefore it is clear that for every 10cm of wire added on with the same diameter, 1.5ohms of resistance will be added. These results support my initial prediction and so my prediction about the relationship between resistance and length was indeed correct.
There are, however some limitations to the conclusion due to the scatter in the range bars. The scatter or size of range bars increases quite a large amount as the length of wire is increased. This increase in the amount of scatter is not coincidence and there is no certain explanation for this. As explained above the simplest explanation is that between each recording, a fragment of heat had been built up in the wire, despite the precaution of turning off the power pack between each reading. No definite conclusion can be drawn from this due to the fact that the reason for this scatter is unsure. This limits the amount or detail of the conclusions that can be made, and therefore decreases the complexity of the investigation, however if I were to re-conduct this experiment, it would be possible to leave more time for the wire to cool down. If then, there was not an increase in the range of scatter, it would give sufficient evidence to support this previously described explanation and therefore a more confident conclusion could have been made and supported with accurate data.
To extend this part of the investigation further I could have drawn a graph that would have shown the results of the calculations of the nth term. This would have enabled me to analyze further, the reasons and causes for the slight increase in the value ‘n’ as length is increased. It would also have more graphically displayed the trend. I would have also been able to include the mean value of ‘n’ on the graph. I could have annotated the graph to explain in more detail how this equation works.
Experiment 2
In the second part of the investigation I am going to use several lengths of nickel-chrome wire with different diameters to find out any change in resistance between the different diameters of wire.
In this second experiment I chose to use only 2v DC of voltage because the test wire was that much shorter than in the first experiment.
To ensure that the results are as accurate as they can be, each reading will be taken 3 separate times and a mean will be calculated from them. The diameter of each wire will be calculated 3 times and a mean taken to ensure an accurate reading. This will improve the accuracy and reliability of the recorded data.
Preliminary Test
I have conducted a preliminary test, to ensure that the second part of my experiment will work and have clear results which show a definite trend. The width of the nickel-chrome wire will make a difference in the resistance of the wire because in a thin wire, there are a lot of electrons which have to travel in a proportionally small channel. This causes a lot of collision with other electrons. This collision causes friction, which produces heat. This heat energy which is produced causes resistance because electrical energy from the current is being transferred into heat energy. These facts are backed up with the data results from my preliminary test, shown below. Resistance was calculated using the formula V÷I = R.
As I was conducting this preliminary test I made absolute certain, that my results were accurate by ensuring that each length of wire was exactly the same length, and I reduced the voltage input from 12v DC down to 2v DC in order that the wires, particularly the thinner wire, did not heat up. This would have altered the resistance of the wire because the more heat energy that the wire has, the faster atoms move in the wire, and so the electrons in the current have more collisions. This causes friction, which produces heat (see figure 1 on page 3b, in the introduction section). Heat is produced using energy from the electrical current. This causes the overall resistance to increase because there is energy being taken from the electrical current. These results show that a thicker wire has a much smaller resistance than a thinner wire. This preliminary data supports my initial prediction which stated that thinner wire will have more resistance than thicker wire. I calculated the resistance of each wire using the formula, R=V÷I. R is resistance in Ohms, V is voltage or potential difference in Volts and 'I' is current, measured in amperes/amps. The higher that the number of Ohms is, the higher the resistance of the wire is. In conducting the preliminary test, I used the following instruments: power supply (set to 2V), 5 copper wires, 2 crocodile clips, an ammeter, a voltmeter, and the nickel-chrome wires both thick and thin.
Method
- Collect apparatus: a voltmeter, an ammeter, 5x wires, 2 crocodile clips, 7 nichrome wires with different diameters and a power pack.
- Set apparatus up as shown:
DRAW DIAGRAM OF CIRCUIT 2
- Set the power pack on as low a voltage as possible, 2v. (So that the voltage doesn’t cause the wire to heat up.)
- Place the nichrome between the two crocodile clips to complete the circuit.
- Turn on the power pack and record the current from the ammeter and the voltage from the voltmeter.
- Turn off the power pack.
- Repeat this process for all the diameters of wires.
- Work out the resistance for all the results using Ohm's law. V = I*R
- Record the results on a graph.
My results are shown to be accurate because I conducted the test 3 times and calculated the mean to 2 decimal places. The results above are the mean values. I also conducted the short experiment using only 2v DC to ensure that neither of the wires began to heat up.
To increase the accuracy of the measurements taken of the diameter of each wire, I conducted an experiment whereby each wire was measured using a micrometer 3 times. A micrometer works by clamping the wire between the spindle face and anvil face. They are adjusted by rotating the ratchet. This moves the spindle and thimble down the sleeve. The sleeve has numbers on it which displays the wires diameter when tightened. The table of results from the measurement of the wires is shown below:
The mean was calculated in the way shown in the calculation: (Test 1 + Test 2 + Test 3) ÷ 3 = mean. So, (0.25 + 0.26 + 0.22) ÷ 3 = 0.24.
These results are clearly very accurate because each measurement for the same wire, are very close to each other, (each within 0.2mm). This is good evidence to support the accuracy of my results. I will use these results when analyzing the data. Due to the fact that these are accurate, any outliers in the graph will be due to an error in the readings or calculations of voltage, current or resistance.
I conducted the second experiment, whereby nickel-chrome wires of 7 different diameters were tested for resistance.
The set up of the circuit is very much similar to the first experiment. I used for this test, an ammeter, a voltmeter, lengths of copper wire, 2 crocodile clips, and a power pack in addition to the test wires. The power pack was adjusted to output only 2v DC. This was to prevent the wires from heating up which would cause additional resistance. The ammeter will be placed in series with the circuit and will record the current flowing through the circuit. The voltmeter will be put in parallel with the test wire using crocodile clips. Any recorded potential difference is in fact that of the test wire only and not of the copper wire since the voltmeter was in parallel, only to the test wire. See diagram above.
Analysis of Experiment 2
I initially planned to use a higher voltage of 10v for this experiment but this caused the wire to rapidly heat up making it impossible to take an accurate reading of the potential difference. The heat as mentioned above causes additional resistance. As I was experimenting before the investigation began I found that 10v did heat up the wire. There was only one outlier or anomaly in this experiment which was the recording of the current of the wire with a diameter of 0.88mm. This was recorded in set 1, as 2.85amps. This reading was 22mm different from the recording in set 2, whereas other recordings of wires with different diameters had been much closer to each other. This is not a major difference, however could have affected the overall pattern. In order to take appropriate action I therefore did not include these results when calculating the mean for this diameter, and therefore did not use the reading for voltage in set 1. I therefore calculated the mean by using only 2 results. This should not however have affected the accuracy of the mean, because the calculation of resistance of this diameter remains to fit in the trend line on the graph.
Here the graph shows the relationship between the diameter of 10cm of nichrome wire, and the resistance it has. Diameter is plotted on the 'X' axis and is the independent variable, however on the 'Y' axis is the resistance which is the dependent variable.
The results from this experiment are shown on the graph comparing diameter with resistance. The displaying of the results indicates that the thicker the wire is, the less resistance it produces. This assumption is based on the narrow range of results shown. As described above, these results are highly accurate. The range bars support this claim as they have a very small range. This shows that the range of data recorded for each diameter of wire is very close to each other and so the possibility that the results are inaccurate from this perspective is very unlikely.
As shown by the graph comparing diameter with resistance, the majority of change in resistance is between 0.24mm to 0.56mm. This means that between these narrow ranges a large percentage of the overall resistance change is lost. In contrast, the range of diameter from 0.9mm to 1.2mm has a much smaller drop in resistance. These figures indicate that when a nichrome wire has a diameter of 1.2mm or more, there is only a small change in resistance is the wire was to increase in diameter. These assumptions do only apply for nichrome wire when a voltage of 2v is passed through them. To expand this experiment, a similar test could be done, however with different ranges of voltage. This would enable me to analyze how the voltage changes resistance, in wires with various diameters
To manipulate this data it is possible to record how much resistance is loosed between different ranges of diameter. This can be done by measuring how much resistance is lost every time the diameter of the wire changes 0.1 of a millimeter. For reasons due to a lack of data, I can only being by recording from 0.3-0.4mm. This is because my results do not cover diameters of 0.2 and below and so this would not be accurate. As shown on the graph, I have drawn a trend line to fill in the gaps between the results to predict the resistance of more detailed diameters. In other word the trend line shows me what the resistance of the diameters of wire which were not recorded was most likely to be. This is a reasonably accurate technique due to the fact that my results are accurate, shown by the range bars.
This trend line enables me to read the resistance of the wires of a diameter with a whole decimal number, e.g. 0.3, 0.4, and 0.5, 0.6 etc.
This table of results shows the recordings.
The cumulative frequency was calculated by adding up the difference in resistance of each previous parameter.
This table of results shows how in general, providing the range bars are of the same difference in diameter, the thinner the wires in the range bar, the greater the change in resistance between them. By calculating the cumulative frequency of these results it becomes clear that this is the case because difference in resistance between each range becomes smaller because the loss of resistance is becoming less after a certain point. The results in the table do follow this idea generally however in detail the differences between some ranges do not follow the pattern. This is not because the idea is the error, but because the reading of the data is in error. When reading the results from the graph I rounded each reading to the nearest single figure. This meant that particularly towards the ranges which included thicker diameters, the results did not follow an exact pattern. This is due to the fact that some readings are close together and therefore were rounded up or down to the same reading of resistance. The markings on the graph show how several reading can be rounded up or down to the same value of resistance. It also shows graphically that the difference in resistance between wire with thinner diameters were bigger. This supports my claim also.
In order to manipulate the available data further and to greater the depth of the investigation, I used the mathematical equation of ‘pi × (radius, squared)’ = the area of the flat circle of the wire. This answer when multiplied by 100 (mm), gave the total area of the wire used in each test. These results are shown on the table below.
The graph of area and resistance shows the relationship between the area of wire and its resistance, only when the wire is nichrome as used in this experiment. The graph indicates a similar pattern to the graph measuring diameter and resistance. The bigger that the area of wire is, the less the resistance of the wire is. This does not however indicate that every 10cm2 of wire has a certain amount of resistance because that is not the way in which the graph was calculated. This graph simply shows the resistance of an area of wire when it is 10cm long. Therefore the change in resistance of different areas shown on the graph is due to the change of diameter because the diameter is the only factor that changes throughout this data manipulation. The area indicating a higher resistance, only has a higher resistance because it has a smaller diameter. The length stays the same, but the change in area between each recording of wire is due to the change of diameter between the wires. This is the reason for the graph looking similar to the initial graph which showed the relationship of diameter and resistance.
A second graph displays 2 variables given using the results from the calculations shown above in the table. These two variables are the area of 10cm of nichrome wire on ‘Y’ axis, and the diameter of the same wire ‘X’ axis. The graph with a trend line shows that the larger the diameter of the wire, the larger the area of the wire. These results also are very accurate due to the fact that the only data used to calculate this data is the diameter of the wire, which was measured 3 times each for precision and accuracy. Calculations were the only other means of manipulating that data to give these results. Pi was multiplied by the radius (half of the diameter) squared. Then, the answer was multiplied by 100 (mm) (10cm), to give the final reading for area. Pi is never ending number used in mathematics to calculate area and circumference of circles. Its first digits 3 are 3.14.
As shown on the graph there is a slight bend in the trend line which implies that as the diameter of the wire increases, the rate of increase in area increases. In other words, the rate that the area increases with diameter is accelerating. This could be due to the fact that as diameter increases, the whole length of wire increases diameter. Therefore area accelerates when the rate of increase in diameter remains constant, because the bigger the diameter of the wire the bigger the increase in overall area because area is added to a larger surface area than it was to a previous diameter. In other words the bigger the diameter of the wire when increased, the more surface area needs to be filled to fulfill the diameter increase for the whole length of wire and therefore the more the added amount of area is.
Despite the fact that my lowest recording in this graph is of a diameter of 0.24mm, one would assume that the trend line would continue to curve down to point (0, 0) because clearly, if a wire has a diameter of 0, then it therefore cannot have an area because there is nothing of it. This can be proven by using the calculation: Pi times 0 squared =0. This is because 0 squared =0 and 3.14 times 0=0.
This graph is a reciprocal graph because it is a curve that is approached, but never reached by the graph... The curve is of the sort of y=a/x (‘y’=‘a’ over ‘x’). For example when ‘x’ is 2, ‘y’ should be 0.5. This is not the actual pattern; however the shape of the graph is similar to this. This type of line represents a line when neither ends of the line become straight, vertical or horizontal.
Conclusion
Secondly the second experiment concluded that the thinner that the nichrome wire is, the larger the resistance. This is also evidence to support my prediction. The prediction made concerning the relationship between resistance and diameter of the wire, was in fact correct also. After conducting further manipulation and analysis of the results from the second investigation, it became clear how resistance is affected by area of wire. Results indicate that the smaller the area of wire, the smaller the resistance, however this cannot be trusted because the larger the diameter as shown in experiment 2, the smaller the resistance, however the larger the diameter of a wire, the larger its area will be.
If more results and data were available, I could have expanded this investigation further to talk about how various wires with different diameters change resistance as voltages are changed. For example I could have recorded how resistance changes in a wire as voltage through the wire is increased. If I had access to this data I could have compared how resistance changes when various voltages are used. I could otherwise have recorded how resistance changes with heat to support the claim that heat causes an increase in resistance. These all could have been used to expand and develop the experiment further.
If I were to conduct this experiment again, I would try to include some of these additional sub-investigations. I would conduct an experiment concerning the relationship between heat in a wire and its resistance. I could conduct this experiment for various diameters and lengths of wire. I may also have conducted an experiment whereby various lengths of wire were tested to see how long it would take for wire of various lengths to heat up to a level that a certain change in resistance was achieved due to the heat. These all would have developed the investigation and made the conclusions all the more in depth and interesting.
There are a range of additional sets of data which could have been beneficial in improving the complexity and reliability of the investigation. To improve the reliability of the experiment, I could have taken more readings of the recordings of each length of wire. This would have meant that I could have calculated a more accurate mean and hade a more detailed range bar. I could have backed up statements by conducting tests challenging them. For example to back up the statement about heat in a wire causing its resistance to be higher, I could have conducted a test whereby a nichrome wire was used to record its resistance at different temperatures, otherwise I could have supported the statement that heat is built up when the circuit is left on over time. I could have done this by measuring resistance of a thin wire every 10 seconds, when the power is left constantly on at a high voltage. This could have given me more to write about and would have increased the complexity of the investigation.
Evaluation
There was a small mistake in the conduction of the first experiment, which if not noticed, could have lead to major inaccuracies in the results of the data. The mistake was that I read the current of the first experiment to be 56amps throughout the investigation. The ammeter was unclear about where the decimal place was and the actual reading was in fact 0.56amps. The results have now been changed by multiplying the resistance by 100. This has been checked several times for accuracy. This mistake was noticed when I realized, after I had calculated resistance, that 56amps in a wire of the diameter used would cause far too much resistance which would have lead to heat in the wire so much that the wire would have broken in two due to the heat. This I did not notice as I was conducting the experiment so my conclusion was that the amp recording must have been wrong. I re-calculated the resistance of each length of wire and spent some time checking my work for other inaccuracies. The likelihood if this is now minimal.
The apparatus in both experiments was carefully considered before any recording of data to prevent any bad recordings or unfair data. The length of copper wire in the circuit was kept to a minimum to prevent the loss of too much voltage as resistance. This would have made the test unfair. I also checked the position of the ammeter and voltmeter, they were in the positions shown on the circuit diagrams, I also check the wire for immediate heating effects. The power output setting was also checked before any recording. All of these precautions were taken in order to maximize the reliability and accuracy of the recorded data and to reduce the chance of any outliers (anomalous readings).
The safety of the experiment was purposefully kept to a maximum. The power packs had a block on them to prevent a voltage higher than 10v. This meant that it was reasonably safe to touch unprotected wire. The only other safety hazard could have been the high temperature of the wire. This was certainly the most hazardous factor of the entire investigation; however was not a major threat to safety of the investigation. It was controlled by using low voltages which prevented the wire from becoming dangerously over heated. A natural safety measure of the wire was that if it because too hot, it broke, thus breaking the connection of the circuit and allowing the wire to cool down.
As mentioned in the introduction, there were a few factors that could have affected the accuracy of the experiments and quality of results (see figure 1 on page 3b, in the introduction section), however as shown in the analysis in previous paragraphs, despite slight inaccuracy, the results are sufficiently trustworthy to be able to be analyzed in detail.
It would have possible for us to improve our investigation by heightening the accuracy of the results. This could have been done by repeating each recording more times. This would have given us more accurate mean. Due to the fact that the experiment was only conducted 3 times, the mean is not as accurate as is could have been. This could have affected the quality of the results. Despite this, the results show a high degree of accuracy because there is very little scatter in the results. Therefore the range bars are very small. This indicates a small range in data which leads to an indication of accuracy in the results and an accurate mean.
In the analysis of experiment 2, I mentioned the anomaly in the recording of current in set 1 of 2.85amps. This recording may have affected the accuracy of the results and could have lead to an unfair conclusion which would have reduced accuracy. I felt it necessary to deduct this result from the calculation of mean, to increase accuracy of the range bars in the graph, and quality of conclusion.
I have high confidence in the reliability of the conclusion, due to the accuracy of the results indicated and explained in the analysis of both investigations. The small range bars indicate a high degree of accuracy in the results. Secondly, the data of which I did not conduct an experiment for, but which I received from another source was also very accurate. This information was taken from the BBC GCSE Bitesize website which includes accurate information concerning resistance in wires. Assumptions and explanations made from this information, I have a great deal of confidence in. For example the explanation for the increase in size of range bars in experiment 1 was based on information from this source which can be relied on.
The first statement, concluded in the first experiment stated that resistance increases at a proportional rate that length of the wire is increased. This is because the longer that the wire is, the more particles of the metal element there are for the electrons to collide with, and so there are more they do collide with. This causes a small amount of friction per electron collision, which all adds up. This friction produces heat. The heat energy is energy transferred from electrical energy in the current. This transfer of energy means that there is less energy that remains as electrical energy. Therefore this removal of electrical energy is resistance. This resistance over a length of wire causes a change in electrical energy or voltage which I recorded as potential difference. The more potential difference that a wire has, the higher its resistance is.
The second conclusion was that taken from the results of the second experiment. It states that the larger the diameter of a wire, the less resistance it has, therefore the thinner the wire or the smaller its diameter, the more resistance it has. This is because a thicker wire allows more space for the same amount of electrons to flow through it and therefore mean that the amount of collisions between electrons I much higher. These collisions cause a lot of friction which causes a production of heat. The heat is transferred to the element or wire and causes the particles in the wire to vibrate; this creates more collisions because it makes it harder for the electrons to pass through. Therefore there is more friction, more heat transferred and a larger increase in resistance.
This investigation has clearly shown that resistance changes proportionally as length increases, and as diameter is increased, resistance rapidly decreases. These two statements are both supported by the results from the enclosed graphs and have been analyzing in their following paragraphs. These two statements also compliment my initial prediction which stated exactly that.
Due to the fact that there is very little scatter in my results, it gives me very little to right about in my conclusions. If the range bars had been bigger or had more scatter, I could have suggested reasons why the results were as they were and attempt to justify the inaccuracies using scientific terminology and detailed explanations or theories as to why the results were as they were. I have explained in detail the reason for the increase in the size of the range bars in the first experiment. Due to the fact that the scatter is so small in the second experiment there is very little to be mentioned. If the results had been inaccurate of had more scatter I could have critically discussed the cause for this.
Bibliography
I used the following websites only for research into resistance:
There was no other resource or external source of data used other than these. All other data was from the results of the experiments and knowledge of this subject.