For this reason, it is important to clarify what changing certain values will do to results, if only in theory. Changing the cross-sectional area and/or length will cause the resistance to vary. Length is what will be examined during the course of this investigation. Cross-sectional area is to be decided upon in some sort of preliminary experiment. As has already been explained, the smaller the piece of wire, the higher the resistance. As resistance causes heating, smaller wires will heat up more and more quickly depending on the current/electrons flowing through them. Cross-sectional area needs to be balanced between to small a diameter causing heating and to big a diameter not having enough resistance.
This brings me onto the next factor which needs to be investigated before any investigation can be done; this is heat. As a wire gets hotter, the resistance increases. This can be explained through the atoms. When the wire heats up either due to large current flow through a small wire or high ambient temperatures, the resistance increases merely because the nuclei vibrate faster. This meant that the gaps between adjacent nuclei are decreased and the resistance increases; conversely, when a wire is cooled, resistance decreases because there is more space between the nuclei as they are vibrating slower.
This is how superconductors work. The material is cooled until the nuclei are vibrating so slowly that the resistance of the wire/material is practically nothing.
Some electrical components such as thermisters use semiconductors to achieve the opposite effect that heat has on wire. When a thermisters is heated, the resistance is decreased because electrons in the semiconductor (silicon) are freed from its nucleus. This decreases resistance. If extreme accuracy is needed, a thermister can be used in conjunction with a suitable wire so that their effects cancel out i.e, because the resistance of wire increases when it is heated and the resistance of a thermister decreases when it is heated, they can be balanced so that when the circuit is heated, the thermister decreases as much in resistance as the wire in the circuit gains. This, however will not be required in most experiments as, if the correct cross-sectional area is chosen which does not create heating and the ambient temperatures are kept quite constant, a reasonable degree of reliability can be kept so that the result are reliable enough to draw valid conclusions from.
Other constants which need to be kept the same include the material used as different ones have different resistances and, hopefully, the equipment used so that the chance of errors being introduced due to different lengths of wire or better/worse connections between components are reduced.
All ideas presented here are based on ideas formulated by scientists such as: John Dalton, J.J Thompson, Niels Bohr etc on electrons and their behaviour. These theories and predictions have been proven correct
Method
To test the hypothesis, a practical experiment needs to be carried out. This will prove my hypothesis correct in a way other than theoretically. This is also necessary in order to convince people that the hypothesis allies in real life and not just theoretically.
The method will mainly include using a variable resistor to keep the current flowing through the circuit the same and a length of wire of which different lengths are measured and used and its resistance tested. This should prove that increasing the length will result in an increase in resistance because when we increase the length, we should see more resistance. A constant should be able to be calculated from the results.
Firstly, we need to define the variables which will be kept the same or varied in order to correctly write the method.
Constant Variables:
The temperature of the entire circuit
The current flowing through the entire circuit (can be decided in the preliminary experiment)
The material that the wire is made of (both in the circuit and for the wire being tested)
The Cross-sectional area or diameter of the wire
The length of all the wire in the circuit (excluding wire being tested)
Preferably the equipment used including all the wires/wire.
Controlled Variables
Length of wire being tested
Independent Variable – Variable that is affected by the controlled variable
Voltage through wire
I will be measuring the resistance and how it varies in accordance with the length of wire being measured. The controlled variable will be what is being changed in order to carry out the aim of the experiment (the length of the wire). The constant variables will be kept the same.
10 Measurements will be made over a range of 100cm, i.e. 10cm, 20cm, 30cm… and so on. This will be so that it is easier to prove my conclusion correct or false. If the measurements were made over a range of 1cm, and slight variation or discrepancy would cause completely inaccurate and unreliable results. This is why a large range will be used. The range is not lengthened too much as a range from 10cm to 10m would be very difficult to set-up and could result in anomalous results caused by something like the wire touching itself and resulting in a shorter length actually being measured. A range from 10cm to 100cm is practical yet easy to spot changes and reliable.
30 measurements will be made altogether. This is 10 actual changes of length: 10cm to 100cm in 10cm increments and 3 repeats. 10 changes in length are used because too big a difference in lengths (i.e. once at 10cm and once at 100cm) will not allow the hypothesis to be proven totally correct as one could ask the question “How do you know what happens at 50cm?” and the experiment and theory would not be able to prove them wrong. Too many measurements (i.e. 10-100cm in 1cm increments would mean that too much time would be spent changing the length and not enough doing work such as repeats. 10 changes in length should be practical enough and give enough material to draw and accurate conclusion
Although 10 changes in length are enough to draw a conclusion, we cannot base our conclusion on experiment that has only been done once. There may be a chance for error to affect our results. For example, if we got one result which was not fitting into a trend which could be spotted using the other points, we would have to accept that that was how the wire behaved and write this in the conclusion. This is why repeats are necessary. If we repeat the same experiment more than once, we can see whether any seemingly discrepant results were genuine or because of error. This is because the repeat will show us the correct result (assuming the error is not present in all of the results taken). This is also why 3 results are the optimum amount that should be performed. If there was a seemingly anomalous result, 2 repeats would not allow conclusive proof that it was definitely wrong. Only 3 would allow this as one would be completely different against two that were similar. The anomalous result can then be repeated. Repeats will make the results more reliable (See the accuracy part of the investigation for more information)
Preliminary experiments can help us in this case as well because any errors that occur in it can be corrected for the real experiment. This can help to stop discrepancies in results obtained.
Method
Safety Precautions
This experiment is generally pretty safe because a person carrying it out will not be subject to dangerous chemicals or hazardous situation; a few measures still need to be undertaken. This includes not using too high a current as this will overheat the wire and cause burning and possible fires. This can be achieved by either lowering the voltage (which also directly affect the current supplied) or by increasing the overall resistance of the circuit.
Equipment Used:
Power Pack or Bench Power Supply
Wires to link up equipment
Rheostat or Variable Resistor
Ammeter to check current
Voltmeter or Multimeter to check resistance
Ruler to check the length of the wire
Diagram
Circuit Diagram
The circuit will be set up as shown in the circuit diagram. This will be used for all the experiments, hopefully with exactly the same equipment.
The experiment will be carried out whilst making all the factors that could possibly vary as static as possible. One such example of this is the temperature of the wire. This is a factor which has to be controlled externally, i.e. , it is not part of the circuit design and could be easily forgotten; it, however, can have quite an important bearing on the result obtained. For this reason, all the factors that could possibly vary whilst testing the circuit are kept as static as possible. This can be greatly helped by doing all of the experimentation in one go and using the same equipment throughout it.
Different equipment can lead to different results. This is because the resistance of the circuit can change when different equipment is used which can affect results. If the experiment is finished during a different time, conditions will have change, which could result in some independent variable factors that have not been considered, changing. This could adversely affect the reliability of my experiment
The resistance will be measured using a combination of an Ammeter and a Voltmeter. This is because the Ammeter is needed (as explained subsequently) for use in the circuit anyway. The resistance will be calculated using the equation V=IR which can be re-arranged to give
(Ecq4) R=__V__
I
The variable resistor or rheostat will be added so that current in the circuit can be kept constant. This is essential because a longer wire (as hypothesised and theoretically proven before) should have a bigger resistance. This will lead to less current being able to pass through it. The variable resistor will control the current/voltage flowing through the wire. The current should be kept constant and the voltage varying according to the length of the wire. This is because the current is effectively the number of electrons flowing through the circuit. The resistance cannot be measured if the current changes as well because resistance causes voltage and current to decrease. If the current changes as well as the voltage, two factors will be changing and this will mean it will not be a fair test (refer to “fair test” for reason why this should be avoided)
Only one factor should be changed. Current should be kept static as there is a maximum amount of current a wire can have passing through it; it also causes heating which can disrupt results. Voltage, however, is not limited by the wire nearly as much. Because of this, only voltage will change and the current should be maintained at one level so that the most reliable set of results are collected.
Fair Test
This experiment will be totally unsuccessful if it is not a fair test. This means that only one factor can vary. The length of the wire will vary according to the lengths being tested. The voltage will vary according to this and allow us to compute the wire’s resistance. The current is always kept the same because when a longer piece of wire is tested, the current will go down. This will mean that the different lengths of wire will not receive the same current and the resistance calculated will be incorrect. Each wire tested needs to receive the same current. The voltage will be measured to what is the actual difference in resistance between the wires. This is why the current is kept constant.
The main way a “fair test” is carried out is by only changing one factor. For example, in this experiment, only the length of the wire being tested will be changed. The other variables will stay the same such as the current and the cross sectional area of the wire. This is because if the length of the wire and the cross sectional area both changed, then we would not know what caused the change in voltage, the change in cross sectional area or the change in length of the wire. This is why the only factor that will be changed is the length of the wire. As the resistance goes up as the cross sectional area goes down and up as the length goes up (this has been proven in the method) the factors will cancel each other out and/or greatly change the results if they are both varied at the same time.
Some other factors that should be taken into account are the temperature of the equipment, as if this varies, Ohm’s law (Equation 4) will not apply as it is only true at a constant temperature.
Accuracy
This is a very important part of the experiment and has been included to some extent in the method part of this investigation. The accuracy of the investigation is reliant purely on the equipment used. It will be impossible to get very accurate results if our equipment is analogue or doesn’t use any decimal places for example. Since we will be using a digital voltmeter, the accuracy will be enough or even too much! The version we will be using will be accurate to 2dp (or 3 figures as this is how many its screen will accommodate). This will be enough for most applications including this experiment. Since we are using a constant current as well to calculate the resistance, it needs to be set up accurately in the first place. The other alternative is to use a digital multimeter to measure resistance across the wire. This will not be necessary as the voltmeter does the same job and is more readily available. The only problem that can be illustrated is that because low current/voltages will be used, we will not really go over 1 volt. This means that the first figure before the decimal point is “wasted”. 2sf though is enough, 3sf would be too accurate. The only other area where accuracy is needed is when the constant variables are tested to see what values they are at
The way to increase the reliability of the experiment is to do repeats. For example, if we got a result that didn’t fit in with a particular trend, with no repeats, we would have to assume that this was how the wire behaved at a particular current level but if we did repeats, we could prove that one or more results were anomalous. The minimum number of repeats needed to do this would be two giving three results altogether. (This has been touched on in the method). This would greatly increase the reliability of the experiment as we would only have the results that are correct (assuming that the cause of anomalous results was not present throughout the entire experiment).
My experiment, so far, is, I think, the best way to test my hypothesis. This can be confirmed/disproved by doing some preliminary work. Some improvements to the method may be needed in order to test the hypothesis in the best way possible.
Preliminary work
This is one of the most important parts of the investigation. A Preliminary experiment enables us
- To see whether the method tests the hypothesis in the most effective way possible i.e. if it is a good way to test the hypothesis and,
- To test which are the best values to keep the constant variables at.
The preliminary experiment that will be attempted will be to find out the best value to keep the current at and to find the best diameter of wire to use. Too thick a wire and only a small range of results will be collected. Too small a wire and heating can occur. Similarly, too large a current will cause heating and too small will cause a small range to be collected. A compromise is needed. It will also decide the best material to use. Ideally, one with the largest resistance should be used as this will give the largest range. Again, as with the other constant variables, too high a resistance will cause heating.
-Obtained from the Standard wire gauge (SWG) sheet handed out in class
From this experiment, we know that Nichrome has the highest resistance by far and will be sufficient for this experiment where the length of the wire being tested will not go over 1m. This is why Nichrome will be used as the material
The next constant factor to be decided on is the SWG and the current that will be used. What will be tested is if the constant chosen has a heating effect and if not, if the range of values are too small. Firstly an SWG of 36 (0.19mm) will be used to test the maximum and minimum current allowed to pass when the power pack was set at 4 volts and the rheostat was moved between maximum and minimum values. When the length of the wire was at 10 and 100cm
This size of wire caused a lot of heating at a higher current. Wire with a larger SWG therefore diameter will be tested.
Using a larger SWG of wire will enable higher current to be used, however, since the voltmeter is very sensitive, a small range of a couple of ohms will be sufficient to draw a valid conclusion. Any sort of heating in the wire will be a very bad effect so must be avoided. This is why a current value of 0.25 Amps will be used. Heating will cause the resistance v length graph not to be directly proportional even if it was before, as the shorter the length of wire, the greater the heating effect. This is why a large diameter and small current will be used. (SWG 28 and current 0.25A)
The aim of the preliminary experiment was also to see all of the possible values of current that could be used without heating i.e. the highest lower bound and the lowest higher bound would be the possible range of current values that I could use to keep constant, in this case, 0.21A to 1.03A. This is why 0.25A was chosen as it is close to the highest lower bound without actually touching it as this would mean that in some cases, due to change of equipment, it might not be possible to go this low again.
The method that was described in the method part of this investigation was correct in that it did not need changing. In the end, the method is as described earlier and the constant values for the wire are Nichrome, 0.25A @ 4volts on power pack.
Conclusion
The hypothesis that was proposed was correct. The hypothesis stated that when the length of the wire was increased, the resistance would increase and they would be directly proportional to each other. The resistance does increase as the length increases. It is (more or less) a straight line. This means that it is directly proportional. This means that Length × constant = resistance and resistance ÷ constant =length of wire
This means that resistance ÷ length = constant. This constant only applies for this circuit or one made under similar conditions.
In this case, the constant would be 1 ÷ 0.3 = 3_13_. This can be checked by doing it again with different values 2 ÷ 0.6 = 3_13_
We can check that the constant is the product of dividing the right numbers by using it for values already known or 0.3 × 3_13_. = 1 and 0.7 × 3_13_. = 2 _13_. This means that the formula relating length, resistance and the constant stated previously is correct.
Length × Constant = resistance and _______Resistance______ = Length
Constant
This formula, that has been calculated and is known to work, proves that resistance is directly proportional to length of wire.
The constant is actually the gradient of the line which is
______Different in y axis________. This is ____2_-_1_ which is the same as is
Different in x axis 0.6 - 0.3 calculated before.
This means that the gradient is the constant. This is very important because it means that to calculate the resistance according to this constant, one needs to have results which form exactly the same gradient that has been obtained here.
Although most of the points fit quite well into the line of best fit, it becomes obvious that as the resistance and length goes up, the point are further and further off the line of best fit. This can be argued to be because of many reasons. The most obvious would be that as the length of the wire increased, so the resistance increased and caused some heating to the wire. This would lead to the resistance changing and not conforming to the line of best fit. This is the simplest explanation as to why the points are not always on the line of best fit
The scientific theory explaining the results are
1. Ohm’s law that relates resistance to current and voltage enabling us to calculate resistance;
2. Equation 3 that helps relate length, cross-sectional area, material of wire and resistance together, and
3. The theory on heat which explains anomalous results.
The results agree with the hypothesis for the most part. The hypothesis states that as the length of the wire increases, the resistance increases. The results also show resistance and length of wire as being directly proportional to each other. My hypothesis, however, does not give any reasons for the results not being exactly proportional with each other i.e. why there are and should be anomalous results. The main reason for this is that there are so many variables that can change that we cannot measure and keep them all constant. There may be some type of undetectable particle in a nucleus which explains my anomalous results. In a perfect world, all of these potential variables in the experiment will be kept constant. In the real world, this will not happen; even so, I can make a guess as to what may be causing the anomalous results.
Firstly, the wire will heat up. This effect will become more apparent when the resistance is high or when the length of the wire is long. This may be why the points conform less and less to a line of best fit when the length of the wire is increased..
Secondly, the reason which probably contributes greatly to why some readings were off the line of best fit was that the entire experiment was carried out using low current and an equation to calculate the resistance in the end. This would mean that there would be a large chance for error as the very small changes in the circuit could result in large changes in the difference. If a large amount of current is used, and small changes would go generally unnoticed. This effect can be compared to the universe. Close up, it seems lumpy and inconsistent as my results could be at low currents; when zoomed out or using larger values, these small discrepancies are ironed out and the results are more consistent.
Thirdly, when the current flows along the wire, it will take a few seconds to ‘stabilise’. This means that there may be a possibility that the wrong reading is taken. This is closely tied in with the fact that small changes when using low currents lead to large discrepancies with the graph. If, for example, the voltage @ 50 cm was measured at .40 instead of .44, the resistance would be 1.6 instead of 1.76. On the graph, this kind of result would have been an anomalous. This is probably the reason for most of the anomalous results.
Evaluation
This experiment was a good way of carrying out the investigation. This is for many reasons. We can mainly say that is way so good because the results needed to be almost spot on or they will not conform to any pattern or in this case, the line of best fit. This is because the current is so small. Because I have got results this accurate, I can say that my method at least was good enough to obtain results of this accuracy in order to draw a conclusion and prove my hypothesis right.
It may be possible to criticise my way of carrying out the investigation because the current used is low. This can be defended by saying that using a low current means that the heating effect is minimized. This means that the chance of anomalous results can be reduced. This can be counter-argued by saying that the chance of getting anomalous results is increased again by having the current low because the values can be subject to changes very easily.
My method can now be proved to be the best way to do the investigation because it combines low current and heating (preventing irregular results) with accurate results due to a good method. This means that the probability of anomalous results is very low (although it is still present).
My results are accurate enough because the graph shows a line of best fit in which most of the points sit on. The anomalous results are not really that far off and as explained before, this is because of the low current which also leads to better results. The equipment is good as the digital voltmeter gives a very accurate reading. There really is not much need for an increase in accuracy as 3dp would be too accurate
I have enough results to draw a valid conclusion. There are two main areas into which this experiment can be expanded into to give more results. A longer length of wire could be used or more repeats could be done. Reasons as to why the lengths chosen are the most accurate have been discussed before. A length of 10m might give me more results but would be impractical to set up and could cause error if used in a small room as the wire could touch itself and cause the length tested to be far shorter. This means that doing the experiment with more lengths would not really be practical.
The other choice would be to increase the number of repeats done. This would be pointless as 3 would be enough to prove one of the results wrong if it did not fit in with a trend. Only if the experiment was very prone to having anomalous results would a 4th repeat be needed. This means that there were enough results to draw a valid conclusion from as no more were really needed.
The results have a wide range. Considering the space in the lab, it would not be feasible to have 20 or so groups doing experiments with 2m of wire, 1m would be the most that could be accommodated. This means that the results that have been attained are really the biggest range and the most feasible number of repeats that could have been done.
The fact that it has been said that the results were accurate and there were enough of them means that there should be enough results for an accurate conclusion to be drawn in which all of the data fits into a pattern. This is the case for most of the results. The anomalous results that were obtained were a consequence of independent variables that I had no/very little control over, such as the placement of the crocodile clips not exactly on the 20 cm mark etc. This means that all of the anomalous results were probably caused by human error and not failure of the procedure to specify how to do certain things.
The 2nd repeat for 40 cm was an anomalous result. Again, this would have probably been caused by human error and not because of failure to comply with the method. We cannot, of course, just say it was this. There is a possibility that it was because of a factor that we did not consider when writing the list for the constant variables such as different particle existing in atoms that has not been detected yet. This probability, however slight, must not be left out of the evaluation.
Some improvements that could be made to the experiment are using a thermister that is perfectly balanced so that as the circuit heats up due to current flow, the thermistor’s resistance also increases. This will mean the resistance of the wire in the circuit that is not being tested has a constant resistance. This, however is not really necessary as it would take a long time to do and may adversely affect the effectiveness of the experiment as if not set up right, the thermister may give higher resistances when not needed
Undoubtedly, the best ‘improvement’ that could be made is to concentrate more on the setting up of the equipment and making sure that the length of the wire is exactly 20 cm (for example) by measuring 20 cm only from the inner edge of the crocodile clips. This will ensure that more accurate results are given.
The alternative to this more rigorous checking would be use a higher current or smaller diameter of wire making the resistance higher which would lead to a larger range and better results due to less influence of small things such as not getting exactly 20cm of wire
Further work that could be done would be to increase the voltage on the power pack from 4 volts to 6 or 8 volts and adjusting the current back down to 0.25A. This should give the same constant (or gradient of line on the graph); directly proportional results should also still be obtained. If this doesn’t happen, we know that there is something that is causing the results to not be the same. If we set up the equipment exactly the same each time, adjust the constant variables to the right levels and do basically everything the same, this different would either be because of human error or because of a constant variable we had not considered before.
© Logan Jayabalan 11 Brown 2002 - OCR Triple Award Higher Physics 1982
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