Aim:
Resistance is a measurement describing the difficulty of electron flow through a conductor. The OHM (W) is its measurement.
In this investigation, I am going to be finding out and investigating one of the four factors, which affects resistance in a wire: Length
Prior Knowledge/Research:
There are many variables that will be relevant to this investigation. Although I am only going to be investigation one of these factors in this experiment, all of the others have a certain degree of relevance making them part of the investigation automatically. These factors are:
· Length
· Thickness
· Temperature
· Material
.Temperature: If the wire is heated up the atoms in the wire will start to vibrate because of their increase in energy. This causes more collisions between the electrons and the atoms as the atoms are moving into the path of the electrons. This increase in collisions means that there will be an increase in resistance.
2.Material: The type of material will affect the amount of free electrons, which are able to flow through the wire. The number of electrons depends on the amount of electrons in the outer energy shell of the atoms, so if there are more or larger atoms then there must be more electrons available. If the material has a high number of atoms there will be high number of electrons causing a lower resistance because of the increase in the number of electrons. Also if the atoms in the material are closely packed then the electrons will have more frequent collisions and the resistance will increase.
Materials that are good conductors, such as copper, allow a large amount of electron flow and so they have very little electrical resistance. Poor conductors, like nichrome, have very high resistance and as such do allow such a current flow even with the same voltage across it.
3.Wire length: If the length of the wire is increased then the resistance will also increase as the electrons will have a longer distance to travel and so more collisions will occur. Due to this the length increase should be proportional to the resistance increase.
4.Wire width: If the wires width is increased the resistance will decrease. This is because of the increase in the space for the electrons to travel through rather than increasing the size of the atoms themselves. Due to this increased space between the atoms there should be less collisions, as the flow of electrons is not interfered by the atoms.
I know that resistance is affected by length and cross sectional area. If the length is increase, so is the number of atoms that collide with free electrons and thus increase resistance. If the cross sectional area is increased so is the space between the atoms rather than the atoms themselves. This means that there are fewer collisions between the electrons and atoms and greater flow of electrons thus decreasing resistance. Therefore the resistance of any material is inversely proportional to its cross sectional area (A):
R=1/A
However, when talking of length and cross sectional area, it is more common to define the resistance of a material instead of a certain aspect. This is known as the Resistivity; P
Resistivity =resistance x area
Length
P = R X A
L
We measure resistivity in the ohm metre (Wm)
The Ohm
In and around 1825, German scientist George Ohm discovered and made a law on resistance that was: The current flowing through a metal wire is proportional to the potential difference (p.d) across it providing that the temperature remains constant. Thus the unit of resistance is now referred to as the Ohm (W).
Resistance (R) = p.d across the wire (v)
Current through the wire (I)
R=V/I V=p.d in volts
I=Current in amps
R=Resistance in a unit ohm
The formula is commonly rearranged though and can sometimes look like this when a different aspect is trying to be calculated:
I=V/R V=IxR
Investigating length on resistance:
Metals conduct electricity because the atoms in them do not hold on to their electrons very well, and so creating free electrons, carrying a negative charge to jump along the line of atoms in a wire. Resistance is caused when these electrons flowing towards the positive terminal have to 'jump' atoms. So if we double the length of a wire, the number of atoms in the wire doubles, so the number of jumps double, so twice the amount of energy is required: There are twice as many jumps if the wire is twice as long. A diagram in my prediction explains these jumps and the collisions between the electrons and atoms.
Prediction:
I predict that if the length increases then the resistance will also increase in proportion to the length. I think this because the longer the wire the more atoms are present and so the more likely the electrons are going to collide with the atoms. So if the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. My graph should show that the length is proportional to ...
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Prediction:
I predict that if the length increases then the resistance will also increase in proportion to the length. I think this because the longer the wire the more atoms are present and so the more likely the electrons are going to collide with the atoms. So if the length is doubled the resistance should also double. This is because if the length is doubled the number of atoms will also double resulting in twice the number of collisions slowing the electrons down and increasing the resistance. My graph should show that the length is proportional to the resistance. I also predict that at 2 volts, the resistance will be less than at 3 volts because the energy between the atoms shall be less thus they will be moving around less. This results in fewer collisions between the flowing electrons and the atoms thus less resistance.
Resistance means the property of anything to constrict the flow of electrons (a current). The electrons that carry the energy within the metal wire collide with "obstacles" (atoms) inside the wire and change direction. (The atoms in the wire are obstacles to the electrons.) This is known as scattering. This causes electrical resistance. Therefore, I can predict that the electrons will collide with the atoms, when the atoms have more energy, more often.
The diagrams below show my prediction and should explain it more clearly:
Given that the length of the wire is only half the length of the wire below there should be half the number of collisions between the electrons and the atoms.
The wire below is twice the length of the wire above and so there should be twice the number of atoms resulting in twice as many collisions and a predicted doubling of the resistance.
Apparatus:
· Power Pack
· 100cm Nichrome Wire
· Ammeter
· Voltmeter
· 2 Crocodile Clips
· Metre Rule
· Sellotape
· Connecting wires
Diagram:
Preliminary work:
Preliminary work is the work that is done beforehand for you to know that the values of the different apparatus you are going to use. It is a way for the person carrying out the experiment to know that it has been set up correctly for when the actual experiment begins.
For my preliminary work, I set up the experiment as said so in my method and took some readings. It helped me realise any mistakes that I was making that would affect the real experiment. These were things such as turning the voltage too high, which would be quite dangerous and could have burnt the wire or the laboratory unit. I also took the readings from the ammeter and voltmeter too quickly and did not let the value settle before taking it. This would only make a marginal difference to the results but accuracy is the main part of any investigation and I wanted mine to be as accurate and reliable as possible so I will have to be a bit more patient when taking down results in the actual experiment. I also need to ensure (although it was not too much of a problem in the preliminary method) that the crocodile clips are at exact points on the wire i.e. 10cm or 50cm to make reading more reliable and exact. Another thing I noticed I would have to watch out for was the independent variables and keeping things like temperature and voltage constant. However, temperature will naturally increase as the voltage is being out through the wire so that is one factor that I can't do too much to control.
I also did the experiment using nichrome wire, which is a poor conductor. This is because I thought that using a good conductor would make the wire too hot and the readings very high so I used nichrome and found that my results were within a viable range.
Safety Precautions:
Throughout this experiment, I made sure that safety was one of my top priorities. I wore a lab coat when working and was extremely cautious when measuring the voltage of the wire in case the wire became very hot. Contrary to this, I did not increase the voltage above the 3 volts so that I would not burn my hands or the metre rule. I wore goggles as a precaution although it was not evident that any sparks etc would be produced in this experiment.
Method:
I firstly plugged a power pack in to a socket. It is this piece of equipment that I will change the voltage with. I connected 2 wires that lead from the power pack to the ammeter and a second wire to the voltmeter. From the ammeter, a crocodile clip was connected with the other end connected to the metre wire at 0cm. This would remain here as it is simply reading the current from this point whilst the wire from the voltmeter varies along the wire. The crocodile clip from the voltmeter was connected at 10cm and this would be repeated at 20, 30, 40, 50, 60, 70, 80, 90, 100cm. The ammeter would remain at 0cm to record the variables easier i.e. the distance from 0 to the recording value does not need to be calculated. The voltage on the power was set at 2V and the recordings were taken three times at each length. The voltage was then set at 3V and the method repeated with an average calculated for each value and the resistance calculated using the V/I formula.
Observation:
For this particular experiment, I found that there was no blatant observation to be made i.e. observing a reaction or change take place. However, there was one observation that can be stated which was taking down the readings from the ammeter and voltmeter. I simply looked and noted down the values of the voltage and current and used them to calculate the resistance.
Fair Test:
To ensure that my experiment was a fair test, I had to take care with a lot of things. I made sure the factors that might affect my experiment working well would attempt to have been suppressed. These were things like temperature, which can affect the wire either by the heat in the laboratory or from the voltage running across the wire. To combat this, I made sure that the power pack was turned off between readings so that the wire did not get hot and thus affect the reliability of my results at each value. I also tried to limit the amount of human error in my experiment with things such as putting the clips on the exact lengths and recording the readings on the ammeter and voltmeter correctly.
I think that these are important factors because it can be detrimental to how accurate and reliable the results were on the whole and it could leave me with anomalous results that have no reason behind their appearance.
Reliable Results:
To make certain that my results are reliable, I will take the readings of each length three times. This means that I will have three sets of data for Voltage, Current and Resistance all from 10cm-100cm. I will calculate an average for each set of data and the range of results will be at 2 and 3volts.
Results:
As stated earlier, I recorded three sets of data and then calculated an average for that data. Below are my three tables and the separate table concerning the average values:
THESE RESULTS ARE AT 2 VOLTS:
Length Voltage(V) Current(I) Resistance
0 0.88 0.47 1.87
20 1.12 0.31 3.61
30 1.26 0.23 5.48
40 1.34 0.18 7.44
50 1.39 0.15 9.27
60 1.44 0.13 11.08
70 1.48 0.11 13.45
80 1.51 0.1 15.10
90 1.52 0.09 16.89
00 1.55 0.08 19.38
Length Voltage(V) Current(I) Resistance
0 0.85 0.47 1.81
20 1.11 0.3 3.70
30 1.21 0.22 5.50
40 1.3 0.17 7.65
50 1.35 0.15 9.00
60 1.4 0.12 11.67
70 1.45 0.11 13.18
80 1.49 0.1 14.90
90 1.52 0.09 16.89
00 1.53 0.08 19.13
AVERAGE RESULTS TABLE
Length Voltage(V) Current(I) Resistance
0 0.84 0.47 1.79
20 1.11 0.3 3.70
30 1.25 0.22 5.68
40 1.32 0.18 7.33
50 1.38 0.15 9.20
60 1.43 0.13 11.00
70 1.47 0.11 13.36
80 1.49 0.1 14.90
90 1.53 0.09 17.00
00 1.55 0.08 19.38
Length Voltage(V) Current(I) Resistance
0 1.98 1.10 1.81
20 2.59 0.70 3.69
30 2.88 0.52 5.57
40 3.07 0.41 7.48
50 3.19 0.35 9.12
60 3.31 0.29 11.28
70 3.41 0.26 13.30
80 3.48 0.23 14.93
90 3.56 0.21 16.94
00 3.60 0.19 19.27
The graphs that I shall be drawing up will be of the average results for the 2 and 3 volts recordings. They shall be on separate paper as a part of the investigation.
Below are the results that I recorded at 3 volts. Again there are three sets of data for accuracy and repeatability and a separate average result table, which the graph I shall be drawing will be constructed of.
THESE RESULTS ARE AT 3 VOLTS:
Length Voltage(V) Current(I) Resistance
0 1.55 0.71 2.18
20 1.95 0.46 4.24
30 2.15 0.34 6.32
40 2.29 0.27 8.48
50 2.38 0.23 10.35
60 2.45 0.19 12.89
70 2.5 0.17 14.71
80 2.53 0.15 16.87
90 2.56 0.13 19.69
00 2.59 0.12 21.58
Length Voltage(V) Current(I) Resistance
0 1.6 0.72 2.22
20 1.97 0.47 4.19
30 2.18 0.35 6.23
40 2.31 0.27 8.56
50 2.39 0.23 10.39
60 2.45 0.19 12.89
70 2.49 0.17 14.65
80 2.53 0.15 16.87
90 2.55 0.13 19.62
00 2.63 0.12 21.92
AVERAGE RESULTS TABLE
Length Voltage(V) Current(I) Resistance
0 1.58 0.73 2.16
20 1.98 0.47 4.21
30 2.17 0.34 6.38
40 2.31 0.27 8.56
50 2.34 0.23 10.17
60 2.46 0.19 12.95
70 2.5 0.17 14.71
80 2.54 0.15 16.93
90 2.57 0.13 19.77
00 2.61 0.12 21.75
Length Voltage(V) Current(I) Resistance
0 1.6 0.75 2.13
20 2.01 0.47 4.28
30 2.19 0.34 6.44
40 2.33 0.27 8.63
50 2.41 0.23 10.48
60 2.47 0.2 12.35
70 2.52 0.17 14.82
80 2.56 0.15 17.07
90 2.59 0.14 18.50
00 2.61 0.12 21.75
Analysis Of Results:
From the tables above, I can see that the resistance in a wire with 2V running across it increases as the length increases. Also, at 3V the resistance increases with the length but to a greater extent than that of 2Volts. An example of this trend can be seen at 10cm with a 2V supply to the wire. The resistance here is 1.81W(from the average table). Looking further along the same table, the resistance at 80cm is 14.93W -an increase of 13.18W. The current also decreases across the wire as there is more wire containing the power, which means that it is spread out thus reducing it at each length.
Analysis Of Graphs:
Graph 1 shows the resistance across a 2V Nichrome Wire. I can see from the graph a clear trend, which is a steep rising line that tells me as the length is increasing, so is the resistance. It is almost a direct straight line showing that the two are proportionate. I drew a line of best fit with each graph to calculate gradient and to calculate the trend of the graph. Graph 2 shows the resistance across a 3V Nichrome Wire. The trend of this line is almost identical to graph 1 but the gradient is steeper, indicting an increase in resistance over the same lengths as the first graph. The line is not as straight as the first but neither indicates any anomalies-all the plots correlate and there are no odd points.
Aside from the two main graphs that showed the average resistances at 2 and 3V, I drew 6 other graphs for each set of data that was repeated. So there are three graphs at 2V and three graphs at 3V. I have drawn a line of best fit for each of them and below is a short summary analysing the graphs.
For all of the graphs at 2V, I noticed that in comparison to the 3V graphs, they have a much less steeper gradient. I can't obviously conform it without mathematically calculating but I have done so for the averages, which can be seen below. The 3V graphs tend to have s steeper slop on their plot than the 2V graph which indicated to me an increase in resistance with an increase in voltage.
I calculated the gradient of each of the average graphs to work out their steepness and if there was a conclusion to be had from them.
20
5
So the gradient of the 2V average graph is 9/47.5= 0.19(2dp)
3V average graph is 12/59.25= 0.20(2dp)
So from the calculation of the gradient that can be seen above and on the graphs themselves, I can see that the 3V graph actually does have a steeper gradient than the 2V graphs and I believe that this is so because the 3V wire give the atoms more energy than the 2V so they collide even more so with the electrons to increase the electrical resistance.
Conclusion:
From my results, I have come to the conclusion that if you increase the length of a wire, you increase the resistance of it as well. The resistance of nichrome wire at 2V increases in proportion to the length. I think that this was because of an increase in the amount if atoms in the wire at each ascending length and so if there were more atoms (that were moving with a lot of energy from the voltage across them) then there would be many collisions between them and the electrons thus causing a lot of electrical friction hence resistance. At three volts, I think that that the resistance was even higher than at 2V because the atoms had even more energy thus they vibrated even more. This resulted in further collisions with electrons and so even higher resistance.
My graphs also clearly showed a steeper gradient with the 3V wire than with the 2V wire and this showed that resistance was indeed higher as the voltage input into the wire was higher.
Linking Prediction To Conclusion:
My original prediction was that increasing the length of a wire would increase the resistance across it. And, from my results, I can see that this is true as at 10cm on a 2V wire, the resistance is 1.81W and at 100cm on the same wire with the same voltage across it the resistance is 19.27W -a differences of 17.46W. This proves that the resistance is increasing as the length is increasing.
Evaluation:
I think that this experiment has been a very successful one as my results supported my prediction. My results were particularly accurate as each length was taken 3 times at the various voltages and calculated an average from my resistance, which was found out using the formula V/I. There were no strange results (anomalies) within my results table and I think that this was because of the extreme caution and care that I put into making sure that the experiment was set up correctly with careful measuring of the length that the second crocodile clip was on.
However I think that I could have repeated my results more however for the reason that I feel although the experiment was repeated four times, the most accurate results in experiments can only come from constant repeatability which I did not display in my experiment. That said, the time allocated did not allow me to do so and I believe as an improvement of what I could do if I did the experiment again, I would have to say that, with more time, I would repeat the results further for even more accurate and reliable results. I would also take even more caution when recording the values as al6though I did my best to turn of the power supply at this time, delaying even for a half of a minute would increase the temperature of a wire and thus make the next set of results not as accurate as the last. This was very important as temperature was one of the possible variables that I wanted to keep constant so feel that I could have taken more care and been more aware of when I was recording the values that the power pack was definitely off.
I believe that I could have improved the method by making it more specific. I stated clearly all the various methods I took in setting the experiment up but I could have been more specific to how all the apparatus was used and perhaps why I used the apparatus I did too. Certainly I could have explained my experiment step by step with numbers explaining carefully in which order that everything needed to be set up.
I believe that I did get a suitable range of results for this experiment. I recorded results from length ranging from 10cm to 100cm. I think that this is a very good range to see any clear trends in my results. One could say however that I could have recorded the lengths at 15, 20, and 25, 30cm and so on to make my range of results even better and accurate. However, I feel that my range of results was good enough to be able to confirm a pattern in my results, as I certainly believe that my range of results was a good one. Perhaps I could have tried the temperature at even higher voltages for more results but I feel that this was not possible with the time allocated and was quite difficult with the temperature factor meaning results could not always be accurate.
Some other areas in the experiment that I feel I could have improved on were factors like controlling the temperature because although difficult, it is a very important factor that can ruin results if not controlled. Measuring the lengths of the wire is also an inaccuracy that could be improved, as the rulers used are not exact, and it is difficult to get an accurate reading of length by eye, as the wire might not be completely straight, it may be of different thickness throughout the length. These would have contributed as well to the error. These results would be difficult to improve on as they are reasonably accurate, and there were no anomalous results.
Nevertheless, if I were to do this experiment again, I would use newer, more accurate ammeters and voltmeters, a more accurate method of measurement, and take a much wider range of readings, and more readings so that a more accurate average can be taken.
Overall, this investigation has been a very successful one. I feel my results and analysis have been as accurate and reliable as they could have been under the time allocated circumstances. However I feel with extra time, I could have repeated the experiment and made it even more accurate and adapted it to try other variables. These would be things like investigating the effect of cross sectional area or temperature on resistance in a wire