To investigate how the resistance of a wire is affected by the length of the wire.
Resistance of a Wire
Task
To investigate how the resistance of a wire is affected by the length of the wire.
Theory
What is resistance?
Electricity is conducted through a conductor, in this case wire, by means of free electrons. The number of free electrons depends on the material and more free electrons means a better conductor, i.e. it has less resistance. For example, gold has more free electrons than iron and, as a result, it is a better conductor. The free electrons are given energy and as a result move and collide with neighbouring free electrons. This happens across the length of the wire and thus electricity is conducted. Resistance is the result of energy loss as heat. It involves collisions between the free electrons and the fixed particles of the metal, other free electrons and impurities. These collisions convert some of the energy that the free electrons are carrying into heat.
How is it measured?
The resistance of a length of wire is calculated by measuring the current present in the circuit (in series) and the voltage across the wire (in parallel). These measurements are then applied to this formula:
V = I ´ R where V = Voltage, I = Current and R = Resistance
This can be rearranged to:
R = V
I
Ohm's Law
It is also relevant to know of Ohm's Law, which states that the current through a metallic conductor (e.g. wire) at a constant temperature is proportional to the potential difference (voltage). Therefore V ¸ I is constant. This means that the resistance of a metallic conductor is constant providing that the temperature also remains constant. Furthermore, the resistance of a metal increases as its temperature increases. This is because at higher temperatures, the particles of the conductor are moving around more quickly, thus increasing the likelihood of collisions with the free electrons.
Variables
Input:
* Length of wire. *
* Material of wire.
* Width of wire.
* Starting temperature of wire.
Output:
*
and thus the resistance of the wire. †
* Voltage across wire.
* Current in circuit.
* Temperature of wire.
The variable marked with a * will be varied, the other input variables will be kept constant. The output variable marked with a † will be measured.
Predictions
* The longer the wire, the higher the resistance. This is because the longer the wire, the more times the free electrons will collide with other free electrons, the particles making up the metal, and any impurities in the metal. Therefore, more energy is going to be lost in these collisions (as heat).
* Furthermore, doubling the length of the wire will result in double the resistance. This is because by doubling the length of the wire one is also doubling the collisions that will occur, thus doubling the amount of energy lost in these collisions.
Method
The following circuit was constructed to perform the investigation:
wire
The two dots ( ) represent the crocodile clips that were placed at the ends of the required length of wire.
. One metre length of 0.4mm diameter "constantan" (a metal alloy) wire is fixed to a metre rule.
2. The first crocodile clip is clipped to the wire at the 0cm position on the metre rule.
3. The second crocodile clip is clipped to the relevant position depending on the required length of wire.
4. The power supply is turned on. The voltage and current are then read off the ammeter and voltmeter, and recorded.
5. The power supply is then turned off and the second crocodile clip is moved to the next position.
The above steps are completed for each length and then the entire investigation is repeated for accuracy.
Rough Trials
In order to decide upon the voltage and lengths of wire to use in the final experiment, the following rough trials were carried out:
At 3V:
Length (cm)
Voltage (V)
Current (A)
Resistance (W) (to 2 d.p.)
0
0.41
0.90
0.46
20
0.51
0.57
0.89
30
0.56
0.42
.33
40
0.60
0.32
.88
50
0.63
0.26
2.42
60
0.64
0.23
2.78
70
0.65
0.20
3.25
80
0.66
0.18
3.67
90
0.67
0.16
4.19
00
0.68
0.15
4.53
At 5V:
Length (cm)
Voltage (V)
Current (A)
Resistance (W) (to 2 d.p.)
0
Could not be carried out as the wire simply melted.
20
2.12
2.07
.02
30
2.25
.56
.44
40
2.34
.24
.88
50
2.41
.02
2.36
60
2.45
0.88
2.78
70
2.49
0.77
3.23
80
2.52
0.68
3.71
90
2.54
0.62
4.10
00
2.56
0.55
4.65
After performing these rough trials, it was decided that 3V would be used in the proper experiment, as it provided results from 10cm up to 100cm and the higher voltage provided no additional ease of measurement.
Furthermore, it was also decided to allow the wire to cool between experiments as considerable heat was noticed at lower lengths and, as mentioned above, an increase in temperature results in an increase in resistance. By allowing the wire to cool between experiments a fair test could be assured.
Safety
In order to perform a safe experiment, a low voltage of 3V was chosen so that overheating was minimilised. Furthermore, lengths lower than 10cm were not tried, which also helped to avoid overheating.
Results
Wire 1, Set 1:
Length (cm)
Voltage (V)
Current (A)
Resistance (W) (to 2 d.p.)
0
0.66
.22
0.54
20
0.84
0.89
0.94
30
0.97
0.70
.39
40
.06
0.57
.86
50
.16
0.50
2.32
...
This is a preview of the whole essay
Safety
In order to perform a safe experiment, a low voltage of 3V was chosen so that overheating was minimilised. Furthermore, lengths lower than 10cm were not tried, which also helped to avoid overheating.
Results
Wire 1, Set 1:
Length (cm)
Voltage (V)
Current (A)
Resistance (W) (to 2 d.p.)
0
0.66
.22
0.54
20
0.84
0.89
0.94
30
0.97
0.70
.39
40
.06
0.57
.86
50
.16
0.50
2.32
60
.22
0.44
2.77
70
.25
0.38
3.29
80
.27
0.35
3.63
90
.31
0.29
4.52
00
.33
0.29
4.59
Wire 1, Set 2:
Length (cm)
Voltage (V)
Current (A)
Resistance (W) (to 2 d.p.)
0
0.51
.02
0.50
20
0.79
0.79
0.97
30
0.91
0.65
.40
40
.02
0.55
.85
50
.08
0.48
2.25
60
.15
0.42
2.74
70
.19
0.37
3.22
80
.22
0.33
3.70
90
.26
0.30
4.20
00
.27
0.28
4.54
Having completed two sets of results for one wire, it was noticed that these was a large black mark towards one end of the wire, where it appeared that it had been melted to some degree at some point. It was therefore decided to conduct experiments on an additional piece of wire that was checked for integrity prior to investigation:
Wire 2, Set 1:
Length (cm)
Voltage (V)
Current (A)
Resistance (W) (to 2 d.p.)
0
0.95
.06
0.90
20
.19
0.67
.78
30
.28
0.48
2.67
40
.35
0.37
3.65
50
.38
0.32
4.31
60
.42
0.27
5.26
70
.45
0.24
6.04
80
.46
0.21
6.95
90
.48
0.19
7.79
00
.50
0.17
8.82
Wire 2, Set 2:
Length (cm)
Voltage (V)
Current (A)
Resistance (W) (to 2 d.p.)
0
0.92
.05
0.88
20
.16
0.66
.76
30
.28
0.47
2.72
40
.34
0.39
3.44
50
.38
0.32
4.31
60
.42
0.27
5.26
70
.45
0.23
6.30
80
.47
0.21
7.00
90
.47
0.17
8.65
00
.48
0.16
9.25
Averages for each wire were then calculated to give these results, which were then graphed:
Length (cm)
Resistance (W) (to 2 d.p.)
Wire 1
Wire 2
0
0.52
0.89
20
0.96
.77
30
.40
2.70
40
.86
3.55
50
2.29
4.31
60
2.76
5.26
70
3.26
6.17
80
3.67
6.98
90
4.36
8.22
00
4.57
9.04
Conclusions
Having performed the investigation, the following conclusions were drawn:
* As predicted, an increase in length resulted in an increased resistance. This can be clearly said for both wires tested.
* Both wires show a strong trend of a straight line, i.e. the length of the wire is shown to be directly proportional to the resistance - double the length and the resistance doubles.
* The overall resistance of the two wires seems to differ considerably. Due to the strong correlation of the results, the explanation of this is unlikely to be the method used to obtain the results. The more likely explanation would be that the first wire was actually of a larger diameter than the second one. Obviously this is a rather important oversight and this will be discussed more in the Evaluation section. The reason why this is the likely explanation is because resistance is known to be inversely proportional to the cross-sectional area, i.e. if you increase the cross-sectional area (by increasing the diameter) then you decrease the resistance. This is because a wider wire means less likelihood of the free electrons having collisions and losing energy.
It is important to realise, however, that despite the fact that it would appear that the resistance of wire 2 is double that of wire 1, that does not mean that the diameter is half that of the wire 1. That is because if you halve the diameter then you decrease the area by a factor of about 3 (A = ?r2)
Evaluation
* As mentioned previously, the biggest downfall of the investigation was the apparent mistakes when choosing the wire, in that they would appear to be of differing diameters. This did not, in this case, cause a big problem as the same wire was used for each set of results so it is known that the results for each wire are correct.
* Generally speaking, wire 1 would appear to contain the most accurate results due to the fact that all of its points bar one sit on the line of best fit for that wire. The only one that does not is the point at 90cm, which was exactly at the point that the black mark (mentioned previously) was found to be.
* Wire 2, on the other hand, had three main anomalous results: at 50, 80 and 90cm. They are by no means that far off but in an experiment such as this, which is generally a very accurate one anyway, such anomalous results should not be quite so common. Possible explanations for these anomalies are as follows:
* The length of wire for that particular measurement was not correct. At 50 and 80cm it is possible that the length was shorter, causing a lower resistance, and at 90cm it is possible that it was longer, causing a higher resistance. The solution to this is to measure the lengths more carefully and ensure that the wire is pulled tight against the metre rule.
* For a particular result, one or more of the connections could have been faulty, causing extra resistance at the connections. A solution to this would be to, before each experiment, connect the connections together without the wire in place and measure the resistance then. If it is higher than it should be then the connections could be cleaned.
* Whilst extremely unlikely, it is conceivable that the power supply was providing a different voltage for some of the results. This is unlikely to be a problem in this investigation but it might have been an issue had we used batteries instead.
NB: If one were to assume that Ohm's Law applies, then another possible explanation could be that at some points (more likely in the lower lengths), the wire was not allowed to cool completely so that the temperature was higher for that measurement. Whilst unlikely (due to the two sets of results), this would cause a higher resistance as explained previously. However, it is now known, after researching the metal alloy "constantan," that the resistivity (the electrical resistance of a conductor of particular area and length) of this alloy is not affected by temperature. Therefore, in these experiments Ohm's Law does not apply.
FULL MARKS:>>>
Before starting my coursework I have decided to chose a factor that will affect the resistance of a wire.
I shall do this by going through all of the factors that affect the resistance of a wire and how I would
measuring each factor to find out which would be the most effective and easiest factor to measure.
Below is a list of factors and reasons why they affect the resistance of a wire. From this list of factors I
shall only pick one factor to investigate. To explain the how the factors would affect the resistance of a
wire I have drawn a diagram to show how resistance occurs.
WIRE
ATOMS=
ELECTRONS=
Resistance occurs when the electrons travelling along the wire collide with the atoms of the wire.
These collisions slow down the flow of electrons causing resistance. Resistance is a measure of how
hard it is to move the electrons through the wire.
Factors
.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.
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. Due to this increased space between
the atoms there should be less collisions.
To chose which factor I am going to investigate I am going to consider how I would measure each
factor and which factor would be the best and easiest to record.
To measure the wire width I would use different widths of the same length and same material of wire
e.g. thin , medium and thick copper wire with thin and thick constantin wire. To record the difference
in widths I would use the same voltage and measure the resistance for each thickness. Although it
would be easy to obtain and record the data the graphs that I would be able to draw up would not be
interesting.
For the temperature of the wire I would not be able to carry out a fair test because it is extremely
difficult to produce and control the range of temperatures needed without the correct equipment.
If I chose to measure the difference in the resistance in different materials I would chose a number of
different materials and using the same voltage I would record the resistance given by each wire of the
same length and width. Although once again it would be simple to record these results the graphs that
could be drawn would not show any connection between the material and the resistance because of the
limited number of materials I could test with the equipment available.
The final factor is the length of the wire. To measure and record the findings for this factor would be
simple and the results collected could show a connection between the length of the wire and the
resistance given by the wire. This is why I have chosen to investigate this factor.
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 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.
The diagrams below show my prediction and should explain it more clearly:
Because 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.
Preliminary Method
In this preliminary experiment I will select a wire that will be used in my main experiment when
investing the connecting between the length of the wire and the resistance of the wire.
To ensure a fair test whilst carrying out my preliminary experiments I am going to be very careful
when selecting my independent variables which are the width of the wire and the wire material. I am
going to use a constant voltage of 2 volts and a constant length of 50 cm.
Apparatus: Meter ruler ¡V To measure the wire being tested to ensure a fair test.
Selection of wires ¡V Different materials and widths but the same length.
Crocodile clips ¡V To connect the wire being investigated to the rest of the circuit.
Voltmeter & Ammeter ¡V To measure the resistance.
Wires ¡V To connect the above items and to complete the circuit.
To measure the resistance of the wire I am going to use the equation RESISTANCE=VOLTS
CURRENT I will obtain the voltage and current readings from the voltmeter and ammeter.
Below is a circuit diagram for my preliminary experiment.
POWER SUPPLY
2 VOLTS
AMMETER
VOLTMETER
CROCODILE CLIPS
WIRE
METER RULER
To ensure a fair test I shall keep the power supply at 2 volts and I shall keep the length of the wire at 50
cm.
Preliminary Results
Below is a table of results which I have collected from my preliminary experiment.
WIRE VOLTS (v) AMPS (A) RESISTANCE (Ohms)
THICK COPPER 0.3 5.13 0.06
MEDIUM COPPER 0.6 4.20 0.14
THIN COPPER 0.9 3.13 0.29
STEEL 0.7 1.20 0.58
MEDIUM CONSTANTIN 1.0 0.41 2.44
THIN CONSTANTIN 2.7 0.49 5.51
From these results I have chosen to use thin constantin for the wire I am going to use in my main
experiment. I have chosen this wire as it has the highest resistance and so it will be easier to notice any
difference in resistance in my main experiment
Main Method
Before I start my main experiment I have chosen to do a risk assessment which is shown below.
Risk Assessment:
"h I will handle the power supply carefully.
"h I am going to only use a voltage of 2 volts.
"h I will be careful when handling live wires.
Apparatus: Power Supply
Ammeter
Voltmeter
Thin Constantin wire
Meter Ruler
Crocodile Clips
Connecting Wires
I have chosen to use thin constantin wire because from my preliminary results I found that this wire had the highest resistance, because it has the highest resistance it will be easier to measure any change in resistance.
To collect the data for my graph I have chosen to take a range of 5 lengths. I have chosen a range of 5
as to plot an accurate graph I will need at least 5 points to mark on the graph . I have also chosen to
take 3 repeats at each length and then take an average. I have chosen this so that if I have any
anomalous results they will not show when I plot the averages on the graph. The lengths that I have
chosen are as follows : 20cm , 40cm , 60cm , 80cm and 100cm. I have chosen these lengths because
they are easily measured by the meter ruler and give a good range.
Below is a circuit diagram of the circuit I am going to use in my main experiment:
POWER SUPPLY
2 VOLTS
AMMETER
VOLTMETER
CROCODILE CLIPS
WIRE
METER RULER
In my main experiment instead of using an ohmmeter I have chosen to use an ammeter and voltmeter ,
I have done this so that instead of relying on the ohmmeter to give the resistance I will calculate the
resistance of the wire , I shall calculate the resistance of the wire using the equation below.
RESISTANCE = VOLTS
AMPS
I have chosen to use a meter ruler because the lengths that I will be measuring are to big for a smaller
ruler and also the meter ruler can be accurate to +1mm or ¡V1mm.
Results
Below is a results table with the results that I collected from my main experiment.
LENGTH 200 mm 400 mm 600 mm 800 mm 1000 mm
VOLTS (v) 1.6 1.5 1.6 1.7 1.7 1.7 1.8 1.8 1.8 1.9
.8 1.8 1.9 1.9
.9
AMPS (I) 0.608 0.609 0.607 0.351 0.352 0.351 0.237 0.238 0.238 0.184 0.184 0.184 0.148 0.149 0.149
RESISTANCE
(Ohms) 2.6 2.5 2.6 4.8 4.8 4.8 7.6 7.6 7.6 10.3 9.8 9.8 12.8 12.8 12.8
AVERAGE
RESISTANCE
(Ohms)
2.6
4.8
7.6
0.0
2.8
From these results I have drawn a graph of the length of the wire and the resistance of the wire.
Analysis
From the graph on the previous page I can see that the resistance of the wire is proportional to the
length of the wire. I know this because the Line of Best Fit is a straight line showing that if the length of the wire is increased then the resistance of the wire will also increase.
Conclusion
In my prediction I said that :
¡§¡K.if the length increases than the resistance will also increase in proportion to the length.¡¨
From my graph I have shown that my prediction was correct, as the Line of Best Fit is a straight line proving that the resistance of the wire is proportional to the length of the wire.
The length of the wire affects the resistance of the wire because the number of atoms in the wire increases or decreases as the length of the wire increases or decreases in proportion.
The resistance of a wire depends on the number of collisions the electrons have with the atoms of the material , so if there is a larger number of atoms there will be a larger number of collisions which will increase the resistance of the wire. If a length of a wire contains a certain number of atoms when that length is increased the number of atoms will also increase. This is shown in my diagrams below:
Electron
Atom
In this diagram the wire is half the length of the wire below and so has half the number of atoms, this means that the electrons will collide with the atoms half the amount of times.
Also if the length of the wire was trebled or quadrupled then the resistance would also treble or quadruple.
Evaluation
From my results table and graph I can see that my results that I collected are very reliable. I know this because my results table does not show any individual anomalous results this means that I did not have to leave any results out of my averages because they were anomalous. Also on the graph I can see that none of the averages plotted are anomalous because all the averages lie along the same straight line.
During my experiment I have noticed several modifications I could make to improve on the Investigation if I was to repeat it.
The first of these modifications would be the circuit that I would use. To be more accurate with my results I would use the circuit layout below:
POWER SUPPLY
2 VOLTS
AMMETER
VOLTMETER
WIRE
METRE RULER
Instead of connecting the voltmeter to the main circuit I would connect it to the wire which is being tested. I would do this so that the voltmeter is measuring the voltage of just the wire being tested and not the wires of the main circuit as well.
To also improve on my results I would use a digital voltmeter instead of an analogue meter. I would do this because a digital voltmeter is a lot more accurate than an analogue because if the needle in the analogue voltmeter is bent then the readings given off will be false whereas a digital voltmeter does not rely on a needle or any other manual movements.
The next modification I would make would be to use pointers instead of crocodile clips , I would do this because pointers would be more accurate. The pointers would be more accurate because the tips have a much smaller area than the crocodile clips giving a more accurate measurement of the length of wire.
As well as making these modifications I would also improve my Investigation by testing the same wire but different widths of that wire. I would do this to expand on my Investigation.