`Resistance of a wire -Electricity Coursework
`Resistance of a wire -Electricity Coursework
Aim:
To see how the length of a wire affects its resistance.
To find the wire to test, I'm going to test 4 different types of wire in another experiment and use the one with the highest resistance.
The Theory behind the Experiment
Theoretically the length of a wire should affect its resistance.
Electricity encounters a certain amount of obstruction when passing through a wire depending on its length, width, temperature and type of metal, this obstruction is called the resistance and is measured in ohms.
The longer and thinner the wire the harder it is for the electrons to flow through, because there are less spaces for it to flow through and more obstructions along the length. It has a similar principal to the flow of water and how it is impeded when passing through a long and narrow pipe. Therefore the longer the wire is the more resistance there should be.
The other factor that can affect the resistance is the metal type, for example the resistance of an Iron wire is about seven times greater than that of a copper wire with the same dimensions, and this is because of the varied amount of ions in the different metal, more ions in Iron mean that electrons find it harder to pass through. This is the reason why copper is used in electrical wire; because it gives little resistance less energy is used to make it flow. I need to test 4 different wires in the first experiment; to find the type of wire with most resistance. It is important that for both experiments I let the wire cool down for a few seconds after taking the reading, as temperature can affect the resistance. This is because the molecules in the wire when heated vibrate more and the electrons find it harder to pass through, thus the resistance will increase.
When connecting the circuits for both experiments I need to make sure the voltmeter is in parallel with the wire and the ammeter is in series. This is shown in a diagram of apparatus later on.
George Simon Ohm (1789-1854) was one of the first people to investigate current and voltage and came up with the following law for metallic conductors.
The current through a conductor is proportional to the potential difference between its ends, provided that physical conditions, such as temperature, remain constant: i.e.
V/I = constant (resistance).
Where v = voltage and I = current.
This means regardless of the size of the current, as long as there is no temperature change the resistance of a wire remains constant. The law is based on experiment (empirical) and holds remarkable accuracy for metallic conductors which are what I'm going to use in my experiment.
It is important to note that the circuits I will be using for my experiments are in series because in parallel and series circuits the methods for calculating the total resistance for more than one component are different. In series the resistance across the components are added together: R = R1+R2. Whereas in Parallel the current divides, the larger part going through the smaller resistance and the smaller part through the larger resistance: 1/R=1/R1 + 1/R2. So the resistance is smaller because it is like a single wire with a large cross section and therefore more spaces in the atoms for the electrons to pass through.
I'm going to prove that resistance is proportional to length. The greater the cross sectional area of the conductor the more electrons available to carry the charge along the conductor's length and so the lower the resistance is. Resistance is inversely proportional to cross sectional area.
Key Variables:
Key Variables
Explanation
Temperature of wire
If the wire is hotter the atoms will be vibrating more, making it harder for the electrons to pass through and increase the resistance.
Thickness of wire
The fatter the wire the easier it is for the electrons to flow through as there is more spaces between the atoms or molecules.
Length of wire
The longer the wire the more difficult it is for electrons to flow through and producing a higher resistance
Type of wire
In different conductors the ease of flow of electrons is different and so conductors have different resistances.
Wires connected to the battery pack
Different wires can produce slightly different resistances and therefore they must me kept the same throughout both experiments.
Experiment
Independent Variable
Controlled Variables
Dependant variable
Type Of Wire:
Constantan, copper, Nichrome and Manganin
Length, Thickness, Temp, Voltage, Wires connected to battery pack
We will find the voltage and current and use this information to find the wire with most ...
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Type of wire
In different conductors the ease of flow of electrons is different and so conductors have different resistances.
Wires connected to the battery pack
Different wires can produce slightly different resistances and therefore they must me kept the same throughout both experiments.
Experiment
Independent Variable
Controlled Variables
Dependant variable
Type Of Wire:
Constantan, copper, Nichrome and Manganin
Length, Thickness, Temp, Voltage, Wires connected to battery pack
We will find the voltage and current and use this information to find the wire with most resistance out of the four.
2
Length Of Wire
Type of wire, temp, thickness, voltage, wires connected to battery pack.
We will find the voltage and current but his time workout the resistance and see if there is a relationship between the length and resistance.
Outline Plan
st experiment
* We have four different types of wire attached to two metre rules they are: Manganin, Nichrome, Copper and Constantan.
* We will measure the current and voltage for each wire separately, one after the other.
* To make it a fair test we will make sure there are no changes in the temperature, thickness, or length that would affect our experiment for reasons explained earlier in "The theory behind the experiment". The voltage will also be kept at 2v for each test to prevent over heating of the wires and subsequent inaccurate results.
* To measure the independent variable accurately we're going use specific apparatus: a metre rule with the different wires attached either end (to measure the voltage and current we're using a standard ammeter and voltmeter).We will also be carrying out the test for each wire 3 times, which will make our results more reliable and accurate when making an average. The wood will not conduct electricity to avoid interference in the results, making it a suitable material to base the wire on.
* The reason we will be using the wire with the most resistance is because it less likely to overheat because it will not let the electrons through as quickly. If the wire overheats, not only will it affect the results of the experiment (ohms law only works at a constant temperature), it would also be a safety hazard as touching it could burn you.
* For both experiments we will be using crocodile clips, for the first experiment this is because they can be attached to the wire easily, safely and without the risk of them falling off.
2nd experiment
* We're going to take the wire with the most resistance from the first experiment a measure its current and voltage at different lengths. We will do this by recording the amps and volts using an ammeter and voltmeter at 10cm intervals for 100cm (10 recordings). This is why we use the metre rule, because it has the measurements on it already.
* After recording every result I will let the wire cool before taking the next reading at the next interval by switching the battery pack off for approximately 30 seconds, this is to prevent a raise temperature from affecting our experiment making it an unfair test.
* We will measure the dependent variable more accurately with more reliable results by repeating the test 3 times and making an average for each length using the 3 results.
* The specific apparatus I'm going to use is a metre rule with the wire attached for the same reasons as in the 1st experiment.
* To make it a fair test the thickness, temperature and type of wire will be kept the same and voltage will be kept at setting 2 as in the 1st experiment.
* The main reason for using crocodile clips in this experiment is because (as well as the reasons mentioned in the 1st experiment) they can slide easily up and down the wire, making It easy to record the results at different lengths.
Safety
Using a low voltage setting (2v) will ensure maximum safety, by preventing over heating of the wire and possible burns on the skin and/or sparks.
Prediction
I predict that the longer the wire the higher the resistance will be, because the electrons will encounter more obstruction when flowing through, the atoms of the wire will be like a blockade and the longer the blockade the harder it will be for the electrons to squeeze through the gaps.
Apparatus
* Crocodile Clips; to attach the wires to the metal being tested.
* Battery Pack; to supply the power for the circuit (voltage setting 2).
* 5 Wires; to allow the electrons to flow in a complete circuit.
* Ammeter; to measure the amps.
* Voltmeter; to measure the volts.
* Meter Rule with different wires; depending on which experiment.
st experiment
Method:
. Firstly assemble the circuit as shown in the diagram of apparatus using one type of wire at a time (you can start with any wire). The length of each wire however must be kept at 30cm.
2. When the circuit is complete turn on the battery pack to voltage setting 2.
3. Let it run for about 5 seconds while the readings fluctuate then record the amps and volts.
4. Turn off the battery pack for about 30 seconds switch it back on a record the results again.
5. Then once more turn off the battery pack let it cool and switch back on and record the results. You should now have three very similar results for one wire.
6. Repeat numbers 2 - 6 for all four wires.
7. Using the three results for each test make an average current and voltage for each wire.
8. With these results you can work out the resistance by using the following equation:
V/I = R
Where current is I, voltage is V and resistance is R.
The wire with the most resistance will be used in the following experiment.
2nd experiment
Method:
. I will Begin the experiment with a similar set up to the 1st experiment, only the wire I'm going to test does not change.
2. Record the voltage and current for the first length (10cm), after recording the results switch off the battery pack, let it cool for about 30 seconds.
3. Whilst the battery pack is cooling move the crocodile clip along the length of the wire to the second interval (20cm).
4. Carry on moving the crocodile clips along the length, letting the battery pack cool and recording the volts and amps until you have the readings for all 10 intervals (100cm).
5. Repeat this test a further 3 times, and make an average of all three measurements for each length.
6. Using the averages for the amps and volts work out the resistance of the wire at each length (the formula is shown above).
7. Use this information to plot a graph, length against resistance and evaluate.
For all the results the decimals are rounded to two decimal places.
For the first experiment, my results were as follows:
Metal
Test 1
Test 2
Test 3
Average= (T1+T2+T3)/3
Volts
Amps
volts
Amps
Volts
Amps
Volts
Amps
Copper
0.17
3.52
0.18
3.52
0.18
3.3
0.176
3.3
Manganin
0.91
.50
0.88
.59
0.88
.62
0.89
.62
Nichrome
.18
0.8
.19
0.84
.18
0.84
.183
0.84
Constantan
0.93
.46
0.93
.46
0.96
.53
0.94
.53
There is hardly any variation in the results for each test.
This is a chart to show the most resistant wire:
Metal
Workings
Resistance (ohms)
Copper
0.176/3.3
0.05 ?
Manganin
0.89/1.62
0.57 ?
Constantan
0.94/1.53
0.63 ?
Nichrome
.183/0.84
.43 ?
ST Experiment
Results
We can clearly see which metals have the highest resistance and which have the lowest, in order from highest to lowest they are: Nichrome, Constantan, Manganin and Copper, because it has such a low resistance copper makes a great wire for electricity to pass through to components around the house because a low voltage can provide such a large current.
The electrons are freed from the battey that is slowly deteriorating letting more and more electrons free, they move from negative to positive - the opposite direction to conventional current (the direction people thought electricity would flow).
The highlighted metal, (constantan) is the metal I'm going to use in the second experiment. Ideally I would use Nichrome but there is a shortage of supplies so we couldn't obtain a length of Nichrome wire so Constantan is the second best as it has the second highest resistance.
Method
The testing for this experiment was sound; no faults were recorded because we had 3 sets of results making the results very accurate when getting an average the results for each test were also very similar anyway.
Improvements
Although the averages were correct, I feel that in some parts of the tests we did not leave the wire to cool for long enough and so the resistance was amplified, next time I do the experiment I will leave the wire to cool for exactly 30 seconds and set a stop watch to records this. Another way of preventing the wire from overheating is by attaching a light bulb to the circuit to absorb the heat. I will also make sure that I record the results immediately otherwise the wire will again overheat and the results will be distorted.
The results for the second experiment are as follows:
Length in cm
Test 1
Test 2
Test 3
Amps
Voltage
Amps
Voltage
Amps
Voltage
0
3.82
0.53
3.75
0.45
3.79
0.44
20
2.76
0.6
2.82
0.67
2.87
0.68
30
2.37
0.73
2.3
0.82
2.3
0.84
40
2.58
0.67
.93
0.92
.97
0.92
50
.88
0.84
.68
0.99
.69
.01
60
2.8
0.79
.47
.06
.49
.06
70
.67
0.9
.3
.1
.32
.1
80
.76
0.8
.19
.14
.19
.14
90
.54
0.92
.09
.17
.1
.18
00
0.97
.14
.01
.19
.02
.2
The circled results are very inaccurate.
Length in cm
Average
(T1 +T2 + T3)/3
Workings
Resistance (?)
Amps
Volts
0
3.79
0.47
0.47/3.79
0.12
20
2.82
0.65
0.65/2.82
0.23
30
2.32
0.8
0.8/2.32
0.34
40
2.16
0.84
0.84/2.16
0.39
50
.75
0.95
0.95/1.75
0.54
60
.92
0.97
0.97/1.92
0.51
70
.43
.03
.03/1.43
0.72
80
.38
.03
.03/1.38
0.75
90
.24
.09
.09/1.24
0.88
00
.12
.18
.18/1.12
.05
From these results I can already see without drawing a graph that as I predicted, when the length increased so did the resistance. Now I will draw a graph to represent my results.
Line of Best Fit
Conclusion
From this graph you can see my prediction is proved correct, for the line of best fit shows as length increases the resistance increases.
As I explained before this relates to the theory; the longer wire the more obstruction the electrons have to push through and consequently the resistance increases.
Using my graph I can see a quantitative relationship in my results; as the length increases by 50cm the resistance increases by about 0.5 Ohms, you could say the resistance = 100 times smaller than the length in cm.
However this graph is not entirely accurate, as you may have noticed the results towards the end are a bit distorted, I believe this is because test 1 was done inaccurately with a different set of wires from a previous lesson. I'm going to produce a graph with an average of the results from just test 1 and 2 and see if the results correlate more clearly.
Test 2
Test 3
Amps
Voltage
Amps
Voltage
3.75
0.45
3.79
0.44
2.82
0.67
2.87
0.68
2.3
0.82
2.3
0.84
.93
0.92
.97
0.92
.68
0.99
.69
.01
.47
.06
.49
.06
.3
.1
.32
.1
.19
.14
.19
.14
.09
.17
.1
.18
.01
.19
.02
.2
Length in cm
Average
(T2 + T3)/2
Workings
Resistance (?)
Amps
Volts
0
3.77
0.45
0.45/3.77
0.12
20
2.85
0.68
0.68/2.85
0.24
30
2.3
0.83
0.83/2.3
0.36
40
.95
0.92
0.92/1.95
0.47
50
.69
.0
.0/1.69
0.59
60
.48
.06
.06/1.48
0.72
70
.31
.1
.1/1.31
0.84
80
.19
.14
.19/1.14
.04
90
.1
.18
.18/1.1
.07
00
.02
.2
.2/1.02
.18
Conclusion
From this graph you can see the results are far more accurate with only one slight anomaly which could just be distorted by temperature or it could have been inaccurately read. Now I have an accurate result I can prove that the resistance is proportional to the length because as you can see at 20cm the resistance is just above 0.2 ohms, if it is proportional at a length of 40cm (doubled) the resistance should also be doubled and sure enough the resistance is just above 0.4ohms, therefore my prediction of proportion is correct.
Evaluation
Results
In my view my results are accurate enough to support the conclusion that as length increases resistance also increases, however the results are not entirely accurate, as two do not correlate with the rest of the results at all. I think I can safely say that despite the results that do not correlate there is a quantative relationship between the length of the wire and the resistance; from the graph I found that the resistance is approximately 100 times smaller than the length in cm. The reason for this is because the difficulty for the electrons to squeeze through the atoms had increased when the length increased and so as the length increased by 50cm the resistance increased by 0.5ohms.
The results were as I predicted and therefore the theory behind the experiment applies, because the theory is what I based my prediction on.
I can say that the resistance is proportional to the length of the wire in one width (the width I am using for my experiment) in cm; R L, when R= 0.5, L = 50 therefore K (the constant) = R/L, 0.01.
So to find the resistance of any length of wire at the width I used in my experiment you use the formula R=0.01L.
Method
I believe my method for finding the first set of results in test 1 was sound, however, I did not check for any faults in the circuit and found in the following test the next lesson that when I checked the circuit the two crocodile clips were touching both wires on the rule, (there are two parallel wires on each rule). It could be possible that this was the case for the previous lesson and by not checking I recorded some anomalous results, circled in my graph. Other wise the testing was fairly accurate and good results were recorded quickly and efficiently by sliding the crocodile clips up the wire and stopping after 10cm recording the results and turning off the battery pack to let the wire cool and make sure temperature (one of our controlled variables) is controlled.
Improvements
If I was to do the experiment again I would check the circuit carefully before every test to make sure there are no faults, this would prevent anomalous results like the ones I had in my experiment.
I could extend my experiment by using different types of wire and see whether the same length and resistance rule applies for them, although the rule would probably not work as well for a wire with more resistance because a higher temperature increases the resistance itself and distorts the readings. If I had access to Nichrome I would use it to test the rule because it has a very high resistance and therefore would be unlikely to get inaccurate readings as a result of overheating. Testing different types of wire of higher resistance would give me more reliable information to support my rule; Ohms law.
Overheating causes the atoms to vibrate more in the wire making more of an obstruction for the electrons to flow through.
If I were to do the experiment again I might try putting 2 wires of the same type in parallel with each other record the resistance of both and see if the length of each wires correlates with the resistance of each wire in the same way as in a series. They should correlate because in the theory I explained how the current divides in a parallel so the resistance will probably be greater per cm of wire because resistance = voltage/ current and if the current is smaller resistance will be greater.
Even though the second graph proves my prediction with more accuracy, the first graph still shows some correlation to also prove my prediction. For in the first graph the results still show vaguely that resistance is proportional to length: at 10 cm resistance 0.1ohms and at double the length (20cm) the resistance is also doubled (o.2 ohms). The only problem with the first graph is that a lot of the results do not show this trend.
