Investigating how the length of wire affects the resistance
Investigating how the length of wire affects the resistance.
Aim: To investigate the affects of the length in the resistance of a wire.
Hypothesis: I predict that when the length of a wire is increased, its resistance will also increase. I also think that the rate at which the resistance increases will be constant and directly proportional to the length.
Apparatus: Voltmeter;
Ammeter;
Connecting wires; Power pack; Constantan wires-SWG value of 30; Ruler; Variable resistor;
Crocodile Clips.
References to support the hypothesis:
"...However, the electron does not accelerate for ever. Eventually, it crashes into one of the atoms in the wire. Since atoms are far more massive than electrons, the electron loses all forward momentum every time it hits an atom (just as we would lose all forward momentum if we ran into a brick wall).. Immediately after the electron hits an atom its forward velocity is zero. The electron is then accelerated by [the battery]..." from the website: http://farside.ph.utexas.edu/~rfitzp/teaching/302l/lectures/node42.html
We can conclude from this that the longer the piece of wire is, the more chance there is of the electron colliding with other atoms. The more collisions that happen, the more resistive the piece of wire is. This text quoted from the science journal confirms this.
"Resistance is caused by electrons bumping into ions. If the length of the wire is doubled, the electrons bump into twice as many ions so there will be twice as much resistance. So
If the cross-sectional area of the wire doubles there will be twice as many ions and twice as many electrons bumping into them, but also twice as many electrons getting through twice as many gaps. If there are twice as many electrons getting through, as there is twice the current, the resistance must have halved. This means that " from the website: http://www.sci-journal.org/vol1no1/v1n1k42.htm
Scientific Knowledge: The Scientific reason why more wire means more resistance can be complicated. Basically, knowledge about structure of atoms is needed to fully explain this. Resistance of wire based on its cross sectional area will be hypothesised and scientifically proven with theory first to help clarify why increasing the length of wire also increases its resistance.
An Atom is made up of a comparatively large nucleus surrounded by shells of electrons. In a metal, these electrons are free to move around. A battery or power supply provides EMF or Electromotive Force. This repels the negatively charged electrons away from the negative terminal and towards the positive. The positively charged nucleuses stay where they are; however, they are still being attracted to the negative terminal.
The electrons have to pass through the gaps in the stationary nucleuses in order to get to the positive terminal and enable electricity to flow. In doing so, they sometimes collide with the nuclei on the way. This slows down their overall speed. In a given time, it cannot go as far. It also impedes the flow of other electrons. This is called resistance. Less electrons (and thus current) can pass through the wire. The electron that has hit the nucleus is holding up other electrons as well as blocking a passage, which electrons can take to get to the positive terminal. This means that fewer electrons can flow through the material.
It can be concluded that thinner wire has less spaces, as there are less nuclei. This greatly increases the probability of a collision (or resistance) because there are fewer spaces to go through. The more spaces a wire has (i.e. the thicker it is) the more gaps there are available and the greater number of electrons that can flow with fewer collisions (it will have less resistance). Basically, thinner wires will have larger resistance than thicker wires, which will allow larger current flows.
When an electron collides with a nucleus (as stated in the first quote) it will lose all kinetic energy only to be speeded up by the power pack. This has a negative implication. When an electron hits a nucleus, its kinetic energy is transferred into heat energy. This is witnessed as the wire heating up when it is too thin or when there are too many collisions. When the thickness is increased, this heating effect is lessened greatly. This is because the number of collisions is reduced greatly.
The reason why the heating effect can be increased dramatically with only a small decrease in diameter is because although
(Ecq1) Resistance = k ____1_____ , (Ecq2) Resistance = k ______1_____
Cross-sectional area , diameter2
This means that resistance is inversely proportional to cross sectional area squared. When the cross sectional area is decreased, the resistance increases in squares. This is because when the diameter of a wire is increased by 2, the surface area is increased by 4, or 22. This means if a 4 mm wire has a resistance of 8 ohms; a ...
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The reason why the heating effect can be increased dramatically with only a small decrease in diameter is because although
(Ecq1) Resistance = k ____1_____ , (Ecq2) Resistance = k ______1_____
Cross-sectional area , diameter2
This means that resistance is inversely proportional to cross sectional area squared. When the cross sectional area is decreased, the resistance increases in squares. This is because when the diameter of a wire is increased by 2, the surface area is increased by 4, or 22. This means if a 4 mm wire has a resistance of 8 ohms; a 2 mm wire has a resistance of 32 ohms. Wire diameter is thus very important as it can have varying levels of resistances depending on its width and also regulate the amount of current that can pass through it.
In a similar way, resistance is affected by length of wire. In a longer length of wire, there are more chances for the electron to bump into a nucleus. If a wire of 4 cm has a resistance of 4 ohm, then in an 8 cm wire, it would be expected to have a resistance of 8 ohms. This is because if the length is doubled, there are twice as many chances for the electrons to bump into a nucleus. Because the resistance is how the material resists the flow of electrons, a twofold increase in length would mean two times as many nuclei to bump into which would also increase the resistance by two also. All of these factors give rise to the formula:
(Ecq3)
Resistance of conductor (R) = Resistivity of Material in Ohm-meters × length (m)
Cross Sectional Area in (m2)
The fact that the diameter is squared to give the cross sectional area confirms that equation (ecq) 2 is correct and that the cross sectional area and/or area squared is directly proportional to resistance.
Equation 3 will be tested using test values to confirm my hypothesis.
Test values: Resistivity of wire = Resistivity of constantan = 2.8
Diameter = 0.05m = 5 cm
Length of the wire doubled.
__2.8_×_4m____ = 224 ohms __2.8_×_8m____ = 448 ohms
0.05 0.05
This confirms that my hypothesis is correct as the equation confirms that doubling the length doubles the resistance when all other factors are kept the same.
The same equation can be used to check whether doubling the cross sectional area halves the resistance
___2.8_×_4m___ ___2.8_×_4m____
0.05 = 224 ohms 0.10 = 112 ohms
This confirms that when you double the cross-sectional area, the resistance halves. This is important in proving my hypothesis correct because if we know and can prove that changing certain values can change the way wire behaves, then we know that keeping it constant will decrease the amount of anomalous results and help prove my hypothesis correct.
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 too 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.
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.
Constant Variables: The current flowing through the entire circuit; The material that the wire is made off; The Cross-sectional area or diameter of the wire;
Preferably the equipment used including all the wires.
Independent Variable: Length of wire.
Circuit Diagram:
Method: 1. Set up circuit as shown in the circuit diagram.
2. Place one crocodile clip at 0 and the other at 50cm.
3. Switch on the power pack and adjust the power supply to get 0.61 amps using the variable resistor.
4. Take the reading at the ammeter and voltmeter and calculate the resistance.
5. Keep on taking the ammeter and voltmeter reading every 5cm until you have reached 5cm.
6. Record the results each time in a table, shown below
7. Repeat the experiment three times.
8. Work out the resistance for all the lengths, using R=V/I.
9. Plot a graph.
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.
I plan to record my results like this:
Length
(cm)
Voltage (Volts)
Current (amps)
Resistance (ohms)
st test
2nd test
3rd test
st test
2nd test
3rd test
st test
2nd test
3rd test
Average
50
45
40
35
30
25
20
5
0
5
I plan to take my results three times to be as accurate as possible. Any anomalous results will be redone. It will start from the highest length to the lowest. The intervals will be done systematically.
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 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 the factors will cancel each other out and/or greatly change the results if they are both varied at the same time.
Preliminary Test: A preliminary experiment is being conducted, in order to determine whether the range of results is large enough to be able to analyse the results conclusively and to test the method to see if it works properly and efficiently, and if not make any necessary amendments.
(cm)
Voltage (volts)
Current (amps)
Resistance (ohms)
50
.97
0.61
3.23
45
.80
0.62
2.90
40
.65
0.63
2.62
35
.45
0.64
2.27
30
.26
0.65
.94
25
.09
0.66
.65
20
0.86
0.67
.28
5
0.68
0.68
.00
0
0.48
0.69
0.70
5
0.23
0.71
0.32
From the results of the preliminary experiment, I conclude that the range of results that I am using for my final experiment will give me good spread of data. I think that these results are very good and they are what I had expected. I will not change my method because my current one gives me accurate and reliable results.
Results:
Length
(cm)
Voltage (Volts)
Current (amps)
Resistance (ohms)
st test
2nd test
3rd test
st test
2nd test
3rd test
st test
2nd test
3rd test
Average
50
2.00
.98
.96
0.61
0.61
0.61
3.27
3.25
3.21
3.24
45
.79
.81
.82
0.61
0.62
0.62
2.93
2.92
2.94
2.93
40
.67
.63
.65
0.62
0.63
0.63
2.69
2.59
2.61
2.63
35
.45
.45
.46
0.64
0.64
0.63
2.27
2.27
2.32
2.29
30
.26
.25
.27
0.64
0.65
0.65
.97
.92
.95
.95
25
.11
.05
.07
0.65
0.66
0.66
.71
.59
.62
.64
20
0.88
0.83
0.85
0.67
0.68
0.67
.31
.22
.27
.27
5
0.71
0.64
0.69
0.68
0.69
0.68
.04
0.93
.01
0.99
0
0.47
0.49
0.48
0.70
0.70
0.69
0.67
0.70
0.70
0.69
5
0.22
0.22
0.26
0.69
0.71
0.70
0.36
0.35
0.43
0.38
Average Resistance = Resistance 1+ Resistance 2 + Resistance3
3
Conclusion: My hypothesis was correct, it 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. My graph also shows that my prediction was correct; as the line of best fit is a straight line through about zero verifying that the resistance of the wire is proportional to the length of the wire. This means:
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.
The line of best fit did not go quite go through the origin because the connecting wires, and the crocodile clips provided their own resistance. So this would have clearly affected the results
The pattern on the graph is of a positive correlation. This is because the resistance rises with the length of the wire. So as the length goes up so does the resistance.
Evaluation: I came to the conclusion after carrying out the experiment, recording the results in table and then drawing graphs, that resistance I directly proportional to the length of the wire meaning that an increase in length would consequently lead to an increase in resistance. As most of the points on my graph lie on the line of best fit, my experiment was accurate enough to prove the prediction I had made earlier in the planning section. Despite this level of accuracy, my experiment could have been more accurate.
I think my results are quite reliable because they agree with my prediction, which is a well-known scientific fact: 'if the length increases then the resistance will also increase directly proportional to the length'. This is shown in the results graph as a diagonal straight line.
From my graph and my results table, I can see that the readings were quite reliable. I know this because the points plotted were very close to the line of best fit, implying that there were no anomalous results. The graph had a strong positive correlation and the best-fit line went very near the origin, which I was pleased about.
I think the method was a well structured because I tried to avoid other affects of resistance so it wouldn't affect the results. However the results could have been even more accurate if we used a timer to time the pauses between collecting each reading. The timing would be the same. Therefore the temperature that has affected the readings will be the same, making it as fair as possible.
The recordings of the experiment were taken 3 times to be as accurate as possible and then averaged to 2 significant figures. To make the results even more accurate I could have left the results as they where and plotted them with 3 digits.
The procedure of the experiment could have been much better and would have explained some of the results being slightly off the line of best fit. This can be explained as follows:
The crocodile clips may not have been placed on the exact point for the length required. The length could have been greater or less than the required length, giving a higher or lower resistance.
The ammeter and the voltmeter were probably not placed exactly at the zero mark prior to the experiment.
The resistance would have been caused to be greater due to small kinks in the wire which I did not notice.
During the experiment, temperature of the surroundings could not be kept constant, this factor affects the results greatly, as the temperature increases the metal ions vibrate more leading to more frequent collisions with the electrons and therefore provide greater resistance to the flow of electrons. Also, if time was available, I should have allowed the wire more time to cool down between readings and to return to its original temperature (I gave the wire approximately only 30 seconds to cool between each reading).
Although the experiment I conducted was efficient to a certain degree but if I were to repeat it; I would make the following changes:
To improve the accuracy I would use pointers rather than crocodile clips. This is because they are pointed at the ends to a particular spot, meaning that a reading for a particular length would be more accurate.
To see if the graph would still produce a straight line, I would use a longer length of wire (i.e. a wider range) such as 0-200cm.
To make sure that the wire has returned to its original temperature, I would leave a five minute gap between each two readings.
In order to control the temperature of the surroundings and keep it at a constant level and if I was able to I would conduct the experiment in a thermostatically controlled room.
My results would have been much more accurate if I had taken these factors into consideration, they would also be better if I make the appropriate improvements.
Further investigation: To extend the work that I have done, I would like to investigate the effect of varying the cross-sectional area of a wire on resistance. I can do this by using wires of different diameters but of the same material. My original method (with the improvements above) would remain the same but without changing the length.
The greater the cross-sectional area of the conductor, the more electrons available to carry the charge along the conductor's length and due to more free space the collisions will be reduced and so the resistance is lower. I predict that the cross-sectional area would be inversely proportional to the resistance, so if I double the cross-sectional area the resistance would half. I predict that the graph of cross sectional area against resistance would be like the sketch below:
Resistance (?)
Cross-sectional area (mm2)
Randip Lochab 10L
