The affect the length of a wire may have on the resistance.
The affect the length of a wire may have on the resistance.
Aim:
The aim of this investigation is to discover how the different lengths of wires affect the amount of resistance.
Prediction:
Metals are good conductors of electricity as electrons are able to move about within them. My research has shown me that this is because the outer electrons of the atoms within the metal are 'de-localized', meaning that they are able to 'swap around' with each other. If electrons are pushed into one end of a piece of wire, they will displace some of the electrons already present in the wire, with the effect that some of them will be forced out of the other end of the wire. However, while the electrons are moving down the wire, they are constantly colliding and interacting with each other. With every one of these collisions, just like a ball bouncing off a wall, as the electron loses a small amount of its energy, which is given off as heat. This effect is called resistance.
If you add potential difference to a circuit, the electrons receive and gain energy. With this energy they move through the wires from positive to negative. The conductivity of the metal has no effect on the overall resistance. The reason for this is that there are always going to be atoms in the path of the electrons, resulting in the current being slowed down. Judging by this theory I believe that if you increase the length of a wire, the resistance will also increase. The relationship between the length of a wire and the resistance is directly proportional.
The following is an equation that can be used to find the resistance using the current and voltage: -
Resistance (R) = Voltage (V)
Current (I)
Resistance is defined as the difference in the amount of volts across the object when there is a flow of current of 1 amp.
The material the object is made of will also have an affect on its resistance. Not every metal is good at conducting electricity. The longer the length of the wire the more resistance it will have. This is because it will become even more difficult for current to flow, as the wire is longer and more resistance is in the path of the electrons.
Temperature is another factor that will have an effect on the resistance. If the metal is warm it will have a much larger resistance compared to one which is not warm.
When temperature rises, the lattice arrangement of atoms vibrate in their own equilibrium more energetically obstructing the flow of electric charge due to more and more collisions.
The main formula that describes the resistance behavior of a piece of uniform metal wire is 'Resistance in ohms = (resistively in ohmmeters x length in meters) / Area of cross-section in square- meters.
Prediction:
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Temperature is another factor that will have an effect on the resistance. If the metal is warm it will have a much larger resistance compared to one which is not warm.
When temperature rises, the lattice arrangement of atoms vibrate in their own equilibrium more energetically obstructing the flow of electric charge due to more and more collisions.
The main formula that describes the resistance behavior of a piece of uniform metal wire is 'Resistance in ohms = (resistively in ohmmeters x length in meters) / Area of cross-section in square- meters.
Prediction:
If you add potential difference to a circuit, the electrons receive and gain energy. With this energy they move through the wires from positive to negative. The conductivity of the metal has no effect on the overall resistance. The reason for this is that there are always going to be atoms in the path of the electrons, resulting in the current being slowed down. Judging by this theory I believe that if you increase the length of a wire, the resistance will also increase. The relationship between the length of a wire and the resistance is directly proportional. So basically if you double the length of a wire you double the resistance. As there will be more atoms for the electrons to get by. Hence the resistance gets doubled as well when the wire does. This is also the case if the wire is tripled and so on.
Equipment:
* 5 pieces of wire
* 1 power pack
* 2 crocodile clips
* A heat proof mat
* An ammeter
* A voltmeter
* 4 nickel-chrome wires. Lengths - 1,2,4,6,8,10,12,14,16,24. These measurements need to be in cm.
The apparatus was set up as shown in the diagram: -
Equipment:
> Gather all the equipment and set it up as shown in the diagram on the previous page.
> The voltage must be kept to 2 volts on the power pack.
> Ensure that direct current (D.C.).
> Place the resistor on the heatproof mat. This is important to do, as they can become very hot.
> Construct a suitable table to record your results.
> The resistance can be worked out by 'R = V/I.'
> In the diagram the nickel-chrome wire will represent the resistor.
> Ensure that the nickel wire is placed in the exact same place as the resistor in the diagram. The resistance may increase due to the wires becoming very hot. For that reason it is important that the circuit is switched on for the minimum amount of time possible.
> To make sure that the best results are obtained; I will record the current and voltage taken from the voltmeter and not any readings from the power pack. As these will be more accurate.
I think that this method is appropriate conducting this experiment. It will enable me to obtain accurate results. The reason I believe this is that all the variables are kept at a constant level, except for the length of the wires.
Fair Test:
In order this experiment to be conducted in a fair and accurate manner: the following things need to be taken into account: -
* Identical sets of equipment should be used wherever possible. E.g. crocodile clips and wires. This is required as these factors can have an effect on the resistance.
* Only one variable should be changed.
* Use a 300-mm ruler each time. Making sure that the length of the wire is cut to the nearest millimeter.
* The same material of wire will be used throughout the experiment. This is nickel-chrome.
* Make sure there is no magnetic fields surrounding the equipment. This can have an effect on the resistance.
Results:
Length of the wire
(cm)
Resistance
(?)
Current
(C)
Voltage
(V)
0.15
4.90
0.73
2
0.25
2.90
0.97
4
0.43
2.95
.28
6
0.65
2.26
.47
8
0.85
.90
.61
0
.08
.55
.67
2
.31
.33
.74
4
.51
.18
.78
6
.66
.09
.81
24
2.54
0.75
.92
Conclusion:
I can see a trend in the results that I have obtained. This trend is that as the length of the wire increases, the resistance along with the voltage also increases. However the current decreases. Also if you look at the graph on the previous page you can clearly notice an almost perfect straight line emerging, through the origin. Thus it is fair to say that as the length of the wire increases so does the resistance. For that reason the length of a wire and the resistance are directly proportional. We can be sure of this by looking at the result table. Below is a section taken from the result table: -
2
0.25
4
0.43
From this we can see that the relationship between the length of a wire is directly proportional to the amount of resistance. E.g. the length was 2 cm and the resistance was 0.25 and when you double the length of the wire to 4 cm the resistance is also doubled from 0.25 to 0.43. This is also the case when the length is tripled.
The results I obtained were not entirely how I expected them to be. The reason for this is that values of resistance are not exactly double to their previous figure. This is due to the inaccuracy readings taken from the voltmeter and ammeter. Luckily the readings which I did obtain displayed a clear trend indicating that the length of a wire is directly proportional to the resistance.
It is fair to say that a current is able to flow through a wire, however it is faced with some degree of resistance. The exact amount of resistance it faces depends on the length of wire. So if you double the length of the wire, you are doubling the number of atoms the electrons have to get through, which results in the resistance being doubled too.
This conclusion and the results match my prediction entirely. That is because I got the results that I had expected to get. The results also back up my theory that the length of wire is directly proportional to the amount of resistance.
Evaluation:
There was a problem I was having with some of the readings taken from the voltmeter and ammeter. The nature of the problem was that the readings displayed where constantly changing little by little. At first this led me to believe I would obtain anomalous results. But this wasn't the case, as the measurements that were moving were not enough to give totally inaccurate results, as I later found out. They did not have an affect on the true readings. The results that I obtained were quite precise. The wires were becoming very hot, as well, I believe this had an affect on the overall resistance. This was also not an entirely fair test, as we did not have the appropriate equipment to cut the nickel-chrome wire. Instead we were resorted to using wire cutters, which were not accurate. The results obtained where rounded up to 2 decimal places. For this reason some of the results may have been anomalous. My results were reasonably accurate. My calculations were fairly accurate too.
So that I could gather more accurate results if I were to do this experiment again; I would take down some more readings. This would limit the possibility of obtaining abnormal results. Using smaller measurements of potential difference would mean the temperature of the wire would also be much lower. Ths a constant temperature is achieved, and the temperature of the wire has no affect on the resistance.
For my experiments to give valid results, they had to be 'fair tests' in which only one variable was altered at one time. By doing this it is reasonable to assume that any change observed is due to that variable, and nothing else. The problem that I expected to be the most significant was that of the 'heating effect' caused by passing an electric current through a wire. Since the energy lost by electrons given out as heat, the temperature of the wire will increase, and since the resistance of a wire increases with temperature, this would introduce another dependent variable. I had thought of various ways that I could get over this problem, including making the wire into a coil and putting under running water from a tap. However, my preliminary experiments showed me that passing the current through the wire for the few seconds necessary for me to take my readings, no discernible change in resistance was seen. Even when passing the current for as long as ten seconds, I was unable to see any change in the readings for the current and voltage, indicating that there was no appreciable change in the resistance.
To extend my investigation even further now, I could investigate different types of wires and see how they affect its resistance. I would also repeat the experiment to see if the results I obtained where constant and accurate.
Overall this investigation went according to plan. I had no anomalous results and they were reasonably accurate. The results backed up my predictions and enabled me to make a good conclusion.
