Also when the width increases I think that the resistance will decrease but not by direct proportion. I think that the thinnest wire will have the highest resistance because there are fewer atoms by which the electrons can be passed along in a given length of wire. Due to the fact there are fewer atoms, which the electrons can jump along, in a given length this means the current will be reduced.
Electric current is the movement of electrons through a conductor. In this experiment a metal wire (Nichrome will be the conductor). So when resistance is high, conductivity is low. Metals such as Nichrome conduct electricity well because the atoms in them do not hold on to their electrons very well. Free electrons are created, which carry a negative charge, to ‘jump along’ the lines of atoms in a wire, which are in a lattice structure.
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 'jumps' 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. This can be explained in an equation as follows: R α1/A. Resistance is when these electrons, which flow towards the positive, collide with other atoms, they transfer some of their kinetic energy. This transfer on collision is what causes resistance. So, if we double the length of a wire, the number of atoms in the wire doubles. This increases the number of collisions and energy transferred twice, so twice the amount of energy is required. This means the resistance is doubled. This means that resistance is proportional to length. Also resistance is inversely proportional to the width. If the width is doubled the resistance will be halved. We can combine these to get: -
Resistance (ohm’s) = Resistivity x Length
Width
Resistivity is a figure, which changes according to the material.
The thinner the wire is the less channels of electrons in the wire for current to flow, so the energy is not spread out as much, so the resistance will be higher: We see that if the area of the wire doubles, so does the number of possible routes for the current to flow down, therefore the energy is twice as spread out, so resistance might halve,
i.e. Resistance= 1/Area.
This can be explained using the formula
R = V/I.
Where there is 2X the current, and the voltage is the same, therefore R will halve. I did some research and in a book called 'Ordinary Level Physics' By A. F. Abbott, it says 'that doubling the area will therefore halve the resistance'- in other words the resistance of a wire is inversely proportional to its area, or R α1/A, but we are measuring diameter, so if the area is: A= Л x (radius) ², A= Л x (diameter/2) ², A= Лd² /4 Where A is area and d is diameter.
Resistance is the property of a substance to resist/oppose the flow of an electrical current. The amount of resistance in a circuit determines the amount of current flowing in a circuit for any given voltage, this is according to Ohm’s law. The resisting property of any material is called resistivity. The resistance is where the electrons give up the potential energy they carry from the battery.
The resistance of a conductor depends upon two things: -
- Its own dimensions,
- The material, which it is made from.
A thin wire has a higher resistance than a thick wire; a long wire has a greater resistance than a short one.
I have information on Ohm’s law which states “The current flowing through a metal wire is proportional to the potential difference across it (providing the temperature remains constant and the resistor is fixed)” So the resistance of a wire is The potential difference, voltage across the wire divided by the current flowing through the wire. So: -
Resistance [ohm’s (Ω)] = Potential Difference [volts (v)]
Current [amps (a)]
The resistance of a conductor is the ratio of the voltage across it to the current through it. We can take the units of potential difference and current, the volt and the ampere, to define the unit of resistance called the ohm. “The ohm is the resistance of a conductor through which the current is 1 ampere when the potential difference between its ends is 1 volt.” (From World Of Physics By John Avison.)
Method
Experiment One - First a length of wire over a metre long is sellotaped to a metre rule. The positive crocodile clip is attached at 0cm. And the negative is moved up and down the wire, stopping at15, 20, 25, 30, 35, and 40. Each time reading the ammeter and voltmeter to work out resistance R = V/I. This is using 32 SWG wire. Other variables, voltage, thickness, and temperature will be kept constant, although the temperature will rise once current is passing through it, which will cause the atoms in the wire to vibrate, and so obstruct the flow of electrons, so the resistance will increase, creating an error.
Experiment Two - The circuit is set up is the same, as is the method apart from the length is constant at 15cm, and the thickness is changed between 16,18, 24, 26, and 32swg. For both experiments the voltage will be kept the same at 2V dc from a power pack. Both experiments will be done twice with different ammeters in case of any damaged or old equipment to gain more accurate results.
Using the micrometer I will measure the thickness of the wires. I will use skill and precision we shall measure the width of the wires in millimetres. I will then compare these widths to the widths, which are shown in the schools catalogue. We shall use a vernier calliper (or micrometer).
Results
Changing width, keeping length the same
Length fixed at 15 cm.
We repeated the experiment
Changing length, keeping width the same
Width fixed at 32 swg.
We repeated this experiment.
Using precision and skill we measured the width of the wires in millimetres (converting from swg). We used a vernier calliper (or micrometer).
Analysis
From my results I have found that the resistance increases with length and decreases with the width. The thinner wire had a higher resistance than the tick wire; the long wire had a greater resistance than the shorter wire.
From looking at my graphs, for the change in the length of the wire, that the graph is a straight line showing that when the length was increased the resistance was also increased proportionally. The resistance increased with the length this shows from the graph, which has a positive slope. The original predictions, which I made on this subject, were correct and my results can be easily said to support this. In my prediction I predicted that that when the length of the wire was increased I also believed that the resistance of the wire would increase by direct proportion because of the electron structure within the wire. The three different types of results I obtained were in the same order of magnitude, which shows I have not made any fatal errors during any calculations. This suggest that the resistance is proportional to length so if I were to double the length the resistance would also double.
As the diameter increased the resistance as previously suggested in my predictions did decrease. I was also correct in suggesting the relationship was not directly proportional, this is proved by the graph not having a straight line. There was a relationship between the two though, it seemed as one increased then the other decreased by a given amount. If I look at the graph for resistance against width the graph has a negative slope, which suggests that maybe the resistance is inversely proportional to width so if I were to double the width then the resistance would be halved.
From looking at my results and from my graphs I can see that there was a relationship between resistance and length hence the straight line on the graph. This tells me that the resistance maybe proportional to the length. I will now check that this is true by looking at my results and proving that this is correct. So if I doubled the length the resistance will also double.
If the length was 15cm and the resistance was 3.09 Ω.
The length would be 30 cm the resistance would be 6.18 Ω.
If the length was 20cm and the resistance was 4.34 Ω.
The length would be 40cm and the resistance would be 8.68 Ω
From my results this is what the resistance would be:
Length 15cm resistance 3.09 Ω
Length 30cm resistance 6.15 Ω
Length 20cm resistance 4.34 Ω
Length 40cm resistance 8.30 Ω
From looking at these results I can see that there were only a few numbers out apart from when the 20cm was doubled which was the same for both sets of results but this proves that the length is proportional to the resistance. I will now see if this is true for the width. With this graph the resistance decreased and mean that the resistance could be inversely proportional to width. If I were to double the width the resistance would halve. From looking at the table of widths from using the micrometer I can see that the width for 32 swg is 0.28 and the width for 24 swg is 0.56, which is double the width. This means that the resistances should be double too.
32 swg 0.28mm
24 swg 0.56mm
32 swg 2.94 Ω
24 swg 0.75 Ω
This shows that there is a difference of 1.5 so the resistance has not been fully halved so the resistance can’t be inversely proportional to width. This is true for length that the resistance is proportional to length. The reason is because from the formula for resistivity we made the assumption that:
R = ρl
A
This is the formula for resistivity and we made the assumption that A (cross-sectional area) was same as the width. It is only when the cross-sectional area is used that the resistance is inversely proportional to area.
When we compare the resistivities of different materials, we actually compare the resistances of conductors. This gives us a definition of resistivity.
“The resistivity of a material is numerically equal to the resistance of a spectrum of unit length and unit cross-sectional area.”
It follows that:
“the resistance R of a conductor is directly proportional to the resistivity ρ of its material; that is R α ρ”
To make sure that the resistance is inversely proportional to width the cross-sectional area needs to be worked out to prove that the width is inversely proportional to width.
Both sets of results for the experiments were linked to the atomic structure of the metal atoms. Each experiment, which was carried out, relied upon the conductivity of the wire and the current, which flowed through it. The electrons of the metals atoms are what create the current by flowing freely through the metals structure. Electrons hence carry the current by “jumping” from one atom to the next and the greater the number of atoms i.e. length of the wire, the further the electrons have to “jump”/travel. E.g. Twice the length, twice the number of atoms therefore the wire had twice the resistance. The thinnest wire had the highest resistance because there are fewer atoms by which the electrons can be passed along in a given length of wire. Due to the fact there are fewer atoms, which the electrons can jump along, in a given length this means the current was reduced.
Resistance is caused when these electrons flowing towards the positive terminal have to 'jumps' 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.
So when resistance is high, conductivity is low. Metals such as Nichrome conduct electricity well because the atoms in them do not hold on to their electrons very well. Free electrons are created, which carry a negative charge, to ‘jump along’ the lines of atoms in a wire, which are in a lattice structure. This was as stated in my prediction. Therefore my predictions were correct.
The conclusion drawn from this is that the thinner the wire the fewer atoms there are in a given space meaning that the flow of electrons is reduced by giving the electrons fewer atoms to “jump” across in that particular space. This means that a good conductor would be a short thick wire because it would have the least resistance. Therefore a poor conductor would be a long thin wire, as it would have a high resistance in a circuit.
Evaluation
From the experiment I obtained good results and I found the experiment most enjoyable. The apparatus was simple and easy to use, the micrometer gave us the exact widths of the wires that we were using and seemed to show a difference from the catalogue of widths. The experiment was safe and the plan was followed and a safe procedure was carried out. We obtained 5 sets of results from this experiment showing which factors alter the resistance of the wire. Our results were accurate and I didn’t have any anomalous results as shown by the graph. As you can see from the graph there were a few results, which did not fit into the line of best fit, but there were no anomalous results. The results for the resistance of the wire were accurate to two decimal places to correlate with the ammeter and voltmeter readings. The results were reliable and proved that my prediction was correct and this proves also that the experiment was carried out correctly.
The results were reliable although there were a few results, which did seem not be correct and there were a few errors. This could be due to human error reading from the meter ruler the wrong length of the wire. The voltmeter and ammeter were both flickering and once it seem to have settled then a value could be read. There may also have been in a kink in the wire meaning that an incorrect length was measured. On the graph, which displayed length, plotted against resistance it showed the larger the length the less accurate the results were, these could be considered anomalous results. In my opinion the results become less accurate the longer the length of the wire, as it is more difficult to have the wire completely straight with no “kinks” in. This would mean that the length measurements were not exactly correct and therefore the resistance’s, which were calculated, should have been plotted on a different part of the graph. Also there was a rise in the temperature of the wire and changes the resistance of the wire. These problems however are only possibilities.
These problems could be overcome by using a meter ruler to three decimal places to make the results more accurate. The wire needs to be nice and taught to measure the length. Also use a voltmeter and ammeter that are accurate and do not flicker. Therefore this would stop any anomalous results and I could have more reliable and accurate results to draw conclusions from.
The conclusions I have made are true for the length and widths of wires that I tested. There is sufficient evidence to support a firm conclusion but further experiments would need to be carried out to prove that my conclusions were true. I cannot say for sure that resistance increase with the length for all lengths of wire and I cannot say that resistance decreases with he width for all widths of wire. Different widths and lengths would have to be tested to see if this is true. I have only tested widths from 16 swg to 32 swg and lengths from 15cm to 40cm. I cannot say for sure what would happen for other lengths and widths. Other materials could be tested too to see if this alters the resistance. Other factors could also be tested such as the different voltage and material etc. Different materials such as gold, steel, silver and copper could be tested to see their effect on the resistance.
I would also use accurate measuring equipment so that no errors occur and good, clear accurate results are obtained. The good results would present a clear idea of which factors alter the resistance of a wire. Further experiments could be carried out, using different equipment to see if my conclusions are true that length and width alter the resistance of a wire
