I also predict that the resistance of a wire will be inversely proportional to its cross sectional area. The reason being that if the wires thickness is increased the space for the electrons to travel through will increase and due to this increased space there should be less collisions between the electrons and the ions. This diminish in the number of collisions would reduce the resistance in the wire. So, if a wires width is doubled then the space that the electrons have to travel through will double and so the number of collisions occurring should halve. If I were to plot the resistances of different wires made out of the same element but with different cross sectional areas on a graph then I think it would look as follows:
Resistances
Cross sectional areas
of wires used
The greater the number of atoms in a material, the more obstruction there will be for an electron to flow from one end to the other in an electric current. For this reason it is possible to say that the greater the density of a conductor, the greater its resistance. For this reason as well as the molecular structure of the conductor and the number of free electrons it has, I predict that not all materials will conduct electricity to the same extent.
When one factor is investigated during the experiment, by carrying out the plans written below, all of the other factors mentioned previously must be kept constant to ensure fair testing however the temperature of the wire cannot be controlled since it rises automatically when a current passes through it. The reason for this is that when a current passes through a wire collisions occur between the electrons and the ions and as I mentioned previously, when collisions occur the electrons lose kinetic energy in the form of heat energy making the overall temperature of the wire increase. However it is possible to minimise heat rise by not using very large currents, this is because it will minimise the number of collisions occurring between the electrons and the ions in any given time and so minimise the amount of heat energy released by the electrons thus reducing the rise in temperature experienced by the wire. This is as constant as it is possible to keep the temperature. Furthermore, as well as the factors listed above there are other variables that must be kept constant to ensure fair testing and these can be seen in the list below:
- The same apparatus must be used throughout the experiment.
- The same method must be used to collect every set of results.
I will now say what apparatus is to be used in the investigation, how the investigation will be carried out and I will also draw a diagram for a visual aid.
APPARATUS:
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A nichrome wire (Ni 80% Cu 20%) 1 meter long with a cross sectional area of 0.40 mm²
A nichrome wire 1 meter long with a cross sectional area of 0.08 mm²
- A nichrome wire 1 meter long with a cross sectional area of 0.11 mm²
- A nichrome wire 1 meter long with a cross sectional area of 0.13 mm²
- A nichrome wire 1 meter long with a cross sectional area of 0.25 mm²
- A constantan (Cu 55% Ni 44% Ma 1%) wire 1 meter long with a cross sectional area of 0.08 mm²
- A copper wire 1 meter long with a cross sectional area of 0.08 mm²
- A manganin (Ma 12% Ni 2% Cu 86%) wire 1 meter long with a cross sectional area of 0.08 mm²
- A rheostat
- A voltmeter
- An ammeter
- 2 crocodile clips
- 6 connecting wires
- A 1 meter ruler
DIAGRAM:
Generator
…….
Ammeter
1 2
Wire
Rheostat
Voltmeter
PLAN (for investigating how the length of a wire affects its resistance):
- The circuit will be set up like the above diagram shows.
-
The crocodile clips will be attached to the wires at points 1 and 2; these will be used to connect one of the loose wires with the cross sectional area of 0.08 mm2 to the rest of the circuit.
- The wire will then be placed in the position shown by the above diagram and the two crocodile clips will then be placed at the far ends of the wire.
- The rheostat will then be placed in a random position ensuring that the current produced isn’t too high to minimise heat rise and the voltage and current present across the wire will then be read off of the meters and noted.
-
The rheostat will then be placed in five new positions with the current and voltage across the wire being noted each time using the meters. This will give me six sets of readings with which resistances will be calculated from using R=V/ I. With all of these resistances, an average resistance will be calculated.
- Using the ruler, the crocodile clip at point 1 will be moved 0.2 meters up the wire and then steps 4 and 5 will be carried out again.
- The previous step will then be carried out another three times so that readings for 5 lengths of the wire are taken.
- All of my results will then be placed in tables and the five average resistances obtained will be plotted on a graph showing the resistances found against the different lengths of the wire used.
-
Step 2 up to step 8 will then be carried out another three times but using a different wire with the cross sectional area of 0.08 mm2 so that results for all of them are found.
PLAN (for investigating how the cross sectional area of a wire affects its resistance):
- The circuit will be set up like the above diagram shows.
- The crocodile clips will be attached to the wires at points 1 and 2; these will be used to connect the loose nichrome wire to the rest of the circuit.
- I will first look at the nichrome wire with the cross sectional area of 0.40 mm². It will be placed in the position shown by the above diagram and the two crocodile clips will then be placed at the far ends of the wire.
- The rheostat will then be placed in a random position ensuring that the current produced isn’t too high to minimise heat rise and the voltage and current present across the wire will then be read off of the meters and noted.
-
The rheostat will then be placed in five new positions with the current and voltage across the wire being noted each time using the meters. This will give me six sets of readings with which resistances will be calculated from using R=V/ I. With all of these resistances, an average resistance will be calculated.
- The nichrome wire will then be replaced by another nichrome wire possessing a different cross sectional area and again the two crocodile clips will then be placed at the far ends of the wire. Steps 4 and 5 will then be carried out again.
- The previous step will then be carried out another three times so that readings are obtained for all of the five nichrome wires possessing different cross sectional areas.
- All of my results will then be placed in tables and the average resistances obtained from the different wires will be plotted on a graph showing the resistances found against the different wires with different cross sectional areas used.
OBSERVATION AND RESULTS:
In order to fit all of my results into the following tables I have had to replace certain words with their symbols instead, I will state which ones below:
- V stands for voltage in volts
- I stands for current in amps
- R stands for resistance in ohms
Furthermore, all of my results are to two decimal places.
Results found concerning how the length of a wire affects its resistance:
Results obtained for the constantan wire:
Results obtained for the manganin wire:
Results obtained for the copper wire:
Results obtained for the nichrome wire:
Results found concerning how the cross sectional area of a wire affects its resistance:
Results obtained for the nichrome wires:
ANALYSIS OF RESULTS AND CONCLUSION
As can be seen from the table of results concerning how the length of a wire affects its resistance, as the length of the wires increase so do their resistances. It can also be seen that as the cross sectional area of the nichrome wire increases its resistance decreases. I will now draw graphs illustrating these above results to see more clearly how they differ. Furthermore, I will draw an additional graph for the results regarding how the cross sectional area of a wire affects its resistance, since these two things show an inversely proportional relationship to each other and on the graph showing resistance against cross sectional area they should show a curve so the additional one which will show 1/ resistance against cross sectional area should form a straight line going through the origin. The following are calculations to find the new Y-coordinates for the graph just described showing 1/resistance against cross sectional area.
For point 1 on the graph: 1/ 13.83 = 0.07 (to 2 d.p)
For point 2 on the graph: 1/ 10.55 = 0.09 (to 2 d.p)
For point 3 on the graph: 1/ 9.80 = 0.10 (to 2 d.p)
For point 4 on the graph: 1/ 4.65 = 0.22 (to 2 d.p)
For point 5 on the graph: 1/ 2.87 = 0.35 (to 2 d.p)
From the previous graphs it can be seen that as the length of the wires increase so do their resistances in a directly proportional manner and as the cross sectional area of the nichrome wire used increases it can be seen that its resistance decreases in an inversely proportional manner.
I noticed that the gradients of the graphs concerning how the length of a wire affects its resistance differ from one another and thought that this must be due to the fact that the graphs illustrate different metals. The nature of the material used in a circuit will therefore affect how well the circuit conducts electricity; this could be due to the molecular structure of the material or the number of free electrons it possesses since these will be the ones that will flow in the circuit producing the electric current. I did some further research on this and discovered something called resistivity, which states that the resistance of an element is directly proportional to its length divided by its cross sectional area i.e. R L/A. So it can be said that R = p L/A where p is the constant known as the resistivity of the element, this is the factor in the resistance which takes into account the nature of the material. To find the resistivity of an element the above formula can be rearranged to make p the subject, which would give p = R . So if I were to draw graphs showing the resistances of the wires used
L/A
against their lengths divided by their cross sectional area, then the gradients of the graphs would correspond to the resistivities of the elements used since
gradient of a graph = change in y-axis .Calculating the resistivity of all the metals
change in x-axis
used in the experiment will allow me to compare how well they all allow an electric current to flow through them. I will now draw the graphs that I described previously.
From these graphs I will now calculate their gradients and hence the resistivity of all the metals used (N.B. the points on the graphs that are to be used in my gradient calculations have been clearly marked on the graphs):
For the constantan graph
GRADIENT = CHANGE IN Y-AXIS
CHANGE IN X-AXIS
GRADIENT = 6.6 - 1
13 - 2
GRADIENT = 5.6
11
GRADIENT = 0.51 (to 2 decimal places)
For the manganin graph
GRADIENT = CHANGE IN Y-AXIS
CHANGE IN X-AXIS
GRADIENT = 6 – 1.3
14 – 3
GRADIENT = 4.7
11
GRADIENT = 0.43 (to 2 decimal places)
For the copper graph
GRADIENT = CHANGE IN Y-AXIS
CHANGE IN X-AXIS
GRADIENT = 0.6 – 0.1
12 – 2
GRADIENT = 0.5
10
GRADIENT = 0.01 (to 2 decimal places)
For the nichrome graph
GRADIENT = CHANGE IN Y-AXIS
CHANGE IN X-AXIS
GRADIENT = 14.4 – 4.4
13 – 4
GRADIENT = 10
9
GRADIENT = 1.11 (to 2 decimal places)
The resistivity of constantan has been found to be 0.51 ohms mm but since the conventional unit of resistivity is ohms meter, the actual answer is 51 * 10-8 ohms m. The resistivity of manganin has been found to be 0.43 ohms mm but since the conventional unit of resistivity is ohms meter, the actual answer is 43 * 10-8 ohms m. The resistivity of copper has been found to be 0.01 ohms mm but since the conventional unit of resistivity is ohms meter, the actual answer is 1 * 10-8 ohms m.
The resistivity of nichrome has been found to be 1.11 ohms mm but since the conventional unit of resistivity is ohms meter, the actual answer is 111 * 10-8 ohms m.
How my results support or undermine my original predictions
- I previously predicted that the resistance of the wires would be directly proportional to their lengths. This was proven to be the case since the graphs showing resistances against lengths of wire used show a straight line going through the origin. This can be explained because as the length of a wire is increased then the distance the electrons will have to travel in an electric current will increase, so more collisions are likely to occur between them and the ions present.
- I also predicted that the resistance of the nichrome wires would be inversely proportional to their cross sectional area. This was proven true since the graph illustrating this shows a straight line descending towards the right side of the graph and ascending towards the left side of the graph. I can explain this because as the wires cross sectional area is increased the space for the electrons to travel through in an electric current will increase and due to this increased space there should be less collisions between them and the ions.
- I also hypothesised that the graphs drawn from the results obtained would resemble the ones that I drew in the PLANNING section. This was the case as can be seen when comparing the graphs I drew with my hypotheses to the ones in this section. This can be explained because the results obtained in the investigation match the patterns that I predicted they would follow i.e. resistance being directly proportional to the length of the wire and resistance being inversely proportional to the cross sectional area of the wire.
- I predicted that not all materials would conduct electricity to the same extent. This was proven true since I discovered something called resistivity by doing some further research, this is the factor in the resistance that takes into account the nature of the material. I found that all of the metals I used had different resistivities and so conducted electricity to different extents. I can explain this because all of the metals contained copper in different proportions and this element has two free electrons able to flow in an electric current, which is quite high. Copper therefore has a very low resistance and so the metals containing the most copper would have the least resistance out of all the metals used in the investigation and hence the least resistivity.
Conclusion
It has been found that the resistance of a wire is directly proportional to its length and inversely proportional to its cross sectional area. This is because as the length of a wire is increased then the distance the electrons have to travel in an electric current increases, so more collisions occur between them and the ions present and as the wires’ cross sectional area is increased the space for the electrons to travel through in an electric current increases and due to this increased space there are less collisions between them and the ions.
It has also been found that the resistivity (this is the factor in the resistance of an element that takes into account the nature of the material) of the copper wire is less than the resistivity of the manganin wire, which is less than the resistivity of the constantan wire and which is less than the resistivity of the nichrome wire. The resistivity of constantan was found to be 51 * 10-8, the resistivity of manganin was found to be 43 * 10-8, the resistivity of copper was found to be 1 * 10-8 and the resistivity of nichrome was found to be 111 * 10-8. The best conductor of electricity was therefore the copper wire and the worst conductor was the nichrome wire.
EVALUATION
Overall, I was pleased with my results. The procedure I used to carry out the experiment seemed to be suitable and good, as my results appeared to be very accurate in respect to my predictions. As can be seen from my graphs, I seem to have only obtained one anomalous result, which appears on graphs 3 and 9 (the ones relating to the copper wire). To improve the results obtained in this experiment and improve the reliability of the evidence I would take more results so that better, more accurate averages could then be made from them and so more accurate graphs could then be drawn. I would particularly take more readings with the copper wire since this is where I obtained the anomalous result, the reason for this I think is that since its resistance was so low the ammeter and voltmeter fluctuated a lot making it hard to take readings from them. I think that it is possible to support a firm conclusion with the results obtained in this experiment since all of the points on my graphs either lie on or near the line of best fit (except for my anomalous result) showing that there is a particular relationship between these results and the factors present while obtaining them.
During this write up I calculated the resistivities of the metals that I used, I looked in an A-level physics book for the values it gave for the resistivities of those metals in order to compare them with the values I found. The following are the resistivity values that I found in the book:
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The resistivity for constantan is 49 * 10-8
-
The resistivity for manganin is 44 * 10-8
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The resistivity for copper is 1.7 * 10-8
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The resistivity for nichrome is 110 * 10-8
It can be seen that my resistivity values calculated in the ANALYSIS SECTION are very close to those found in the book. This further emphasises my opinion that my results are accurate enough to draw conclusions.
Further Work
To improve the experiment in order to provide additional and more reliable evidence for a conclusion I would carry out the experiment using additional different metals to see how their resistances would change as their lengths and cross sectional areas were varied. Such examples of these metals could be for example titanium, silver, steel, brass etc…