I will not vary material in this experiment because it is more difficult to get different wires of different materials than to keep one piece of wire and shorten it and still keep the experiment a fair test. I will use constantan wire throughout this experiment to keep it fair.
Width: the narrower a conductor is, the greater its resistance. This is because the narrower a piece of wire is the less electrons can travel through it at once making them collide more with the protons and produce more resistance. The resistance R of a piece of material of uniform length is inversely proportional to the area of cross-section, A.
R ∝ 1
A
I will not investigate width in this experiment because it is more difficult to get different wires of different widths than to keep one piece of wire and shorten it and still keep the experiment a fair test.
Length: the longer a piece of wire is the more resistance it has. The resistance R of a piece of wire of a certain cross-section is proportional to its length, l:
R ∝ l
The length of a wire affects resistance in this way because the longer the wire is the further distance the electrons have to travel making it more likely that they will collide with the protons, losing their kinetic energy and slowing them down therefore creating more resistance.
Temperature: the more the material heats up, the greater the resistance. Resistance of most metals increases uniformly with temperature. An increase in the temperature of a metal causes a greater vibration of the atoms in the lattice framework of atoms therefore there is more interaction between the vibrating atoms and the flowing electrons. It is more difficult for the electrons to get through since they are colliding more with the protons. A semi-conducting material such as carbon will be the other way round. As the temperature rises its resistance falls. This is because electrons get sufficient energy to escape from a particular atom if the temperature is higher. They can then contribute towards the electric current and therefore reduce the resistance of the semi-conductor. I am investigating length in this experiment therefore it is imperative that I keep temperature the same. This will be difficult because during a day the temperature can change so I will do this experiment in one hour therefore the temperature will not change significantly. I will conduct the experiment at room temperature. I will not investigate temperature because that would be a hard variable to control and I do not have the correct apparatus.
I will keep all these factors the same except length, which I am investigating, in order to keep it a fair test. I will also use the same equipment throughout the experiment including the same piece of wire.
Apparatus -A piece of constantan (resistivity at 25˚C=49 x 10 Ω/m) wire 1.1m long to use to measure resistance at different lengths. I will cut it at 1.1m and wind it round the safety pins so that it is kept firmly in the desk
-A metre rule to measure how far down the wire to clip the crocodile clips for each reading
-Two drawing pins to keep the wire fastened to the desk
-A multimeter set to ohmmeter setting to measure the resistance
-Two leads to attach the multimeter to the constantan wire
-Two crocodile clips to attach the leads to the wire
-Wire cutters to cut the wire at the beginning of the experiment
Prediction- I predict that as the length of my wire increases so will my resistance and it will do this in proportion to the length. I predict that my resistance at 1m will be double that at 0.5m because there will be double the amount of atoms for the electrons to collide with so there should be twice the number of collisions. I also predict that my resistance at 0.9m will be three times my resistance at 0.3m. I know this because R ∝ l. This is because as the electrons flow through the wire they collide with the protons in the atomic lattice structure. The longer the wire is, the further the electrons have to go through the lattice structure therefore they will make more collisions therefore more kinetic energy will be lost giving the wire more resistance. Also I have seen from my preliminary experiment that as voltage and current increase so does resistance.
Diagram-
If I wanted to I could set up my experiment using a power pack, an ammeter and a voltmeter instead of a multimeter set to ohmmeter setting. I will not do my experiment like this because that would make the wire heat up more because I would be running a current through it and the increase in temperature would make my resistance higher. That would make the experiment unfair.
Another thing I will do to keep my experiment fair is I will make sure my crocodile clips are attached right at the end of the length of wire I am measuring so as to keep it accurate.
Risk assessment-
I will be careful when I use the wire cutters so that I do not hurt myself
I will keep my work area tidy
Method-
-Set up electrical circuit as shown in diagram including cutting the piece of constantan wire to 1.1m with wire cutters
-Record resistance for lengths of wire varying from 10cm to 100cm in 10cm intervals.
-Vary the length of the wire by clipping the crocodile clip to different lengths along the wire in order to get different lengths to measure
-Repeat experiment three times to improve reliability in case some results were incorrect and take an average
I will control the width and material of the wire by keeping the same piece of wire for the whole experiment therefore making all factors apart from length the same. This is because I already know that these factors can affect electrical resistance and I need to make this experiment a fair test. I will vary the length of the wire so as to investigate what affect it has on electrical resistance. If I let the wire get kinks in it I could affect the resistance so I will try to keep the wire as straight as possible. I will also make it a fair test by not leaving the circuit connected in between recording my results so as not to make the wire heat up too much which if it got hotter would make the resistance greater. It is important to keep it a fair test so that my results are correct and also accurate.
Results:
All averages are rounded to one decimal place.
Conclusion: I conclude from my results that as the length of my wire decreases so does my resistance and it does this proportionately. This is because R l. This is because as the electrons flow through the wire they collide with the protons in the atomic lattice structure. The longer the wire is, the further the electrons have to go through the lattice structure therefore they will make more collisions therefore more kinetic energy is lost giving the wire more resistance. My reading for 0.5m was 5.9 and my reading for 1m was 11.5. 5.9 x 2= 11.8. My results were not exact but they were basically what I predicted. My reading for 0.3m was 3.7 and my reading for 0.9m was 10.3. 3.7 x 3= 11.1. This result was further off but it was not too far from what I predicted to make my results invalid. From my graph I can see that the resistance of a wire is directly proportional to the wire’s length. I know this because my graph nearly passes through the origin and my graph is a straight line. My graph does not pass through the origin and it does not show the shape I would expect from a graph showing direct proportionality. This is because as I can see from the results table there is a resistance of 0.5 when the length of the wire is at zero. This means that the other apparatus I used had resistance therefore my results are not completely accurate. To have a graph which showed only the resistance of the constantan wire I should minus 0.5 from each of my readings for resistance.
I can prove numerically that resistance is directly proportional to length:
If Resistance = R and wire length = l and k = a constant then
R ∝ l
Therefore R = k l
In order to find the constant I should substitute some of my results into the equation.
Wire length = 0.5m and resistance = 5.9 Ω
5.9 = k x 0.5
k = 5.9/0.5
5.9/0.5 = 11.8
Now to find the resistance of a known length
Wire length = 0.2m, constant = 11.8
R = k l
R = 11.8 x 0.2
11.8 x 0.2 = 2.36
My actual value was 2.6 but if my results had been more accurate I would have got a calculation closer to my reading for 0.2m.
Evaluation: When I was doing this experiment I didn’t have any major problems, however I did have a slight problem in clipping the crocodile clips onto the piece of wire at the right place. It was difficult to get the connecting leads clipped to the exact measurements of length that the metre rule showed. If I repeated the experiment to make this better I would cut my wire to the correct length after each reading and clip the crocodile clips onto the end of the wire not move them along according to where they needed to be along the metre rule. This would improve the accuracy of my results.
To make the results reliable I used a good range of lengths and kept other variables the same. I knew these results were reliable because they fitted in with my prediction and previous scientific knowledge, the line of best fit was the shape I expected it to be if I took away 0.5 from each reading and I took all appropriate measures to keep it reliable. To increase my confidence in the reliability of this experiment I could do it with more different lengths of wire within the 0-1m range, for example in intervals of 0.05m, and therefore make my line of best fit better.
My results were very close to my line of best fit. There were no odd results in my experiment. This is because I had very few problems in my practical work. I tried to carry out my experiment accurately by using the setting on the multimeter that went to one decimal place. I could get even more accurate results by using a multimeter or ohmmeter that goes to two or three decimal places. I kept it a fair test by keeping all variables the same (temperature, width of wire, material of wire) except the one I was varying (length of wire) and keeping the same other apparatus for each reading.
I have a lot of confidence in my results because I have repeated my experiment a few times and every time I have repeated it I have come up with the same results. To make my experiment even more reliable I could repeat it again but I think that to repeat it three times is sufficient.
To further this experiment I could investigate longer lengths of wire or shorter lengths of wire. I would carry out the experiment very similarly to how I carried out this one. I would collect a range of values from 1.1m to 2.0m in 10cm intervals. I would keep other things constant as in original experiment. I would carry out the method as following:
-Set up electrical circuit as shown in diagram including cutting the piece of constantan wire to different lengths with wire cutters
-Record resistance for different lengths of wire, clipping different wires in between the two crocodile clips
-Repeat experiment three times to improve reliability in case some results were incorrect and take an average
I could also investigate length using different materials such as . I would use the method I used in the original experiment to do this and I would just change the material to .
Bibliography - Key Science Physics by Jim Breithaupt
- University of Bath science: Physics by Robert Hutchings
