The power pack will supply the variable voltage to the circuit. The ammeter is used to measure the current flowing through the circuit. The volt meter is used to measure the voltage across the length of wire. Connecting wires are used to connect the circuit as shown. Crocodile clips are attached to the ends of the connecting wires to hold the constantan wire.
The planning of the experiment is described in detail in the method below. I have chosen this set-up because of its simplicity and also because it is one of the most reliable ways to find the resistance of a wire.
METHOD
There are a few things I will have to be careful about when I set-up my experiment. First I will have to check that all of the equipment needed is functioning properly. Once I have made sure that none of the equipment is defective, I can set the circuit like shown in the figure above. As I have to use different lengths of the wire, I will start with the longest length of the wire which is 1 metre. Using sticky-tape I will stick the metre-rule onto a table. Then the full length of wire will be stuck on to the metre ruler. The extra wire (10 cm) will be used to stick the wire down from the edges and will not be used in the experiment itself. Fixing the wire in one position will help me to take better measurements of the length and will also stop the wire from curling up (curling up of the wire can be a problem - explained below). Once the wire is in place, a crocodile clip (connected to the circuit) will be attached at one end of the wire. The second crocodile clip will be attached at the required length of wire (which will be 1 metre to start with, and after taking all the measurement needed for that length it will be reduced). The voltage from the power pack will be set at a lowest and the power will be turned on. Next I will record the reading from the ammeter and the volt meter onto a table alongside with the length of wire in the circuit. Once the reading has been taken I will switch the power pack off. The voltage will be increased and the process of taking the readings will be repeated. This will be repeated for all the different voltages (4 different ones will be enough). Once I have a set of readings for that length, I will decrease the length by just moving one crocodile clips, and repeat the whole process again. Then I will reduce the length again and so on till I have a set of readings for all the lengths. All the lengths and the results for them are recorded on the results page (page 5).
By just moving one of the crocodile clips instead of cutting the wire to a shorter length I will avoid using the wire cutter again and again. This will save a lot of time and will also reduce the risk of cutting myself. Moving one of he crocodile clips down the wire will decrease the length of the wire being used in the circuit. This procedure will work because of the fact that the current will only pass through the wire between the two crocodile clips.
Here although the length of the wire is more than
90 cm, but the length of the wire between the two
crocodile clips is only 90 cm, therefore the length
of the wire in the circuit is only 90 cm.
If one of the crocodile clips is moved
down the wire so that the length of the wire between
the two clips is 50 cm, the length of the wire in the
circuit will also be 50 cm.
The readings from the ammeter and volt meter should be taken as carefully as possible to reduce the effect of human error, which is usually the largest of all errors.
The main precaution to be taken is to make sure that the wire is kept straight. If the wire curls up and touches itself (overlaps) somewhere it will reduce the effective length in the circuit. In other words a short-circuit. This is explained with the aid of the example and the diagram:
In this diagram the wire between the crocodile
clips is 40 cm i.e. the wire being used is 40 cm long.
Here in the second figure the same length of
wire curls up and overlaps itself as shown.
The effective length of the wire is reduced.
Although the length of the wire between the
Clips is still 40 cm, but the effective length
of the wire is only about 25cm. This change in the length of the wire will cause huge errors in the results if it is not taken care of.
So to avoid the problem of getting a short circuit in my circuit I will have to take extra care that the wire is not curled and does not ovelap itself anywhere. I will take the metre rule and stick the wire on to it from the ends to hold it down. This way the wire will not curl and It will also be a lot easier to measure the length of the wire. This overcomes the short circuit problem but it also creats a new one. Using this method the wire might get stretched. If I stretch the wire too much, it might reduce its diameter, which is also a problem I will have to be careful about.The change in the diameter of the wire means the cross sectional area is being changed. The resistance of a wire is inversely proportional to its cross sectional area. This means if the cross sectional area is doubled, the resistance will be halved – or if the cross sectional area is halved, the resistance will be doubled. The equation below defines this principle.
Here is a list of the precautions to be taken during the experiment:
- I should be careful not to let the wire curl/overlap to avoid a short circuit.
- I have to be careful that I don’t stretch the wire too much; as that might change the wire’s cross sectional area.
- I have to be careful not to touch the wire while the power is on as the wire might be very hot.
- I have to read the ammeter and volt meter carefully, and should make sure I am using the appropriate scale.
PREDICTION FOR THE RESULTS OF THE EXPERIMENT:
According to the theory the increase in the length of a wire should be proportional to the increase of its resistance. Thus if I plot a graph of resistance against length, the result should be a straight line (y=mx+c). This is true taking experimental errors into account. As experimental results are never perfect, I am expecting my graphs to be a ‘best fit’ straight line. This means that a straight line is drawn going through as many points as possible, and some points might not be on the line but are very close to it.
The resistance should be higher in a longer piece of wire. Electricity is the flow of electrons. Resistance is the stopping of the flow of these electrons. When the electrons flow through the wire they keep on colliding with the particles inside the wires (atom etc). This knocks the electron from the flow. In a longer wire there will be more particles to collide with hence the resistance will increase.
After doing the experiment I have recorded the results on the next page.
RESULTS:
After doing the experiment I got the following results. I have plotted graphs for all these results on the following pages.
Then I calculated the gradient for the straight line on each graph and it gave me the average resistance for that certain length.
The darker lines on the graphs are the best fit straight lines which have been used to in working out the gradient. The lighter lines are the actual lines going through all the points. As it can be seen from most of the graphs, both the lines overlap most of the time, hence showing that accuracy of the results is really good.
CONCLUSIONS
I used the above graphs to get an average value for the resistance for each length. The table below shows the values obtained.
Using the above table I plotted the graph shown below (resistance against length). I have drawn the line as a best fit to all the points. I have made error boxes around all the points with a height of 0.02 ohms. The straight line in the graph touches all the error boxes which means that all the results have an accuracy of ±0.02 Ohms. The darker line is the best fit straight line and the lighter line is the actual line.
In the above graph, all the points are accurate to ±0.02 Ohms. Although this is a very small error, it is still an error. Therefore I have listed below the possible causes.
- Human error: I might not have read the ammeter or the voltmeter properly.
- The wire might have been elongated by stretching.
- I might have lost some accuracy during the calculations.
All these factors might or might not have contributed towards the errors.
As it can be seen from the graph that the best fit line to all the points is a straight line (y=mx+c). This fits with my prediction of the result. This proves that resistance is proportional to the length of the wire.
By this experiment I have reached the conclusion that resistance is proportional to the length of the wire taking experimental errors into account.
Using the above graph I calculated the average resistance for 1 unit length (which is 1 metre). I did this by finding the gradient of the straight line on the graph.
Resistance of 1 metre of the wire = 1.971 Ω
As this is an average from a lot of values the accuracy is increased to ±0.005 Ohms.
The main aim of this experiment was to find the resistivity of the wire. To find the resistivity of the wire I have to use the formula:
The data I need to work out the resistivity is:
- A length of wire and its resistance: I have got these values from the above experiment and calculations.
- The cross sectional areas of the wire.
I had to work out the cross sectional area of the wire. I measured the diameter of the wire ‘’ using a micrometer. To increase accuracy I took 3 readings from different places on the wire and took an average of the three as my measurement.
= metres.
A= A=
The cross sectional area of the wire (to 5 s.f.) = A = 2.4630*10-7 m2
Data: = 1.00 m R = 1.971 Ω A = 2.4630*10-7 m2
= = 4.855*10-7 Ωm (to 4 s.f)
RESISTIVITY of 24 swg consantan wire =
4.855*10-7 Ωm (to 4 s.f)
Physics experiment write-up by Sarwar Akeel Akbar –6M
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