By using the equations above I can also re-arrange them to make this equation;
V ÷ I = ( l ÷ A) x P
And from here;
1 ÷ I = ((V x A) ÷P ) x l
By using this last equation I’m able to plot a graph, from which I can work out the resistivity, as it is part of the gradient (1÷ I against l).
As voltage and the radius of area of the circle are constants, I can alter the length of wire and record the change of current, to attain a value for resistivity.
To carry out the experiment I will need to set out a circuit like this;
Method
- As you can see, from the diagram I will need;
- A power source
- A voltmeter
- An ammeter
- 5 x Connecting wires
- 2 x Crocodile clips
- A length of Constanton wire
- A meter rule
The first thing I did after setting up the circuit is, to measure the diameter of the Constanton wire, using a micrometer.
I then took 5 readings to get an average.
- I cellotaped my length of wire to the meter rule, so I could measure (in intervals of 10 cm) with to crocodile clips attached.
- At every interval of 10 cm on the meter rule, I varied the resistor so that the voltmeter read at a constant of 1 volt. The 1 volt I worked out in my preliminary work, by varying the voltage across the wire, using a variable power source, so I could read the ammeter at a suitable scale and for safety reasons; to make sure the wire didn’t get to hot and burn.
- I made a table recording the current for a total of 10 readings, from these results I was able to work out the average current for each length, but only from one set of results as I ran out of time.
Results
- Results for the diameter of the Constanton wire;
I added the readings together getting a total of 1.32 mm, and then divided by 5 to get an average of 0.264 mm.
I lastly divided 0.264 mm by 2000 to convert the millimetres (mm) into meters (m).
0.264 ÷ 2000 = 0.000132 == radius ( r )
π x (0.000132) = 5.47391104 –08
Area of wire ( A ) = 5.5 x 10 –08
- Results of actual experiment;
Calculations
As mentioned before I can work out the resistivity of my piece of constanton wire using the gradient of my graph.
To begin with, I took the co-ordinates of the two points on my graph.
(0.04, 0.40) and (0.86, 6.70)
I then minus the two x-axis co-ordinates, and then minus the two y-axis co-ordinates;
0.86 – 0.04 = 0.82
6.70 – 0.40 = 6.30
I then divided the two answers to get the gradient
6.30 ÷ 0.82 = 7.683 to 3 d. p.
From here to work out resistivity I times the gradient by the area of circle, which I worked out to be 5.5 x 10–08
7.683 x (5.5 x 10–08) = 4.226 x 10–07 Ωm
Conclusion
To conclude I say that the resistivity of my constanton wire is
4.226 x 10–07 Ωm with an error of ±1.429
I worked out the error by drawing a line on the widest point on both sides and taking the gradient of each. With the gradient I made two more values for resistivity and took the difference, from the original value of 4.226 x 10–07 Ωm.
Minimum Value: (0.20, 1.50) and (0.96, 7.10)
0.96 – 0.20 = 0.76 and 7.10 – 1.50 = 5.60
5.60 ÷ 0.76 = 7.368 to 3 d. p.
Maximum Value: (0.16, 1.40) and (0.90, 7.90)
0.90 – 0.16 = 0.74 and 7.90 – 1.40 = 6.51
6.51÷ 0.74 = 8.797 to 3 d. p.
So the error is 8.797 – 7.368 = ±1.429
Evaluation
I realise that my experiment may not be entirely reliable because I have a large error due to working conditions, equipment and the results produced (anomalies shown on the graph).
I don’t think that the heat affected the experiment at a measurable amount because I made sure the volt stayed down to 1, not getting hot. However other conditions such as time may have affected the experiment, if I had time I would have left so long in-between each reading, to leave no room for the wire to heat up even slightly. Also I would have taken more results to obtain a better average.
In terms of equipment I would see about getting a piece of wire which is straight with no kinks in it, and tried to make the measurements of lengths more accurate. There is also the diameter variation of the micrometer readings which may have an affect on the gradient result.
I finally needed to take into account if my reading the meters was accurate.