The 10 different lengths I will be using in this experiment are 10cm, 20cm, 30cm, 40cm, 50cm, 60cm, 70cm, 80cm, 90cm and 100cm. I will be measuring current at voltage readings 0.05V, 0.10V, 0.15V, 0.20V, 0.30V, 0.35V, 0.40V, 0.45Vand 0.50V. I have decided to take 10 different readings because I’ll have a range of values and it’s also manageable. I have decided to use a range of low voltages because this means I will get low current readings and therefore, the wire heats up less resulting in more accurate results.
Safety considerations
- Safety goggles will be worn in order to prevent the wire from damaging the eyes
- I will turn the power off between readings so that the wire doesn’t heat up
- I will make sure I do not touch the wire until it has cooled down and I will avoid the wire from touching my clothes or the desk
- I will also make sure the experimental desk is clear of any objects apart from the necessary apparatus.
Accuracy
In order to minimise errors and for a fair test, I will measure the diameter of the wire using a screw gauge at several different places and at different directions across the wire. I will then work out an average of these measurements. This should compensate for any variations in thickness along the wire. I will also use the same equipment throughout my experiment. I will make sure the wire is straight and exactly 1m long when I stick it down onto the ruler. I preferred using digital multimeters instead of analogue meters. This was because reading off a digital multimeter was much easier and therefore, meant fewer chances of inaccurate readings.
Trial run
Before I begin my actual experiment, I have done a trial run for practice. This was because if I made any mistakes I’d know before the real experiment and could fix them. I measured current and voltage readings for a 10cm length of wire with a diameter of 0.35mm. Below are my table of results:
From this table of results, you can see that as voltage increases, currents decreases. Now I know that I should be looking for this kind of pattern for my real experiment.
After I have collected my results, I will plot 10 graphs; one for each length. Using the gradient of a best fit line, I will work out the resistance of that particular length. I will then plot resistance against length to see its relationship. I will then work out resistivity using the equation:
p=RA
l
Results
10cm 20cm
30cm 40cm
50cm 60cm
70cm 80cm
90cm 100cm
(All working of gradients is shown on the graphs).
When I was measuring current for the 50cm length of wire, I could not measure current at 0.05V so instead I began from 0.10V up to 0.55V. This was the only modification I had to make during my experiment.
I have recorded all my measurements to 3 significant figures.
Below is a table of results for the length and its resistance:
As you can see from the graph, as length increases resistance also increases. This shows that resistance is directly proportional to length. I can say this because of the straight line I’ve got. I have also worked out an average for the diameter which is shown in the table below:
Diameter = 2r so r = diameter
2
Radius = 0.1475cm = 0.001475m
My next task is to work out resistivity. To do this I will be using the resistivity equation mentioned earlier. To calculate area I will be using the equation Л r 2:
Л r 2 = Л x 0.0014752 = 0.000006834m2
p=RA 10cm: p = 0.70 x 6.834x10-6 = 4.78x10-7 Ωm
l 10
20cm: p = 1.40 x 6.834x10-6 = 4.78x10-7 Ωm
20
30cm: p = 2.10 x 6.834x10-6 = 4.78 x10-7 Ωm
30
40cm: p = 3.00 x 6.834x10-6 = 5.12 x10-7 Ωm
40
50cm: p = 3.25 x 6.834x10-6 = 4.44 x10-7 Ωm
50
60cm : p = 4.25 x 6.834x10-6 = 4.84 x10-7 Ωm
60
70cm : p = 5.00 x 6.834x10-6 = 4.88 x10-7 Ωm
70
80cm : p = 6.50 x 6.834x10-6 = 5.55 x10-7 Ωm
80
90cm : p = 6.67 x 6.834x10-6 = 5.06 x10-7 Ωm
90
100cm : p = 7.50 x 6.834x10-6 = 5.12 x10-7 Ωm
100
Average:
(4.78x10-7) + (4.78x10-7) + (4.78x10-7) + (5.12 x10-7) + (4.44 x10-7) + (4.84 x10-7) + (4.88 x10-7) + (5.55 x10-7) + (5.06 x10-7) + (5.12 x10-7)_________________________________
10
= 4.935x10-7 Ωm
Conclusion
From the graph I drew of resistance plotted against length, I got a straight line through the origin which indicates that resistance is directly proportional to length. The scientific explanation for this is that if you double the length, you are doubling the number of atoms in that wire and therefore, increasing the possibility chances of successful collisions between the delocalised electrons carrying current in constantan and the fixed particles thus doubling resistance.
The value I found for the Resistivity of constantan is 4.94x10-7 Ωm measured to 3 significant figures. I believe this is very close to the actual value which is 4.9x10-7 Ωm. This leads me to believe my experiment was successful although there have been some errors.
Anomalies
There was one anomalous result when I was using the 10cm wire. The reason why I got this result was because of the length of wire being so small and hence, heating up quickly giving high current values which lead to more uncertainty.
Errors
- Systematic errors – Ammeter not zeroed
- Rounding off errors – length ± 0.5cm
Screw gauge ± 0.005cm
Voltmeter ± 0.01V
Ammeter ± 0.01A
When there was no current going through the circuit, the reading on the ammeter was not 0. I could have also made a mistake in reading when rounding off.
Heating up of the wire could have altered the resistance values calculated. V=IR only works if temperature is kept constant.
The systematic errors were very small and therefore measurements were still accurate. Overall, the errors did not cause a great difference as I got a calculated resistivity value extremely close to the actual resistivity value.
Evaluation
I feel that I have collected some fairly accurate readings as there was no need to repeat any readings. The points on the graph I drew were close to the line of best fits. Although there were some errors, it didn’t make a huge difference. The fact that the wire was not totally straight may have affected my results reliability. There were also kinks in the wire which may have also affected my results. I tried to overcome the problem of making sure the diameter was measured accurately by measuring it at 6 different places and then finding an average of those readings. I also made sure the power pack was set to 6V throughout the whole experiment. In order to ensure temperature did not make a huge difference, I carried out all the experiment in one room on the same day. However, heating up of the wire could not be avoided even though I did switch off between readings.
I did experience other problems such as trying to get the digital voltmeter to stay constant as it kept moving form one reading to another.
If I were to do this experiment again, I would not use a length of 10cm of wire again in the experiment due to the amount of uncertainty you get. I would also use more accurate equipment for example, a stainless steel ruler as the wooden ruler was worn out especially around the edges and the scale was unclear. I would also try to find a better method of measuring the distance between 2 crocodile clips. I will also try to make sure I could get a wire that would be either 100% (or nearly 100%) straight in order to minimize errors. Taking more readings and repeats increases accuracy and so I would do this to improve my method as I had not taken any repeats for this experiment.
I could also expand my experiment by changing area and investigating its affect on resistivity.