- Level: AS and A Level
- Subject: Science
- Word count: 2614
Measurement of the resistivity of Nichrome
Extracts from this document...
Introduction
Measurement of the Resistivity of Nichrome (NiCr)
Introduction
In this coursework, I am going to measure the resistivity of Nichrome.
Nichrome is a non-magnetic alloy of nickel and chromium. It is a good conductor of electricity and heat, and has a high melting point. Due to its relatively high resistivity and resistance to oxidation at high temperatures, the wire made of Nichrome is widely used in heating elements, such as in hair dryers, electric ovens and toasters.
What does Resistivity mean?
Resistivity (also known as electrical resistance) is a measure of how strongly a material opposes the flow of electric current. It is normally static and could be varied by changing the temperature. In general, resistivity of metals increases with temperature, while the resistivity of semiconductors decreases with increasing temperature.
High values of resistivity imply that the material making up the wire is very resistant to the flow of electricity. Low values of resistivity imply that the material making up the wire transmits electrical current very easily.
The unit of resistivity is the ohm meter (Ω m).
The resistivity ρ (rho) of a material is given by
- ρ is the static resistivity (measured in ohm metres, Ω·m);
- R is the electrical resistance of a uniform specimen of the material (measured in ohms, Ω);
- L is the length of the piece of material (measured in metres, m);
- A is the cross-sectional area of the specimen (measured in square metres, m²).
From this equation, I can see that the resistivity will be the resistance over length multiplied by the cross-sectional area.
Middle
12.947
70
7.538
13.778
75
8.000
14.706
80
8.478
15.750
85
9.091
16.933
90
9.476
18.286
95
10.100
19.111
100
10.895
20.077
Then I used those data to plot graphs separately for Wire A and Wire B with Excel.
Add a straight best fit line across those points.
Graph plotting
Error bar
To find the error bar on the y-axis, I need to calculate the percentage uncertainty of resistance.
But how to work out that?
From Table A, I could find that the wire is not uniform. So I calculate the standard deviation of the values I got for the diameter. The standard deviation of a collection of numbers is a measure of the dispersion of the numbers from their mean value. If many data points are close to the mean, then the standard deviation is small; if many data points are far from the mean, then the standard deviation is large.
Use the equation:
ρ = R1L /A1 ①
ρ = R2L /A2 ②
Let ①over②, I would get R1/A1 = R2/A2
Rearrange the equation R1/R2 = A1/A2
As A = πd²/4
Therefore R1/R2 = d12/d22
Rearrange it R1 = d12 × R2 / d22
From the equation above I could get that the Rmax = dmax2×R /d2
Maximum value of percentage uncertainty of resistance (Max) = (Rmax - R) / R
Substitute Rmax = dmax2×R /d2 into the equation above,
Max = (dmax2/d2) -1
d = the mean of d
dmax = the mean of d + standard deviation
Use the same method; I got the Minimum percentage uncertainty of resistance
Minimum value of percentage uncertainty of resistance (Min) = (Rmin- R) / R
Rmin = dmin2×R /d2
Min = (dmin2/d2) -1
dmin = the mean of d-standard deviation
The data in the table below is in 3 decimal place
Graph A (Wire A) |
Conclusion
5
0.380
0.277
6
0.370
0.272
7
0.370
0.273
8
0.375
0.272
9
0.368
0.271
10
0.368
0.270
Table B
Length (cm) | Voltage (V) | Current (A) | Resistance (Ω) (3 d.p.) | |
1 | 5 | 0.70 | 1.05 | 0.667 |
2 | 10 | 1.02 | 0.85 | 1.200 |
3 | 15 | 1.20 | 0.64 | 1.875 |
4 | 20 | 1.33 | 0.56 | 2.375 |
5 | 25 | 1.43 | 0.50 | 2.860 |
6 | 30 | 1.53 | 0.45 | 3.400 |
7 | 35 | 1.64 | 0.41 | 4.000 |
8 | 40 | 1.62 | 0.36 | 4.500 |
9 | 45 | 1.65 | 0.32 | 5.156 |
10 | 50 | 1.72 | 0.31 | 5.548 |
11 | 55 | 1.79 | 0.29 | 6.172 |
12 | 60 | 1.88 | 0.27 | 6.963 |
13 | 65 | 1.90 | 0.27 | 7.037 |
14 | 70 | 1.96 | 0.26 | 7.538 |
15 | 75 | 1.92 | 0.24 | 8.000 |
16 | 80 | 1.95 | 0.23 | 8.478 |
17 | 85 | 2.00 | 0.22 | 9.091 |
18 | 90 | 1.99 | 0.21 | 9.476 |
19 | 95 | 2.02 | 0.20 | 10.100 |
20 | 100 | 2.07 | 0.19 | 10.895 |
28-gauge Nichrome wire (Wire A)
Table C
32-gauge Nichrome wire (Wire B)
Length (cm) | Voltage (V) | Current (A) | Resistance (Ω) (3 d.p.) | |
1 | 5 | 1.02 | 0.92 | 1.109 |
2 | 10 | 1.48 | 0.67 | 2.209 |
3 | 15 | 1.72 | 0.56 | 3.071 |
4 | 20 | 1.95 | 0.44 | 4.432 |
5 | 25 | 2.03 | 0.40 | 5.075 |
6 | 30 | 2.12 | 0.35 | 6.057 |
7 | 35 | 2.20 | 0.31 | 7.097 |
8 | 40 | 2.28 | 0.28 | 8.143 |
9 | 45 | 2.32 | 0.25 | 9.280 |
10 | 50 | 2.36 | 0.23 | 10.261 |
11 | 55 | 2.40 | 0.21 | 11.429 |
12 | 60 | 2.44 | 0.20 | 12.200 |
13 | 65 | 2.46 | 0.19 | 12.947 |
14 | 70 | 2.48 | 0.18 | 13.778 |
15 | 75 | 2.50 | 0.17 | 14.706 |
16 | 80 | 2.52 | 0.16 | 15.750 |
17 | 85 | 2.54 | 0.15 | 16.933 |
18 | 90 | 2.56 | 0.14 | 18.286 |
19 | 95 | 2.58 | 0.14 | 19.111 |
20 | 100 | 2.61 | 0.13 | 20.077 |
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Here's what a star student thought of this essay
Response to the question
Response to question - To what extent has the student answered the set question? How explicit is their response?
The writer has approached the set title very well and therefore produced a very high standard lab report. It was ...
Response to the question
Response to question - To what extent has the student answered the set question? How explicit is their response?
The writer has approached the set title very well and therefore produced a very high standard lab report. It was nice to see that the writer before he had started explaining the experiment they were doing, decided to go through all the theory that was involved in both experiments they were planning. It was also good that the writer explained what resistivity was and how it can affect materials. It was very good that the writer looked at the equations they were using and how it could be related to the standard equation of a straight line.
The discussion of the actual experimentation was at a really high standard. It was very good that the writer explained as he chose particular apparatus to take particular measurements. Diagrams of the set up are of a high standard. At first, it wasn't clear why the writer was calculating the mean and standard deviation as it wasn't explained in the theory. Although it was used later when calculating the error, this calculation should have been explained beforehand or calculated the the topic of error was in discussion.
Graphs where drawn to a high standard, where error bars were used in the correct way. Although it is an accurate graph, if you have access to a better graph drawing program (such as QTIPlot) then use it. However, the graphs are really good. Conclusion is written very well and looks at the reasoning as to why their values of resistivity might not have been the value quoted from one of their sources. However, a recommendation is when you are sourcing/referencing, try to use websites such as Wikipedia to the minimum.
Level of analysis
Level of analysis - To what extent does the writer show appropriate analytical skills for this level of qualification? Have they made evaluative judgements using suitable evidence? Have these examples been developed throughout the response and has an appropriate conclusion been reached?
The scientific language behind the report is correct. Units were consistent throughout the writers report. The writer could discuss precision and accuracy in more detail. But a very well produced report.
Quality of writing
Quality of writing - Is the writing accurate in terms of spelling, grammar and punctuation? Has the writer used technical terms expected at this level of qualification? To what extent does the writer follow conventions and expectations for written work at this level?
Spelling and grammar are of a very good standard. The layout was very good. However, I think it would be good if all the pages were numbered. In addition, referencing should try and follow "Harvard referencing"
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