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Measurement of the resistivity of Nichrome

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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

class="c2">0.273

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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5 star(s)

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"

Reviewed by cpdavis 18/02/2012

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