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        RESISTIVITY

Confusion existed in the past regarding the first data table on the data sheet. The data table is called "Resistance Versus Length." At the expense of sounding trivial (or maybe mudding the waters even more), here is an attempt to clear up the confusion.

In general, whenever you see a column with dotted borders (See the picture below. Look at 3rd column) this means that a calulation is required. Whever you see a column with solid borders, this means data should be entered directly as measured.

It is crucial in a laboratory setting to record all data in its most raw form. (The only exception might be to convert the measurement; ie. centimeters --> meters.)

The first data table requires that the student measure the short distance in between each of the screw pairs. These are raw data values.

The second column calls for the length of the wire. The length is a calculation because it is the sum of all the screw pair distances up to that point.

Take the following example:

There is a new version of the data table in Spring 2013.
The new data table gives values for Wire Diameter, rather than wire area.
You will need to calculate the area.
There is also a new row allowing you to record the uncertainty values.
See the Diameter to see where to place these uncertainties.
There is also a movie below dealing with the details for the uncertainties.
Here is the pdf for the new data table.

Here is the MSExcel File (be sure to right click this link to download the file.)

MOVIES

Please note: If the movie is too small,
please watch via youtube using the YOUTUBE button on bottom right of each video.
And, some videos have much higher quality. Find the HD version using the gear icon.

Resistivity: Theory



Resistivity: Procedure



Resistivity: Uncertainties



DMM-01- Inputs and Selector for Amprobe 37XR-A Digital Multimeter



DMM-02- Measure Resistance with DMM Amprobe 37XR-A 



What about a plot? If you need a semi-quick review, watch this movie.
7.5 minutes will get you enough. The whole movie shows a little more.
If you need a longer movie on spreadsheets and plots, 
go to lab 1 schedule and see Spreadsheets link.



Resistivity - Quickie Plot




Begin Q&A Forum for "RESISTIVITY"

Questions concerning the first pre-lab quiz:
1. Question #8 asks for the area of the largest wire we will be using. I am not seeing this anywhere. The lab book just says that the areas are listed on the resistivity board. Am I missing something?
2. Concerning question #9....I am understanding from the lab manual that rho=(1/sigma). So, if rho=.95, then sigma = 1/.95 = 1.052...which is 1.1 with two significant figures (with the appropriate units). However, this also is wrong.
Sorry so many questions. Never had any problems with the pre-lab quizzes for Lab I.
Thanks
Anonymous
Sat. 24, Aug 2002, 23:02
J,
Q#8: You answered N/A and then 0.3.
In the lab manual exists a write-up for each lab.
There is a section for Resistivity. In that is a data table that you will use in class.
Q#9: My algorithm was incorrect for rounding. I have fixed it. Try again.

Don't apologize for asking questions. You are here to learn.
:)
Douglas
Sun. 25, Aug 2002, 05:28

Douglas,
I am getting an incorrect answer for problem # 9, even though I am using the rho=(1/sigma) equation mentioned in the book, and the previous post. Is it possible there is still a problem?
Thanks
Anonymous
Sun. 25, Aug 2002, 14:46
Yes. I normally use three significant figures. With this quiz I asked for two. That creates problems (so I have discovered). I fixed it and your answer is recorded properly. No need to re-login. Sorry; and thank you for asking.
Hey, check this out; (σ) gives a sigma symbol (σ) on a web site.
Douglas
Sun. 25, Aug 2002, 15:11

I'm from a 5-6:50P 2341-002 PhysLab II class. I bought MSCD&UCD LAB II Manual 2040 and 2341 (all sections), but instead of resistance there is section on resonance. What's up with that? Is it a wrong manual?Anonymous
Mon. 02, Sep 2002, 17:52
Dear Student,
Look again for the Table of Contents in the front of the lab manual.
You should find "Resistivity" and "Ohms Law" as they were last week's lab and this week's lab respectively.
There are experiments in the lab manual that we won't be doing this semester, such as "Resonance."
Douglas
Mon. 02, Sep 2002, 18:55

Douglas -
As far as our lab reports go ought we to include excel graphs in our turned in work or simply our graphs that we filled out in the write up literature. Additionally, when the write up asks us to fill in the "k for the least squares fit," where could I find that? I've made all three graphs and have them plotted with equations and trendlines on excel but where can I find "k"?
Thanks
Hotchkiss, John
Fri. 31, Jan 2003, 18:31
jhhotchkissiv@hotmail.com
John, You may turn in your printed-out spreadsheet graphs in place of the hand-written graph paper. (But, Peter may want you to turn in the hand-graphs. You'll know if he said that in class.) On the cover page for your write-up is information about the k for least squares fit. K is the number of data points used in the regression. For this lab, I think you took five measurements.Douglas
Sat. 01, Feb 2003, 06:58

Douglas, just had a quick question about post lab quizes. Is it possible to log into the quiz and print it and exit without submitting it, without losing your one try at it? Anonymous
Mon. 02, Jun 2003, 13:56
Yes. One submit, but multiple prior logins.Douglas
Mon. 02, Jun 2003, 15:41

I can go ahead and login to print out the pre and post labs before I fill things in, right? Then what? Instead of hitting "Submit" can I just close the window? Or will that end up in "spurious results" as my grade for the lab?
Thanks,
Angie
Anonymous
Fri. 22, Aug 2003, 10:30
Don't hit "Submit." Just close the window. Nothing is stored unless you hit submit.Douglas
Fri. 22, Aug 2003, 13:22

Howdy Douglas,
My lab book has a procedure for the resistivity lab, but no write-up (and therefore no explanation of "k" and no sample data table). Do I have a defective manual, or was the write-up jettisoned in favor of the MSExcel template?
Thanks,
Josh
Anonymous
Sun. 24, Aug 2003, 17:09
The write-up's are in the back of the lab manual.
You also have the data table on the CD-Rom.
I will have the entire lab manual online in the next week or so.
Douglas
Mon. 25, Aug 2003, 10:51

Douglas,
For question #4 in the Resistivity postlab, you ask for each measurement name, an average and the uncertainty. Do you want us to include calculated data as well (ex: L/A)?
Thanks,
Megan
McCarthy, Megan
Wed. 27, Aug 2003, 11:02
mccarthymegan@yahoo.com
{Best if viewed on web site.}
State only measured values.
Here is a plausible, complete sample.

Position of Screws, 0.210[m] ± 0.002 [m] (We each repeated the measurement four times and this was our uncertainty.)
Length, 1.000 meters ± 0.003 meters (the wires had a stretch of maybe 3mm)
X-sec Area, 0.05 mm² ± ?? mm² (values given to us)
Resistance, 24.6 Ω ± 0.2 Ω (σ for 5 measurements)
Douglas
Wed. 27, Aug 2003, 11:15

On the post-lab, question #1, we are only aloud 50 words for six pages to summarize, so am I to assume that the summary won't really have any detail of the experiment?
Also, on question #4, do you want us to include all measured values? So there would be 5 Lengths and resistances from table #1, and 5 Lengths, 5 resistances, and 5 areas from table #2, and 1 measured resistivity and 1 measured conductivity.
Thanks.
Anonymous
Sat. 30, Aug 2003, 19:03
You did not measure resistivity nor conductivity. You calculated them from measurements.
Please see my response on the Q&A forum about this very question.
It is just above my response to you (this response.) :)
Douglas
Sun. 31, Aug 2003, 15:07

Hi, I have a question for you. If from the experiment, we found our equation
y=0.97 x + 0.8. And then we need to test the longer wire (but same material), how do we
calculate resistance for that wire? Do we need to use only general formula R = p L/A, or do we need to use R = p L/A + 0.8?
Thank You, Elena
Timoshina, Elena
Sat. 30, Aug 2003, 19:06
elenatimoshina@comcast.net
Please ask your question FROM the web page that relates to your question. Thank you; that helps me organize answers for others to reference.
Visit the Resitivity web page to view the answer to your question because the formating will look better on the web...And because I moved your answer to the Resistivity page... :)

Translate your equation first.
y = 0.97 x + 0.8 becomes
Resistance = 0.97 [Ω mm2m-1] Length Area-1 + 0.8 [Ω]
From that form of the linear fit, we can see the relationship Length and Area have to the Resistance for the nicrome wire. The +0.8 [Ω] is the measurement offset as found through experimentation. Anyone doing the experiment as you did should find the same offset using the same equipment. So the newly predicted resistance measured needs to include the +0.8 [Ω].
Douglas
Sun. 31, Aug 2003, 15:16

How do I make a squared number for answer in the postlab, Ex. 0.57[mme2]? Am I suppose to write it like that or is the way to make it superscript?
Also, we are suppose to put our units is brackets. What about this example, 1.036 [ohm * m]e-1, where it's already in brackets, do we us double brackets, 1.036 [[ohm * m]e-1]?
Thanks
Anonymous
Mon. 01, Sep 2003, 15:59
{Best viewed on website.}
Please use the answer formats button at the top of the quiz to learn how to make superscripts, subscripts, and greek symbols.
0.57[mm<sup>2</sup>] → 0.57[mm2] is what you will find. Also the sample quiz discusses this.

I prefer square brackets simply to be uniform. It helps the units stand out as separate from the variables, but this is in no wise some sort of scientific standard.

e is not good here because it either means the natural number e or it means scientific notation as in 2.3E3 = 2.3*103. It does not mean raise my base to the power of...
Use superscript notation, if powers are what you mean.

I don't know of a unit in Resistivity where you have [Ω-1m-1], but if you wanted this unit, write it as just shown by me or use parenthesis within your single brackets. i.e. [(Ωm)-1] or no parens' as in [Ωm]-1.
I hope this helps.
Douglas
Mon. 01, Sep 2003, 18:14

Hi for question 4 on the post lab. I see that you gave an example above but i'm still comfused. We had similar lengths of wires so i uderstand that example. However, we had different areas of the cross section of the wires, screws unequally spaced and many different resistance readings. How would i narrow down my data to give one general answer. Do i average all the different readings together for that particular set. for instance all the areas of the wires? Also how do you come up with the uncertainty.
My second question invovles question 1 of the post lab. It says to include the theoretical equation, how do you get the y-intercept for this. Is it Resistance=1.1 [? mm2m-1] Length Area-1 + (our experimental y-intercept +/ - our percent discrepancy)? would this formula yield a theoretical equation? also the lab manuel states "if there was a theoretical equation..." does this mean that there isn't one to begin with, since the data is consistant.
thank you kindly,
Im new to this lab style and am very confused at the moment
I guess it will take some getting used to
sorry for the overload on questions
Anonymous
Wed. 26, Jan 2005, 13:04
J,
Good questions.
Yes, an average is fine. Other people like to state a range.
The uncertainty question requires a lengthy answer. Summary: evaluate two numbers and use the bigger one.

First method: what is the resolution of the measuring device? The meter stick can be resolved to about 0.5mm (0.0005m). So the uncertainty is ± 5E-3[m] due to resolution of meter stick.

Second Method: How repeatable was the measurement? Did you have each lab partner independently measure the distance between two screws? If so, what was the "spread" in that data? Let's just say it was a 2mm spread. This number is higher than the resolution, so we choose the higher number for uncertainty. Thus the uncertainty is
± 2E-2[m] due to standard deviation in repeated measurements.
This analysis can be done for most measurements in lab 2. Evaluate both methods and choose the bigger.

Theoretical question don't usually have y-intercepts. Theory normally doesn't contain experimental values (numbers.)
R = ρ L A-1 + Roffset (That is a theoretical equation.)

I think the "if there was..." was within the context of trying to discover the final equation
R = ρ L A-1 + Roffset.
Douglas
Wed. 26, Jan 2005, 13:32

I'm not getting prelab question 7 right. This led me to flip through a CRC handbook, and now I have two questions -
First, it seems like the "expected" resistivity answer would be "N/A", considering that the lab procedure doesn't even officially tell us that the wire is nichrome, never mind which alloy. Am I not thinking straight?
Second, I notice that resistivity in the CRC book is in units of [10^-8 Ohm * meter], which does not appear equivalent to [Ohm * meter / mm^2] since it isn't divided by an area. Any comment on this?
Thanks
Anonymous
Fri. 28, Jan 2005, 10:35
Read the lab manual. It says in bold print:
The expected resistivity of this wire is
ρ = 1.1 Ω mm2 m-1.
This is the theoretical value for ρ. Your slope should be close to this value.

As for your second question:
Sometimes, the units are simplified by reducing the length and area measurements together as m instead of mm2m-1.
1.1 Ω mm2 * (1[m]/1000[mm] * 1[m]/1000[mm]) * m-1
= 1.1 Ω m * 10-6 m-1
= 11 Ω m * 10-8


Douglas
Fri. 28, Jan 2005, 11:07

Hi Douglas,
On question 3 in the post lab, I am struggling with the units for sigma. The pre-formatted cell on the Resistivity Excel file gave a label of (Ohm m)^-1, but I disagree. If rho equals the reciprocal of sigma, then shouldn't the units be reciprocals also? Thus, the units for concuctivity should be [m/(Ohms*mm2)]... If I'm correct, I'll correct my data sheet. If I'm wrong, I need explanation for #3 in my post lab!
Please help (and thank you),
Sara
Pauquette, Sara
Thu. 01, Sep 2005, 19:01
rayelana@msn.com
I am glad you disagree. The units for σ
are indeed [m Ω-1mm-2].
The data tables for lab2 purposefully have some incorrect and missing units in hopes students are carefully checking everything.
Douglas
Fri. 02, Sep 2005, 03:40

Hi Douglas,
For the resistivity post lab #2, when stating the equation of our data for resistance versus length/area, do we include values for L/A and resistance? That is do we just say, Resistance [ohms]= 0.9... [ohms mm squared /m] * L/A + 1.1[ohms] or do we need to put values for resistance and L/A?
oladiran, seun
Mon. 04, Sep 2006, 11:57
seun_diran@yahoo.com
Good question. Don't put values for L/A nor Resistance. You built a "model" equation that is based upon your data for your experimental set-up. Leave L/A and Resistance so that "someone" can use your equation to predict values given some input.
Oh, don't forget, you need to format the equation when you are in the quiz software. I realize you didn't have the tools when you composed this post. But, this is what it should look like
Resistance [Ω]= 0.973 [Ω mm2m-1] * L/A + 1.1[Ω]
Douglas
Tue. 05, Sep 2006, 05:04

Hi Douglas,
For postlab #2, I don't understand what the expected (theorectical) resistance is suppose to be. I guess I'm confused on what the vertical intercept is supposed to be for this equation. The slope is given as 1.1 ohm mm^2m^-1, but I don't know what the vertical intercept is suppose to be.
Anonymous
Fri. 01, Jun 2007, 01:28
The theory equation will look like your data's equation except for two things: the slope will be the value for the expected ρ for nichrome; and intercept is zero because it is theory (no offset.)Douglas
Fri. 01, Jun 2007, 06:04

Hi Douglas,
I had few questions about the postlab #3. I read the forum already but I am still confused. I understand the format but I am not clear on how to get the values. For the position of screws, do we take the length of the wire between each screw or is it the length of the wire between one screw and the left side of the resistance board? How do we know the uncertainty. For the given example, you wrote that we performed the experiment four time but I am confused on how that brings the value of uncertainty. For the length measurement, how do we know the wire stretch and how is that an uncertainty to the measurement? For cross-sectional area, resistance and position of screw, we perfomed the experiement 5 times, so how do we get one measured value? Do we take the average of the range? How do we know the uncertainty in cross sectional area and resistance? I am totally confused by the whole question! I also had a question about the write-up. Do we need a theory line for resistance vs. L/A graph? Sorry about asking too many questions. Thanks for the help.
Monil
Shah, Monil
Wed. 29, Aug 2007, 23:09
Monil.Shah@email.cudenver.edu
Wow! Let's start at the beginning. Once upon a time... :)

We measured the distance between screws with a meter stick that had ±1mm resolution, but one can argue for 0.0005m (1/2 mm) readability. But, is that a valid uncertainty for how we used or utilized the meter stick? Was parallax an issue? Was stretched wire an issue? Yes, and yes. Therefore, you may estimate your uncertainty. We can reason (just by using the physical measurement on that wired system) that ±0.0005m is out of the question; 0.5mm is way to small for uncertainty. Parallax probably offers a resolution of about 1.5mm for each side of the measurement, therefore 3mm for the whole measurement. One way to discover the 1.5mm is to repeat the same measurement multiple times and take the standard deviation. So, we could say ±3mm(σ found by repeated measurement, uncertainty comes from parallax on both sides of the measurement.)

On a side note: You may want to report your uncertainty as a relative uncertainty. σ/Measurement*100%. This is a dimensionless value, a percentage, a relative uncertainty. (How does the uncertainty σ relate to the actual measurement ---> relative uncertainty.)

Was the wire bent severely? If so, then you might need to note an offset as well as an uncertainty.

For the other measurements you can just list a range instead of an average. For instance Area from 0.03 - 0.20 mm2 (not measured by us; therefore uncertainty unknown.)

Resistance uncertainty should be discovered in the lab during the experimentation. You probably would have found the meter resolved to 0.1[Ω] but showed a repeatability of ±0.2[Ω]. Again, it is important to not only look at the resolution of a device but also the ability it (or you and the device) has to repeat a measurement.

Theory line for R vs. L/A graph? Technically, No, since we didn't specify it for this particular experiment; but it is a worthy exercise, if you have a little time.

I hope I covered your questions.
:)oug
Douglas
Thu. 30, Aug 2007, 13:13

I think that there is a small error in the spreadsheet provided on the CD. Specifically, the units provided for Length/Area in cell C17 are m/mm^-2. Should this not be m*mm^-2 or m/(mm^2)?Beckman, David
Sat. 26, Jan 2008, 12:48
beckmada@msudenver.edu
Nice work! Lab 2 has "purposeful" errors on the spreadsheet templates that students have to find and correct before handing in the "Write-Up."
Douglas
Mon. 28, Jan 2008, 13:17

Hi Douglas,
I just took the resistivity prelab and missed question 7. The question asked the value for resistivity, given y=0.9723x +1.0915, with two sig figs for answer. My answer was 0.97 [ohm *(mm)^2 / m]. I got this answer marked wrong, however, I am convinced this is the right answer. Am I missing something here? Thank you !!
Anonymous
Tue. 25, Jan 2011, 11:58
The question states:
What is the value for the expected resistivity of the wire?
The expected value is not from your data, but rather from some look-up table of expected values. The lab manual reports the expected value for nichrome wire.
Douglas
Wed. 26, Jan 2011, 03:47

This might be a silly question, but I'm a little confused. In the equation R=(rho)(L/A) +b I see that rho is the resistivity, which is also the slope. So in question #3, when we are asked to list the measurements, you ask for resistance. Is resistance the same as resistivity, or is resistance the R in the equation above (which would be the b value when we listed our measurement)? Thanks!Anonymous
Sat. 29, Jan 2011, 00:04
R is resistance measured in [Ohm].
rho is resistivity measured in [Ohm mm^2/m].
Douglas
Mon. 31, Jan 2011, 18:55

Hello, I have a few questions about what you were looking for on the post lab. For question number 6 it is asking for the resistivity of Nichrome, which in our lab says it is 1.1. I answered 1.10 because it asked for 3 sig figs and I got the question wrong.
Along the same lines, I thought to figure out the conductivity you just divided 1/resistivity so i thought for the Nicrome it would be 1/1.1 which would be 9.09e-1 but that was also incorrect. Could you help me figure out what I am doing wrong? Thanks for the help.
Anonymous
Wed. 25, Jan 2012, 14:08
Question 6 says "...for this wire..."
The expected resistivity is indeed 1.1 [Ω mm2 m-1]. But did your wire in the lab behave exactly that way? Or does the graph reveal the resistivity for that wire?
Yes, ρ = 1/σ But again, interpret the linear trend from the plot to find the value for ρ.

In a laboratory we have to be careful to distinguish between real data and theory.
Douglas
Sat. 28, Jan 2012, 19:39

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