I assume that you know:

- how to do the wiring
- how to set the multimeter on the right type of measurement
(function choice: current, voltage, resistance) and how to switch it to the right range; if you forgot ... read again Appendix 1 (pp 118, 119) of the Lab. Manual.
- how to connect the milliammeter (in series with the device through which you are measuring the current)
- how to connect the voltmeter (in parallel with the element of circuit across which you measure the voltage drop)
- how to take the measurements

Without these basic skills, this page, which deals mainly with the analysis side of the experiment, is of no help!

 

Foreword on errors

Use the 1% of the reading + 1 digit rule as advised in the guide-sheets.

Of course, this accuracy specification contradicts the specs sheet of the multimeter (true values are: for voltage 0.25% , for mA 0.75% a.s.o.) but that  was for the regular lab hours.

They ask you to use this increased accuracy error to make sure you have a chance to plot error bars and do some error calculation easier and faster.

Reading error on a digital instrument is 1/2 of the last displayable digit.

Example: on the "20V" scale you have readings like 7.34 V, 11.35 V a.s.o. For this scale 1 last digit is 0.01 V. The reading error on this scale would be 0.005 V.

Accuracy (calibration) error is ( 1% of the reading + 1 digit).

According to the explanatory web-pages to the ErrorAnalysis assignment (see the "Accuracy Error" section) this rule for accuracy (calibration) error has to be understood indeed as "plain adding" of the (1% of the reading) to the (1 digit), with appropriate rounding to significant digits. You can see how this works in the table of Section 12 of the above mentioned document.

A few other comments regarding DC-I error estimation can be found here. I discuss there the ( 1% of the reading + 1 digit) rule for the accuracy error, and explain why it is important to measure things on the right scale (so that the effect of 1- and 1/2-digit errors is minimized).

Regarding the same issue of precision vs. accuracy errors you may read an article on the newsgroups (or the local version of it, in case the original is missing).
For even more information on the digital and analog multimeters see the "Making Electrical Measurements: Part 1" section on the R.S.R. Electronics equipment manufacturer tips pages. I must warn you: the information there is a bit of overkill for the LabTest, so you may safely ignore it (if you are not interested in the nitty-gritty details of how the multimeter works).
For those interested in nitty-gritty details you may read about digital instruments and their specifications here, on Tektronix's site. The same warning applies: the level of description there is too high for 1st year student (unless you're a "geek").

A-meter before/after V-meter ?

Regarding the wiring: make sure you are able to explain why one has to choose the scheme (7c) instead of (7d) or vice-versa (see Lab. Manual, pg. 57). This might be a nice interview question (say, for an A+) :-)

Hint 1:   According to the multimeter's specs posted on UPSCALE, the internal resistance of the V-meter is about 10-MOhm on all scales, while the A-meter's inner resistance is (0.25V / 2mA) = 125 Ohms (on 2mA scale), 12.5 Ohms (on 20mA scale) and 1.2 Ohms on the 200mA scale.
Given these values, you are now in the position to calculate which values of R are better measured with the scheme (7c) and which ones go better with (7d).
Do this calculation before the lab. test since you don't have time for it during the test. Ideally, you should remember one typical value for the threshold value of R and decide accordingly - once you have R measured with the Ohmmeter you'll know which circuit to use.

Hint 2:   If you encounter difficulties with the above calculation (and even if you don't, read it anyway) take a look at the 2 pages (.pdf)   that I wrote on this matter.
The rule of choosing the right circuit is as follows: if R is large (say, larger than 10KOhms, with V-meter on the 20V scale and A-meter on the 20mA scale), then you should use the circuit in which the V-meter is before the A-meter (looking at the circuit left-to-right). If not, then the opposite applies.

Note:  Although it is important, in principle, to choose the right circuit [ (7c) or (7d) ], in practice (at the LabTest) it makes little difference which one you choose. This is due to the large accuracy (1%) error that you have, which luckily enough overcomes the error of method (i.e. systematic (accuracy) error) you introduce by using the wrong scheme.
Please note, however, that the error of method shifts your results either up or down, while the (1%) accuracy error is used here with "±".

Moral 1:  Try to use the right circuit from the very beginning. Use Ohm-meter first, to see which is the value of the resistance and then choose the appropriate circuit.

Moral 2:  for the LabTest, unless your R value is either very low (say, below 2kOhms) or very large (say, above 50kOhms), the accuracy error induced by a wrong choice of the circuit ( (7c) instead of (7d) or vice-versa) is smaller than the accuracy error of 1%. You still get an acceptable agreement, (but with the wrong method...).
Note however, that you'll lose points for the wrong choice of the circuit - even if your results look reasonable (as per Moral 2).

Taking measurements with enough significant digits

For the measurements of resistance, current and voltage choose the range which gives you 3 or 4 significant digits.
Do not use an inadequate range, which gives you only 2 digits.
For the purpose of the lab. test the optimum is 3 digits (it's enough and it's not overkill - see some comments on this matter).

Why ? 
Readings of voltage and current with 3 or more significant digits minimize the effect of the 1-digit or/and 1/2-digit errors, and leave you with only the 1% accuracy error as your error for your measurements of V and I.
This makes your life (and error calculations) a lot easier! Make sure you understand why this happens!

Examples (of choice of the range):
Good: 0.545mA (on 2mA scale) 7.13V (on 20V scale), 1.785V (on 2V scale)
Bad: 0.5mA (on 200mA scale), 1.5V (on 200V scale)

Try to take all the V  and I  measurements on one scale (avoid changing the range). Say, measure the voltage on the 20V scale and the current on the 20mA scale (or the 2mA scale - use the one which gives you 3 significant digits).
No need to go beyond 20V with the test voltage.
Why?
This simplifies the assessment of scale-related errors (say, the 1/2 reading error and 1 last digit (accuracy) error are negligible compared to 1% accuracy error).

What is important to do in this lab. test experiment?

Measure the resistance R with 2 (two) methods and COMPARE the results!

a) First you measure R with the multimeter set as Ohm-meter.

Say, you got R = (1.80 ± 0.03) kOhm

Details: If this R is measured on the 20kOhm scale, then this would be the right quotation: (1% of the reading) is 0.018 kOhm, and (1 last displayable digit) is 0.01 kOhm. Using the formula for the reading error this gives you 0.028 which is to be rounded up to 0.03.
Here, an error quoted as 0.02 kOhm seems to me a bit of underestimation (0.02 would result as a rounding of 0.018 only)... I know looks tricky, but nevertheless it's true. Quote it 0.03 kOhm.

On the other hand, once you've seen that R = 1.8 kOhm you may switch the Ohm-meter to the 2-kOhm range, and measure the resistance more precisely.
Say, you get R = 1.805 kOhm. The (1% of the reading) is still 0.018 kOhm, but now the (1 last displayable digit) is a mere 0.001 kOhm.
Hence the total error is 0.019KOhm, which of course gets rounded to 0.02kOhm.

Above we've just seen how important is to choose the right range if you want (and you definitely want) to get a better precision of the measurement.
On the 20-kOhm scale the relative error turned out to be 1.6% while for the 2-kOhm scale the relative error is 1.1%.
Eventually, you know that you did the right choice of the measurement range because the relative error turned out to be close to the accuracy of the device, which is the best you may expect (1%, in our case).

b) Take the measurements of (V,I) for the "unknown" resistor.
Plot your data on a (V vs. I ) graph.

Error bars would be probably visible only for larger values of V and I
(typically 1% of the value plotted, for both V and I , but this 1% is big enough to be represented only for large values of V and I)
(see how to figure out whether the error bars are displayable in my Free Fall notes)
I strongly suggest that you compare (during your home preparation for the lab. test) your graph with what the Faraday's fit program gives you.

c)   Determine the resistance R from the slope of the graph.

The error in the slope may be determined by "swinging" a bit the fit line.
READ the Lab manual for details on fitting techniques (pp 133-140)!

Show on the graph which are the extreme fit lines that can be drawn through your points.

BE careful: the extreme fit lines MUST cross the origin (0,0) of the graph, as DOES the best fit line!
Why?
Read your lab. notebook to see my comments (if you did this plot wrong during the year I'm sure I wrote something on that matter).

Read Lab manual (page 136 ...) on how to get the error with the method of maximum an minimum slope lines !

Let's assume that you got from the graph: R = ( 1.78 ± 0.04 ) kOhms

Conclusion

Well, in this case you may be happy! The two estimates for R agree within the errors (because the error intervals overlap).
Nevertheless, don't assume the reader sees this (or wants to see...).
You should write this clearly in your report (at the very end)!

 

Last but not least: your report must be SHORT, CLEAR and NEAT !

The TAs have only a few minutes (3-5) to mark each report.
Apply the strategy: "better less, but better"!

Be short but precise at discussions and explanations ...since TAs (me included...) look mainly after tables, graphs and the right measurement and result quotations (='insider' information what I'm telling you...)

Perhaps, I oversimplify the real life situation...so, write as much as you feel is needed to explain your point!
The grader always finds time to read your report completely :-)

 

Summary

The error calculus (propagation), is not that important at the Lab. test. Long introduction and extensive explanations are to be avoided!
Please, concentrate your efforts on getting the correct data, with proper error quotations. The final result should be the correct mean value of the resistance with 2(two) methods:

(a)  using the multimeter as an Ohmmeter
(with error quotation, accounting the reading and accuracy errors, as discussed above)

and

(b)  from the slope of the graph (V vs I )
(with or without error; better with :-) time permitting ...)

Besides, your goal is to show that you can fit your (V,I) data to a straight line (of constant slope). This actually tells you that Ohm's Law is verified.

 
Last revised: July 06, 2003
© Sorin Codoban, 2003.

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