Download Exercise 8

Exercise 8
Resistors and Multimeters
I. Purpose
The purpose of this exercise is to teach you a little bit about resistors, electrical resistance,
multimeters, and wiring up electrical circuits. First, you will build some resistors of different
shapes and sizes and measure their resistance using a multimeter. Then you will find out what
happens when you connect together resistances in series and see how the total resistance adds.
In the last part, you will examine what happens when you connect resistors in parallel.
II. References
If you have had no prior experience with electrical circuits, you should read this write-up
before coming to the lab and you should do some additional reading about current, voltage,
resistance, and Ohm’s law. Most introductory physics texts have at least one chapter on such
things; see for example Chapter 22 from "Physics for Scientists and Engineers-Volume 2" by
Tipler. There are also many books written for people who want to build circuits and want a
more practical-minded discussion, see for example: "Getting Started in Electronics" or
"Engineers Mini-Notebook: Formulas, Tables and Basic Circuits" both by Forest M. Mims
(Radio Shack).
III. Equipment
#2 pencil
resistor board
multimeter
IV. Building your own resistors
(1) Resistors can be made from many different materials and come in a wide variety of shapes
and sizes. The most basic requirement is that the material from which a resistor is built has
to let electrical current flow through it; i.e., it is an electrical conductor. In practice, most
resistors are made from metal wire, thin-films of metal, or amorphous carbon which is a noncrystalline semiconductor. Very roughly speaking, a semiconductor is a relatively poor
conductor of electricity.
(2) In this lab, you will start by constructing your own resistors using a pencil and a piece of
paper. The pencil "lead" is actually made of graphite, which is a form of carbon. Graphite is
a semiconductor and so can be used to construct resistors.
(3) Turn to the next page, which shows two rectangular regions. Tear this page out of your
manual.
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Physics 174 - Exercise 8 - Graphite Resistors
NAME:
SECTION:
Endcap
tab
tab
R1
R2
tab
For this lab, do all your shading and make all your measurements on the above resistors!
( in case you mess up the first one…)
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(4) Now use your pencil to fill in the two rectangular regions labeled R1 and R2. Stay within the
solid lines and include the tabs. To get a good consistent resistor, you have to put down a
fairly uniform coating of graphite. The best way is to use a sharp number 2 pencil and place
the paper directly on a hard smooth surface (i.e. on your desktop) - press firmly and shade in
the regions darkly and you shouldn't have a problem. However, don't spend more than a few
minutes total on this.
(5) When you are done, show your instructor and get your checksheet signed.
V. Measuring the Resistance of a Single Resistor
(1) Set up your spreadsheet as indicated in the diagram below.
PAPER RESISTOR MEASUREMENTS
SERIES
PARALLEL
R1 (kohms)
R2 (kohms)
RA (kohms)
RC (kohms)
Avg R1 (kohms)
Avg R2 (kohms)
Avg RA (kohms)
SD of R1
(kohms)
SD of R2
(kohms)
SD of RA (kohms)
SD of RC
(kohms)
sigma_R1
(kohms)
sigma_R2
(kohms)
sigma_RA (kohms)
sigma_RC
(kohms)
SERIES
PARALLEL
RESISTOR BOARD
MEASUREMENTS
Expected RA
Avg RC
(kohms)
R3 (ohms)
R4 (ohms)
RB (ohms)
Expected RB
RD (ohms)
uncert_R3
(ohms)
uncert_R4
(ohms)
uncert_RB (ohms)
uncertainty
uncert_RD
(ohms)
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Expected RC
Expected RD
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(2) Use your multimeter to measure the resistance of R1. To do this, switch to the  scale and
place a lead on the tab at each end of the first resistor. Let things settle down for a few
seconds. You should find a value between about 700 k and 5 k. A value in the 50-100
krange is best. If the meter shows a much larger resistance or indicates that the resistance
is off scale, then go back and shade in the resistors more with your pencil. Once you are
happy with the value, for the rest of this lab don't shade in the body of this resistor
anymore or you'll have to repeat all the measurements.
Show your instructor and get your checksheet signed.
(3) Measure the first resistance R1 five times, each time picking up the leads and putting them
down again on the tabs near the end of the resistor. This should only take you about a minute
to do. Record your values in your spreadsheet.
QUESTION 1: You may find a noticeable spread in the data. What's causing this variation?
Briefly explain.
(4) Repeat your measurements for resistor R2. If R2 looks unusually large, just shade it in some
more, but don't worry about it if it’s within a factor of 2 of R1’s value. Once you are happy
with the value, for the rest of this lab don't shade in the body of this resistor anymore or
you'll have to repeat all the measurements.
(5) Calculate the average resistance and the standard deviation of the 5 measured resistances of
R1. Do the same for R2.
(6) You learned in Exercise 2 that the uncertainty can be reduced by averaging together a set of
measurements of the same quantity. Here, you measured the resistance in the paper resistors 5
times, so the uncertainty in the average of these 5 measurements should be smaller than the
standard deviation you just computed.
QUESTION 2: What is the uncertainty in the average resistance for each resistor? Call these
sigma R1 and sigma R2 in your spreadsheet.
(7) Now take a look at the resistor board in front of you. The carbon resistors are the cylinders
with the color bands on them. These bands tell you the resistance value of the resistor. The
code gives you the resistance as two digits and a power of ten. To use the bands, first identify
which band is closest to an end of the resistor (this is the orange band in the picture below,
because it is much closer to the left end of the resistor than the brown band is to the right end
of the resistor). This is the starting band. Using the color code table below, write down the
digit corresponding to the color for this first band. Next, write down the digit corresponding
to the color of the second band. Next to these two digits, write "x10 " and in the exponent of
the ten, write down the digit corresponding to the color of the third band. A fourth band, if it
exists, shows the tolerance. Gold corresponds to 5% variation and silver to 10% variation.
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Black
0
Brown
1
Red
2
Orange
3
Yellow
4
Green
5
Blue
6
Violet
7
Grey
8
White
9
Thus a resistor marked with Orange (first band), Black (second band), and Brown
(third band) is read as 3 0 x 101 = 300.
(8) Find the 300  resistor and the 1 k resistor and measure and record their values and
uncertainties as R3 and R4 . You only need to record these once.
Show your instructor and get your checksheet signed.
(9) Manufacturers of resistors specify the accuracy of the labeled resistance value by the
color of the fourth band on the resistor. If the fourth band is silver, then this means
that the true value of the resistance is supposed to be within 10% of the value given
by the first three colored bands. Thus a 300 nominal resistor with a silver band
should have a true value of resistance within the range 270 to 330.
However if you measure the resistance with an ohmmeter then the situation is
completely different. The resistance is the best estimate of the measured value and
the uncertainty is given by the uncertainty in this measured value. Here, we’re going
to ignore the “accuracy” of the meters, and consider only their “precision”.
QUESTION 3: What are the uncertainties in R3 and R4 ? Explain how you arrived at
your answer, and record these as sigma R3 and sigma R4 in your spreadsheet.
QUESTION 4: How close are R3 and R4 to their expected values? These resistors are
sold as being 5% tolerance, is this reasonable?
Fill in your spreadsheet. Show your instructor and get your checksheet signed.
VI. Resistance in series
(1) Now use your pencil to connect the two resistors R1 and R2 on the torn-out page in series by
connecting the top of resistor R1 to resistor R2 (so that it looks like the figure below). Make
sure the top endcap connection is well-shaded in. Note: do not fill in the resistors below,
make the connection on your resistors on the tear out page by shading in the top endcap
so that it looks like the sketch below.
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(2) Measure RA , the resistance of the series connected strips R1 and R2, by placing the ohmmeter
leads on the tabs at the bottom of R1 and the bottom of R2. Also, find the uncertainty RA,
using the same method you did to find the uncertainty in R1 and R2 .
Show your instructor and get your checksheet signed.
QUESTION 4: Qualitatively, how well does your result agree with RA=R1+R2?
Show your instructor and get your checksheet signed.
(3) Now go to the resistor board and connect the 1 k and 300 resistor in series as
shown below and measure the combined resistance RB and find its uncertainty. Use
the same method for the uncertainty as you did for R3 and R4.
1k
300
Series
Now we want to compare the measured series resistance RB with the sum of the two resistors on
the resistor board. For this result, you can be somewhat quantitative in answering the
question.
You can compute the quantity RBR3+R4, which should be close to zero. Let’s call this Rdiff .
Using error propagation, you can compute the uncertainty in Rdiff . (see labs 5 or 5* if you need
reminding on how to propagate uncertainties). If Rdiff is closer to zero than its uncertainty,
then we can say the result agrees with expectation. If it is not, then ideally we’d need to do a
chi-squared test to find out what is the probability of getting the result that we did.
QUESTION 5: How well does your result agree with RB = R3+R4 ? Use the technique above to
answer this question.
VII. Resistors in parallel
(1) Now use your pencil to connect resistors R1 and R2 in parallel. Do this by filling in the
endcap at the bottom of resistors R1 and R2 so that in the end, your resistors look like the
sketch below. Note: do not fill in the resistors below, make the connection on your
resistors on the tear out page so that it looks like the sketch below
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Show your instructor and get your checksheet signed.
(2) Now measure the resistance RC , the parallel combination of R1 and R2 , and find its
uncertainty, Rc , by placing the ohmmeter leads in the middle of the cross bars.
QUESTION 6: Qualitatively, how well does your result agree with the expected result
RR
RC  1 2 )?
R1  R2
Show your instructor and get your checksheet signed.
(3) Now go to the circuit board and connect the 1 kand the 300 resistors in parallel as
shown below and measure the combined resistance, RD and its uncertainty Rd.
1k
300
Parallel
QUESTION 7: Qualitatively, how well does your result agree with the expected result
RR
RD  3 4 )?
R3  R4
Show your instructor and get your checksheet signed.
(4) Email a copy of your work to yourself, submit via WebCT, and turn in your
checksheet.
VIII. Homework
(e-mail in your revised version of the lab as well as the homework)
No homework this week
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