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EE 1105
Pre-lab 1 Data logging, Basic
Instrumentation, and Resistors and
Ohm’s law
Introduction
This lab is concerned, in a first part, with an electrical component called resistor and
some of its properties such as color coding to know its value, its voltage/current
relationship (referred to as Ohm’s Law) and the equivalence of resistors in parallel
and in series are addressed. The properties of a resistor are also compared with
those of a light bulb. In the second part, we are going to work with data logging. We
will be able to analyze data, using statistical tools such as mean, mode, median,
variance and standard deviation.
I. The Resistor
The primary characteristics of a resistor are the resistance, the tolerance, maximum
working voltage and the power rating. Other characteristics include temperature
coefficient, noise, and inductance. Less well-known is critical resistance, the value
below which power dissipation limits the maximum permitted current flow, and
above which the limit is applied voltage. Critical resistance is determined by the
design, materials and dimensions of the resistor. Several varieties of resistors may
be seen on a printed circuit board (PCB) that for instance could be in your car or
computer. The one below on the left is the surface-mount type and is glue-soldered
to wire contacts on the PCB while the one on the right is the through-hole type and
requires that the resistor’s metal wires be placed in holes on the board and then
using a drop of metal solder the resistor is connected to the board.
100
The size of many resistors on a PCB can be read directly off a label as on the left
above, or via a color code as is the case on the right. The color code is defined below
and on the next page. When color-code bands are used to record the size of the
resistor, one starts reading the code from the side where the bands are the closest to
one another.
EE 1105
Color
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Grey
White
Gold
Silver
None
1st
band
0
1
2
3
4
5
6
7
8
9
2nd
band
0
1
2
3
4
5
6
7
8
9
band
(multiplier)
×100
×101
×102
×103
×104
×105
×106
×107
×108
×109
×0.1
×0.01
1ST 2 ND 3 RD
3rd
Accuracy
4th band
(tolerance or
accuracy)
±1%
±2%
±0.5%
±0.25%
±0.1%
±0.05%
±5%
±10%
±20%
Quality
For example, after orienting a resistor as pictured above, let the colors bands
starting from the left be brown, black, orange and gold. Using the chart on the
previous page one can determine that the resistor is of size 1 0 103 with a
manufacturing accuracy of ±5%. Thus, such a resistor would ideally be 10x103
Ohms ( i.e., 10 K Ohms) but due to its manufacturing accuracy could be as little as
9.5 K Ohms or as much as 10.5 K Ohms. The quality band, when present, is used by
some manufactures to indicate the temperature rating of the resistor or the
predicted failure rate of the resistor based on a particular set of operating
conditions.
As indicated above the units of resistance are Ohms, which is symbolized as Ω (i.e.,
10 KΩ). In a schematic one would generally indicate the placement of a 10 kΩ
resistor using the symbol and label
10 kΩ
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EE 1105
Standard Resistor Values
Typically only certain resistor values are available for use in a circuit. In this lab the
normally available resistors are of the ±10% accuracy type. Further when using
±10% resistors the available values in the marketplace are limited to 10, 12, 15, 18,
22, 27, 33, 39, 47, 56, 68, and 82 with multiplier exponents of 0 to 5 (a few similar
standard value resistors with multiplier exponents of 6 can also be found).
Ohm’s Law
Ohm’s Law states that the voltage across a resistor (V) is equal to the electrical
current flowing through the resistor (I) multiplied times the size of the resistor (R),
i.e. V = IR. A resistor does not have a polarity. Note that the current in Ohm's Law is
defined as entering the positive side (+) of the voltage polarity.
I
+
V
―
R
Series and Parallel Resistance
A. Resistors in series
R1
R2
Rn
Resistors in series exhibit properties that are complementary to those of the
resistors in the parallel case. For instance, resistors in series share one wire
(connection point) with only one other resistor. Further, the current through
resistors in series is the same in each, but the voltage across each resistor in
a series of resistors is divided between both of them.
Thus, the voltage across the Req of resistors in series is equal to the sum of
the voltage across each of the resistors in the series of resistors, while the
current through Req is equal to the current flowing through each resistor in
the series.
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The total equivalent resistance (Req) of resistors in series is given by
Req = R1 + R2 +
. . . .
+ Rn
B. Resistors in parallel
R1
Req
R2
. . .
R3
Rn
Resistors are in "Parallel" when both of their terminals are respectively connected
to each terminal of the other resistor or resistors.
As shown on the next page, resistors in a parallel configuration share both of their
wires (connection points) and each has the same voltage across it. This latter
voltage would also be the same as that across the total equivalent resistance, Req.
The electrical currents through the parallel resistors can however be different.
To find the current through Req, one must thus sum the currents through each of the
resistors to obtain the total current that would be measured entering all the parallel
resistors together.
The total equivalent resistance (Req) of resistors in parallel is given by
1
1
=
Req
1
+
R1
1
+
. . . .
+
R2
Rn
To find the equivalent resistance of two parallel resistors, one can use the formula
R1 R2
Req = R1 || R2 =
R1 + R2
Note that as in the above equation that the parallel property can be represented in
an equations by two vertical lines "||" (as in geometry) to simplify equations.
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Data Entry
Before any other work (creating graphs, etc.) it is useful to first record data in a
table. When making a graph, make sure that each axis is labeled (including units)
and that the graph has a title. Further, the controlled quantity (or the quantity for
which you are trying to show a result) is normally plotted on the horizontal axis,
while the measured quantity should be on the vertical axis. Also, attempt to use
reasonable numbers or labels for the axes (i.e., 1, 2, 3, … or 10, 20, 30, … and not
1.23, 3.14, 5.27, … or 7, 14, 21, …).
II. Data Logging
When performing experiments, various statistical and summary data may be useful.
This lab introduces some of these useful parameters, functions and data logging
concepts.
Arithmetic or simple average (Also called the mean and designated as µ.)
X1 + X2 + … + XN
XAVG = µ =
N
Mode
The mode of a set of values is the value that occurs most often. Some data can have
more than one mode.
Median
If data is arranged from least to greatest value, the median value is the one that falls
in the center of the sorted data.
Variance and Standard Deviation
The variance or standard deviation (symbolized with σ) of a set of data indicates the
amount of “spread” that exists in the data around the mean value.
Variance is the subtraction of the mean or average to every single number of the
data collected. After that it will be squared, each results are added together. Then
the whole result will be divided by N(the number of results) minus 1.
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( X1 - µ )2 + ( X2 - µ )2 + … + ( XN - µ )2
var =σ2 =
N-1
St. dev. = σ = √ var
In order to obtain the standard Deviation, you simply obtain the square root of the
variance obtained.
Percent error
The percent error of a measurement indicates the amount of “error” that exists
between the measured value and a predicted value.
Histograms
Histograms are graphs which show the distribution of data in various ranges. In one
form, the histogram can show the total number in each category (Fig.1). In another
form (Fig.2) one can show the relative frequency (or percentage) of each category.
Lab grades
number of students
8
7
6
5
4
3
2
1
0
A
B
C
D
F
grade
Fig.1 Histogram of Lab grades
The following histogram was obtained by calculating the relative frequency. In
order to obtain the relative frequency you will have to follow the next steps:
1. Get the total number of students, from the above histogram in this case is 23
students.
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2. To get the relative frequency of the first grade (A) you simply divide the number
of A’s in the class by 23. 4/23 giving you as a result .17.
3. Repeating step two, you obtain the relative frequencies for the other four grades.
4. The relative frequency helps you to get the probability of a grade in a class.
5. In order to gain the probability of getting an A in a class will be multiplying the
.17 by 100, giving you as a result of 17%. In the class there is a probability of
17% to obtain an A.
Lab grades
0.35
relative frequency
0.3
0.25
0.2
0.15
0.1
0.05
0
A
B
C
D
F
grade
Fig.2 Histogram of Lab grades (relative frequency)
If the data set is large, showing results in the latter form (the relative frequency
histogram) allows one to easily determine the probability of a particular quantity.
For example, the probability of a student earning a “B” in the lab grades shown is
about 30%. Thus, this latter form is also referred to as a probability density
function.
Normal distribution
A quantity (say the variation in the manufacturing accuracy of a resistor) that
exhibits normal distribution produces a special probability density function that is
shaped like a bell curve.
(µ = 0, σ = 1)
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Normal Distribution
0.45
relative frequency
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-4
-3
-2
-1
0
1
2
3
4
x
The continuous normal distribution has the following properties:
1) It can mathematically be described by the exponential function:
- ( x - µ )2 /(2 σ 2)
f(x) = e
√2 π σ 2
where x is the measured quantity, µ is the mean value and σ2 is the standard
deviation.
2) The median and mode are equal to the mean and the distribution is symmetric
around the mean.
Data Entry
When data is entered into your lab notebook/write-up; it is often very important to
note the number of data points used to calculate a quantity. For instance, an
average taken from a large number of data values is much more meaningful than
one take from just a few. Also, before any other work is done it is useful to first
record the data in a table.
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III. Prelab
Do the following work before attending lab:
a) Resistors and Ohm’s law
1) What would the color-band codes be for ±20% 1200 Ω and 300 Ω resistors?
What would be the effective resistance for a 1200 Ω and 300 Ω resistor in
parallel? How about in series?
2) The voltage/current data below was obtained for a pair of resistors. Plot the data
for each resistor and estimate (by eye) a line that best fits each set of data. What
are the slopes of the lines? What resistances are suggested by these slopes?
V-I measurements
for a 1200 Ohm
resistor
V
Volts
0
10
20
30
40
50
60
70
80
90
100
110
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I
Milli-Amps
0
8.4
16
24.1
32.2
40.8
46.4
54.3
62.7
70.5
78.4
86.1
V-I measurements
for a 300 Ohm
resistor
V
Volts
0
10
20
30
40
50
60
70
80
90
100
110
I
Milli-Amps
1.7
29.9
63.1
95.5
128.6
162.5
185.9
228
250
283
315
346
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EE 1105
b) Data Logging
Find the mean, median, mode and standard deviation of the measurements of the
68 Kilo-Ohm resistors. Using this mean value calculate the average percentage
error in these resistors versus the ideal value.
A group of resistors measured with a multimeter
10% 68 Kilo-Ohm
Resistors
69.9
66.2
66.4
64.8
71.8
66.1
65.1
67.5
67.7
67.6
69.4
67.8
66.2
67
67.3
68.5
65.4
65.7
69.3
65.1
69.4
67.1
67.1
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