Photo by: pixabay.com @ pexels.com
By:
Huixin Wu
Ohbong Kwon
Version 1, February 2019
Introduction to Circuit Analysis Laboratory
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This Introduction to Circuit Analysis Laboratory Manual, by Huixin Wu and Ohbong Kwon is
copyrighted under the terms of a Creative Commons license:
This work is freely redistributable for non-commercial use, share-alike with attribution
Published by Huixin Wu and Ohbong Kwon via CUNY OER @ February 2019
About the Authors:
Professor Wu was the course coordinator of the ac circuit analysis course when she worked
as an instructor in NYCCT. As the course coordinator, professor Wu updated the course outline
and also created homework and exercises to complement the learning materials for the course. She
also has participated in grants and has experiences in creating new teaching terminologies for
engineering technology students. She was the PI of the PSC CUNY Adjunct-CET grant titled
“Training courses on MATLAB Fundamentals”, and the CO-PI of the National Science
Foundation (NSF) STEM grant titled “A video Lecture Library and an Interactive Systems for
Computer Programming Concepts”. Currently professor Wu works as a lecturer at QCC.
Besides from her teaching schedule, she is the lead of the curriculum development
of TechWorks grant, and a faculty mentor of the students Undergraduate Research Project
program at QCC. Professor Wu has taught both the circuit analysis, dc and ac, course and
laboratory in NYCCT and QCC.
Professor Kwon is an assistant professor in the department of the Computer Engineering
Technology. He is the EMT program coordinator and the course coordinator of the ac circuit
analysis in NYCCT. He has been teaching dc and ac circuit analysis courses for several years and
updated curriculums for the lecture and lab of circuit courses. He participated in a series of Open
Educational Resources workshops in Spring 2016 and developed the supplementary OER website
for EMT Laboratories which provides students more information about lab components,
equipment, and breadboarding in the lab.
For more information or feedback, contact:
Huixin Wu, Professor
Engineering Technology Department
Queensborough Community College
222-05 56th Avenue, Bayside, NY 11364
hwu@qcc.cuny.edu
Introduction to Circuit Analysis Laboratory
Ohbong Kwon, Assistant Professor
Computer Engineering Technology
Department
New York City College of Technology
300 Jay Street, Brooklyn, NY 11201
okwon@citytech.cuny.edu
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Preface
This lab manual is intended for use in DC circuit analysis laboratory for a two and four year
engineering technology program. The laboratory manual contains 15 weekly lab experiments that
include brief introduction of the experimental topics, step by step procedures, tables and graphs to
record measurements, and questions to reinforce the understanding of the theory with the
experimental results.
Each lab experiment is designed to be completed using a two to three hour practicum period. The
topics range from basic laboratory procedures and resistor identification through series-parallel
circuits, mesh analysis, superposition theorem, Thévenin’s theorem, maximum power transfer
theorem, and concludes with an introduction to capacitors and inductors. For equipment, each lab
station should include a dual adjustable DC power supply and a quality DMM capable of reading
DC voltage, current and resistance.
A Note from the Authors
This collaborative project between the department of Engineering Technology in Queensborough
Community College, QCC, and the department of Computer Engineering Technology in New
York City College of Technology, NYCCT, is based on creating two laboratory manual for the
course of dc circuit analysis and ac circuit analysis. In QCC, the circuit analysis courses are major
required courses for students on most of the engineering technology majors. In NYCCT, the
circuit analysis courses are major required courses for students in the Electromechanical
Engineering Technology and Computer Engineering Technology programs. Creation of these two
laboratory manuals that covers the appropriate materials to a sufficient depth of learning circuits
analysis while remains readable and accessible manner for the students.
Acknowledgements
I want to give my thanks to my mother Wanxia who has taught me to trust in myself, in my abilities,
and in my dreams. As my mom says: “always do with the best you can offer!”
I also want to give thanks to the support of OER in QCC that helped me organize the necessary
documentation for the publication of this manual. To the professors of the department of
Engineering Technology who contributed ideas for the development of this laboratory.
Huixin Wu
I would like to thank to the support of OER in CityTech to give all information how to initiate
and organize this lab manual. Special thanks to Prof. Cailean Cooney for sharing her expertise
and Prof. Jeremy Seto for his technical assistance. I am also grateful to Sunghoon Jang, Chair of
Computer Engineering Technology, Julia Jordan, Director of Faculty Commons, Associate
Provost Pamela Brown, and Provost Bonne August for their continuous support.
Ohbong Kwon
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CONTENT
Lab Experiment 1 – Math Review
1.1 Powers of Ten ......................................................................................................................................... 6
1.2. Scientific and Engineering notation ....................................................................................................... 8
Lab Experiment 2 – Resistance
2.1 – Resistors and Color Coding ................................................................................................................ 25
2.2 – Breadboard/Protoboard .................................................................................................................... 31
Lab Experiment Procedure.......................................................................................................................... 32
Questions .................................................................................................................................................... 36
Lab Experiment 3 – Voltage and Current Measurement
3.1 – Voltage and Current ........................................................................................................................... 37
Lab Experiment Procedure.......................................................................................................................... 39
Questions .................................................................................................................................................... 52
Lab Experiment 4 – Multisim
4.1 – Introduction to Multisim .................................................................................................................... 53
Lab Experiment Procedure....................................................................................................................... 57
Lab Experiment 5 – Ohm's Law and Series Circuits
5.1 – Ohm’s Law .......................................................................................................................................... 67
5.2 – Series Circuits ..................................................................................................................................... 68
5.3 – The Voltage Divider Rule (VDR).......................................................................................................... 70
5.4 – Non-Resistive Series Circuits .............................................................................................................. 71
Lab Experiment Procedure.......................................................................................................................... 72
Questions .................................................................................................................................................... 77
Lab Experiment 6 – Parallel Circuits
6.1 – Kirchhoff’s Current Law (KCL) ............................................................................................................ 78
6.2 – Components Connected in Parallel .................................................................................................... 79
6.3 – Total Resistance and Conductance in a Parallel Circuit ..................................................................... 80
6.4. – The Current Divider Rule (CDR) ......................................................................................................... 82
6.5 – Applications of Parallel Circuit ........................................................................................................... 83
Lab Experiment Procedure.......................................................................................................................... 83
Question...................................................................................................................................................... 88
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Lab Experiment 7 – Series-Parallel Circuits
7.1 – Series-Parallel Circuits ........................................................................................................................ 89
Laboratory Experiment ............................................................................................................................... 92
Questions .................................................................................................................................................... 99
Lab Experiment 8 – Power
8.1 – Introduction to Power ...................................................................................................................... 100
Lab Experimental Procedure ..................................................................................................................... 101
Questions .................................................................................................................................................. 106
Lab Experiment 9 – Short & Open Circuits and Switches & Relays
9.1 – Short & Open Circuits....................................................................................................................... 107
Lab Experiment Procedure........................................................................................................................ 110
Lab Experiment 10 – Mesh Analysis
10.1 – Method of analysis: Mesh analysis ................................................................................................ 117
Lab Experiment Procedure........................................................................................................................ 123
Questions .................................................................................................................................................. 128
Lab Experiment 11 – Superposition Theorem
11.1 – Superposition-Two Energy Sources ............................................................................................... 129
Lab Experiment Procedure........................................................................................................................ 130
Question.................................................................................................................................................... 135
Lab Experiment 12 – Thévenin's Theorem and Maximum Power Transfer
12.1 – Thevenin’s Theorems ..................................................................................................................... 136
12.2 – Maximum Power Transfer.............................................................................................................. 136
Lab Experiment Procedure........................................................................................................................ 137
Questions .................................................................................................................................................. 144
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Lab Experiment
1
Math Review
1.1 Powers of Ten
It should be apparent from the relative magnitude of the various units of measurement that very
large and very small numbers are frequently encountered in the sciences. To ease the difficulty of
mathematical operations with numbers of such varying size, powers of ten are usually employed.
This notation takes full advantage of the mathematical properties of powers of ten. The notation
used to represent numbers that are integer powers of ten is as follows:
1
1 = 100
10 = 101
100 = 102
1000 = 103
10
1
100
1
1,000
1
10,000
=
0.1 = 10-1
=
0.01 = 10-2
=
0.001 = 10-3
=
0.0001 = 10-4
where, an expression 104 is called a power, read “ten to the fourth power.” The exponent 4
represents the number of times the base 10 is used as a factor as shown below.
A quick method of determining the proper power of ten is to place a caret mark to the right of the
numeral 1 wherever it may occur; then count from this point to the number of places to the right
or left before arriving at the decimal point. Moving to the right indicates a positive power of ten,
whereas moving to the left indicates a negative power. For example,
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1.1.1 Properties of Powers of Ten
100 = 1
1) Zero exponent:
1
2) Negative exponent:
10𝑛
= 10−𝑛 ,
1
10−𝑛
= 10𝑛
Example 1.1
a.
b.
1
104
= 10−4
1
10−5
= 105
3) Product of powers of ten:
(10𝑚 )(10𝑛 ) = 10(𝑚+𝑛)
Example 1.2
a. (1000)(10,000) = (103 )(104 ) = 10(3+4) = 107
b. (0.000001)(100) = (10−6 )(102 ) = 10(−6+2) = 10−4
4) Quotient of powers of ten:
10𝑚
10𝑛
= 10(𝑚−𝑛)
Example 1.3
a.
b.
100,000
1000
0.0001
100
105
= 103 = 10(5−3) = 102
=
10−4
102
= 10(−4−2) = 10−6
5) Power of a power of ten:
(10𝑚 )𝑛 = 10𝑚𝑛
Example 1.4
a. (1000)4 = (103 )4 = 103×4 = 1012
b. (0.00001)3 = (10−5 )3 = 10−15
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Exercises 1.1 – Properties of Powers of Ten
Solve the following exercises and write the answer using powers of ten
1. (1000)(10,000) =
2. (0.001)(1000000) =
3.
4.
100
10,000
=
0.0000000001
1000
=
5. (100)3 =
6. (0.000001)5 =
Show work here:
1.2. Scientific and Engineering notation
In electronics, technicians very often have to deal with measurable values that might be very large
or very small numbers. For example, the distance from the Earth to the sun, which is 92960000
miles, or the thickness of the aluminum foil, which is 0.000963 inches. These numbers are
impractical to write out because of the length, the amount of space required, and the difficulty to
reading them. Due to it, scientists have developed a shorter method to write very large or very
small numbers. Those methods are known as scientific notation and engineering notation.
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1.2.1 Scientific Notation
Scientific notation is based on powers of 10. It is a method to represent very large or very small
number by representing the number with a coefficient, named Mantissa, greater or equal to 1 and
less than 10, times powers of 10. For example, the distance from the Earth to the sun written in
scientific notation is 9.296×107 miles. In this case, the number 9.296 is the mantissa which must
be a number greater or equal to 1 and less than 10. The second part must be powers of 10.
Scientific notation: c × 10n
where 1 ≤ mantissa (c) < 10 and the exponent n is an integer.
How to write a number in scientific notation?
To write the distance from the Earth to the sun which is 92960000 miles in scientific notation:
Step 1: Identify the number where the decimal point should be placed, so the mantissa will be
greater or equal to 1 and less than 10. In this case, the decimal point must be placed in between 9
and 2 to make the mantissa to 9.296.
92960000
Step 2: Check how many decimal places you must move from the lowest digit of the given
number so the mantissa will become 9.296. In this case, the decimal point must move 7 decimal
places.
92960000
Step 3: Now, pay attention if the decimal point must be shifted to the left or to the right.
Always remember:


If the decimal point is shifted to the left, the base exponent increases. (positive
exponents)
If the decimal point is shifted to the right, the base exponent decreases. (negative
exponents)
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In this case, the decimal point is shifted to the left by 7 places, meaning that the base exponent is
increased by 7.
92960000
+7 6 5 4 3 2 1
Step 4: Write the number in scientific notation
9.296 × 107
Exercises 1.2a – Scientific Notation
Write the following number into scientific notation. Include the unit for all exercises:
1. A human hair has an average diameter of about 0.0000165 meter.
2. An asteroid has an average orbital speed of 25000 meters per seconds.
3. Scientists have recorded that the average speed of oxygen molecules in air is about
1700000 meters per hour.
4. An E. coli bacterium has a diameter of about 0.000000498 meter.
Show work here:
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1.2.2. Engineering Notation
Scientific Notation is a notation widely used in science field to display very large or very small
numbers. But a common method used in the field of engineering or engineering technology is the
Engineering Notation. In Engineering Notation, numbers are expressed with power of ten with a
base exponent that is divisible by 3 and a mantissa greater or equal to 1 and less than 1000. For
example, to write the distance from the Earth to the sun in engineering notation will be: 92.96 ×
106 miles.
Engineering notation: m × 10n
where 1 ≤ mantissa (m) < 1,000 and the exponent n is restricted to multiples of 3.
How to write a number in engineering notation?
To write the distance from the Earth to the sun which is 92960000 miles in engineering notation:
Step 1: Shift the decimal point three places and stop to check if the mantissa is greater or equal to
1 and less than 1000. If the mantissa is in between this range, then stop shifting the decimal point.
If the mantissa is not between the ranges, shift the decimal point three more places, stop and check
the mantissa again. Continue to do so until the mantissa is between the ranges.
92960000
+3 2 1
If we shifted the decimal point three
times, the mantissa becomes
92960.000. Since 92960 is not less
than 1000, then we need to shift the
decimal point three more places.
92960000
+6 5 4 3 2 1
If we shifted a total of 6 decimal places, the
mantissa becomes 92.96. Since 92.96 is less than
1000 but greater or equal to 1, then we stop the
shifting, and 92.96 is the mantissa in engineering
notation.
Note: There is no need to write the zeros of the
right side of the mantissa because there are not
significant.
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Also, always pay attention if the decimal point must be moved to the left or to the right. If the
decimal point is shifted to the left, the base exponent increases. If the decimal point is shifted to
the right, the base exponent decreases. In this case, the decimal place is shifted 6 places to the left,
then the base exponent is +6.
Step 2: Write the number in engineering notation
92.96 × 106
Exercises 1.2b – Engineering Notation
Write the following number into engineering notation. Include the unit for all exercises:
1. A human hair has an average diameter of about 0.0000165 meter.
2. An asteroid has an average orbital speed of 25000 meters per seconds.
3. Scientists have recorded that the average speed of oxygen molecules in air is about
1700000 meters per hour.
4. An E. coli bacterium has a diameter of about 0.000000498 meter.
Show work here:
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1.1.3 Prefixes
Prefixes are alternative way to write the powers of ten. It is very useful in engineering notation
because it has a specific name to each power of ten which make them easy to write and read.
Some of the prefixes for engineering notation are listed in Table 1.1
Prefixes
Name
Symbol
Power of ten
18
Decimal value
exa
E
10
peta
P
1015
1,000,000,000,000,000
tera
T
1012
1,000,000,000,000
giga
G
10
9
1,000,000,000
mega
M
106
1,000,000
k
3
1,000
0
kilo
1,000,000,000,000,000,000
10
-
-
10
1
milli
m
10-3
0.001
micro
µ
10
-6
0.000001
nano
n
10-9
0.000000001
pico
p
10-12
0.000000000001
femto
f
10
-15
atto
a
10-18
0.000000000000001
0.000000000000000001
Table 1.1 Most common powers of ten used in electrical and electronic work
For example, the distance from the Earth to the sun, which is 92960000 miles, written in
engineering notation using the respective prefix symbol will be:
Replace the unit miles with its abbreviation
“mi”
92.96 × 106 miles = 92.96 Mmi
Replace 106 with prefix
symbol “M”
Table 1.2 displays each decimal quantity in engineering notation with its respective prefixes.
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Use of prefixes in power of ten
Quantity in
Decimal notation
120,000,000,000 hertz
Quantity in
Engineering notation
120 × 109 Hz
Quantity in
Prefix notation
120 GHz
30,000,000 bytes
30 × 106 b
30 Mb
14,500 ohms
14.5 × 103 Ω
14.5 k
9 volts
9 × 100 V
9V
0.092 amperes
92 × 10-3 A
92 mA
0.000005 henrys
5 × 10-6 H
5 H
0.0000000385 seconds
38.5 × 10-9 s
38.5 ns
0.0000000000012 farads
1.2 × 10-12 F
1.2 pF
Table 1.2 Typical electrical quantities in decimal, engineering and prefix notation
Example 1.1. Convert 23000 W in engineering notation using prefixes
23000. W = 23.000 × 103 W = 23.0 kW
Example 1.2. Convert 0.0000215 s in engineering notation using prefixes
0.000021.5 s = 21.5 × 10-6 s = 21.5 µs
Exercises 1.3a - Engineering notation with prefixes
Convert each of the following measurements into engineering notation with its respective
prefixes:
1. The electron volt of a charge is 562000000000000000 eV
2. The resistivity of a copper wire is 0.00001234 Ω-CM
3. The speed of sound is 32060 m/h
4. The current through a resistor is measured to be 0.0000000135 A
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Show work here.
1.4 Converting between prefixes
There are different methods to convert numbers of the same unit to a different prefix. One of the
method is by using the power of ten. For example, if the number 0.03205 ms (milli-seconds) is
converted to ns (nano – seconds), the steps to follow are:
Step 1: Convert each prefix by its corresponding power of ten.
0.03205 ms

ns
0.03205 × 10-3 s

10-9 s
Step 2: Indicate the distance from one exponent to the other exponent.
10-3

10-9
From -3 to -9 there are 6 decimal places.
Step 3: Determine if the distance of decimal places should be shifted to the right or to the left.
Always remember:


If the exponent is converting from a larger to a lower exponent, the decimal point of
the number must be shifted to the right.
Otherwise, if the exponent is converting from a lower to a larger exponent, the decimal
point of the number must be shifted to the left.
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From Step 2, the exponent is converting from the larger exponent to a lower exponent, therefore,
the decimal point of the number must be shifted six places to the right.
0.03205 ms 
10-3

ns
10-9
Note: Any empty spaces after or before the decimal point is filled with zero
0.032050
Step 4: Write the answer using prefixes
32050 × 10-9 s  32050 ns
Exercise 1.3b – Converting between prefixes
Convert the following measurements to quantities indicated
1. 23500 pF to µF
2. 0.11827 V to mV
3. 0.03716 mA to µA
4. 927300 kHz to GHz
Show work here
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1.1.5. Order of Operations
Order of operation in math, including the use in a calculator, and computer programming is a set
of rules where indicates which procedures to perform first in order to solve for a mathematical
expression. Indeed, the order of operation in math is Parentheses, Exponents, Multiplication and
Division, and Addition and Subtraction or simply PEMDAS. The operations of multiplication and
division have the same level of priority. To decide when to multiply or divide, always perform the
one which appears first from left to right. In the same manner, addition and subtraction are coequal in terms of importance. Perform the operation that comes first as you work it out from left
to right.
For example, evaluate −9+3× (2 − 8) ÷ 6 + 2 using the order of operations
Parenthesis
−9+3× ( −6) ÷ 6 + 2
Exponent
None
Multiplication −9 −18 ÷ 6 + 2
Division
−9 − 3 + 2
Addition
−9 − 1
Subtraction
−10
Then −9+3×(2 − 8) ÷ 6 + 2 = −10
Try to confirm the answer in a calculator by entering the whole mathematical expression, −9+3×
(2 − 8) ÷ 6 + 2 in the calculator.
When you have an expression where the division comes before multiplication, then you perform
the division operation first and then multiplication.
For example, evaluate (3 + 8) + 112 ÷ 7 × 23
Parenthesis
(11) + 112 ÷ 7 × 23
Exponent
11 + 112 ÷ 7 × 8
Division
11 + 16 × 8
Multiplication 11 + 128
Addition
139
Subtraction
None
Then (3 + 8) + 112 ÷ 7 × 23 = 139
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Try to confirm the answer in a calculator by entering the whole mathematical expression, (3 + 8)
+ 112 ÷ 7 × 23, did you have the same answer?
Exercise 1.5 – Order of operation
Evaluate the following mathematical expression using order of operation. Check your answer
using a calculator.
1. 6 − (10÷5)2 × 3 + 3
2. (5 × 33 − 5) − 3 × 3
3. 10 − 10 × (3 − 10)3 +11
4. (2 × 42 − 2) − 4 × 4
Show work here
1.6 Equation with unknown variables
Solving equations that contain one unknown variable is basically to make the unknown variable
to be equal to a value or equation. To do so, the rule of operation to the other side of the equal side
is applied.
Example 1.3 – Solving equations with an unknown variable
Given the equation 3x – 5 = 16, solve for the unknown value x
Solution:
Solving for x means to find what x is equal to, to do so:
Add 5 to both sides of the equation 
Introduction to Circuit Analysis Laboratory
3x – 5 + 5 = 16 + 5

3x = 21
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Divide both sides of the equation by 3 
3𝑥
3
=
21
3

x=7
Example 1.4 – Solving equations with the variable on both sides
If there are variables in both sides of the equation, first move all like variables to one side and the
numbers to the other side. Try to collect the variables on the side of the equation where the
coefficient will be positive.
Given −5z − 26 = 12z + 8, solve for z
Solution:
Check which side has the variable with the greater coefficient. In this case, the right side has 12z
and the left side has -5z. Since 12z is greater than -5z, then we move -5z to the right side by
adding 5z to both sides.
− 5z − 26 + 5z = 12z + 8 + 5z  −26 = 17z + 8
Now, collect all numbers to the left side by subtracting 8 on both sides.
− 26 −8 = 17z + 8 − 8  −34 = 17z
To solve for z we need to divide both sides by 17
−34
17
=
17𝑧
17
 –2 = z or z = –2
Example 1.5 – Solving equations with the Distributive Property
When solving an equation that involves variables and numbers inside a parenthesis, it is important
to apply the Distributive Property to each variable and number inside the parenthesis, and then
simplify on both sides of the equal sign before trying to isolate the variables.
Given 3(5x + 4) – 8 = –3x + 10, solve for x
Solution: According to the order of operation, the item inside of the parenthesis must be solved
first. But since 5x and 4 can’t be combined, in order to break the parenthesis, the Distributive
Property must be applied by multiplying each term inside the parenthesis with 3.
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3(5x + 4) – 8 = –3x + 10  15x + 12 – 8 = –3x + 10
Now, we combine like variables in one side, since 15x is greater than -3x, then all x variable will
be combined on the left side. To do so, we add 3x in both sides.
15x + 12 – 8 + 3x = -3x + 10 + 3x
18x + 12 – 8 = 10  18x + 4 = 10
To simplify, all numbers must be on the right so. For it, we subtract 4 in both sides.
18x + 4 – 4 = 10 – 4
18x = 6
To solve for x, we divide both side by 18
18𝑥
18
=
6
18
 𝒙=
𝟔
𝟏𝟖
or 𝒙 =
𝟏
𝟑
Example 1.6 – Solving equations with the rational numbers
To solve an equation with a variable on one or both sides that involves fractions, first get rid of
the fractions and solve the unknown variables using the methods learned in Example 1.3, 1.4,
and 1.5.
Given
3
2
𝑚 + 2 = 3 𝑚 + 5, solve for m
4
Solution:
Multiple both sides of the equation by the Least Common Multiplier, LCM, of 4 and 3, which is
12
3
2
4
3
𝟏𝟐 ( 𝑚 + 2) = 𝟏𝟐 ( 𝑚 + 5)
(
𝟏𝟐×3
4
𝟏𝟐×2
𝑚 + 𝟏𝟐 × 2) = (
3
 Apply the Distributive Property
𝑚 + 𝟏𝟐 × 5)  Simplify the equation
9𝑚 + 24 − 𝟖𝒎 = 8𝑚 + 60 − 𝟖𝒎
 Solve for m
𝑚 + 24 − 𝟐𝟒 = 60 − 𝟐𝟒
 𝒎 = 𝟑𝟔
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Exercise 1.6 – Solving for unknown variables
Given the following equations, solve for the unknown value:
1. 9i + 2 = 3i – 10
i=
2. 4(-9Ix + 12) = -26 -32Ix
 Ix =
3.
3
2
5
𝑡 + 6 = 5𝑡 −
125
t=
3
4.
6𝑉𝐴 −7
4
+
3𝑉𝐴 −5
7
=
5𝑉𝐴 +78
28
 VA =
Show work here
1.7 Equation in Engineering Technology with unknown variables
It is very important to know how to solve for unknown variables. There are scenarios where they
might need to formulate an equation to analyze an object behavior, or simply a calculation where
they have to estimate a constant by using given formulas.
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Example 1.7 – Find the unknown value
Given the voltage formula
𝑉=
𝑊
𝑄
Where V is the voltage between two points, in volts, W is the amount of energy, in
Joules, needed to move a negative charge Q, in Coulombs, from one point to the other
point.
Find the energy expended moving a charge of 48.5 µC between two points if the voltage
between the points is 5.2 V.
Solution: For this problem, it is important to identify the unknown variable first from the given
equation. Since the voltage and the charge is given, the unknown variable here is work, W.
𝑉=
𝑾
𝑄
Multiple both side of the equation with Q
𝑉×𝑄 =
𝑾
𝑄
×𝑄

𝑉×𝑄 =𝑊

𝑊 =𝑉×𝑄
Substitute the given value for Q and V
W = 48.5 µC × 5.2 V
𝑊 = 48.5 × 10−6 𝐶 × 5.2 𝑉
𝑊 = 252.2 × 10−6 𝐽  𝑊 = 252.2 𝜇𝐽
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Exercise 1.7 – Equation in Engineering Technology with unknown variables
1. The current formula is given to be: 𝐼 =
𝑄
𝑡
Where I is the current in Amperes, Q is the charge in Coulomb, and t is time in second.
How many coulombs of charge pass through a lamp in 1.2 minutes if the current is
constant at 250 mA? Hint: 1 minute = 60 seconds
2. The life of a battery is calculated by the life formula:
𝐿𝑖𝑓𝑒 𝑜𝑓 𝑏𝑎𝑡𝑡𝑒𝑟𝑦 (𝑖𝑛 ℎ𝑜𝑢𝑟𝑠) =
𝑎𝑚𝑝𝑒𝑟𝑒 − ℎ𝑜𝑢𝑟 𝑟𝑎𝑡𝑖𝑛𝑔 (𝐴ℎ)
𝐷𝑟𝑎𝑖𝑛 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 (𝐴)
What is the current drain of an Energizer D cell with ampere-hour rating of 12 Ah after 3
hours of use?
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Questions
1. The thickness of a copper wire is measured as 0.00036 inches. Show step by step how to
convert the thickness in engineering notation with its respective prefix symbol.
2. Analyzing a circuit a student found the following equation:
1
2
𝑉𝐵 + 2 = 𝑉𝐵 − 1
4
5
Using the different mathematics method learned in session 1.6, solve for VB. Show all
calculation steps
3. A student enters the following operation 70 +
1
1
1
1
+ +
200 120 500
in his calculator and the result
shows in the calculator is: 70.0153
He shows the answer to the lab instructor and the instructor tells him that the answer is
wrong. Solve the equation using the order of operations method and justify why the
student's answer is incorrect.
------------------- LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT ---------------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab instructor’s signature
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Lab Experiment
2
Resistors and Resistance
2.1 – Resistors and Color Coding
Resistors are electronic components that introduce a specific amount of resistance into electric
circuits. If you went to the store to buy a resistor you would have to know the required power
rating, the required resistance value, the tolerance you can allow, and the material that the resistor
should be made of.
The power rating of a resistor is an indication of how hot the resistor can get before burning up.
Power rating is expressed in watts. Some common power ratings range from 200W down to 1/8
W. Usually, the power rating of a resistor is directly proportional to the physical size of the resistor:
the higher the power rating, the bigger the physical size of the resistor. Carbon composition
resistors are very popular. These resistors come in power ratings of 2W, 1W, 1/2W, 1/4W and
1/8W. The 2W resistor is as thick as a pencil while the 1/8W resistor is the size of a grain of rice.
Figure 2.1 shows the different size of resistors and its respective power rating.
Resistors and Power Rating
1/8 W resistor
¼ W resistor
½ W resistor
1 W resistor
2 W resistor
5 W resistor
Table 2.1 – Resistors with difference power rating
2.1.1 Resistance representation
The resistor is usually identified by the letter R and either another letter or a number. Its resistance
value is written next to it. The unit for the resistance value is the ohm, which is represented by
upper case Greek omega (). It is customary to use the omega next to resistor values smaller than
1,000 ohms. Resistor values in the 1,000-ohm range or bigger are usually shown without the ohm
symbol. Examples: 10 , 330 , 1.2 k, 1 M.
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2.1.2 Resistor Color Code
The value of the resistor in ohms and its tolerance are usually indicated by several bands of color
grouped together on the left side of the resistor body. Most resistor has 4 bands together, the first
and second band indicate the first two significant figures of the resistor value, the third band
indicates the multiplier and the fourth band indicates the tolerance. Usually, the first three bands
are close together and the fourth band is a little bit apart. Also, the bands are always read from the
end that has a band closest to the edge.
Figure 2.1 Resistor with four color bands
Resistors that have more than four colors, the other colors usually indicate the reliability (failure
rate) of the resistor in % over 1000 hours of operation. It means how many resistors out of 100
will change their values to fall outside the allowed tolerance range after 1000 hours of operation.
Also, some resistors with five colors means that the three first colors are the three resistance digit
respectively, the forth color is the multiplier, and the fifth band is the tolerance.
In order to indicate resistor values, manufacturers agreed to use the following value for each color:
Value
0
1
2
3
4
5
6
7
8
9
0.1
0.01
Color
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Gray
White
Gold
Silver
Table 2.2 Color code for resistance value
Introduction to Circuit Analysis Laboratory
Tolerance
20%
10%
5%
4%
3%
2%
1%
0.5%
0.25%
0.1%
0.005%
Color
No color
Silver
Gold
Yellow
Orange
Red
Brown
Green
Blue
Violet
Gray
Table 2.3 Color code for tolerance
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Reliability (failure rate) is indicated by the following colors.
Reliability (failures)
Color
1/100
(absolute)
1/1,000
(absolute)
1/10,000
1/100,000
Brown
Red
Orange
Yellow
Table 2.4 Color Code for Reliability (failures) per 1,000 hours of operation
Example 2.1 – Finding the resistance value using color coding
For the following resistor,
read the resistance value of the following resistor and
find the lowest and highest resistance value
Solution:
Identify the order of the color band and read the equivalent value for each color:
-
1st band = Blue
2nd band = Gray
3rd band = Red
4th band = Gold
=6
=8
=2
= + 5%
Combining all digits together, we have 6 8 × 102 + 5% Ω
Converting the value in engineering notation, we have 6
. 8 × 102+1 = 6.8 × 103
6.8 k Ω + 5% (Actual resistance value)
To find the lowest and the highest resistance, we find the tolerance resistance first:
5
𝑇𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 𝑟𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 5% 𝑜𝑓 6.8 𝑘Ω = (100) × 6.8 𝑘Ω = 𝟎. 𝟑𝟒 𝒌𝛀
Lowest resistance = actual resistance – tolerance resistance = 6.8 kΩ – 0.34 kΩ = 6.46 kΩ
Highest resistance = actual resistance + tolerance resistance = 6.8 kΩ + 0.34 kΩ = 7.14 kΩ
2.1.3 Electrical test equipment: multimeter
Multimeters are the most common piece of electrical test equipment. They have the ability to
measure voltage, current, resistance, and often many other function such as checking the reverse
biasing of a diode.
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Understand the multimeter parts
Multimeter typically has a set of terminal sockets marked as VΩ, A, COM, and a function selector
switch, measure dial, or set of push buttons to select ranges and measurement functions as shown
in Figure 2.2
Terminal socket VΩ stands for Volts and Ohms, which are the electrical unit of voltage and
resistance, respectively. This terminal is used to measure voltage and
resistance. Terminal A stands for Ampere, which is the unit for electric
current. This terminal is used to measure current. Some multimeters have
mAVΩ in one socket and some others have them separated as VΩ and A.
The terminal COM stands for common terminal and it is the common
terminal for all measurements.
The function selector switch or measure dial has different measurement positions, the most of the
basic multimeter has five selections: two V settings, two A settings,
and one Ω setting. The two settings, one have a pair of short horizontal
lines, one solid line above one dashed line
. This pair of parallel
lines represent “DC”, direct current. In other words, if you want to
measure dc voltage, your measure dial must be position among the dc
volts
. The other setting has a wave
which represents “AC”,
alternating current. If you want to measure ac voltage, the measure dial
must be position among the ac volts
The multimeter comes with testing leads or probes. There are many different testing probes
available for multimeter. Some of the most common probes use in lab for multimeters are:
o Banana to alligator clips: good to connect large wires or pins on a breadboard.
o Banana to IC hook: good to work on smaller ICs and legs of ICs.
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o Banana to test probes: good to work on one test measurement.
The red test lead is plugged in the VΩ or A socket and the black lead is plugged in the COM. As
reference, the black lead is always plugged in the common socket.
2.1.4 Resistance Measurement using a multimeter DMM
Reading resistance using a multimeter is very simple:
-
To begin, make sure that no current or voltage is running through the resistor or circuit.
Set the multimeter to read resistance. Always try to set the DMM to read the highest resistance
and then gradually adjusted the dial until it reads the resistance.
Figure 2.2 shows the setup of a simple DMM to measure resistance. Also from Figure 2.2, the
Display window shows “1” meaning “Open Circuit” or that the meter leads are not connected to
everything. Open Circuit reading is different from meter to meter, some meters show OL (OverLoaded) to represent an open circuit.
Display window
Positive Lead is connected to VΩmA.
Usually the red lead is used to identify +
terminals
Measure dial
Negative Lead is connected to COM. Usually
the black lead is used to identify - terminals
Resistance range
Figure 2.2 (a) DMM set to measure resistance
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Display window
Positive Lead is connected to VΩmA. Usually
the red lead is used to identify + terminals
Measure dial
Negative Lead is connected to COM. Usually
the black lead is used to identify - terminals
Resistance range
Figure 2.2 (b) DMM set to measure resistance
-
Place the measurement leads parallel to the resistor.
Figure 2.3 Resistance Measurement
-
Record measurement from DMM’s display window.
2.1.5 Variable Resistance: Potentiometer, POT
A potentiometer is a variable resistor that has 3 terminals. The value of a potentiometer is the
maximum resistance of the potentiometer. This means that a potentiometer can be set between any
resistances from around 0 Ω to its maximum resistance. As shown in Figure 2.4, the 2 outside
terminals are connected to the ends of a distributed resistor. The middle terminal is connected to a
wiper arm that moves along the resistor as the shaft is turned or as the slider is moved. The wiper
arm always divides the total potentiometer resistance into 2 parts so that the total resistance is
always the sum of the two parts.
R T = R 1 + R2
Introduction to Circuit Analysis Laboratory
Figure 2.4 Potentiometer
30 | P a g e
There are 2 types of potentiometers (also abbreviated as ‘pots’). One has a linear distribution of
resistance while the other has a logarithmic distribution. The linear potentiometer is said to have a
‘linear taper’ while the logarithmic potentiometer is said to have an ‘audio taper’. The reason for
the audio taper name is that the human ear responds logarithmically to sound energy. Audio taper
pots are used in volume controls while linear taper pots are used in balance controls.
A potentiometer is linear if it measures half the total resistance when the wiper arm is set in the
middle. If the resistance in the middle setting is not half the total, then the pot is logarithmic.
Potentiometers also have power ratings. Usually, the bigger (physically) the potentiometer, the
more power it can handle (it can get hotter without burning up).
2.2 –Protoboard/Breadboard
The protoboard (in the past most commonly called a breadboard) that will be used in this lab is a
very simple plastic block with holes onto which circuit elements are plugged in and interconnected.
In order to use it properly, you must understand its construction. This particular protoboard has
two lines of holes on each long side of the board. 0n each long side, one is identified with a red
line (labeled with a +), and one with a blue line (labeled -). All the holes in each long line of holes
are connected together underneath the board. Each line of connection is known as a node. In other
words, there is a short circuit between any two holes on any long outside line that is identified with
red or blue. In the middle (running the long way), there is an indentation in the board. This
indentation separates the two halves of the board. Each line of 5 holes on either side of the
indentation is a short circuit. Each five holes on either side of the indentation are connected
together. Check Figure 2.6 for reference.
Protoboard Front View
Protoboard Internal Connections
Figure 2.6 - Protoboard Connections
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Lab Experiment Procedure
Part 1 – Resistors and Color Coding
Exercise 2.1 – Resistance reading using color coding
Given the following nominal or actual resistance, find the color of each band, the tolerance
resistance, and the maximum and minimum resistance. Record all results in Table 2.5
Nominal Value
1st band
2nd band
3rd band
4th band
Tolerance
resistance
Minimum
resistance
Maximum
resistance
57  + 20%
0.68  + 5 %
260 k + 5%
3.9 M + 10%
Table 2.5 – Resistance Reading and Color Coding
Show Calculations Here.
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Exercises 2.2 – Measuring the resistance value using a DMM
a. Using the table below, pick one resistor from each column. Circle your choice
Resistor 1, R1
240 kΩ
430 kΩ
470 kΩ
560 kΩ
1 MΩ
Resistor 2, R2
15 kΩ
18 kΩ
27 kΩ
47 kΩ
68 kΩ
Resistor 3, R3
1.3 kΩ
1.5 kΩ
1.8 kΩ
3.6 kΩ
3.9 kΩ
Resistor 4, R4
470 Ω
560 Ω
620 Ω
680 Ω
820 Ω
Resistor 5, R5
47 Ω
120 Ω
150 Ω
270 Ω
390 Ω
b. Obtain the five resistors from step a. from your components’ kit.
c. Write the actual resistance in Table 2.6.
d. Prepare a DMM to measure resistance. Remember to set the resistance reading to the
highest resistance first.
e. Using as reference Figure 2.3, measure each resistor and record its resistance value in
Table 2.6. Write your measurement in engineering notation with its respective prefix and
unit.
f. Find the Percent of Difference % using the following formula and write the answer in
Table 2.6.
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐴𝑐𝑡𝑢𝑎𝑙 − 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑
% 𝑜𝑓 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (
) × 100 %
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐴𝑐𝑡𝑢𝑎𝑙
Resistor
Actual Resistance
Measured Resistance
Percent of Difference %
R1
R2
R3
R4
R5
Table 2.6 – Measured resistance value using a DMM
g. Turn off the DMM and place the resistors back to the components’ kit.
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Part 2 – Potentiometer
Exercises 2.3 – Potentiometer
a. From your component kit, take all the potentiometers for examination.
b. Look at the value code of the potentiometer (check Figure 2.5) and write its
resistance value in increasing order:
_
,
,
__________,
,
Figure 2.5 Potentiometer value code location
c. Place a 50 kΩ potentiometer in a breadboard as the following
Node 7
Node 5
Node 6
d. Turn on the DMM and set it to the appropriate resistance range to measure 50 kΩ.
Measure the different nodes and record measurement in Table 2.7
Node
Measured Resistance
5 to 6
6 to 7
5 to 7
Table 2.7 Potentiometer
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Exercises 2.3 – Protoboards
Obtain a protoboard from your components’ kit. Have a look at the protoboard and complete
Table 2.8 using as reference Figure 2.6.
Description
Number nodes
Number of
connections in a node
Power supply nodes: Each long red or blue
line
Basic nodes: Each short line (on each side
of the indentation)
Table 2.8 – Protoboard Description
Part 3. Resistance Measurement Practice
Exercises 2.4 – Connected resistors
a. Obtain 470 Ω, 330 Ω, 220 Ω, 47Ω, and 1 kΩ resistors from the components’ kit.
b. Connect the resistors together as a chain in the protoboard. Check Figure 2.7.
Figure 2.7 Connecting resistors together as a chain
c. Set the DMM to measure resistance.
d. Measure from node to node according to Table 2.9. To measure from node to node, it is
always recommended to use the DMM measurement leads as reference. For example, if
you are measuring from node A to node B, then the red lead of the DMM is connected to
A and black lead to B.
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Node
Measured Resistance Value (include unit)
A to B
A to C
C to A
F to C
F to A
B to D
C to E
F to E
Table 2.9. Resistance measurement in a chain resistive circuit
Turn off all lab and testing equipment, dissemble the circuit, and place all components back in
the lab kit. Answer the following lab questions.
Questions
1. A student was building a circuit with two resistors, 100 Ω and 470 Ω, connected in a chain as
the following:
Now she turned on the ohmmeter and measured the resistance from Node 5 to Node 15. The meter
read: OL. Why the DMM display OL? Justify your answer
2. A technician measured a resistor with an ohmmeter and got a reading of 940 Ω. The resistor
was color coded Gray Green Brown Silver. Explain whether the resistor is within
specifications.
3. If the resistor in the previous question had only three colors (Gray Green Brown), how would
it affect your previous answer?
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT -----------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab instructor’s signature
36 | P a g e
Lab Experiment
3
Voltage and Current Measurement
3.1 – Voltage and Current
A basic electric circuit is built of a source, such as a battery, a switch, interconnection wires, and
a load, such as a lamp. When the electric circuit is built and the switch is closed, flow of charges
will travel in a closed path causing the light of the lamp to come on. These flow of electrons are
known as electric currents. Electric currents has magnitude and direction. The magnitude and
direction of each current is a measurable fact using an ammeter.
Even ammeters are available as individual instruments, they are combined instruments called
Multimeter or Volt-Ohm-Milliammeter, VOM. Figure 3.1 shows both digital and analog
multimeters. Digital multimeter uses a numerical readout, while analog multimeter uses a needle
pointer to indicate the measure values.
Figure 3.1 Digital and Analog multimeter
3.1.1 How to set the multimeter to measure voltage and current
How to measure voltage?
Before placing the testing probes in the circuit to measure voltage, you have
to set your multimeter to measure voltage. To set up the multimeter, make
sure that the red probe is connected to the VΩmA socket and the black probe
to the COM socket.
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To measure a dc quantity, set the measure dial to the desired dc voltage range
. For example,
if you are measuring no more than 9 V, you can set the measure dial to 20 V dc volts. But if you
want to measure 9 V and you set the measure dial to 2 V, the multimeter will show an Over Load
message, why? Because the voltage range in the multimeter presents the highest measurable
voltage. That is why, if the measure dial is selected to 2 dc V, then the highest voltage that you
can measure is 2 dc V.
Once the multimeter is set up to measure voltage, the next step is to measure the
voltage across a component in the circuit. Once the circuit is power, you can place
the multimeter leads across the component whose voltage you want to measure.
This technique is applied because voltage is the potential difference between two
points. It is also good to remember that to measure the voltage across a component, the multimeter
has to be in parallel to the measure component.
How to measure current?
Measuring current is more complicated than measuring resistance or voltage. There are two main
reasons for this:
1. The connection of the multimeter with the measure component. In order for the multimeter to
measure the current through a component, the multimeter has to be connected with the measure
component in a way that the current can go through the
multimeter and the component. This means that the
multimeter must be made part of the current path of the
circuit. In order to make the multimeter part of the
current path of the circuit, the original circuit must be
“broken” and the meter connected across the two points
of the open break. When the multimeter is part of the
open break, the multimeter is connected in series with
the measure component.
2. The fuse of the multimeter. One of the most common mistakes with the use of the multimeter
to measure current is to connect the probes in parallel with the measure component. This will
immediately short power to ground through the multimeter causing the power supply current
going through the multimeter. As the current rushes through the multimeter, the internal fuse
will heat up and then burn out as 200 mA flows through it.1
1
How to Use a Multimeter, https://learn.sparkfun.com/tutorials/how-to-use-a-multimeter/fuse, retrieve on 8/16/18
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Remember that a fuse is a safety device consisting of a strip of wire that melts and breaks if
the current exceeds a safe level. A fuse that is burned becomes an open circuit in an electric
circuit.
fuse
Lab Experiment Procedure
Part 1 – Resistive Circuit
Exercise 3.1 - Building a Resistive Circuit from a Circuit Schematic
-
Obtain the resistors needed to build the circuits according to Table 3.1.
Before building the following circuits, measure the resistance of each resistors using a
DMM and record the measurements in Table 3.1.
Elements
Actual Value (include a unit)
R1
100 Ω (brown, black, brown, gold)
R2
330 Ω (Orange, orange, brown, gold)
R3
47 Ω (yellow, violet, black, gold)
R4
470 Ω (yellow, violet, brown, gold)
R5
220 Ω (red, red, brown, gold)
Measured Value (include a unit)
Table 3.1 Components measurements
-
Having the components, we can start making the connection of each resistor according to
circuits.
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a) Building a resistive circuit with one resistor
Circuit 3.1 Resistive circuit with 1 resistor
There are different ways to build and make connections among the elements within the circuit.
One way to do so is by the order of the elements:
Circuit Schematic
Step 1)
Description
To build the circuit, we need to
place the switch first. Put the
middle leg of the switch in a node
5 and Row H, which needs to be
connected to “+”.The right leg of
the switch needs to be connected to
one side of R1. So put a jumper
wire in a hole of “+” and in a node
5 and Row J. And put another wire
between nodes 6 and 13 of Row F.
It should be OFF when you slide
the button to the left and ON when
the button to the right.
Protoboard Connection
Switch: OFF
Switch: ON
Place R1 between nodes 13 and 22 of Row H.
Step 2)
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Step 3)
Connect the other side of R1 to the Ground.
Once the circuit is built, turn the switch to a close or ON position and measure the total
resistance, by placing the multimeter testing probes in between the + and – node of the
breadboard. Record the measure resistance in Table 3.2.
b) Building a resistive circuit with 3 resistors
Circuit 3.2 Resistive circuit with 3 resistors
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Circuit Schematic
Step 1)
Step 2)
Step 3)
Description
Protoboard Connection
From the Circuit 3-1, remove the jumper wire to the Ground.
Place R2 between nodes 22 and 31 of Row G and put jumper
wires between Row F and E of nodes22 and 31.
Place R3 between nodes 22 and 31 of Row C and connect the
other sides of R2 and R3 to the Ground.
Once the circuit is built, turn the switch to a close or ON position and measure the total
resistance and record the measure resistance in Table 3.2
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c) Building a resistive circuit with 5 resistors
Circuit 3.3 Resistive circuit with 5 resistors
Circuit Schematic
Description
Protoboard Connection
From the Circuit 3-2, remove the jumper wire to the Ground. And
place R3 and R5 between nodes 31 and 40 of Row H and Row B,
respectively. And put a jumper wire between Row F and E of a
node 40 and connect the other sides of R3 and R5 to the Ground.
Step 1)
Once the circuit is built, turn the switch to a close or ON position and measure the total
resistance and record the measure resistance in Table 3.2
Element
Total Resistance
(Circuit 3.1)
Total Resistance
(Circuit 3.2)
Total Resistance
(Circuit 3.3)
Actual Value (include a unit)
Measured Value (include a unit)
100 Ω
293.875 Ω
343.796 Ω
Table 3.2 Total resistance measurement
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Part 2 - Measuring the current in a resistive circuit
Exercise 3.2 – Measuring the current through each resistor in Circuit 3.3
To measure current, we need to provide power to the circuit:
- Set the power supply to 9 V or use a 9 V battery.
- Connect the red lead of the power supply to the “+” node of the protoboard.
- Connect the black lead of the power supply to the “-” node of the protoboard.
- Double check the circuit connection with the lab instructor.
- Set the DMM to measure current: set it to read the highest current first.
- Always remember: to measure current of an element, one terminal of the element must
be “broken” and the DMM must be placed in between the ‘break’. In order words, the DMM
is used as a bridge between the measured element and the other element on the circuit. Check
Figure 3.2.
1. To measure the current through 100 Ω.
2. Connect the 9 V battery to the circuit. Make sure that the switch should be OFF.
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3. Break one of terminal of 100 Ω resistor
4. Optional: place a jumper wire where the terminal was connected
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5. Switch ON the circuit and place the DMM probes in between the break to measure current through 100 Ω
resistor.
Measure
the open
Switch ON
Circuit diagram of step 5: measuring current through R1.
Figure 3.2 Steps to measure current through a resistor
-
Repeat the previous step and measure the current through each resistor. Record the
measurements in Table 3.3
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Elements
Measured value (include a unit)
IR1
IR2
IR3
IR4
IR5
IS = Current through the battery
Table 3.3 – Current measurements from Circuit 3.3
Note: The current distribution and flow for Circuit 3.1 is showed in below, Figure 3.2. You can
use the measured current value in Table 3.2 and compare them with Figure 3.1
Figure 3.2 Current flow within a resistive circuit
Part 3 - Measuring the voltage in a resistive circuit
Exercise 3.3 – Voltage measurement across a resistor
-
Before measuring the voltage, check the circuit connections with the lab’s instructor.
Prepare the DMM to measure voltage.
To measure the voltage drops at a resistor, simply place the DMM measurement’s
leads “across” the resistor as shown in Figure 3.3.
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Figure 3.3 – Measuring voltage across a resistor
-
Following the previous step, measure the voltage across each resistor and record the
measurements in Table 3.4.
Voltage Label
Measured value (include a unit)
Vs
VR1
VR2
VR3
VR4
VR5
Table 3.4 Voltage Measurement from Circuit 3.3
Exercise 3.4 - To measure the voltage at a node with respect to ground
Be aware that in the field of electronics the word ground is often used to indicate the reference
point rather than physical ground. In this case, the reference point is the negative node of the
protoboard.
-
Clip one negative lead of the DMM to the circuit ground (point E) or reference point (the
negative – node)
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-
To measure the voltage at each node of Circuit 3.1, clip the other meter lead, (the one connected
to the meter jack labeled with a plus sign, usually the red lead) to each node in succession
(namely point A, B, C and D) as shown in Circuit 3.2.
Circuit 3.4 Resistive circuit, Circuit 3.3, with label in each node
-
Record each measured voltage in Table 3.5.
Include the polarity of the voltage with respect to ground in Table 3.4. Positive voltages are
displayed with no sign by the DMM, while negative voltages are shown with a minus sign. For
Circuit 3.1, all the nodes are positive with respect to ground because the battery’s negative
terminal is taken to be reference (ground).
NOTE: If an analog meter were used, a negative voltage would cause a meter deflection off the
left side of the scale possibly causing meter damage. An analog meter can only measure positive
voltages. To fix this error, swap the DMM’s leads position, measure the voltage again, and mark
the reading as a negative value.
Node
Display number
in DMM
Voltage written as
A
(sample)
9
VA= + 9V
B
C
D
Table 3.5 Voltages from different node to ground
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Measuring the voltage between two nodes (Double subscript notation)
In the electronics field, it is common to represent the voltage between two points in the circuit
using a double subscript. VAB indicates the voltage at point A with respect to point B. If one were
to measure this voltage with a DMM, one would put the black meter lead at the point indicated by
the second (reference) subscript and the red meter lead at the point indicated by the first subscript.
Therefore, to measure VAB, the black meter lead is connected at node B and the red meter lead at
node A. This is exactly the same as measuring the voltage across the resistor R1.
For example, to measure VBA, one would put the red meter probe at node B, and the black meter
probe at node A. This would obviously result in the same voltage but the meter would indicate a
negative sign because the voltage in node B is lower than the voltage in node A. This shows that
VBA = VB – VA
Exercise 3.5 Measuring and calculating voltage between nodes
 From Circuit 3.3, measure the voltages indicated in Table 3.6
 It is also important to notice that VAB = VA- VB, where the voltage of VA and VB is obtain
from Table 3.5. Using those information, calculate each node voltage as indicated in Table
3.6.
 Complete Table 3.6.
Written as
Calculation using Table 3.5
Voltage at first node minus
voltage at second node
-2.6 V
VBA = -2.6V
VBA = VB – VA
VBA = 6.4V – 9V= - 2.6V
- sign indicates B is lower in
voltage than A
+5.6 V
VBC = +5.6V
VBC = VB – VC
VBC = 6.4V – 0.8V = + 2.6V
+ sign indicates B is higher
in voltage than C
Voltage to
Measured
be measured Voltage
Comment
VAB
VBA
(Sample)
VBC
Sample)
(
VCB
VDB
VCA
VAC
Table 3.6 Measuring and calculating voltage between nodes
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Measuring the voltage rises and the voltage drops
When moving around a circuit in a particular direction, if one goes across a circuit element and
encounters a voltage polarity from – to + then the voltage is considered a voltage rise and is usually
assigned a + sign. For example, going from B (black probe) to A (red probe) goes from – to +
therefore it is considered a voltage rise of 2.6V (or VAB = +2.6V). Alternately, if one encounters a
voltage polarity from + to – then the voltage is considered a voltage drop and is usually assigned
a – sign. Here for example, going from A (black probe) to B (red probe) goes from + to – therefore
it is considered a voltage drop of 2.6V (or VBA = –2.6V). Note that a voltage is either a rise or a
drop depending on the direction taken, which is usually use the test probe as reference.
Exercise 3.6 Measuring the voltage rises and voltage drops
Don’t forget that all voltage measurements were done across elements or from one terminal to
another.
-
Using the information from Table 3.5 complete Table 3.7
To
point
From
point
A
C
D
A
Ground
(E)
C
D
Ground
(E)
B
D
Calculation using Table 3.5
Rise or
drop?
Write + for rise
Write - for drop
Table 3.7 Voltage rises and voltage drops
Turn off all lab and testing equipment, dissemble the circuit, and place all components back in
the lab kit. Answer the following lab questions.
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Questions
1. According to this experiment, which is/are the most difficult step/s to measure the current
through a resistor? Explain your answer.
2. You are trying to measure the current through a resistor, you power the circuit, set the
multimeter to measure the current, and connect the multimeter in series with the circuit.
The multimeter shows ‘OL’. How would you troubleshoot this error? Mention three
alternatives to troubleshoot this error and explain.
3. According to this experiment, which is/are the most difficult step/s to measure the voltage
across a resistor? Explain your answer.
4. For a given circuit, when you measure a voltage from node C to node A, the multimeter
displays -3.5V. What does the negative sign mean? Which node has the lower voltage?
Explain your answer
-------------------LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT -------------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab instructor’s signature
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Lab Experiment
4
Multisim
4.1 – Introduction to Multisim
Circuit simulation software allows us to predict circuit behavior by modeling and simulating an
electronic circuit. It is used to find errors and make corrections to the circuit before we even build
or manufacture the circuit under study.
Many circuit simulation tools are based on SPICE which is an acronym for Simulation Program
with Integrated Circuit Emphasis. SPICE is a general-purpose circuit simulation program for DC,
AC and transient analyses. Circuits may contain resistors, capacitors, inductors, independent
voltage and current sources, as well as switches, semiconductor diodes, and BJTs, JFETs,
Transistors. SPICE was originally developed at the Electrical Engineering and Computer Science
Department of the University of California at Berkeley. PSpice is a free version of this program.
There are a variety simulation software packages available including PSpice, Circuit Maker and
Multisim. Today we will look at Multisim.
Multisim is a schematic capture and simulation application that assists you in carrying out the
major steps in the circuit design flow. Multisim can be used for both analog and digital circuits
and also includes mixed analog/digital simulation capability, and microcontroller co-simulation.
Simulating the circuits before building them, catches errors early in the design flow, saving time
and money. The Multisim’s user interface and its main elements can be seen in Figure 4.1
Figure 4.1 Multisim Interface
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Multisim Interface
1. Menu Bar
2. Standard
Toolbar
3. Component Toolbar
4. Simulation Toolbar
Figure 4.2 Multisim Interface
1. Menu Bar
Menu bar contains the tabs or commands for all main functions: File, Edit, View, Place,
MCU, Simulate, Transfer, Tools, Reports, Options, Window, and Help
2. Standard Toolbar
The standard toolbar contains buttons for commonly-performed functions: New, Open,
Open Sample, Save, Print Circuit , Print Preview, Cut, Copy, Paste, Undo, Redo, Zoom In,
Zoom Out, Zoom to Specific Area, Zoom Sheet, and Full Screen button
3. Component Toolbar
Component toolbar contains button that launches to the component browser of a selected
Group: Source, Basic, Diode, Transistor, Analog, TTL (Transistor-Transistor-Logic),
CMOS (Complementary metal–oxide–semiconductor), Mixed, Indicator, Power
Component, Miscellaneous, Advance peripherals, RF, Electromechanical, Educational
resources, and Connectors button
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4. Simulation Toolbar
Simulation toolbar contains the buttons to run, pause, or stop the simulation of the circuit.
7. Instruments
toolbar
6. Circuit Window
5. Active Bar
Figure 4.3 Multisim lab equipment
5. Active Bar
Active bar shows the current workspace.
6. Circuit Window
Circuit window is the active workspace where the circuit is built.
7. Instruments Toolbar
Instruments toolbar contains buttons that place a specific instrument on the workspace:
Multimeter, Function generator, wattmeter, oscilloscope, four channel oscilloscope, bode
plotter, frequency counter, word generator, logic converter, logic analyzer, IV analyzer,
distortion analyzer, spectrum analyzer, network analyzer, Agilent function generator,
Agilent multimeter, Agilent oscilloscope, Tektronics oscilloscope, and LABView
instruments.
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Searching for components
The main components that are used for circuit analysis are located at Group Sources and Basic.
There are three different ways to search for Sources and Basic components:
Alternative 1: Search for Sources and Basic components from Menu bar.
- In the Menu bar, select the tab Place
- From the Place list, select Component… a Select a Component window will appear.
- In the Select a Component window, you will see the Group selection on the left of your
window.
- Click on the pointing down arrow and select the Group of components that you are
looking for.
Each Group of component is organized by a Family of components, for example, when you
select Group: Sources or Basic, the following Family components will show:
Figure 4.4 - Component list window: Group Sources
-
Figure 4.5 Component list window: Group Basic
Select the component that you need from the list of Component.
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Alternative 2: Search for Sources and Basic components from Component Bar:
- Move the cursor to the Basic or Sources icon
Figure 4.6 Component Toolbar
-
When you do so, the Select a Component window appears
From the window, select Group: Sources or Basic
Alternative 3: Using combination key Ctrl + w
- From your keyboard, press the combination Ctrl + w
- When you do so, the Select a Component window will appear
- From the window, select Group: Sources or Basic
Lab Experiment Procedure
Exercise 4.1. Building a series resistive circuit
For today’s lab, you will need to build a circuit as shown in Circuit 4.1 using Multisim. In
Multisim, you will learn how to obtain components, make connections between components, use
lab instrument, and measure the current and voltage through an element.
Circuit 4.1 Series circuit
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Open Multisim and save the Multisim file
To save the Multisim file:
 Open Multisim  Click on File from the menu bar  select Save As
 Save the file as “LastName_Lab4A.ms14”. Note: remember where the file is saved.
Placing components in a worksheet
 Obtain the components from the following Group and Family, and also position them in
their respective location in the workspace:
 Ground  Group: Sources, Family: POWER_SOURCES, Component: GROUND;
Location: 3E
 10 V DC power source  Group: Sources, Family: POWER_SOURCES,
Component: DC_POWER; Location: 3D.
By default, the voltage source is automatically set to 12 V. To change the value of the
voltage source, double click on the voltage source to open the DC Power window. In
the window, click on the Value tab and change the voltage to 10 V. The voltage source
label can also be changed to Vs instead of V1. Check Figure 4.7.
Figure 4.7 DC Power window
 150 Ω resistor  Group: Basic, Family: RESISTOR, Component: 150; Location:
between 4C and 5C.
 220 Ω resistor  Group: Basic, Family: RESISTOR, Component: 220; Location:
6D.
Note that resistors by default are position horizontally. If the resistor needs to be
rotated or flipped, right click on the resistor to open the resistor’s properties. In the
properties, select Rotate 900 clockwise. Another alternative to rotate is by using
combination keys Ctrl + R. Check Figure 4.8
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Figure 4.8 Properties of a 220 Ω resistor
All components should be position in the workspace as Figure 4.9.
Figure 4.9 Components position in a workspace
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Wiring the components
All the components are placed. However they need to be connected or “wired together”.
To wire them together from the ground:
 Place the mouse cursor on the terminal of the Ground and click. Once it is clicked, a wire
appears from the ground’s terminal. Check Figure 4.10
Figure 4.10 First connection of ground component.
 Drag the wire to the negative terminal of the voltage source and click to make the
connection.
 Click on the positive terminal of the voltage source, drag the wire to one terminal of 150
Ω resistor, and click to make connection.
 Click the other terminal of 150 Ω resistor, drag the wire to one terminal of 220 Ω resistor,
and click to make connection.
 Click the other terminal of 220 Ω resistor, drag the wire to ground, and click to complete
the circuit connection. The complete wired circuit should be as Circuit 4.1.
 Click on the Save icon
to save the work.
Exercises 4.2. Current Measurements in a resistive circuit
To take current measurements in Multisim you need to “break the circuit” and add a DMM in line with
the circuit along the component we intend to measure. The DMM is the uppermost item in the instrument
panel. Check Figure 4.11
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Multimeter
Figure 4.11 Multimeter location in Multisim
 Break the connection of one terminal of 150 Ω resistor. Note: To break a connection,
click on the wire and hit the Delete key.
 Obtain one multimeter from the instrument toolbar and connect the multimeter in
between the break. Check Figure 4.12.
Figure 4.12 Measuring the current through 150 Ω resistor
 Break the connection of one terminal of 220 Ω resistor.
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 Obtain another multimeter from the instrument toolbar and connect the multimeter in
between the break. Check Figure 4.13.
Figure 4.13 – Measuring the current through 150 Ω and 220 Ω resistors
 Run the simulation circuit by clicking the Run button
from the simulation toolbar.
 Double click on the multimeters to open the display window. Check Figure 4.14.
Measured value
To measure resistance = ohmmeter
To measure current = ammeter
To measure voltage = voltmeter
To measure noise = decibels
To measure dc values
To measure ac values
Figure 4.14 Display window of a multimeter in Multisim
 Since the circuit at Figure 4.13 is set to measure dc current, to do so, click on Ammeter
to measure the current flowing the circuit in a branch between the two nodes. Check
Figure 4.15.
 Record the current through R1 and R2 in Table 4.1.
 Stop the simulation
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 Double click on the voltage source to change the voltage from 10 V to 16 V.
 Run the simulation again and record the current through R1 and R2 in Table 4.1.
 Stop the simulation, delete the connection of the nodes with the multimeter, and connect
the components back as Circuit 4.1.
Figure 4.15 To measure current through R1 and R2
VINPUT
Current through R1, IR1
Current through R2, IR2
VS = 10 V
VS = 16 V
Table 4.1. Current measurements through R1 and R2
Exercises 4.3. Voltage measurements in a resistive circuit
To take voltage measurements, the multimeter has to be connected across the intended
component to measure.

Place the multimeter above or next to the component to be measured. Optional: rotate the
2nd multimeter to set it in parallel with R2.
 Attach the multimeter’s probes in between two nodes of R1 and R2 respectively. Check
Figure 4.16
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Figure 4.16 To measure voltage across R1 and R2
 Run the simulation.
 Doule click on the multimeters to display the measurement window.
 Since the circuit at Figure 4.16 is set to measure dc voltage, to do so, click on Voltmeter
to measure the voltage between two nodes. Check Figure 4.17.
Figure 4.17 Voltage measurement across R1 and R2





Record the voltage across R1 and R2 in Table 4.2
Stop the simulation.
Double click on the voltage source to change the voltage from 10 V to 16 V.
Run the simulation again and record the voltage across R1 and R2 in Table 4.2.
Stop the simulation.
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VINPUT
Voltage across R1, VR1
Voltage across R2, VR2
VS = 10 V
VS = 16 V
Table 4.2 Voltage measurements across R1 and R2
Exercises 4.4 Building and measuring voltage and current in a resistive circuit
To insert and modify a Title Block
 Open a new workspace and save it as “Lab4_LastName”
 Insert a Title block. The title block is located at Place tab  Title Block. Select the
DefaultV6.tb7 title block.
 Position the title block to the right-lower corner of the worksheet and click once to place
the title block.
 Double click on the title block to open the Title Block window. The Title Block window
is used to fill up information about the circuit schematic.
 Fill up the Title block with the following information:
Title: Exercise 4.4 - Series-Parallel Resistive Circuit
Description: Practice circuit to measure voltage and current through each resistor
Designed by: Student’s name
Date: Enter today’s date
 Click Ok to save the information in the Title Block.
 Build Circuit 4.2.
Circuit 4.2 Series-parallel circuit





Obtain three multimeters and set the circuit to measure the current through each resistor.
Run the simulation.
Measure the current through each resistor and record measurement in Table 4.3.
Stop the simulation.
Change the voltage source to 16 V.
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 Run the simulation and record the current through each resistor. Record measurement in
Table 4.3.
VINPUT
Current through R1,
IR1
Current through R2,
IR2
Current through R3,
IR3
VS = 10 V
VS = 16 V
Table 4.3 Current measurements through R1, R2, and R3
 Stop the simulation, delete the connection of the nodes with the multimeter, and connect
the components back as Circuit 4.2.
 Place each multimeter in parallel with each resistor. Optional: rotate the 2nd and 3rd
multimeter to set it in parallel with R2 and R3 respectively.
 Run the simulation and record the voltage across R1, R2, and R3 in Table 4.4
 Stop the simulation
 Change the voltage source to 16 V.
 Run the simulation and record the voltage across each resistor. Record measurement in
Table 4.4.
VINPUT
Voltage across R1, VR1
Voltage across R2, VR2
Voltage across R3, VR3
VS = 10 V
VS = 16 V
Table 4.4 Voltage measurements across R1, R2, and R3
Save all your work in a portable memory and close Multisim.
-------------------LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT ------------------Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab instructor’s signature
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Lab Experiment
5
Ohm’s Law and Series Circuits
5.1 – Ohm’s Law
George Ohm formulated the relationship among Voltage (V or E), Resistance (R) and Current
(I). Knowing two of the values, the third value may be computed using the following:
I
V
V
, V  IR , or R 
R
I
where, i) I is the electronic current measured in amperes (A)
ii) V is the voltage measured in volts (V) and
iii) R is the resistance measured in ohms ()
Formula 5.1 Ohm’s Law
Circuit 5.1. 2.2 kΩ resistor across 9V DC Supply
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Circuit 5.1 shows a 2.2 k resistor connected across a 9-volt battery. Using Formula 5.1 the
current can be calculated to be 4.09 mA.
I
V
9

 4.09 mA
R 2.2k
Plotting Ohm’s law behavior
The relationship between the current and voltage through a resistor is a linear response. This
means that the slope of the line is the value of the resistance.
Current vs voltage through R1
Current (mA)
20
15
10
5
0
0
1
2
3
4
5
6
Voltage (V)
5.2 – Series Circuits
Circuit elements are said to be in SERIES when they are connected TERMINAL-TO-TERMINAL,
like a chain.
Elements connected in series configuration:



Have the same current, because after the current goes through one component it has to go
through the other. It has no other place to go.
The total applied voltage gets divided between the series components in such way that the
sum of all the voltages across the series components is equal to the total applied voltage.
This is also known as Kirchhoff’s Voltage Law (or KVL).
The equivalent or total resistance is the sum of all individual resistance.
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Circuit 5.2 shows a circuit with two resistors connected in series. The 1.5 k resistor is in series
with the 2.2 k resistor, because they are connected in chain fashion. Notice that they have one
connection in common and nothing else is connected to that point (or node).
Circuit 5.2 Series resistive circuit
When the 9V battery “looks” out, it doesn’t know what is connected to it. It only “knows” the total
resistance. In this case, the battery “sees” 3.7 k. Since all batteries know Ohm’s Law, it puts out
2.43mA. The calculations are shown here.
IS 
VS
9V

 2.43 mA
RT 3.7k
This current comes out of the positive side of the battery, goes through the connecting wire, goes
through the 1.5k resistor (R1), comes out of the 1.5k resistor, goes through the 2.2k (R2)
resistor, comes out of the 2.2k resistor and finally goes back to the negative side of the battery
through the connecting wire. So you see that the current is the same in the whole loop or closed
circuit, IS = IR1 = IR2. The current direction is clockwise. Check Circuit 5.3.
Circuit 5.3 Current flow in a series circuit
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Ohm’s Law may be applied to each resistor to find the voltage dropped across each resistor. Note
that the voltage polarity across a resistor is positive at the terminal where the current enters the
resistor and negative at the terminal where the current leaves the resistor. Figure 5.1 shows this
relationship. Make a mental picture of Figure 5.1 and never forget it.
I
R
+
V
-
Figure 5.1 Voltage Polarity Across a Resistor
Since the current direction is clockwise, it comes down through the two resistors. According to
Figure 5.1, the voltage polarity across each resistor caused by the downward current is positive on
top and negative on the bottom of each resistor. Ohm’s Law allows us to calculate the magnitude
of each resistor voltage.
VR1  I R1 R1  (2.43mA)(1.5k)  3.65V
VR 2  I R 2 R2  (2.43mA)(2.2k)  5.35V
Kirchhoff’s Voltage Law (KVL) can be confirmed, because the 9V rise provided by the battery
is equal to the sum of the 3.65V drop across the 1.5k resistor and the 5.35V drop across the
2.2k resistor.
5.3 – The Voltage Divider Rule (VDR)
The Voltage Divider Rule is another way to obtain the voltage drop across series resistors. It says
that the voltage dropped across one of two resistors in series is the product of the applied voltage
and the ratio of the particular resistor divided by the sum of the two resistors. This is shown
symbolically as follows.
𝑅𝑥
𝑉𝑅𝑥 = 𝑉𝑇 ( )
𝑅𝑇
Formula 5.2 – Voltage Divider Rule Formula
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Using voltage divider rule, Formula 5.2, we can calculate the voltage across R1 and R2:
𝑉𝑅1 = 𝑉𝑇 (
𝑉𝑅2 = 𝑉𝑇 (
𝑅1
𝑅𝑇(𝑠𝑒𝑟𝑖𝑒𝑠 𝑟𝑒𝑠𝑖𝑠𝑡𝑜𝑟𝑠
𝑅2
𝑅𝑇(𝑠𝑒𝑟𝑖𝑒𝑠 𝑟𝑒𝑠𝑖𝑠𝑡𝑜𝑟𝑠
) = 9𝑉(
1.5 𝑘Ω
) = 9 𝑉(0.405) = 3.65 𝑉
1.5 𝑘Ω + 2.2 𝑘Ω
) = 9𝑉(
2.2 𝑘Ω
) = 9 𝑉(0.595) = 5.36 𝑉
1.5 𝑘Ω + 2.2 𝑘Ω
Notice that these were the same values that we obtained using Ohm’s Law. The main advantage
of using the VDR is that once the multiplying factors are obtained for the two resistors, they will
never change. In other words, the 1.5k resistor will always drop 0.405 or 40.5% of the applied
voltage while the 2.2k resistor will always drop 0.595 or 59.5% of the applied voltage. If the
power supply voltage is increased to 18V. The voltage drop in 1.5 k is also 40.5% of the applied
voltage, and 2.2 k is also 59.5% of the applied voltage.
5.4 – Non-Resistive Series Circuits
In practical circuits, resistors in series are very seldom seen. Usually, a resistor is in series with
another circuit component. Circuit 5.4 shows a resistor in series with a standard size light emitting
diode, LED. It is a well-known fact that a standard size light emitting diode needs 2 V and 20 mA
to operate. Since the applied voltage is 9V, according to KVL the voltage across the resistor must
be 7V (9 V – 2 V = 7 V). Since the two elements are in series and the LED needs 20 mA, the
current must come through the resistor. Knowing the voltage drop in the resistor, Ohm’s law can
be applied to find the resistance. In this case, a resistor of 350  must be used to produce a current
of 20 mA with a voltage drop of 7 V.
R
7V
 350 
20 mA
Since 350  produces exactly 20 mA, for safety purposes a larger resistance is needed to limit the
current to a safe value that is less than 20 mA. In this case, a 470  resistor is used because it
produces a current flow of 15 mA.
I 
7V
 0.0 1 5
A  1 5mA
47
0
The brightness of an LED is proportional to the LED current. 20mA is the rated current for good
brightness for a standard LED. Currents higher than 20mA should be avoided. In our case, 15mA
is enough to light the LED with sufficient brightness without exceeding the 20mA rating.
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Circuit 5.4 A Resistor in Series with a Light Emitting Diode
An LED is a semiconductor light source widely used in the field of electronics. Its function is to
emit light when it is active or when current flows through the diode from the anode to the
cathode. Check Figure 5.2.
Figure 5.2 LED terminals
Lab Experiment Procedure
Notation: All measurements and calculations must be written in engineering notation rounded off
to the hundredth.
Part 1: Ohm’s Law






Obtain a 2.2 kΩ resistor from the component kit.
Measure the resistance and record the measurement in Table 5.1.
Build Circuit 5.1 into a protoboard.
Measure the voltage across the resistor.
Measure the current through the resistor.
Record the measurements in Table 5.1.
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
Power OFF the circuit.
Resistor Value
Measured Resistance
(Unit)
Measured Voltage
(Unit)
Measured Current
(Unit)
2.2 kΩ
Table 5.1 Ohm’s law
Plotting Ohm’s law behavior








Obtain a second resistor 1.5k (color code: BROWN, GREEN, RED, GOLD).
From the circuit, replace the 2.2 k resistor with a 1.5 k resistor in its place.
Turn on the power supply and the set the voltage to 0 V.
Connect the power supply to the circuit.
Measure the voltage and current across the resistor, and record the values in Table 5.2.
Set the voltage in the power supply to the values in Table 5.2, measure the voltage and
current, and record the values in Table 5.2.
Repeat the previous step until you complete Table 5.2.
Disassemble the circuit.
Power Supply Voltage (V)
Measured Voltage (V)
Measured Current (A)
0V
1.0 V
2.0 V
3.0 V
3.5 V
4.0 V
4.5 V
5.0 V
5.5 V
6.0 V
6.5 V
7.0 V
Table 5.2 – Measured voltage and current
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
Using the value from Table 5.2, sketch the Ohm’s law behavior graph below.

Using the measured values from Table 5.2 or the graph above, pick two sets of voltage
and current through R1, record these two sets in Table 5.3, and calculate the resistance
value of the line using the slope formula:
𝑆𝑙𝑜𝑝𝑒 =


Δ𝐼
𝐼2 − 𝐼1
1
=
=
ΔV
𝑉2 − 𝑉1 𝑅
Record the calculate slope resistance in Table 5.3.
Calculate the percent of difference between the resistor value and the calculated slope
resistance value.
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐴𝑐𝑡𝑢𝑎𝑙 − 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑
% 𝑜𝑓 𝐷𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (
) × 100 %
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐴𝑐𝑡𝑢𝑎𝑙
Formula 5.3 – Percentage of difference between the measured and calculated value
Resistance Value
1.5 kΩ
Slope Resistance
% of difference
Table 5.3 – Measured resistance
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Part 2: Series Circuit





Obtain 1.8 k and 3.6 k resistors and measure each resistor individually. Record the
measured resistance in Table 5.4.
Build a series circuit in a protoboard using the resistors (1.8 k and 3.6 k) obtained in
the previous steps.
Measure the current flow through R1 and R2 resistors and record the measurements in
Table 5.4.
Measure the voltage across each resistor, VR1 and VR2. Record measurements in Table 5.4
Disassemble the circuit.
Measured Resistance
(Include unit)
Measured Voltage
(Include unit)
Measured Current
(Include unit)
R1 (1.8 k)
R2 (3.6 k)
Table 5.4 Voltages & Currents in a Series Circuit
Part 3: Voltage Divider Rule




Use the voltage divider formula, Formula 5.2, and calculate the voltage across R1 and R2.
Record calculations in Table 5.5.
Using Table 5.4, record the measured voltage in R1 and R2, VR1 and VR2, in Table 5.5
Find the percentage of difference between the calculated and measured of voltage VR1
and VR2 using Formula 5.3.
Record calculation in Table 5.5.
Show Calculations Here.
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Calculated Voltage
Measured Voltage
from Table 5.4
% of difference
VR1
VR2
Table 5.5 Confirmation of the Voltage Divider Rule
Part 4 - Non-Resistive Series Circuit






Obtain a 470  resistor and a red LED.
Build Circuit 5.4. Make sure that the cathode of your red LED is connected to the
negative of the voltage source (Observe Figure 5.2 to find the cathode of the LED).
Power ON the circuit.
Measure the voltage across R1 and the red LED. Record your measurement in Table 5.6
Measure the current through R1 and the red LED. Record your measurement in Table 5.6
Disassemble the circuit.
Measured
voltage across R1
(VR1)
Measured voltage
across LED
(VLED)
Measured current
through R1
(IR1)
Measured current
through LED
(ILED)
VLED + VR
Does the sum of the LED voltage and the resistor voltage equal or almost equal the
applied voltage? In other words, does KVL hold? Justify your answer.
Table 5.6 Voltage & Current Measurements for the LED & KVL Confirmation
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Questions
Question 1 and 2. A student measured and sketch the current and voltage through a resistor, R1:
Current vs Voltage through R1
Current (mA)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
Voltage (V)
1. The student recorded a resistor value of 2.7 kΩ. Is this the correct resistor value? Explain
and justify your answer.
2. Which do you think was the student's error, if any, during the experiment? Justify your
answer.
Question 3 and 4. A student built a series circuit with a 470 Ω connected in series with a red
LED as below:
3. The red LED will light up completely if a 20 mA flows through it. The student measured
the voltage across R1 as 2 V. Would the student be able to observe the red LED lights
up? Justify your answer.
4. If the student wants to generate a 20mA current through the red LED, what would be the
total voltage, Vs, that would have to apply to the circuit? Justify your answer.
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT -----------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab instructor’s signature
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Lab Experiment
6
Parallel Circuits
6.1 – Kirchhoff’s Current Law (KCL)
Kirchhoff’s Current Law, KCL, was introduced by German mathematician and physicist Gustav
Kirchhoff. Gustav described that the sum of the currents leaving the node, junction point, was
equal to the sum of the currents entering the same junction or node. A simple way to say this is
that at any node, what goes in must come out.
Figure 6.1 Illustration of water distribution in water pipes
Figure 6.2 Current Distribution
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𝑆𝑢𝑚 𝑜𝑓 𝐼𝑖𝑛(𝑛𝑜𝑑𝑒 𝐴) = 𝑠𝑢𝑚 𝑜𝑓 𝐼𝑜𝑢𝑡(𝑁𝑜𝑑𝑒 𝐴)
𝑆𝑢𝑚 𝑜𝑓 𝐼𝑖𝑛(𝑁𝑜𝑑𝑒 𝐴) + 𝑠𝑢𝑚 𝑜𝑓 𝐼𝑜𝑢𝑡(𝑁𝑜𝑑𝑒 𝐵) = 0 𝐴
Formula 6.1 Kirchhoff’s Current Law (KCL)
6.2 – Components Connected in Parallel
Components are connected in parallel if their component terminals are connected to the same
common node respectively, and have the same voltage drop. In other words, two or more
components are in parallel if they are connected between the same two connection points or nodes.
The shortcut notation for a parallel connection is two slashes “//” sometimes “||” is also used. If a
1kΩ resistor and a 4.7kΩ resistor are connected in parallel, one could write 1kΩ || 4.7kΩ. This is
read as: 1kΩ in parallel with 4.7kΩ.
Circuit 6.1 1kΩ resistor in parallel with 4.7kΩ resistor
The voltage across parallel components is the same because the voltage between two points is
always the same.
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Circuit 6.2 Voltage across parallel components
The total current entering a junction with two parallel paths, however, divides between the two
paths in such a way that the sum of the currents in the two paths is equal to the total current entering
the parallel combination. As stated above, this is known as Kirchhoff’s Current Law (KCL).
Circuit 6.3 Current flow in a parallel circuit
6.3 – Total Resistance and Conductance in a Parallel Circuit
Conductance is the reciprocal of resistance, is represented by the letter G and is measured in
siemens [S]. In parallel, the conductance value of the resistors adds.
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(Conductance)
RT 
G
1
1
1
1

 ....
R1 R2
RN
1
R
where N is the total number of resistor connected in parallel.
Formula 6.2 Total Resistance and Conductance formula
For
 example, to find the total resistance of the circuit Figure 6.1, the total resistance can then be
obtained by taking the reciprocal of the total conductance.
G

1
R1
G 4.7 k 
G1k 
1
R2
1
 1mS
1k
G4.7 k 
1
 0.2128mS
4.7k
GT  G1k  G4.7k  1mS  0.2128 mS  1.2128 mS  1.21mS
RT 
1
 0.82645k  826.45
1.21mS
In lab, the total resistance can me measure by placing the measuring leads of your DMM across
the resistors connected in parallel as it is shown in Figure 6.3
Figure 6.3 Parallel Resistive Circuit Measurement with a DMM
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There is a special case for two resistor connected in parallel. The total resistance for two parallel
resistors can also be calculated using the “product over sum” formula.
RT 
R1 R2
R1  R2
Formula 6.3 Special case for two resistor connected in parallel
Once we have the total resistance, the total current can then be obtained by dividing the applied
voltage by the total resistance.
IT 
9V
 0.0109149A  10.91mA
824.56
6.4. – The Current Divider Rule (CDR)
The current divider rule is a computational method that allows you to calculate how the current
divides between two paths of known resistance. The current divider rule says that the current
through one of two parallel paths is equal to the total current that comes into the junction
multiplied by the ratio of the resistance of the other path divided by the sum of the resistance of
the two paths. In symbolic form this is as follows:
IX  IT
RT
RX
Where X is the unknown current of resistor X
Formula 6.4 Current Divider Rule
The advantageof using the Current Divider Rule (CDR) is that you obtain the percentage of the
division of current between the paths. For this circuit, the current through the 1kΩ resistor will
always be 0.82456 or 82.46% of the total. The current through the 4.7kΩ resistor will always be
0.17544 or 17.54% of the total. This current division ratio will always hold no matter what the
total current is.
𝑅𝑎𝑡𝑖𝑜 𝑜𝑓 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑅1 =
𝑅𝑇 0.82456𝑘Ω
=
= 0.82456 = 82.46%
𝑅1
1𝑘Ω
𝑅𝑎𝑡𝑖𝑜 𝑜𝑓 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑡ℎ𝑟𝑜𝑢𝑔ℎ 𝑅2 =
𝑅𝑇 0.82456𝑘Ω
=
= 0.17544 = 17.54%
𝑅2
4.7𝑘Ω
 Measured _ Value  Calculated _ Value 
 * 100 %
% _ difference  
Calculated _ Value


Formula 6.5 Percent of Difference between the Calculated and Measured Value Formula
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6.5 – Applications of Parallel Circuit
Every residence in the US has usually one or two electrical energy feeds. Each one of these
feeds breaks out into several branch circuits. Each one of these circuits has many lighting loads
and receptacles. All the electrical loads and receptacles connected to the same feed are in
parallel. Therefore, all the electrical appliances in your house that are connected to the same
feed are connected in parallel.
Each branch circuit has a fuse or a circuit breaker to protect the wiring against current overload
in case you connect too many appliances in parallel, and therefore, exceed the current rating of
the wires. Branch circuits in modern residences are wired with AWG # 12 wires which is capable
of safely carrying 20 amperes. The circuit breakers used, therefore, are set to trip and interrupt
the circuit if the current demand exceeds 20 amps.
Lab Experiment Procedure
Part 1 – Two Resistors Connected In Parallel
Part 1 of your lab experiment is to measure the total resistance, and voltage and current through
each element of a two resistors parallel circuit. For calculations, the current distribution in a
parallel circuit can be found by applying Ohm’s law, Kirchhoff’s Current Law, and Current
Divided Rule.
 Obtain a protoboard, jumper wires, and 1 kΩ and 4.7 kΩ resistors from your component kit.
 Build Circuit 6.1 in your protoboard
 Before powering your circuit, measure the total resistance (RT) is indicated in Figure 6.3.
Record this measurement in Table 6.1
 Set your circuit and DMM to measure current
 Power Circuit 6.1
 Measure the current through R1, R2, and voltage source, and record measurement in Table 6.1
 Set your circuit and DMM to measure voltage
 Measure the voltage across R1, R2, and voltage source, and record measurement in Table 6.1
 Calculate the total resistance using Formula 6.3. Record calculation in Table 6.1
 Calculate the current through R1, R2, and IT using Ohm’s law. Record calculation in Table 6.1
 Using the % of difference formula, Formula 6.5, calculate the percentage of difference between
the measured and calculated value. Record calculation in Table 6.1
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Measured Value
(Include Unit)
Calculated value
(Include Unit)
% of Difference
Total Resistance, RT
Total Current, IS = IT
Current through R1 (1 kΩ),
IR1
Current through R2 (4.7
kΩ), IR2
Voltage source, VS
Voltage across R1 (1 kΩ),
VR1
Voltage across R2 (4.7 kΩ),
VR2
Table 6.1 Two Resistors Circuit: Total resistance, Voltage, and Current Measurements
 Use the measured current IT, IR1, and IR2 from Table 6.1 and fill up the corresponding cell in
Table 6.2.
 Use the Current Divider Formula, Formula 6.4, and calculate IR1 and IR2. Show calculation in
Table 6.2.
 Use KCL formula in Circuit 6.3 to find IT. Show calculation in Table 6.2.
 Use the current divider rule formula, Formula 6.3, to find the current through IR1 and IR2. For
this calculation, RT and IS values are the calculated value from Table 6.1.
 Using the % of difference formula, Formula 6.5, calculate the percentage of difference between
the measured and calculated current. Show calculation in Table 6.2.
 Ask lab instructor to check Table 6.1 and 6.2.
 Once both tables are checked, disassembled circuit, organize your components in your
components kit, and proceed to Part 2.
IT
Total Current
(Include Unit)
IR1
Current in R1
(Include Unit)
IR2
Current in R2
(Include Unit)
Measured value
(Table 6.1)
Calculated value
% of Difference
Table 6.2 Current divider rule in two resistors circuit
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Part 2 – Three Resistors Connected in Parallel Configuration
Experiment Part 2 is to measure the total resistance of a three resistors parallel circuit, as well as
the voltage and current distribution through each element of the parallel circuit. For the
calculations part, the current distribution in a parallel circuit can be found by applying Ohm’s
law, Kirchhoff’s Current Law, and Current Divided Rule.
 Obtain a 1 kΩ, 3.3 kΩ, and 5.6 kΩ resistors from your component list
 Build Circuit 6.4
Circuit 6.4 Three Resistors Connected In Parallel Configuration
 Before powering your circuit, measure the total resistance and record this measurement in Table
6.3
 Set your circuit and DMM to measure current
 Power up circuit 6.4
 Measure the current through R1, R2, R3, and voltage source, and record measurement in Table 6.3
 Set your circuit and DMM to measure voltage
 Measure the voltage across R1, R2, R3, and voltage source, and record measurement in Table 6.3
 Calculate the total resistance using Formula 6.2. Record calculation in Table 6.3
Show Calculations of total resistance
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 Calculate the current through R1, R2, R3, and voltage source using Ohm’s law. Record calculation
in Table 6.3
 Using the % of difference formula, Formula 6.5, calculate the percentage of difference between
the measured and calculated value. Record calculation in Table 6.3
Show Calculations of the current through R1, R2, and R3
Measured Value
(Include Unit)
Calculated value
(Include Unit)
% of Difference
RT
IS = ITotal
IR1
IR2
IR3
VS
VR1
VR2
VR3
Table 6.3 Three Resistors Circuit: Total resistance, Voltage, and Current Measurements
 Use the measured current IT, IR1, IR2, and IR3 from Table 6.3 and fill up the corresponding cell
in Table 6.4.
 Use the Current Divider Formula, Formula 6.4, and calculate IR1, IR2, and IR3. Show calculation
in Table 6.4. For this calculation, RT and IS values are the calculated value from Table 6.3.
 Use KCL formula in Circuit 6.3 to find IT. Show calculation in Table 6.4.
 Use the current divider rule formula, Formula 6.3, to find the current through IR1 and IR2.
 Using the % of difference formula, Formula 6.5, calculate the percentage of difference between
the measured and calculated current. Show calculation in Table 6.4
 Ask lab instructor to check Table 6.3 and 6.4
 Once both tables are checked, disassembled circuit, organize your components in your
components kit, and proceed to Part 3.
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ITotal
IR1
IR2
IR3
Measured value
(Table 6.3)
Calculated
value
(Show
calculations)
% of Difference
Table 6.4 Current divider rule in a 3 resistors circuit
Part 3. Non-Resistive Components in Parallel
Circuit 6.5 shows a 1.5kΩ resistor connected in parallel with a computer chip cooling fan. The
parallel combination is powered by a 9V supply. According to the fan’s specifications, the fan
current should be less than 50mA. Here, however, we are energizing the fan with 9V, therefore
the fan current will be less.
Circuit 6.5 A Typical Heater and a fan in Parallel Circuit





Obtain a 1.5 kΩ resistor from your component kit
Obtain a cooling fan from lab technician
Build Circuit 6.5
Set your circuit and DMM to measure current
Measure the current throgut voltage source (total current), 1.5 kΩ resistor, and the cooling
fan. Record measurement in Table 6.5
 Ask lab instructor to check Table 6.5
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 Once both tables are checked, disassembled circuit, organize your components in your
components kit, and proceed with lab report.
ITotal
IR=1.5 kΩ
ICooling Fan
Does KCL Hold?
(Yes/No) Explain
Measured
Table 6.5 - Parallel Components and KCL
Question
1. Three resistors, 5.6 kΩ, 8.2 kΩ, and 2.7 kΩ, are connected in parallel. When a student
measured the total resistance, the DMM read 6.027536 kΩ. Without calculations, do you
think this measurement may be correct? Justify your answer.
2. A global outlet power strip has a maximum current load of 15A. If a 10A air conditioner
and a 1A desk lamp is already connected in the power strip. What do you think it would
happen if you connect a 12 A hair dryer to the same power strip? Explain your answer.
3. A student built a circuit with two resistors, 2 kΩ and 3 kΩ, connected in parallel. The
student measured the current through 3 kΩ and the DMM displayed 4 mA. Using this
measurement, how can the student predict the total voltage of the parallel circuit? Justify
your answer.
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT ----------------Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab Instructor’s Signature
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Lab Experiment
7
Series-Parallel Circuits
7.1 – Series-Parallel Circuits
Most practical circuits in electronics are made up combinations of both series and parallel circuits.
These circuits are made up of all sorts of components such as resistors, capacitors, inductors,
diodes, transistors and integrated circuits. Such a circuit, where the components are not strictly in
series or in parallel, is called series-parallel circuit. There is no real world application for a seriesparallel circuit made up of only resistors. In this lab however, we investigate series-parallel circuits
made up of only resistors to learn about such circuits. The concepts we investigate here can then
be applied to real world circuits. In this experiment, we will investigate a series-parallel circuit.
The voltages and the currents in the circuit will be measured and then compared to the expected
values.
Remember that you can only combine resistors that are in series or resistors that are in parallel.
Series resistors add. Resistors in parallel can be combined using either the conductance method or
the “product over sum” method (two resistors at a time). The conductance method, you remember,
is easier to use with the calculator. Two resistors may be recognized to be in series if they have
one node in common and nothing else is connected to that node, it means that the node has a degree
of two. Resistors may be recognized to be in parallel, if they are connected between the same two
nodes. If two resistors are neither in series nor in parallel, they cannot be combined. Only resistors
in series or in parallel can be combined.
Circuit 7.1 shows a series-parallel circuit. Note that R1 cannot be combined with either R2 or R3;
R1 is neither in series nor in parallel with either R2. However, R2 is in parallel with R3, because they
are connected between the same two nodes (node B and ground).
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Circuit 7.1 Series-Parallel Resistive Circuit
The equivalent combination of R2//R3 is easily found by using the equation the reciprocal of total
conductance formula
𝑅2 ||𝑅3 =
1
1
1
(𝑅 + 𝑅 )
2
3
=
1
1
1
(330Ω + 680Ω)
= 222Ω
You can also use the special formula, product over the sum, for two resistors connected in
parallel
𝑅2 ||𝑅3 =
(𝑅2 × 𝑅3 ) (330Ω × 680Ω)
=
= 222Ω
(𝑅2 + 𝑅3 ) (330Ω + 680Ω)
This parallel combination can now be seen to be in series with the 100 resistor R1.
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Circuit 7.1A Equivalent Circuit from Circuit 7.1 (R2 || R3)
The total resistance can be calculated as follows:
RT  R1  ( R2 // R3 )  100  222  322
The 9V power supply therefore “sees” 322. Ohm’s Law allows us to predict the total current.
IT 
VT
9

 0.028 A  28mA
RT 322
About the current distribution in Circuit 7.1, you can note since the positive of the voltage source
is connected in series with R1, the current through R1 is the same as the voltage source. At node
B, the current source or current coming out from R1 divides in two paths. Check Circuit 7.2 for
reference.
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Node A: Total current flows through R1. IS = IR1
Node B: Total current slips to R2 and R3. The
amount of slipped current depends on the
resistance value of R2 and R3. IS = IR1 + IR2
Node C: Current R2 and R3 recombines and
becomes the total current again. IR1 + IR2 = IS
Circuit 7.2 Current distribution for Circuit 7.1
Laboratory Experiment
Part 1 – Resistance Measurement in a Series-Parallel Circuit
1. Obtain a protoboard, jumper wires, and 100 Ω, 330 Ω, and 680 Ω resistors from your
component kit.
2. Build Circuit 7.1 into your protoboard, but don’t make the connection to voltage source
yet.
3. Measure total resistance for the circuit in step 2 as shown in Figure 7.1. Record your
measurement in Table 7.1. Do not forget the unit.
Figure 7.1 Total resistance measurement using a DMM
4. Calculate the percentage of difference between your calculated and measured total
resistance and record your result in Table 7.1.
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Show Calculation Here
Calculated RT
Measured RT
𝑹𝑻(𝑪𝒂𝒍𝒄𝒖𝒍𝒂𝒕𝒆𝒅) − 𝑹𝑻(𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅)
% 𝒅𝒊𝒇𝒇 = (
) × 𝟏𝟎𝟎%
𝑹𝑻(𝒄𝒂𝒍𝒄𝒖𝒍𝒂𝒕𝒆𝒅 )
Total Resistance
RT
Table 7.1 Total Resistance Analysis in a Series-Parallel Circuit, Circuit 7.1
Part 2 – Current Analysis in a Series-Parallel Circuit
5. Power circuit in step 2 to complete Circuit 7.1.
6. Set up the DMM and Circuit 7.1 in Step 5 to measure current. Measure the current
through each element in Circuit 7.1 and record the measurements in Table 7.2.
7. Calculate the current through each resistor and voltage source in Circuit 7.1. Record
calculation in Table 7.2.
Show Calculation Here
8. Find the percentage of difference between the measured and calculated current. Record
the result in Table 7.2.
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Show Calculation Here
Is
IR1
IR2
IR3
Does KCL Hold? (Yes/No) Explain.
Measured
Value
Calculated
Value
% Difference
Table 7.2 Current Analysis in a Series-Parallel Circuit, Circuit 7.1
Part 3 – Voltage Analysis in a Series-Parallel Circuit
9. Set the DMM and Circuit 7.1 in Step 5 to measure voltage. Measure the voltage across
each resistor and voltage source. Record the measured value in Table 7.3.
10. Calculate the voltage across each resistor and voltage source in Circuit 7.1. Record
calculation in Table 7.3
11. Find the percentage of difference between the measured and calculated voltage. Record
the result in Table 7.3.
12. Disassemble the circuit and place your component in their respective kit. Proceed with
Circuit 7.2.
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Show Calculation Here
Vs
VR1
VR2
VR3
Does KVL Hold? (Yes/No) Explain.
Measured
Value
Calculated
Value
% Difference
Table 7.3 Voltage Analysis in a Series-Parallel Circuit, Circuit 7.1
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Part 4 – Resistance, Voltage, and Current Analysis in a Series-Parallel Circuit
Circuit 7.2 Series-Parallel Resistive Circuit
13. Obtain resistors: 100Ω, 330Ω, 220Ω, and 470Ω.
14. Build Circuit 7.2 into your protoboard, but don’t make the connection to voltage source
yet.
15. Measure total resistance for Circuit 7.2 in step 14. Record your measurement in Table
7.4. Do not forget to include the unit.
16. Calculate the percentage of difference between your calculated and measured total
resistance and record your result in Table 7.4.
Show Calculation Here
Calculated RT
Measured RT
% 𝒅𝒊𝒇𝒇 = (
𝑹𝑻(𝑪𝒂𝒍𝒄𝒖𝒍𝒂𝒕𝒆𝒅) − 𝑹𝑻(𝒎𝒆𝒂𝒔𝒖𝒓𝒆𝒅)
) × 𝟏𝟎𝟎%
𝑹𝑻(𝒄𝒂𝒍𝒄𝒖𝒍𝒂𝒕𝒆𝒅 )
RT
Table 7.4 Total Resistance Analysis in a Series-Parallel Circuit, Circuit 7.2
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Part 5 - Current Analysis in a Series-Parallel Circuit
17. Set 9 V to circuit in step 14 to complete Circuit 7.2.
18. Set the DMM and prepare Circuit 7.2 in Step 17 to measure current. Measure the current
through each element in circuit from step 17 and record the measured value in Table 7.5.
Is
IR1
IR2
IR3
IR4
Measured Value
Calculated Value
% Difference
Table 7.5 Current Analysis in a Series-Parallel Circuit, Circuit 7.2
19. Calculate the current through each resistor and voltage source in Circuit 7.3. Record
calculation in Table 7.5.
20. Find the percentage of difference between the measured and calculated current. Record
the result in Table 7.5.
Show Calculation Here
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Part 6 - Voltage Analysis in a Series-Parallel Circuit
21. Set DMM and prepare Circuit 7.2 in Step 17 to measure voltage. Measure the voltage
across each resistor and voltage source. Record the measured value in Table 7.6
22. Calculate the voltage across each resistor and voltage source in Circuit 7.2. Record
calculation in Table 7.6
Show Calculation Here
23. Find the percentage of difference between the measured and calculated voltage. Record
the result in Table 7.6
Vs
VR1
VR2
VR3
VR4
Measured Value
Calculated Value
% Difference
Table 7.6 Voltage Analysis in a Series-Parallel Circuit, Circuit 7.2
24. Disassemble the circuit and place your component in their respective kit.
25. Call instructor to check your circuit and tables.
26. Pack your lab components and clean your workstation before leaving lab room.
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Questions
1. A student built Circuit 7.1 and measured the voltage through each resistor. The student
measured 9 V for all three resistors. What was the mistake that the student made?
Explain your answer.
2. A student built Circuit 7.2 and measured the total resistance using a DMM. The recorded
total resistance was around 101 Ω. What was the mistake that the student made? What
should the student do to measure total resistance correctly? Explain your answer.
3. For Circuit 7.2, if a student measured the current through R1, R2, and R3 and found that
they were the same current. Just by observation, how can you justify that the measured
currents are wrong?
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT -----------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab Instructor’s Signature
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Lab Experiment
8
Power
8.1 – Introduction to Power
Power is familiar to us since we see the power value in electric circuit and devices like light bulbs,
hair dryer, power adapter, heater, etc. The higher the watt rating of a device, the more energy it
can get out of it per unit time. For example, the greater the power rating of the heater, the more
heat energy it can produce per second. In general, the rate at which electric energy is handled is
called power. The symbol for power is P and its unit is Watts “W”.
Power is related to energy, which is the capacity to do work or the rate to transfer energy, in an
interval of time:
𝑃=
𝑊
𝑡
Since our interest is in electrical power, if W and t is substitute from the current and voltage
formula, respectively:
𝑡=
𝑸
𝑰
𝑊 = 𝑸𝑽
𝑃=
𝑄𝑉
= 𝑽𝑰
𝑸
𝑰
To express the power in terms of electrical quantities, the three basic relationships for power in
electrical quantities are:
P  VI
P  I 2R
P
V2
R
Formula 8.1 Power Formula
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Lab Experimental Procedure
Part 1: Resistance Measurements
Circuit 8.1 shows a series-parallel resistive circuit built of three resistors.
Circuit 8.1 Voltages & Currents in Series-Parallel Circuit
1. Obtain resistors 120 Ω, 220 Ω, and 470 Ω from your components’ kit
2. Measure the resistance of each resistor individually and record the measurement in Table
8.1
3. Using wiring practices, assemble the Circuit 8.1 on your protoboard
4. Before connecting the power source to Circuit 8.1, measure the total resistance as seen by
the source terminals and record the measurement in Table 8.1. Check Figure 8.1 for
reference.
Figure 8.1 - Total Resistance Measurement from Protoboard
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5. Calculate the total resistance and record the answer in Table 8.1
Show calculation for total resistance here
6. Calculate the percent of difference between the measured and the given resistance of each
resistor.
% 𝑜𝑓 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐴𝑐𝑡𝑢𝑎𝑙(𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑) − 𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑
) × 100 %
𝑅𝑒𝑠𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝐴𝑐𝑡𝑢𝑎𝑙(𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑)
7. Record calculation in Table 8.1
Actual Resistance Value
Measured Resistance
% of difference
R1 = 120 Ω
R2 = 220 Ω
R3 = 470 Ω
Calculated RT = ________
Table 8.1 Resistance measurement
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Part 2: Current Measurements and Calculations
8. Connect 9 V from the power supply or 9 V battery to the + and – node of the protoboard.
9. Prepare the circuit and the DMM to measure the current through each resistor.
10. Measure and record the current through each resistor in Table 8.2.
11. Calculate the current through each resistor in Circuit 8.1 and record the calculated value
in Table 8.2.
12. Find the percent of difference between the measured and calculated current through each
resistor. Record result in Table 8.2.
Show calculation for the current through each resistor.
Component
Measured Current
Calculated Current
% of difference
IR1(120 Ω)
IR2(220 Ω)
IR3(470 Ω)
IS
Table 8.2 Measured and calculated current of Circuit 8.1
Part 3: Voltage Measurements and Calculations
13. Prepare the circuit and the DMM to measure the voltage across each resistor.
14. Measure and record the voltage across each resistor in Table 8.3
15. Calculate the voltage across each resistor using Ohm’s law or Voltage Divider Rule.
Record the calculated voltage in Table 8.3.
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16. Find the percent of difference between the measured and calculated voltage through each
resistor. Record result in Table 8.3
17. Disassemble the circuit, put your components in your lab kit, and turn OFF all lab
equipment.
Component
Measured Voltage
Calculated Voltage
% of difference
VR1(120 Ω)
VR2(220 Ω)
VR3(470 Ω)
VS
Table 8.3 Measured and calculated voltage of Circuit 8.1
Part 4: Power Dissipation Calculations Using Three Different Power Formula
For this part of lab, you will need to calculate the measured and calculated power using three
different power formula:
P  VI
P  I 2R
P
V2
R
Formula 8.1 Power Formula
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18. Using the Measured Current from Table 8.2 and the Measured Voltage from Table 8.3,
calculate the power dissipation for each resistor using the first power formula from
Formula 8.1  P = VI
Component
Measured Power
Calculated Power
P = VI
% of difference
PR1(120 Ω)
PR2(220 Ω)
PR3(470 Ω)
PS
Table 8.4 Measured and calculated power dissipation in Circuit 8.1 using P = VI
19. Record calculation of Measured Power in Table 8.4
20. Using the Calculated Current from Table 8.2 and the Calculated Voltage from Table 8.3,
calculate the power dissipation for each resistor using the first power formula from
Formula 1  P = VI
21. Record calculation of Calculated Power in Table 8.4
22. Find the Percent of Difference between the Measured and Calculated Power and record
result in Table 8.4.
23. Using the Measured Current from Table 8.2, calculate the power dissipation for each
resistor using the second power formula from Formula 1  P = I2R
Component
Measured Power
Calculated Power
P = I2 R
% of difference
PR1(120 Ω)
PR2(220 Ω)
PR3(470 Ω)
PS
Table 8.5 Measured and calculated power dissipation in Circuit 8.1 using P = I2R
24. Record calculation of Measured Power in Table 8.5
25. Using the Calculated Current from Table 8.2, calculate the power dissipation for each
resistor using the second power formula from Formula 1  P = I2R
26. Record calculation of Calculated Power in Table 8.5
27. Find the Percent of Difference between the Measured and Calculated Power and record
result in Table 8.5
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28. Using the Measured Voltage from Table 8.3, calculate the power dissipation for each
resistor using the third power formula from Formula 1  𝑃 =
Component
Measured Power
𝑉2
𝑅
Calculated Power
𝑽𝟐
𝑷=
𝑹
% of difference
PR1(120 Ω)
PR2(220 Ω)
PR3(470 Ω)
PS
Table 8.6 Measured and calculated power dissipation in Circuit 8.1 using
𝑃=
𝑉2
𝑅
29. Record calculation of Measured Power in Table 8.6
30. Using Calculated Voltage from Table 8.3, calculate the power dissipation for each
𝑉2
resistor using the third power formula from Formula 1  𝑃 = 𝑅
31. Record calculation of Calculated Power in Table 8.6
32. Find the Percent of Difference between the Measured and Calculated Power and record
result in Table 8.6
Questions
1. Explain the possible reason why the powers to the components using the three different
formulas are slightly different. (Compare result from table 8.4, table 8.5, and table 8.6)
2. For circuit 8.1, if the power rating for R1, R2, and R3 is ¼ Watts, what would happen
with the power dissipation at each resistor if the voltage source is increased to 18 V?
Explain and justify your answer.
3. From table 8.4, 8.5, and 8.6, the highest percent of difference between the measured and
the calculated power is by using which of the three power formula? Explain your answer.
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT -----------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab Instructor’ Signature:
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Lab Experiment
9
Short & Open Circuit and Switches &
Relays
9.1 – Short & Open Circuits
Short and open circuit are important circuit concept in electronics because they allow us to make
or break connections. A short circuit is a path with very little resistance, close to zero resistance,
such as a piece of wire. In some circuit application, a closed switch or a switch in ON position and
a good fuse in a DMM (Figure 9.1) are examples of short circuits. Since a short circuit has very
low resistance, current will flow through the path to the rest of the circuit. On the other hand, an
open circuit is a broken connection or wire in a path that consequently will interrupt the current
flow, and produce an extremely high resistance across it, usually mega or giga ohms. Examples of
open circuit are the OFF position in a switch or a “blown” fuse of a DMM (Figure 9.1). Open
circuit interrupts the current flow
The following pictures of a “good” fuse and a “blown” fuse:
Good fuse (Short circuit)
Blown Fuse (Open Circuit)
Figure 9.1 Short and Open Circuit
9.1.1 Short and open circuit detection
A short or an open circuit may be detected using an ohmmeter or a continuity tester. When a test
is placed to a short circuit using an ohmmeter, the resistance measurement will show very low
resistance such as milliohms (Figure 9.2A). Instead, when an ohmmeter detects an open circuit, it
usually displays the letters “OL” which stand for Over Load.
A continuity tester from the DMM
usually indicates a short circuit with either a sound or
a small light bulb being lit, while the absence of a sound or the small light bulb being not lit is an
indication of an open circuit.
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Short Circuit Resistance (A)
Open Circuit Resistance (B)
Figure 9.2 Short and Open Circuit Resistance Measurement using an Ohmmeter
9.2 Switches and Relays
Switches are devices use to control the flow of current in through a circuit. They can turn electronic
or electrical devices ON or OFF and enable circuits to perform various tasks. Some example of
switches are doorbell switch, computer keyboard keys, car ignition key, an ON/OFF light switch,
etc. Switches come in different shapes and mechanical or electrical operations. Examples of
mechanical switches are momentary contact switches, slide switches, toggle switches, rotary
switches and rocker switches. There are also electrical operate switches as relays.
9.2.1. Mechanical Operation Switches
Momentary Contact Switches
Momentary contact switches are activated by pushing a button and come in two types; normally
open (N/O) and normally closed (N/C). When the button is pushed on a N/O switch, the contact is
made. When the button is pushed on a N/C switch, the contact is broken. The make or the break is
active for the whole time that the button is held depressed. Figure 9.3 shows the circuit diagram
for these two types of momentary contact switches.
N/O
Pushbutton Make
N/C
Pushbutton Break
Normally Open
Normally Closed
Image of a
push-button
switch
Figure 9.3 Momentary Contact Switches
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Pole and throw switches
In a toggle switch, a rocker switch or a slide switch, one terminal of the switch is permanently
connected to the traveling arm of the switch. This is called the pole. The other terminal of the
switch is in contact with the traveling arm during a ‘make’, and is not in contact during a ‘break’.
This terminal is called the through. A switch that has one pole and one through is called a ‘single
pole single through’ switch (SPST). A switch that has one pole and two through paths is called
‘single pole double through’ (SPDT). This kind of a switch is used when one point of the circuit
has to be connected to two separate points (at different times of course). When the handle of a
SPDT switch is “throw”, the contact to one through-path is made while the contact to the other
through path is broken. This can be accomplished in two ways. The break to the first contact can
be accomplished before the contact to the second through path is made. This is called a ‘break
before make’ switch. Alternately, the contact to the second through path can be made before the
break to the first through path is accomplished. This is a ‘make before break’ switch. Usually, only
‘make before break’ switches are identified. If nothing is said, a ‘break before make’ switch is
implied. When two SPST are built on the same switch body, usually, there is only one switch
handle, which operates both switches at the same time. The switch is referred to as ‘Double Pole
Single Throw’ (DPST). When two SPDT switches are built on the same switch body, the switch
is called ‘Double Pole Double Throw’(DPDT). See Figure 9.4 for reference.
9.2.2. Electrical Operation Switches
Relays
Relays are switches that are operated electrically. Relays offer isolation between the control circuit
and the load circuit. Relays allow a circuit to control other circuits without direct connection
between them. A typical relay consist of a coil that when energized attracts the traveling arm of a
SPDT switch. It opens the N/C contacts and it closes the N/O contacts. Figure 9.5 shows the
schematic representation of a typical relay.
Single Pole Single Throw (SPST)
Single Pole Double Throw (SPDT)
Double Pole Double Throw (DPST)
Figure 9.4 Switches
When the coil is energized the pole breaks from throw 1 and makes with throw 2
Figure 9.5 Typical Relay
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Lab Experiment Procedure
Part 1 – Open and Short Circuit
 Set up the DMM as an ohmmeter to the lowest resistance range, and connect the DMM
leads across a short piece of wire.
 Record your observations in Table 9.1.
 Disconnect one of the DMM leads from the wire. Record your observations in Table 9.1.
Some DMMs also have a ‘continuity tester’ built-in. If your DMM has this feature, put the DMM
in this mode and first place the DMM leads across the wire, and then disconnect one of the leads.
Record your observations in the continuity indication column of Table 9.1
Circuit Element
DMM
reading
Resistance
Value
Is it an open or
short circuit?
Continuity
indication
(Yes / No)
Short piece of wire
Wire Disconnected
from meter lead
Table 9.1 Short Circuit & Open Circuit Measurements
Part 2 – Protoboard connections
Use the DMM as an ohmmeter or a continuity tester, verify which holes are connected together on
your protoboard, and fill up Table 9.2. With your results in Table 9.2, describe how the nodes in
the protoboard is organized and fill up Table 9.2.
Test node
Measured
Resistance
Short or Open
Circuit?
Are they connected?
(Yes/No)
A5 and A6
D10 and F10
C20 and D20
F50 and I50
+ 10 and + 20
+30 and -30
Table 9.2 – Protoboard connections
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Part 3 – Switches
 Pick an ON/OFF (SPST) switch from your component kit. If you don’t have a SPST
switch, you can use a jumper wire to simulate the switch.
 Set the DMM either as an ohmmeter or as a continuity tester.
 Connect the meter across an ON/OFF switch.
 Operate the switch and fill your observation in Table 9.3
Switch Position
Measured Resistance
Short or Open?
ON
OFF
Table 9.3 On/Off Switch Operation
 Pick a SPDT switch from your component kit.
 Set the DMM either as ohmmeters or continuity testers.
 Connect the first ohmmeter from the pole of the switch to the first throw. Remember that
the pole of the switch is the middle terminal.
 Connect the second ohmmeter from the pole to the second throw.
 Operate the switch and fill in Table 9.4
Switch Position
Measured Resistance
Short or Open?
Position 1
Position 2
Table 9.4 SPDT Switch Operation
Part 4 - Application of Momentary Contact Switches
 From you component kit, obtain two filament light bulb and build the circuit in Figure
9.6 on a protoboard.
 Build the circuit with the Normally Open push-button switch.
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N/O
Pushbutton
Switch
Bulb
1
VT
9V
Battery
Bulb
2
a) Normally Open Push-button Switch
b) Normally Closed Push-button Switch
Figure 9.6 – Momentary contact switch
 Measure the voltage across the switch and the voltage across both bulbs and record in
Table 9.5A
 Depress the switch and hold, and measure the voltage across the switch and the voltage
across both bulbs. Record measurement in Table 9.5A
Figure 9.5A
Push to make
Measured Voltage
Across Switch
Measured Voltage
Across both Bulbs
Light bulbs condition
(ON or OFF?)
Pushbutton
not depressed
Pushbutton
depressed
Table 9.5A Switch & Bulb Voltages N/O Pushbutton Switch
 Change the switch to a Normally Closed Push-button Switch.
 Measure the voltage across the switch and the voltage across both bulbs and record in
Table 9.5B.
 Depress the switch and hold, and measure the voltage across the switch and the voltage
across both bulbs. Record measurement in Table 9.5B.
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Figure 9.5B
Push to make
Measured Voltage
Across Switch
Measured Voltage
Across both Bulbs
Light bulbs condition
(ON or OFF?)
Pushbutton
not depressed
Bulbs are ON
Pushbutton
depressed
Bulbs are OFF
Table 9.5B Switch & Bulb Voltages N/C Pushbutton Switch
Part 5 - Application of ON/OFF Switches
 On your protoboard interconnect the circuit shown in Figure 9.7 by replacing the
momentary contact switch with a SPST switch. If you don’t have a SPST switch in your
component kits, you can use a jumper wire to simulate the switch.
 With the switch in the OFF position, measure the voltage across the switch and the
voltage across the bulbs. Record in Table 9.6 Turn the switch to the ON position, and
repeat the measurements.
 Disassemble the circuit.
Figure 9.7 Operation of an ON/OFF Switch (SPST)
Figure 9.4
(Push to make)
Describe the bulb
(ON or OFF?)
Measured Voltage
Across Switch
Measured Voltage
Across Bulbs
Switch in the OFF position
Switch in the ON position
Table 9.6 Switch & Bulb Voltages for on/off Switch
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Note that the Momentary contact switches are stable only in one condition, while the ON/OFF
switch (SPST) is stable in both the ON and the OFF condition.
Part 6 - Application of a Two-way Switch (SPDT)
 Obtain a red and green LED, and a SPDT switch from your component kit.
 Build the circuit in Figure 9.8 in a protoboard. Use the following LED connection as
reference
 For this experiment, the SPDT switch used to control 2 separate circuits. Operate the
switch and measure the voltage across the R1 and R2. For a SPDT switch, pick a position
to be position 1 and 2.
 Record your observation and measurement in Table 9.7
 Disassemble the circuit.
Figure 9.8 Two-way Switch (SPDT) Used to Control 2 Circuits
Switch
Position
1
Green LED
(on or off?)
Red LED
(on or off?)
VR1
VR2
2
Table 9.7 Control of 2 circuits with a SPDT switch
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Part 7 - Control of a Light from Two Different Locations
A light can be controlled from two different locations with the use of two SPDT switches as
shown in Figure 9.9
 Obtain a red, green, and yellow LED and two SPDT switches from your component kits.
 Interconnect the circuit on your protoboard as shown in Figure 9.9. Make sure you connect
the switches correctly. The pole is the center terminal on the SPDT switch while the throws
are the two outside terminals.
Figure 9.9 Controlling 3 LEDs From Two Separate Locations
 Operate the two SPDT switches as shown in Table 9.8 and record the LED operation (ON
or OFF) in Table 9.8
SPDT1
SW Position
SPDT2
SW Position
1
1
1
2
2
1
2
2
Green LED
(ON or OFF?)
Red LED
(ON or OFF?)
Yellow LED
(ON or OFF?)
Table 9.8 Control of 2 SPDT Switches
 Disassemble the circuit.
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Part 8 – Relays
 Obtain two 150 Ω resistor, one green and red LED, one N/O push-button, and one 5 V dc
relay from your component kit.
 Built the circuit shown in Figure 9.8 and apply the indicated power supply.
Relay Connection
Figure 9.10 Control of 2 Separate Circuits with a SPDT Relay
 With the push button not depressed, observe which LED is ON, and measure the current and
voltage through resistor R1 and R2. Record measurement in Table 9.10.
 Push the button of the switch, observe which LED is ON, and measure the current and
voltage through resistor R1 and R2. Record measurement in Table 9.10.
 Disassemble the circuit.
 Place your components in your component kit.
 Disconnect all lab equipment.
Pushbutton
Switch
Which LED
turn ON?
Current
through R1
Current
through R2
Voltage
across R1
Voltage
across R2
Not Depressed
Depressed
Table 9.10 Control of 2 Separate Circuits With a SPDT Relay
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT ----------------Student’s name:
Introduction to Circuit Analysis Laboratory
Lab Instructor’s Signature
116 | P a g e
Lab Experiment
10
Mesh Analysis
10.1 – Method of analysis: Mesh analysis
Method of analysis is a technique used to solve complex circuit with one or more sources that
cannot be solve using the tradition series, parallel or series-parallel method.
One of the method of analysis is mesh analysis. Mesh analysis applies Kirchhoff’s Voltage Law,
KVL, along with Ohm’s law to solve for a circuit. The goal of mesh analysis is to find a set of
simultaneous linear of equation that then can be solved to obtain the required mesh current.
There are different math method to solve for the linear equation with two or more unknown
variables such as elimination and/or substitution rule and Cramer’s rule, which allows us to
calculate variables as a quotient determinant.
10.1.1 Solving Systems of linear equation with two variables using elimination
For systems with two variables with different coefficient in both equations, one way to solve for
the system is by elimination with multiplication. The steps for this method are:
Step 1: Decide which variable to eliminate.
Step 2: Find the Least Common Multiple (LCM) of the coefficient of both equations.
Step 3: Multiply both equations by a constant so the coefficient on both equation can be
cancelled when adding them.
Step 4: Add both equation and solve the resulting equation for the other variable.
Step 5: Pick one original equation and substitute the value to find the value of the eliminated
variable.
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Example 10.1 – Solving linear equation with two variables using elimination
For the following system of equation with two variables I1 and I2, use the elimination method
and solve for i1 and i2
6I1 – 5I2 = -27
2I1 + 4I2 = -26
Following the previous steps:
Step 1: Decide which variable to eliminate.
In this case, if you want to eliminate I1, you can see that the Least Common Multiple (LCM) for
both I1 is 6. Then, if you want to eliminate I1, the first equation must be multiplied by 1 and the
second by 3. On the other hand, if you want to eliminate I2, the LCM for both I2 is 20. Then, to
eliminate I2, you multiply the first equation with 4 and the second with 5. Which variable should
be eliminated first? It really does not matter, but I personally recommend to eliminate the
variable that will result with a lower coefficient. In this case, I will eliminate I1 first because the
LCM for both equation is 6.
Step 2: Find the Least Common Multiple (LCM) of the coefficient of both equations.
The LCM of the coefficient of I1 for both equations is 6.
Step 3: Multiply both equations by a constant so the coefficient on both equation can be
cancelled when adding them.
For our example, one coefficient for I1 must be -6 and the other +6. For it, you will multiply the
first equation with -1 to make the coefficient to be -6
- 1× (6I1 – 5I2 = -27) 
-6I1 + 5I2 = +27

6I1 + 12I2 = -78
3× (2I1 + 4I2 = -26)
Step 4: Add both equation and solve the resulting equation for the other variable.
-6I1 + 5I2 = +27
6I1 + 12I2 = -78
17I2 = -51
𝐈𝟐 =
−51
= −3
17
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Step 5: Pick one original equation and substitute the value to find the value of the eliminated
variable
6I1 – 5I2 = -27  since I2 = -3
6I1 – 5(-3) = -27
6I1 -15 = -27
6I1 = -27 + 15
6I1 = -12
𝐈𝟏 = −
12
= −2
6
10.2. Mesh analysis with two voltage sources
Mesh analysis applies Kirchhoff’s Voltage Law, KVL, along with Ohm’s law to find the
simultaneous linear of equation. There are different ways to find the linear equations, this lab
experiment will show you how to find those equation by general analysis using independent
loops. The steps to find the linear equations are:
Step 1: Identify the number of independent loops.
Step 2: Set the direction of current flow for each independent loop and label the loop/mesh
current as I1, I2… IN, where N is the number of independent loops.
Step 3: Set the polarity of the voltage drop for the unknown voltage according to the direction of
current flow set in Step 2.
Step 4: Apply KVL to each independent closed loop and write the linear equation.
Step 5: Using the equations from Step 4, apply Ohm’s law to represent the unknown voltage
(voltage drop at each resistor)
Step 6: Use elimination and solve for each mesh current I1, I2…, IN
Step 7: Solve for the circuit using the mesh current found in Step 6.
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Example 10.2 – Mesh analysis with two voltage sources
For the following circuit 10.1, use mesh analysis to find the voltage and current through each
resistor.
Circuit 10.1 Resistive circuit with two voltage sources
Using the steps mentioned before:
Step 1: Identify the number of independent loops.
For Circuit 10.1, there are two independent loops. This means that the resulting linear equation
will have two unknown.
Step 2: Set the direction of current flow for each independent loop and label the loop/mesh
current as I1, I2,…, IN.
Setting the current of flow (clockwise
or counterclockwise
) is ready up to the student, at
the end, when you solve for the linear equations, the magnitude of the mesh current will be the
same. But you need to keep in mind that if the resulting mesh current is positive, it means that
the mesh current was set to the conventional flow of current. On the other hand, if the mesh
current is negative, it means that the mesh current was set to the electrons flow of current.
Usually, I use the polarity of the voltage sources to set the direction of the current flow. For
example, for Circuit 10.1, I will set the mesh current for Vy clockwise because the current will
flow from negative to positive. Likewise, the mesh current for Vx counterclockwise.
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Step 3: Set the polarity of the voltage drop for the unknown voltage according to the direction of
current flow set in Step 2.
Step 4: Apply KVL to each independent closed loop and write the linear equation.
KVL for mesh I1
KVL for mesh I2
Vy – VR1 – VR2 = 0V
Vx – VR3 – VR2 = 0V
Vy = VR1 + VR2
Vx = VR3 + VR2
Step 5: From the equation in Step 4, use Ohm’s law to represent the unknown voltage (voltage
drop at each resistor)
KVL for mesh I1
Vy = VR1 + VR2
The Ohm’s law equation for VR1 is:
VR1 = I1×R1
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To find the Ohm’s law equation for VR2,
Since there are two mesh currents going through R2, which are I1 and I2, and both
currents flow down through R2, then the total current through R2 is the sum of I1
and I2. On the other hand, if the mesh currents through R1 flow in different
direction, then the total current through R2 shall be their difference.
VR2 = (I1 + I2)×R2 = I1×R2 + I2×R2
Another observation on this step is the order of I1 and I2. I1 goes before I2
because we are writing the KVL equation for mesh I1. This procedure is
important if we are subtracting the mesh currents.
Replacing the Ohm’s law equation into the KVL equation:
Vy = I1×R1 + I1×R2 + I2×R2
Vy = I1×R1 + I1×R2 + I2×R2
Vy = I1(R1 + R2) + I2×R2  Linear equation for mesh I1
KVL for mesh I2
Vx = VR3 + VR2
The Ohm’s law equation for VR3 is:
VR3 = I2×R3
To find the Ohm’s law equation for VR2,
VR2 = (I2 + I1)×R2 = I2×R2 + I1×R2
I2 goes before i1 because we are writing the KVL equation for mesh I2.
Replacing the Ohm’s law equation into the KVL equation:
Vx = I2×R3 + I2×R2 + I1×R2
VX = I1×R2 + I2(R3 + R2)  Linear equation for mesh I2
Step 6: Use elimination and solve for each mesh current I1 and I2.
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Step 7: Solve for the circuit using the mesh current found in Step 6.
Once you have the mesh current, according to Circuit 10.1
IR1 = I1
VR1 = IR1×R1
IR2 = I1 + I2
VR2 = IR2×R2
IR3 = I2
VR3 = IR3×R3
Lab Experiment Procedure
Part 1 – Resistive Circuit with Two Voltage Sources
 Obtain 1.5 kΩ, 2.7 kΩ , and 3.9 kΩ resistors from your component kit, measure their
resistance, and record the measured values in Table 10.1
Percent of difference
Measured Resistance
𝑴𝒆𝒂𝒔𝒖𝒓𝒆𝒅 − 𝑮𝒊𝒗𝒆𝒏
(
)
𝑮𝒊𝒗𝒆𝒏
∗ 𝟏𝟎𝟎%
R1 = 1.5 kΩ
R2 = 2.7 kΩ
R3 = 3.9 kΩ
Table 10.1 – Resistance measurement
Circuit 10.1 Resistive Circuit with Two Voltage Sources
 Build Circuit 10.1 in a protoboard. For this step, it is very important to remember which
power nodes are used for Vs1 and Vs2. For example, you can identify the top + and –
node as for Vs1 and the bottom + and – node as for Vs2.
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 Since Circuit 10.1 is using two power supplies with different voltages, before connecting
the power supplies to the circuit, the two power supplies have to be connected in a way
that they will have one common ground.
 Set one power supply to 9 V and the other to 6 V and connect them to the circuit in the
protoboard.
 Prepare the multimeter and the circuit to measure current.
 Measure the current through R1, R2, and R3 and record the values in Table 10.2
Measured value
Calculated value
% of Difference
IR1
IR2
IR3
Table 10.2 Current Measurement through each resistor of Circuit 10.1
 Prepare the multimeter and the circuit to measure voltage.
 Measure the voltage through R1, R2, and R3 and record the values in Table 10.3
Measured value
Calculated value
% of Difference
VR1
VR2
VR3
Table 10.3 Voltage Measurement through each resistor of Circuit 10.1
 Turn off the power supplies.
 Use mesh analysis to calculate the current and voltage through each resistor. Record
the calculation in Table 10.2 and 10.3 respectively.
Show mesh analysis calculations here.
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 Find the percentage of differences between the measured and calculated value and
record the answer in Table 10.2 and 10.3 respectively.
% 𝑜𝑓 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = (
𝑀𝑒𝑎𝑠𝑢𝑟𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 − 𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
) × 100%
𝐶𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
 Ask lab instructor to check the calculations and tables.
 Once the tables are checked, disassembled the circuit, and organize your components
in your components kit.
Part 2 – Exercises: Analyzing circuits using mesh analysis
For this part of the lab, you will practice how to analyze different type of circuit using mesh
analysis.
Exercise 10.1 Given Circuit 10.2, use mesh analysis to:
Circuit 10.2 Resistive Circuit with Two Voltage Sources
a. Find the linear equation (from Kirchhoff’s Voltage Law and Ohm’s law) for mesh current
I1 and I2
Equation Mesh I1:
, Equation Mesh I2:
Show your calculations here.
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b. Using the mesh equations, apply elimination method or Cramer’s law to find the mesh
current I1 and I2
I1 =
, I2 =
Show your calculations here.
c. Using the mesh current i1 and i2, find the current through each resistor:
IR1 =
IR2 =
IR3 =
Show your calculations here.
d. Find the voltage across each resistor using Ohm’s law:
VR1 =
VR2 =
VR3 =
Show your calculations here.
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Exercise 10.2 Given Circuit 10.4, use mesh analysis to:
Circuit 10.4 Resistive Circuit with Three Independent Sources
Find the linear equation (from Kirchhoff’s Voltage Law and Ohm’s law) for mesh current I1, I2,
and I3.
Equation Mesh I1
Equation Mesh I2
Equation Mesh I3
Show your calculations here.
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Questions
1. For Circuit 10.1, if a student by mistake reversed/flipped the polarity of Vs2 when building
the circuit in a protoboard, how this mistake would affect his measurements? Explain
and/or justify your answer.
2. Analyzing a circuit using mesh analysis, a student is measuring the current through the
resistors R1, R2, and R3. The student measured that the current through R1 is the mesh
current I1 and the current through R2 is the mesh current I2. What experimental procedure
should a student apply to find if the mesh currents I1 and I2 are flowing clockwise or
counter-clockwise? Explain and/or justify your answer.
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT ----------------Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab Instructor’s Signature
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Lab Experiment
11
Superposition Theorem
11.1 – Superposition-Two Energy Sources
In a scenery of complex circuits or circuits that have more than one sources (voltage and/or current)
as shown in Circuit 11.1, regular method of series and parallel analysis is not enough to predict
the voltage and current distribution within the circuit. One way to predict the currents and voltages
for each resistor is to use superposition theorem. The method of superposition consists of finding
the voltage and current contribution to each element by each source and then combining the effects.
Circuit 11.1 Resistive circuit with two voltage sources (Original Circuit)
To find the contribution of one source, all of the other sources have to be removed from the circuit.
Current sources are replaced by open circuits while voltage sources are replaced with short circuits.
Once with one source active, find the voltage and current distribution through each of the resistors.
At the end of superposition, remember that currents in the same direction add, keeping the original
direction. Currents in opposite directions subtract, keeping the direction of the larger current.
Voltages with the same polarity add, keeping the original polarity. Voltages with opposite
polarities subtract, keeping the polarity of the larger voltage.
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Lab Experiment Procedure
Part 1: Original Circuit Measurement
1. Obtain 100 Ω, 220 Ω, and 330 Ω from your components’ kit
2. Measure each resistor’s value and record the measured resistance in Table 11.1
Resistor
Measured value
R1 = 100 Ω
10
R2 = 330 Ω
330
R3 = 220 Ω
220
Table 11.1 Resistance Measurement
3. Build Circuit 11.1 in a protoboard.
4. Prepare the circuit and the multimeter to measure current.
5. Measure the current through each resistor, IR1, IR2, and IR3. Record measurement in Table
11.2, don’t forget to include the direction of current flow for each resistor.
Current
Measured value
(Include direction of current flow)
IR1(100 Ω)
IR2(330 Ω)
IR3(220 Ω)
Table 11.2 Current Measurement of Original Circuit
6. Prepare the circuit and the multimeter to measure voltage.
7. Measure the voltage across each resistor, VR1, VR2, and VR3. Record measurement in
Table 11.3, don’t forget to include the voltage polarity for each voltage drop.
Voltage
Measured value
(Include voltage polarity)
VR1(100 Ω)
VR2(330 Ω)
VR3(220 Ω)
Table 11.3 Voltage Measurement of Original Circuit
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Now, prepare to analyze Circuit 11.1 using superposition theorem. For this, each voltage source is
active one at the time, and measurement of current and voltage through each resistor is done for
each active source independently.
Part 2: Current and Voltage Measurement with “ONLY” V1 Voltage Source Active
8. To deactivate V2 voltage source, change the connection of R3 from the positive of the
voltage source V2 to Ground (“-” of protoboard). This will ground the voltage source V2
and only V1 will be active. Check Circuit 11.2 for reference.
Circuit 11.2 Original Circuit with VR1 active
9. Prepare the circuit and the multimeter to measure current.
10. Measure the current through each resistor, IR1, IR2, and IR3. Record measurement in Table
11.4, don’t forget to include the direction of current flow for each resistor.
Current
Measured value
(Include direction of current flow)
IR1(100 Ω)
IR2(330 Ω)
IR3(220 Ω)
Table 11.4 Current Measurement of Original Circuit with ONLY V1 Voltage
Source Active
11. Prepare the circuit and the multimeter to measure voltage.
12. Measure the voltage across each resistor, VR1, VR2, and VR3. Record measurement in
Table 11.5, don’t forget to include the voltage polarity for each voltage drop. Hint: The
polarity can be found by knowing the direction of the current flow through each resistor
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Measured value
Voltage
(Include unit and voltage polarity)
VR1(100 Ω)
VR2(330 Ω)
VR3(220 Ω)
Table 11.5 Voltage Measurement of Original Circuit with ONLY V1 Voltage
Source Active
Part 3: Current and Voltage Measurement with “ONLY” V2 Voltage Source Active
13. Reconnect R3 from Ground to the positive polarity of V2. By doing this, you should have
the original Circuit 1.
14. Change the connection of R1 from the positive of the voltage source V1 to Ground (“-”
of protoboard). This procedure will ground the first voltage source, V1, and only V2 will
be active. Check Circuit 3 for reference.
Circuit 11.3 Circuit 11.1 with VR2 active
15. Prepare the circuit and the multimeter to measure current.
16. Measure the current through each resistor, IR1, IR2, and IR3. Record measurement in Table
11.6, don’t forget to include the direction of current flow for each resistor.
Current
Measured value
(Include unit and direction of current flow)
IR1(100 Ω)
IR2(330 Ω)
IR3(220 Ω)
Table 11.6 Current Measurement of Original Circuit with ONLY V2 Voltage
Source Active
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17. Prepare the circuit and the multimeter to measure voltage.
18. Measure the voltage across each resistor, VR1, VR2, and VR3. Record measurement in
Table 11.7, don’t forget to include the voltage polarity for each voltage drop.
Measured value
Voltage
(Include unit and voltage polarity)
VR1(100 Ω)
VR2(330 Ω)
VR3(220 Ω)
Table 11.7 Voltage Measurement of Original Circuit with ONLY V2 Voltage
Source Active
19. Disassemble the circuit and place all components back to the lab kit. Also, turn off all
equipment and organize all measurement leads. Now, you are proceed to analyze the
measured data.
Part 4: Superposition Theorem Analysis
20. Record the measured current through each resistor from Table 11.2 to Table 11.8
21. Record the measured current through each resistor from Table 11.4 and Table 11.6 to Table
11.8.
22. Find the total current through each resistor using measured currents from Table 11.4 and
11.6. Remember, currents flowing in the same direction add and keep the direction of
current flow; currents flowing in opposite direction subtract and keep the direction of the
larger current. Record result in Table 11.8.
23. Find the percent of difference between the current from the original circuit and the total
current from the superposition theorem (Step 22). Record the percent of different in Table
11.8.
% 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 = (
Current
Measured current
from Original
Circuit (Table 10.2)
IOriginalCircuit
𝑰𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍𝑪𝒊𝒓𝒄𝒖𝒊𝒕 − 𝑰𝒔𝒖𝒑𝒆𝒓𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
) × 𝟏𝟎𝟎%
𝑰𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍𝑪𝒊𝒓𝒄𝒖𝒊𝒕
Superposition Theorem Analysis
Measured
current from
Table 10.4
Measured
current from
Table 10.6
Total Current
through each
resistor (step 22)
% difference
Isuperposition
IR1(100 Ω)
IR2(330 Ω)
IR3(220 Ω)
Table 11.8 Superposition Theorem Current Measurement and Analysis
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24. Record the measured voltage across each resistor from Table 11.3 to Table 11.9
25. Record the measured voltage across each resistor from Table 11.5 and Table 11.7 to Table
11.9.
26. Find the total voltage across each resistor by using measured voltage from Table 11.5 and
11.7. Remember, voltages with the same polarity add and keep the original polarity;
voltages with opposite polarity subtract and keep the polarity of the larger voltage. Record
result in Table 11.9.
27. Find the percent for difference between the voltage from the original circuit and the total
voltage from the superposition theorem (step 26). Record the percent of different in Table
11.9.
𝑽𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍𝑪𝒊𝒓𝒄𝒖𝒊𝒕 − 𝑽𝒔𝒖𝒑𝒆𝒓𝒑𝒐𝒔𝒊𝒕𝒊𝒐𝒏
% 𝒅𝒊𝒇𝒇𝒆𝒓𝒆𝒏𝒄𝒆 = (
) × 𝟏𝟎𝟎%
𝑽𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍𝑪𝒊𝒓𝒄𝒖𝒊𝒕
Voltage
Superposition Theorem Analysis
Measured voltage
from Original
Circuit (Table 10.3)
VOriginalCircuit
Measured
voltage from
Measured
voltage from
Table 10.5
Table 10.7
Total Voltage
through each
resistor (step 26)
% difference
Vsuperposition
VR1(100 Ω)
VR2(330 Ω)
VR3(220 Ω)
Table 11.9 Superposition Theorem Voltage Measurement and Analysis
28. Using the superposition current from Table 11.8 and superposition voltage from Table
11.9, calculate the power dissipation in each resistor. Record calculation in Table 11.10
Table 11.10 – Superposition Theorem Power Analysis
Power
Dissipation
Using current from
Table 11.4 and voltage
from Table 11.5
PR1
PR2
PR3
Using current from Table 11.6
and voltage from Table 11.7
PR1
PR2
Using Itotal from Table 11.8 and
Vtotal from Table 11.9
PR3
PR1
PR2
PR3
Table 11.10 Superposition Theorem Power Analysis
Notice that the total power to each resistor is neither the sum nor the difference of the power
supplied by each source when considered separately. In other words, power does not
superimpose.
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Question
1. According to your measured voltage in Table 11.8 and the current in Table 11.9, does the
measured data prove the superposition theorem? Explain your answer.
2. According to the calculated power in Table 11.10, why the power calculation using
superposition analysis does not superimpose? Explain your answer.
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT -----------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab Instructor’s Signature
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Lab Experiment
12
Thévenin’s Theorem and Maximum
Power Transfer
12.1 – Thevenin’s Theorems
Thevenin’s Theorem is applied to analyze a load does not care where it gets its energy from. As
a matter of fact, as long as a load gets the same required energy, it “does not know” what circuit it
is connected to. To this, Thevenin said that instead of using the original circuit to supply the
required energy to the load, he will substitute the original circuit with a battery in series with a
resistor, each of the proper value of course, and this combination will supply the load with the
same required energy as the original circuit.
Figure 12.1 Thevenin’s Equivalent Circuit
12.2 – Maximum Power Transfer
One important fact of circuit analysis is to find the conditions that should be imposed on the
source and load resistance to ensure that it will deliver the maximum power to the load.
The maximum power transfer theorem states that a load will receive maximum power from a
network when its resistance is exactly equal to the Thevenin resistance of the network applied to
the load.
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𝑹𝑳 = 𝑹𝑻𝑯
Lab Experiment Procedure
Part 1: Original Circuit Measurements
Circuit 12.1 shows a circuit with a 12V battery connected to a series parallel circuit consisting of
R1, R2 and R3. This circuit feeds energy to a load resistor RL (1 kΩ potentiometer). The
expected values of load current, load voltage and power to the load are also shown. You will be
asked to confirm these values in your write-up.
Circuit 12.1 Original Circuit Feeding Load Resistor
 Obtain 220 Ω, 330 Ω, and 100Ω resistor from your components kit. Measure their resistance
individually, and record the measured values in Table 12.1.
 Obtain a 1 kΩ potentiometer and measure the highest resistance of the 1 kΩ potentiometer.
Record measurement in Table 12.1
 Set the potentiometer to 500 Ω and record the measurement in Table 12.1
 Build Circuit 12.1 in a protoboard.
 Prepare the DMM and circuit to measure current
 Measure the current through RLoad. Record measurement in Table 12.2
 Prepare the DMM and circuit to measure voltage
 Measure the voltage across RLoad. Record measurement in Table 12.2
 Multiply the voltage and the current through RLoad to obtain the power. Record the power in
Table 12.2
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Voltage across the
load resistance, VL
Current through the
load resistance, IL
Power dissipation at the load
resistance, PL
Measured
Value
Table 12.2 Original Circuit Measurements
Part 2 - Thevenin’s Equivalent Circuit
Circuit with RLoad Removed - Thevenin’s Voltage
Circuit 12.2 shows the circuit with the load resistor removed. The open circuit voltage from
Node A to ground is the Thevenin Voltage [VTH].
 Remove the load resistor, 500 Ω (potentiomenter), from the circuit and place jumper
wires where the connections of RLoad were. Check Circuit 12.2 for reference
 Prepare the DMM to measure voltage (VOM)
 Measure the voltage across the open circuit where RLoad was connected, between Node A
and ground. This voltage is known as the Thevenin’s voltage.
 Record this measured value in Table 12.3
Given Resistance
Measured Resistance
(Include unit)
Percent of difference
 Measured  Given 

 *100 %
Given


R1 = 220 Ω
R2 = 330 Ω
R3 = 100 Ω
RLoad = 1 kΩ pot
Table 12.1 – Resistance measurement
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Circuit 12.2 Thevenin Voltage Measurement
Measuring the Thevenin’s resistance
 Move one terminal of R1, the one that is connected to + power, to ground. Check Circuit
12.3 for reference.
 Prepare the DMM to measure resistance
 Measure the resistance in between the open circuit where RLoad was connected, between
Node A and ground. This resistance is known as the Thevenin’s resistance.
 Record this measured value in Table 12.3.
 Disassemble the circuit, turn off of lab equipment, organize the equipment leads, and
organize the lab components.
 Proceed with calculations.
Circuit 12.3 Thevenin’s resistance measurement
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Thevenin’s Equivalent Circuit Measurements
Voltage across the open
circuit Thevenin’s voltage,
VTH
Resistance between the open
circuit
Thevenin’s resistance, RTH
Measurements
(Include all unit)
Table 12.3 Thevenin Equivalent Circuit Measurements
Calculating the voltage, current, and power at the RLoad using the Thevenin’s Equivalent
circuit
Fill up the Circuit 12.4, which is the Thevenin’s equivalent circuit, with measured values from
Table 12.4.
Circuit 12.4 – Thevenin’s equivalent Circuit
 Calculate the voltage, current, and power through RL = 500Ω
 Record calculation in table 12.4
Load Resistance calculation using the Thevenin’s Equivalent Circuit
Voltage across the
load resistance, VL
Current through the
load resistance, IL
Power dissipation
at the load
resistance, PL
Calculations
(Include all unit)
Table 12.4 – Load analysis from the Thevenin’s Equivalent Circuit
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 Use the information in Table 12.2 and Table 12.4, and calculate the percent of difference
between the original circuit and the Thevenin’s equivalent circuit in Table 12.5
Load Resistor Analysis
Voltage across
the load
resistance, VL
Current through
the load
resistance, IL
Power dissipation
at the load
resistance, PL
Original Circuit
Table 12.2
Thevenin’s Equivalent
Table 12.4
𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍 − 𝑻𝒉𝒆𝒗𝒆𝒏𝒊𝒏′𝒔
%=(
)
𝑶𝒓𝒊𝒈𝒊𝒏𝒂𝒍
× 𝟏𝟎𝟎%
Table 12.5 – Load Resistance Analysis
Part 3 – Maximum Power Transfer Analysis
 Build the Thevenin’s equivalent circuit with its respective RTH and VTH values as shown
in Circuit 12.4. Note: if you don’t have the exact RTH resistor in your components’ kit,
you can use another potentiometer and set it to the resistance of RTH.
 Set the RLoad potentiometer to 0 Ω
 Prepare the multimeter and circuit to measure voltage.
 Measure the voltage across RLoad and record the measurement in Table 12.6
 Increment the resistance of RLoad according to Table 12.6, measure the voltage across
RLoad, and record the measurement in Table 12.6.
 Once all data are recorded, disassemble the circuit, turn off of lab equipment, organize
the equipment leads, and organize the lab components.
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Power Analysis Through RLoad
RLoad
Ω
Measured VLoad
(Include unit)
(𝑽𝑳𝒐𝒂𝒅 )𝟐
𝑳𝒐𝒂𝒅 𝑷𝒐𝒘𝒆𝒓, 𝑷𝑳𝒐𝒂𝒅 =
𝑹𝑳𝒐𝒂𝒅
(Include unit)
0Ω
25 Ω
50 Ω
75 Ω
100 Ω
125 Ω
150 Ω
175 Ω
200 Ω
225 Ω
250 Ω
275 Ω
300 Ω
325 Ω
350 Ω
375 Ω
400 Ω
425 Ω
450 Ω
500 Ω
550 Ω
600 Ω
700 Ω
800 Ω
900 Ω
1000 Ω
Table 12.6 – Power dissipation through RLoad
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-
Using the graph paper below, plot PLoad versus RLoad
Graph 12.1 Maximum Power Transfer Plot - PLoad vs RLoad
-
From Graph 12.1, estimate or measure the Maximum Power Transfer through load resistor,
RLoad and record the measurement in Table 12.7
Calculate the Maximum Power Transfer through the load resistor using Formula 12.1.
Record calculation in Table 12.7
Maximum Power Transfer Analysis
Measured Maximum
Power from Graph 12.1
(Include Unit)
Calculated Maximum
Power using Formula 12.1
(Include Unit)
% of difference
Table 12.7 – Maximum Power Transfer Analysis for Circuit 12.1
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Questions
4. Does Thevenin’s Equivalent supply the load with the same power as the original
circuit? Explain your answer.
5. From the Thevenin’s Equivalent circuit, Circuit12.4, would the polarity of VTH affect
the load voltage and current measurement? Explain your answer.
6. From Table 12.6, explain the power behavior with respect to the RLoad .
7. Can you estimate the maximum power through the load by using the data from
Table 12.6? How? Explain your answer.
8. Thevenin’s equivalent circuit, Circuit 12.4, was used to obtain the power behavior
for Table 12.6. If the original circuit, Circuit 12.1, was used instead of Circuit 12.4,
would the power behavior be the same or different? Explain your answer.
------------------ LAB EXPERIMENTS ENDS HERE, PROCEED WITH LAB REPORT -----------------
Student’s Name:
Introduction to Circuit Analysis Laboratory
Lab Instructor’s Signature
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