1 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
BASIC
ELECTRICAL ENGINEERING
Author
Joshua P. Tejada, REE, RME Michael L. Pascua, REE, RME Marvin P. Amoin, ECE, Ph.D
Marlon A. Bautista, REE, RME, MAT John Neil B. Herrera, REE Rene A. Ariston, REE, RME Roy C. Andrada, REE, MIT
2 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
To the College of Engineering student: Welcome to EE 8 (Basic Electrical Engineering). This course guide will be the alternative assessment for the knowledge and skills you attained from the electrical engineering lessons and practical guides. This course guide covers the requirements, schedule of assignments, SAQs and Activities throughout the semester.
I am Engr. Joshua P. Tejada your course coordinator for EE 8. I am currently a Part Time Instructor in the College of Engineering of this university, a freelance Electrical System Designer and Consultant for different companies and was a solo book author of Electrical Shop Theory and Practice.
The other members of the course are: Engr. Michael L. Pascua is a professor in the college of engineering and an
engineer in University Physical Facilities Development Unit of this university. He was a Registered Electrical Engineer and a Registered Master Electrician at the same time and authored books Electrical Circuits I along with Engr. Bautista and Basic Electrical Engineering along with Engr. Tejada.
Dr. Marvin P. Amoin is the current campus director of the University of Rizal System Morong Campus. He was a graduate of BS in Electronics and Communications Engineering in Rizal Technological University and graduates his Masters and Doctoral degree in University of Rizal System. He authored the book entitled Advance Engineering Mathematics and Engineering Economy.
Engr. Marlon A. Bautista is the former dean of College of Engineering and a former Program Head for Electrical Engineering Department for 15 years. He authored many books such as Mathematics in the Modern World, Integral Calculus, Discrete Mathematics, and many more.
Engr. John Neil Herrera is the current president of the college of engineering faculty. At present, he takes his graduate studies in EARIST. He was also a former advisor for the student organization of electrical engineering,
Engr. Roy C. Andrada is a Master in Information Technology and a Registered Electrical Engineer. He is also the research coordinator for electrical engineering program. Engr. Andrada was a former Program head of the Electrical Engineering Department.
Engr. Rene A. Ariston is a Part Time Instructor which link the industry knowledge with academe. Currently, he was working in Solid Cement Corporation- Cemex Philippines which he works as Cement Mill Operations at CCR Shift Supervisor. He also was a Professional Electrical Engineer Aspirant 2020 of the IIEE Metro East Chapter.
3 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Course Description
EE 8 (Basic Electrical Engineering) deals with the general principles and methods in electrical circuits, Ohmβs law, as well as the use of instruments for electrical applications such as multimeter/tester, and resistor laboratory activities.
Course Objectives General Objectives: Apply the principles and methods of Electrical Engineering
Circuits in different situations concerning electricity.
Specific Objectives:
At the end of the course, the student should be able to:
1. Analyze the characteristics, components, quantities regarding electrical circuits in direct current application.
2. To understand the flow of electricity in different methodology such as: 2.1 kirchhoffβs Law 2.2 Maxwellβs Mesh 2.3 Superposition Theorem 2.4 Millmanβs Theorem 2.5 Nodal Node Voltage Analysis
3. To differentiate the procedures and considerations in Alternating Current to the Direct Current.
4. Be able to apply the basics of electrical engineering to the different fields of engineering.
4 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Course Structure
The course EE8 consists of three (3) Instructural Units divided into fifteen (15) Modules namely:
Unit 1 β Basics of Electrical Engineering Circuits
Module Writers
1. Introduction - Michael L. Pascua, REE, RME 2. The Power, Energy and Ohmβs Law - Roy C. Andrada, REE, MIT 3. The Multimeter - Joshua P. Tejada, REE, RME 4. The Resistor - John Neil Herrera, REE 5. Batteries - Marlon A. Bautista, REE, RME, MAT
Unit 2 β Network Theorems Laws and Methods
Module Writers
1. Kirchhoffβs Law - John Neil Herrera, REE 2. Maxwell Mesh - Rene A. Ariston, REE, RME 3. Superposition Theorem - Michael L. Pascua, REE, RME 4. Millmanβs Theorem - Joshua P. Tejada, REE, RME 5. Nodal Node Voltage Analysis - Marvin P. Amoin, ECE, Ph.D
Unit 3 β AC Circuits
Module Writers
1. AC Circuit Introduction - Marvin P. Amoin, ECE, Ph.D 2. Impedance and Admittance - Michael L. Pascua, REE, RME 3. Network Theorems in AC Circuits - Marlon A. Bautista, REE, RME, MAT 4. Resonance - Joshua P. Tejada, REE, RME 5. Power factor Correction - Roy C. Andrada, REE, MIT
5 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Course Requirements
The following are the major course requirements:
1. The circuit familiarization activities
Each student is required to conduct activities regarding electrical circuits. This activity is equivalent to one laboratory activity. This activity may be one of the following.
1.1 Create your own electrical circuit design 1.2 Breadboard activities 1.3 Simulation of circuits using simulation applications
2. Examination, quizzes and self-assessment questions. 3. Other requirements enumerated by the instructor.
GRADING SYSTEM Basic Electrical Engineering is a three (3) unit subject. Final grade will be based
on your performance in the written assignments and reports for the lecture (40% or 1 units) and laboratory activities (60% or 2 units).
Lecture (40%)
β’ Examination 40% β’ Quizzes 30% β’ Activities 20% β’ Class Participation / Recitation 10%
Laboratory (60%)
β’ Examination 40% β’ Activities 40% β’ Class Participation / Recitation 20%
6 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 RUBRIC FOR ASSESSMENT
CRITERIA EXEMPLARY
4
SATISFACTORY
3
DEVELOPING
2
BEGINNING
1
RATING
Comprehensive Ability
The score of the SAQ and Activities is around 90% to 100% Correct.
The score of the SAQ and Activities is around 70% to 89% Correct.
The score of the SAQ and Activities is around 40% to 69% Correct.
The score of the SAQ and Activities is around 0% to 39% Correct.
Workmanship The neatness of the solution for the SAQ and Activities is very good quality.
The neatness of the solution for the SAQ and Activities is good quality.
The neatness of the solution for the SAQ and Activities is standard quality
The neatness of the solution for the SAQ and Activities needed improvement
Accuracy The submitted work manifests qualities which go beyond the requirements
The submitted work manifest the required qualities
The submitted work partially manifest the required qualities. Certain aspects are either incomplete or incorrect.
7 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 ACADEMIC INTEGRITY
Due to COVID β 19 pandemic, alternative learning sessions must be produced. Even the course is delivered online, as a student you are expected to observe intellectual honesty at all times. This means doing your assignments and term papers yourself, acknowledging indebtedness to sources of original ideas and quoted materials which you used, and taking examinations yourself.
SCHEDULE
The schedule making depends on the schedule given by the memorandum from the university. The time allotment from the syllabus can be also a factor but the huge factor for the scheduling is on the instructor. The instructor can give his/her schedule of dates for submission of different requirements.
8 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Unit 1 Basics of Electrical
Engineering Circuits
9 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Module 1: Introduction Table of Contents Introduction
Lesson 1: Electron Theory
Lesson 2: Circuit Elements
Lesson 3: Circuit Parameters
Lesson 4: The Resistance
10 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 1: Electron Theory
Matter is whatever has mass and volume that occupies space. The fundamental unit of matter is the atom. The atom is basically consisting of the Nucleus and orbits. The orbit contains electron, while the Nucleus contains proton and neutron. Proton and Neutron are often called nucleons because they are found inside the nucleus. The number of protons usually gives the atomic number of an element, while the sum of protons and neutrons gives the atomic mass of an element.
π΅π΅π΅π΅π΅π΅π΅π΅π΅π΅π΅π΅ ππππ π΅π΅πππ΅π΅πππππ΅π΅ππππππ ππππ ππππππ πΆπΆπ΅π΅π΅π΅ππππ = ππππππ
Where: n = the number of the desired orbit of the material
Example 1. Find the maximum number of electron in the 4th orbit
Solution. N = 2n2 = 2 x 42 = 32 electrons.
Example 2. If the maximum number of electron in the orbit is 8, what orbit contains those electron?
Solution. n = sqrt(N/2) = sqrt(8/2) = 2. It means it is in the 2nd Orbit
11 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions
Answer the following neatly
Find the maximum number of electron in the 3rd orbit
If the maximum number of electron in the orbit is 2, what orbit contains those electron?
Activity 1
On a clean sheet of paper, answer the following neatly. Send a photograph of your work to your designated GDrive
1. Find the maximum number of electron in the 5th orbit 2. Find the maximum number of electron in the 4th orbit 3. If the maximum number of electron in the orbit is 72, what orbit contains those
electron?
12 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 1
Find the maximum number of electron in the 3rd orbit
18 electrons
If the maximum number of electron in the orbit is 2, what orbit contains those electron?
1st Orbit
13 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 2: Circuit Elements
Figures are from
book β Basic Electrical Engineering by Joshua Tejada and Michael Pascua β
Source β Provides the necessary voltage to force the current to flow throughout the circuit.
Conductors β The path where the current flows though out the circuit. It may be copper, aluminium, silver or any low resistance materials.
Protection β It is used to protect the load and the circuit from the sudden change in current.
Load β The purpose of electrical energy is to be used in many ways, to convert into other kinds of energy.
Control Device β The control of the circuit when and when not to let current pass though the circuit.
14 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 2
Identify the following symbols
Activity 2
On a clean sheet of paper, draw the symbols with their identification for familiarization of electrical symbols. Send your output to your designated GDrive
15 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Answers to Self-Assessment Questions 2
Source: Basic Electrical Engineering by J. Tejada and M. Pascua
16 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 3: Circuit Parameters Electric Charge
The electric charge represents the volume of electricity. The electric charge is denoted as βQβ or βqβ. the lowercased letter denotes time varying quantities while uppercased letters are not. The unit for Electrical Charge is Coulomb (C).
ππ πͺπͺπππ΅π΅πππππ΅π΅π΅π΅ = ππ.ππππ ππ ππππππππ Electrons
Example. If the total number of charge pass through a conductor is 13Β΅ Coulomb. How many electrons it contains?
Solution. ππππππππππππ ππππ πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ = ππ π₯π₯ 6.28π₯π₯1018 πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ ππππππ πΆπΆπππππΈπΈππππππ
ππππππππππππ ππππ πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ = 13π₯π₯10β6 πΆπΆπππππΈπΈππππππ π₯π₯ 6.28π₯π₯1018 πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ ππππππ πΆπΆπππππΈπΈππππππ
ππππππππππππ ππππ πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ = 8.164π₯π₯1013 πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ
Electric Current
The electric current is the rate of flow of current at a point per unit of time and is denoted as βIβ or βIβ because it is also called Current Intensity. The unit of electrical current is Ampere (A). To produce a one (1) ampere of current, it requires a one coulomb or 6.28 x 1018 Electrons to pass a point in a second. The steady state of current is given by the formula:
π°π° = πΈπΈ/ππ
Where: I β Electric Current
Q β Electric Charge
t - Time (seconds)
Example. When checking through a circuit, it observes that a current of 200 mA is passing through a circuit in 1.2 seconds. Find the total charge in the circuit.
Solution. ππ = πΌπΌπΈπΈ = 0.2π΄π΄ π₯π₯ 1.2πΈπΈ = ππ.πππππͺπͺ
The Voltage
are the force that pushes the electrons to move. It may be denoted as βVβ or βEβ. The unit for voltage is volts (V). To produce a voltage of 1 volt, you need an electrical energy of 1 Joule divided by 1 Coulomb of charge. Mathematically, it is expressed as:
π½π½ = πΎπΎ/πΈπΈ
17 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Where: V β Voltage
W = Work / Energy
Q = Electric Charge
Example. In a given circuit, the available energy is 2 joules where the system voltage is 1.2v. How many available electrons are in the circuit?
Solution. ππ = ππ/ππ = 2π½π½ / 1.2ππ = 1.667πΆπΆ
ππππππππππππ ππππ πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ = ππ π₯π₯ 6.28π₯π₯1018 πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ ππππππ πΆπΆπππππΈπΈππππππ
ππππππππππππ ππππ πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ = 1.667 πΆπΆπππππΈπΈππππππ π₯π₯ 6.28π₯π₯1018 πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ ππππππ πΆπΆπππππΈπΈππππππ
ππππππππππππ ππππ πΈπΈπΈπΈπππΈπΈπΈπΈπππππΈπΈπΈπΈ = ππ.ππππππππππππππππππ π¬π¬πππ΅π΅πππππ΅π΅ππππππ
18 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 3
Answer the following neatly
If the total number of charge pass through a conductor is 2.2 Coulomb. How many electrons it contains?
The total number of Electrons passes through is 2.164x1018. The total charge available is?
If the total number of charge pass through a conductor is 2.5 Coulomb in 3 seconds, find is the current passing in the conductor.
When checking through a circuit, it observes that a current of 200 mA is passing through a circuit in 1.2 seconds. Find the total charge in the circuit.
If the total energy available is 3 Joules, find the total number of charge if the potential difference available is 2 volts.
Activity 3
On a clean sheet of paper, answer the following neatly. Send a photograph of your work to your designated GDrive
1. If the total number of charge pass through a conductor is 2000 nC. How many electrons it contains?
2. If the total number of charge pass through a conductor is 12 mC. How many electrons it contains?
3. If the total number of charge pass through a conductor is 1.6 Coulomb in 10 seconds, find is the current passing in the conductor.
4. The total number of Electrons passes through is 9.62x1018 in 2 seconds. Find is the current passing in the conductor.
5. In a given circuit, the available energy is 3000 mJ where the system voltage is 3.6V. How many available electrons are in the circuit?
6. The total energy available is 300 Joules; find the total number of charge if the potential difference available is 230 volts.
19 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Answers to Self-Assessment Questions 3
If the total number of charge pass through a conductor is 2.2 Coulomb. How many electrons it contains?
ππ.ππππππππππππππππππ π¬π¬πππ΅π΅πππππ΅π΅ππππππ
The total number of Electrons passes through is 2.164x1018. The total charge available is?
0.345C
If the total number of charge pass through a conductor is 2.5 Coulomb in 3 seconds, find is the current passing in the conductor.
πππππππ΅π΅ππ
When checking through a circuit, it observes that a current of 200 mA is passing through a circuit in 1.2 seconds. Find the total charge in the circuit.
ππ.πππππͺπͺ
If the total energy available is 3 Joules, find the total number of charge if the potential difference available is 2 volts.
ππ.πππͺπͺ
The total energy available is 3 Joules, find the total number of charge if the potential difference available is 2 volts.
ππ.ππππππ
20 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 3: Circuit Parameters The Resistance
The resistance is the opposition given by a material to the flow of electricity. The resistance is denoted as βRβ and has the unit of ohms (Ξ©).
The Cross Sectional Area of Wires
Wire also offers electrical resistance and the cross sectional area of wire gives a major factor to this. The size of wire is denoted by its cross sectional area such as mm2 for metric, Circular Mil for English and American Wire Gauge (AWG) for US. Mils and Circular mils are often used and the conversion for it is enumerated as follows
1000 πππππΈπΈ = 1 πππΈπΈπΈπΈβ
(ππππππππ)2 = 1 πΆπΆπππππΈπΈπππΈπΈπΆπΆππ πππππΈπΈ
1πππΆπΆππ = 1000 πΆπΆπππππΈπΈπππΈπΈπΆπΆππ πππππΈπΈ ππ4
(πΆπΆπππππΈπΈπππΈπΈπΆπΆππ πππππΈπΈ) = 1 πππππππΆπΆππππ πππππΈπΈ
Example 1. Convert 20 Mil wire to inches.
Solution. 20 πππππΈπΈ π₯π₯ 1 πππΈπΈ1000 πππππΈπΈ = ππ.ππππ ππππ
Example 2. Convert 3 inches diameter wire to mils.
Solution. 3 in π₯π₯ 1000 πππππΈπΈ1 πππΈπΈ = ππππππππ π΄π΄ππππ
The Resistance offered by Wires
It would be expected that a wire's electrical resistance would be greater for a longer wire, less for a wire of a larger cross sectional area, and would be expected to depend on the material from which the wire is produced. Mathematically, it is expressed as:
π π = πππΈπΈπ΄π΄ =
πππππ΄π΄2 =
πππΈπΈ2
ππ
Where: R β Resistance offered
ππ β Resistivity ( Ξ©-m, πΊπΊβπΆπΆππππππ
)
πΈπΈ - Length (m, ft)
π΄π΄ - Area (ππ2, ft2, CM)
21 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 ππ - Volume (ππ3, ft3)
MATERIAL RESISTIVITY (at 20Β°C, in unit of 10-8 Ξ©-m)
Aluminum 2.83 Brass 6.16
Carbon (graphite) 800 Copper (annealed) 1.72
Copper (hard-drawn) 1.77 Iron (electrolytic) 9.95
Lead 22 Mercury 96 Silver 1.64 Gold 2.44
Tungsten 4.37 Table 1.1; Resistivity of Metals
Source: basic Electrical Engineering by J. Tejada and M. Pascua
Example 3. Find the resistance of an aluminium wire of length 1.5 km long and has a diameter of 0.1 m.
Solution. π΄π΄ = ππππ2
4= ππ(0.1ππ)2
4= ππ
400ππ2
π π = πππππ΄π΄
= 2.83π₯π₯10β8Ξ©βm(1500ππ)ππ400ππ
2 = ππ.ππππππππβπππ΄π΄
The effect of Temperature in Resistance
Experiments have shown that resistance of all wires commonly used in electrical systems in operation is increasing as the temperature rises. The formulas for the effect of Temperature are enumerated as follows.
π π 1/π π 2 = (|ππ| + πΈπΈ1) / (|ππ| + πΈπΈ2) π π 2/π π 1 = 1 + πΌπΌππ1βπΈπΈ πΌπΌππ1 = 1 / (|ππ| + πΈπΈ1)
βπΈπΈ = πΈπΈ2 β πΈπΈ1
Where: π π 1 β Initial Resistance
π π 2 β Final Resistance
ππ - Inferred Zero, temperature when resistance of a given material is zero.
πΈπΈ1 β Initial temperature
πΈπΈ2 β Final temperature
βπΈπΈβ Change in temperature
22 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 πΌπΌ - temperature coefficient of resistance
Material
Inferred Absolute Zero (T), Β°C
Aluminum -236
Copper, annealed -234.5
Copper, hard-drawn -242
Iron -180
Nickel -147
Silver -243
Steel, soft -218
Tin -218
Tungsten -202 Zinc -250
Table 1.2; Inferred Absolute Temperatures for several Metals Source: basic Electrical Engineering by J. Tejada and M. Pascua
Example 1. A coil of copper wire has a resistance of 54Ξ© at a room temperature of 20α΅C. What will be its resistance at 30α΅C?
Solution. π π 1π π 2
= (ππ + ππ1) (ππ + ππ2)
; π π 2 = π π 1(ππ + ππ2) (ππ + ππ1)
= 54 (234.5+ 30) (234.5+ 20)
= ππππ.ππππΞ©
Example 2. A wire in a substation is made up of 2 inches round, 20 ft. long. If the resistance of the wire is 5.185x10-5 Ξ©, What is the material used in the wire?
Solution. π π 1π π 2
= (ππ + ππ1) (ππ + ππ2)
; πΈπΈ2 = π π 2(ππ + ππ1)π π 1
β T = (5+15)(236+ 20)5
β 236 = ππππππα΅ππ
Example 3. What is the temperature rise in Example 2?
Solution. βπΈπΈ = πΈπΈ2 β πΈπΈ1 = 788α΅C β 20α΅C = ππππππα΅ππ
23 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 4
Answer the following neatly
1. Convert 160 Mil wire to millimeter. 2. Convert 52 mm diameter wire to mils. 3. Convert 54 Mil wire to MCM. 4. Convert 0.06 MCM wire to Mil. 5. Convert 12Ο wire to Circular Mil. 6. Convert 48Ο wire to MCM. 7. Convert 300 mm2 wire to CM. 8. Convert 500 mm2 wire to MCM.
Self-Assessment Questions 5
1. A wire in a substation is made up of 2 inches round, 20 ft. long. If the resistance of the wire is 5.185x10-5 Ξ©, What is the material used in the wire?
2. Find the length of a copper wire that has a cross sectional area of 0.00025m2. The resistance of the wire is 3.06 ohms.
3. What is the temperature coefficient of resistance of silver at 20α΅C? 4. At the room temperature of 290.15 kelvin, find the temperature coefficient of
resistance of Zinc.
Activity 4
On a clean sheet of paper, answer the following neatly. Send a photograph of your work to [email protected]
1. A brass wire, that has a cross sectional area of 0. 12m2 and its resistance is 80Β΅ ohms. Find the volume of the brass wire
2. If a 1 ohm copper wire of unknown length passes through drawing dies, the length of wire increased by 2 times of its original length. Determine its new resistance.
3. An iron wire has a resistance of 2.78Ξ© at room temperature of 20α΅C. when placed near the engine of a vehicle, the resistance raised to 3.614Ξ© at its new temperature. What is the change in temperature given that the coefficient of temperature for iron at 20 degree Celsius is 0.005?
24 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 4
Convert 160 Mil wire to millimeter. ππ.πππππππ΅π΅π΅π΅
Convert 52 mm diameter wire to mils. ππππππππ.ππππ π΄π΄ππππ
Convert 54 Mil wire to MCM. ππ.ππππππ π΄π΄πͺπͺπ΄π΄
Convert 0.06 MCM wire to Mil. ππ.ππππ π΄π΄ππππ
Convert 12Ο wire to Circular Mil. ππππ πͺπͺπππ΅π΅πππ΅π΅πππππ΅π΅ π΄π΄ππππππ
Convert 48Ο wire to MCM. ππ.ππππππ π΄π΄πͺπͺπ΄π΄
Convert 300 mm2 wire to CM. ππππππππππππ.ππππ πͺπͺπππ΅π΅πππ΅π΅πππππ΅π΅ π΄π΄ππππ
Convert 500 mm2 wire to MCM. ππππππ.ππππππ π΄π΄πͺπͺπ΄π΄
Answers to Self-Assessment Questions 5
1. A wire in a substation is made up of 2 inches round, 20 ft. long. If the resistance of the wire is 5.185x10-5 Ξ©, What is the material used in the wire? Copper (annealed)
2. Find the length of a copper wire that has a cross sectional area of 0.00025m2. The resistance of the wire is 3.06 ohms. 44.47kΞ©
3. What is the temperature coefficient of resistance of silver at 20α΅C? 0.0038 4. At the room temperature of 290.15 kelvin, find the temperature coefficient of
resistance of Zinc. ππ.ππππππππππππ
25 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
End of Module 1
26 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Module 2: The Power, Energy and Ohmβs Law Table of Contents Lesson 1: The Ohmβs Law
Lesson 2: Electrical Power
Lesson 3: Electrical Energy
27 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Source: Basic Electrical Engineering By J. Tejada and M. Pascua
Lesson 1: The Ohmβs Law The Ohmβs Law
Ohmβs law is the relationship between Voltage, Current and Resistance. The ohmβs law can be applied in DC circuits as well as AC circuits. It states that βthe current flowing in the circuit is proportional to the applied Voltage and inversely proportional to the circuit resistanceβ. Figure 2.1 shows the different formulas derived from the ohmβs law.
Conditions for Ohmβs Law
Ohmβs Law may be extended either to the entire
circuit or to a circuit section. Ohmβs Law can be applied to DC as well as AC
Circuits. However, in AC circuits, Impedance is used in place of Resistance.
When Ohmβs Law is applied to a branch of a circuit, the branch resistance, voltage or current should be used.
In Ohmβs Law, the temperature must be constant.
Example 1. Find the current I through a resistor of resistance R = 3 Ξ© if the voltage across the resistor is 6 V.
Solution. Current, πΌπΌ = ππ/π π = 6ππ / 3Ξ© = ππ ππ
Example 2. A resistor with a 100 kilo ohms resistance is connected to a 230 volts alternating current. Find the value of the current flowing in the resistor?
Solution. Current, πΌπΌ = ππ/π π = 230ππ/100 Ξ© = ππ.ππ π΅π΅ππ
28 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 6
1. Find the voltage V through a resistor of resistance R = 2.1 Ξ© if the current across the resistor is 6 A.
2. A resistor with a 100 ohms resistance is connected to a 5 amps alternating current. Find the value of the voltage across the resistor?
3. Find the resistance R through a circuit of voltage 12V if the current across the resistor is 6 A.
4. A resistor across a 230V AC is known to produce a 5 amps alternating current. Find the value of the resistor?
Activity 5
On a clean sheet of paper, create ten electrical energy questions and answer it. Send a photograph of your work to your designated GDrive
29 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 6
1. Find the voltage V through a resistor of resistance R = 2.1 Ξ© if the current across the resistor is 6 A.
2. A resistor with a 100 ohms resistance is connected to a 5 amps alternating current. Find the value of the voltage across the resistor?
3. Find the resistance R through a circuit of voltage 12V if the current across the resistor is 6 A.
4. A resistor across a 230V AC is known to produce a 5 amps alternating current. Find the value of the resistor?
30 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 2: Electrical Power Electrical Power
Source: Basic Electrical Engineering By J. Tejada and M. Pascua
The Electrical Power is the rate at which electrical energy is being transferred in a given time. It is denoted as βPβ or βpβ and has the unit of Watts (W). The Electrical Power is usually used as the rating of devices and machines such as motors, pumps and other devices.
Example 1. Find the Power dissipated through a resistor of resistance R = 3 Ξ© if the voltage across the resistor is 6 V.
Solution. Power, P = ππ2/π π = (6ππ) 2/ 3Ξ© = ππππ πΎπΎ
31 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 7
1. A resistor with a 100 kilo ohms resistance is connected to a 230 volts alternating current. Find the value of the power dissipated in the resistor?
2. Find the Power dissipated through a resistor of resistance R = 2.1 Ξ© if the current across the resistor is 6 A.
3. A resistor with a 100 ohms resistance is connected to a 5 amps alternating current. Find the value of the power dissipated in the resistor?
4. Find the Power dissipated through a circuit of voltage 12V if the current across the resistor is 6 A.
Activity 6
On a clean sheet of paper, create ten electrical energy questions and answer it. Send a photograph of your work to your designated GDrive
32 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 7
1. A resistor with a 100 kilo ohms resistance is connected to a 230 volts alternating current. Find the value of the power dissipated in the resistor? ππ.πππππππΎπΎ
2. Find the Power dissipated through a resistor of resistance R = 2.1 Ξ© if the current across the resistor is 6 A. ππππ.πππΎπΎ
3. A resistor with a 100 ohms resistance is connected to a 5 amps alternating current. Find the value of the power dissipated in the resistor? ππ.πππππΎπΎ
4. Find the Power dissipated through a circuit of voltage 12V if the current across the resistor is 6 A. πππππΎπΎ
33 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
End of Module 2
34 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Module 3: The Multimeter Table of Contents Introduction
Lesson 1: The Ohmmeter
Lesson 2: The Voltmeter
Lesson 3: The Ammeter
35 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Introduction The Multimeter
Source: Basic Electrical Engineering By J. Tejada and M. Pascua
A Multimeter or a tester is a necessary tool for an electrical practitioner and technicians. It is used to measure values and is used for trouble shooting. A common Multimeter has 5 parts known as ohmmeter, ammeter, DC voltmeter, AC voltmeter, and continuity/semiconductor tester.
Parts of a Multimeter
1. Pointer β It is the needle indicating the measured value that can be seen on the scale.
2. Scale β It is the list of values to be indicated by the pointer. It is usually consist of three parts, the ohmmeter, ammeter and the voltmeter.
3. Adjustment Screw β It is used to adjust the pointer to zero position.
4. Zero-Ohm adjustment knob β It is used for adjusting the pointer to zero for measuring resistance.
5. Ranges Selector Knob β It is used to choose from different function of the tester, and for selecting the proper multiplier to be used.
6. Test Probe β Are commonly in two colors. Red colored test probe is used for positive terminal while black colored test probe is used for common terminal.
36 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Multimeter usage and Maintenance
First and Foremost, Always read the manual oh how to operate the multimeter.
Check if the battery connected is in good condition. Low battery level may affect
the precision of measured values, and also it can affect the internal setting of the multimeter.
Check if the multimeter is set to correct setting and multiplier. Ohmmeter measuring resistance, voltmeter measuring voltage, and ammeter measuring current.
When not in use, Range selector knob must be set on βOFFβ or the highest voltage range available. It is to ensure that the battery will not drain.
Do not drop or break the multimeter. The multimeter is not designed as shockproof type of device.
37 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Activity 8
Photograph an analog multimeter. Print it or edit it as a photo and identify the different parts of the multimeter. Send your work to your designated GDrive
38 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 1: The Ohmmeter The Ohmmeter
Source: Basic Electrical Engineering By J. Tejada and M. Pascua
Things to remember
For Analog ohmmeter, four things must be checked before taking any resistance test and enumerated as follows:
1. Select first the proper multiplier in the function selector. 2. Adjust the pointer to zero reading by shorting the test prods together as shown in
figure. It is necessary because without the zero adjustment, it may affect the accuracy of the measurement.
3. The component under test must be DE ENERGIZED during the test. This is to protect both yourself and the device from the electric current. Must be vigilant to ensure the safety of the device and the one using it.
4. You must not touch the metallic part of the test prods to prevent measuring your own body resistance. Although it is not harmful, the ohmmeter reading will be incorrect.
Reading exercise of Ohmmeter
There are many ways you can measure a specific resistance as long you have proper multiplier for the multimeter read resistance value. Suppose we have a 100 ohm resistor and we have to check the actual value of it, we can usex1, x10, and x100 multiplier as shown in the following figures.
Multimeter Display when measuring 100 ohm resistor in x1 multiplier
39 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Activity 9
Answer the following values using analog multimeter. Send your work to your designated GDrive
40 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 2: The Voltmeter The Voltmeter
Source: Basic Electrical Engineering By J. Tejada and M. Pascua
A Voltmeter is used to measure electromotive force. The scale under the ohmmeter readings in the analog Multimeter is used for voltage readings. Common Multimeter has two voltmeter functions: one for AC and one is for DC. The figure shows the set of scales used for measuring electromotive force
Things to remember
For Analog voltmeter, four things must be checked before taking any resistance test and enumerated as follows:
1. Check first the polarity of the source being tested. An analog multimeter is incapable of testing a negative voltage, and if so, it may dislocate the needle of the tester.
2. It must be observed that the test probe will never touch each other when testing. It may cause short circuit.
3. When measuring an unknown voltage using a Voltmeter, it must be set in the highest range and then setting down one by one. This is used to protect the device from measuring values that exceeded the maximum value of the said range.
4. When measuring the voltage drop across a component, it must be tapped in parallel across the component.
Reading exercise of Voltmeter
When measuring voltage, the multiplier must be set in the proper range. Also, the proper range in the multiplier has its own scale in the multimeter screen. In the Philippines, we have a standard voltage of 230v in our outlet. We will try to test it using a multimeter.
41 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Multimeter Display when measuring 230v AC in 250 Multiplier
The needle stops between 200 and 250 in the highest voltmeter scale. It means, the voltage is around 200 to 250. For more precise look, it stops one line after the middle that has a value of 225v. So it means it is measuring 230 volts potential.
42 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Activity 10
Answer the following values using analog multimeter. Send your work to your designated GDrive
43 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 3: The Ammeter The Ammeter
Source: Basic Electrical Engineering By J. Tejada and M. Pascua
An Ammeter is used to measure Electrical Intensity or current. The scale under the ohmmeter readings in the analog Multimeter is used for voltage readings. The following figure shows the set of scales used for measuring electrical current.
Things to remember
For Analog ammeter, four things must be checked before taking any resistance test and enumerated as follows:
1. Check first the polarity of the source being tested. An analog multimeter is incapable of testing a negative current, and if so, it may dislocate the needle of the tester.
2. It must be observed that the test probe will never touch each other when testing. It may cause an open circuit.
3. When measuring an unknown current using an ammeter, it must be set in the highest range and then setting down one by one. This is used to protect the device from measuring values that exceeded the maximum value of the said range.
4. When measuring the current across a component, it must be tapped in series across the component.
Reading exercise of Ammeter
When measuring current, the multiplier must be set in the proper range. Also, the proper range in the multiplier has its own scale in the multimeter screen. A normal ammeter in the multimeter has only 0.25A capacity. If your goal is to measure a value above that, it is required to use a current transformer. We will try to test it using a multimeter.
44 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Multimeter Display when measuring 10mA in 25DCmA Multiplier
The needle stops exactly at 1.0 in the scale. It terms of 25mA scale, stopping at 2.5 means it has exactly 25mA. Using ratio and proportion, 1.0 at 25mA scale means it has 10DCmA.
45 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Activity 11
Read the following values using analog multimeter. Send your work to your designated GDrive
46 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
End of Module 3
47 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Module 4: The Resistor Table of Contents Introduction
Lesson 1: Resistor Color Coding
Lesson 2: Series β Parallel Resistors
Lesson 3: Network Reduction (WYE-DELTA)
48 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Introduction The Resistor
Source: Basic
Electrical Engineering By J. Tejada and M. Pascua
Resistors are electronic components made up of high resistive materials and is used to control and limit the current flow to a circuit
Different Types of Resistors
β’ Wire wound resistors β’ Metal film resistors β’ Thick film and Thin film resistors β’ Network and Surface Mount Resistors β’ Variable Resistors β’ Special resistors
Symbol Actual Component
49 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Activity 12
In a document file (maybe hardcopy or softcopy), attach the different types of resistors and their identification. Send your work to your designated GDrive
50 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 1: Resistor Color Coding Resistor Color Coding
Carbon Resistors are usually small in size depends on their wattage capacity. Color code is used to represent their resistance value in ohms. Note that BLACK color can never be the first band.
Self-Assessment Questions 9
Color Digit Multiplier X10^(-)
Tolerance (%)
Mnemonics
Black 0 0 Bad Brown 1 1 Β±1 ( F ) Boys Red 2 2 Β±2 ( G ) Race Orange 3 3 Our Yellow 4 4 Young Green 5 5 Β±0.5 ( D ) Girls Blue 6 6 Β±0.25 ( C ) But Violet 7 7 Β±0.1 ( B ) Violeta Gray 8 8 Gave White 9 9 Willingly with None Β±20 No Silver -1 Β±10 ( K ) Silver and Gold -2 Β±5 ( J ) Gold
51 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Find the resistance of the resistors
1.
2.
Self-Assessment Questions 10
Identify the color codes of the resistor
Activity 13
On a clean sheet of paper, draw and color resistors with values as given. Send your work to your designated GDrive
VALUE 1ST 2ND 3RD 4TH 12 Ξ© Β±10% 3.6 Ξ© Β±1% 740 Ξ© Β±5% 2600 Ξ© Β±10% 100 Ξ© Β±10%
160 kΞ© Β±10% 130 kΞ© Β±5% 2.65 Ξ© Β±5%
52 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 9
1.
2.
Answers to Self-Assessment Questions 10
VALUE 1ST 2ND 3RD 4TH 12 Ξ© Β±10% brown red black silver
3.6 Ξ© Β±1% orange blue gold brown 740 Ξ© Β±5% violet yellow brown gold 2600 Ξ© Β±10% red blue red silver 100 Ξ© Β±10% brown black brown silver
12x10^(5) = 1.2MΞ©
100 ohms
53 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 2: Series β Parallel Resistors Series connection of resistors
Series connection of resistors is used to create a chain like circuit that is used to raise the circuit resistance while lowering the circuit current.
Example 1. Find the total Voltage in the Circuit shown
Solution. πΌπΌππ = πΌπΌ1 = πΌπΌ2 = πΌπΌ3 = 3π΄π΄
Voltage at 5Ξ© Resistor,
ππ1 = πΌπΌ1π π 1 = 3π΄π΄ π₯π₯ 5πΊπΊ = 15ππ
Voltage at 6Ξ© Resistor,
ππ2 = πΌπΌ2π π 2 = 3π΄π΄ π₯π₯ 6πΊπΊ = 18ππ Voltage at 7Ξ© Resistor, ππ3 = πΌπΌ3π π 3 = 3π΄π΄ π₯π₯ 7πΊπΊ = 21ππ
Getting the total voltage, ππππ = ππ1 + ππ2 + ππ3 = 15ππ + 18ππ + 21ππ = πππππ½π½
54 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Parallel connection of resistors
is used to reduce the circuit resistance and to get the desired constant voltage per branch. It is commonly used in designing for all the ranch circuit have the same voltages especially in the Lighting outlet and convenience outlet designing
Example 1. Find the total Current in the Circuit shown
Solution. ππππ = ππ1 = ππ2 = ππ3
Current at 5Ξ© Resistor,
πΌπΌ1 = ππ1/π π 1 = 24ππ/5πΊπΊ = 4.8π΄π΄
Current at 6Ξ© Resistor, πΌπΌ2 = ππ2/π π 2 =24ππ/6πΊπΊ = 4π΄π΄
Current at 7Ξ© Resistor, πΌπΌ3 = ππ3/π π 3 = 24ππ/7πΊπΊ = 3.43π΄π΄
Getting the total current, πΌπΌππ = πΌπΌ1 + πΌπΌ2 + πΌπΌ3 = 4.8π΄π΄ + 4π΄π΄ + 3.43π΄π΄ = ππππ.ππππππ
55 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Series β Parallel connection of resistors
are the combination of series circuitry and parallel circuits that is commonly used by technicians to create the best possible circuit design.
Example 1. Find the resistance reading in the ohmmeter given in Figure 4.5A.
Solution. By analysis, The 6 ohms and the 10 ohms are in series with each other. That is also true with 5 ohm and 12 ohm resistors.
Using the equation of resistances in series circuit, the total resistance for the upper branch is
π π ππππππππππ = 6πΊπΊ + 10πΊπΊ = 16 πΊπΊ, And for lower Branch,
π π πΏπΏπΏπΏπΏπΏππππ = 5πΊπΊ + 12πΊπΊ = 17 πΊπΊ.
The circuit may be written as a two parallel resistor circuit as shown in Figure 4.5B.
Solving for Total Resistance,
π π ππ = 1
1π π ππππππππππ
+ 1π π πΏπΏπΏπΏπΏπΏππππ
= 11
16πΊπΊ+1
17πΊπΊ = 8.2424Ξ©
Figure 4.5A
56 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 11
Answer the following
1. A two identical 15 kΞ© resistors are connected in series with a fixed 34 volt power supply. Find the current being supplied in the circuit. Find also the voltage on each resistor.
2. Three 13 kΞ© resistors and a 4 kΞ© resistor are connected in parallel with a fixed 34 volt power supply. Find the current being supplied in the circuit. Find also the current on each resistor.
Activity 14
On a clean sheet of paper, create your own circuit and answer it. Send your work to your designated GDrive
57 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 11
Answer the following
1. A two identical 15 kΞ© resistors are connected in series with a fixed 34 volt power supply. Find the current being supplied in the circuit. Find also the voltage on each resistor. I = 1A, V1 = 15 V V2 = 15 V
2. Three 13 kΞ© resistors and a 4 kΞ© resistor are connected in parallel with a fixed 34 volt power supply. Find the current being supplied in the circuit. Find also the current on each resistor. IT = 8.508A, IR1 = 2.615mA, IR2 = 2.615mA,
IR3 = 2.615mA, IR4 = 8.5A,
58 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 3: Network Reduction (WYE-DELTA)
Source: Basic Electrical Engineering By J. Tejada and M. Pascua
In certain circuits resistors are neither in series nor in parallel, so it is difficult to apply the rules for series or parallel circuits. Converting from one circuit type to another may be important for such circuits to simplify the solution.
Example. A circuit consist of three resistors rated: 10 ohms, 12 ohms, and 15 ohms connected in delta. What would be the resistances of the equivalent wye connected load?
Solution.
ππ = π΄π΄πΆπΆ
π΄π΄ + π΅π΅ + πΆπΆ=
10π₯π₯1210 + 15 + 12
= ππ.ππππ π΄π΄
ππ = π΄π΄π΅π΅
π΄π΄ + π΅π΅ + πΆπΆ=
10π₯π₯1510 + 15 + 12
= ππ.ππππ π΄π΄
ππ = π΅π΅πΆπΆ
π΄π΄ + π΅π΅ + πΆπΆ=
15π₯π₯1210 + 15 + 12
= ππ.ππππ π΄π΄
Delta to Wye:
ππ = π΄π΄πΆπΆ
π΄π΄ + π΅π΅ + πΆπΆ ππ =
π΄π΄π΅π΅π΄π΄ + π΅π΅ + πΆπΆ
ππ = π΅π΅πΆπΆ
π΄π΄ + π΅π΅ + πΆπΆ
Wye to Delta:
π΄π΄ = ππππ + ππππ + ππππ
ππ π΅π΅ =
ππππ + ππππ + ππππππ
πΆπΆ = ππππ + ππππ + ππππ
ππ
59 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 12
Answer the following
1. A circuit consist of three resistors rated: 12 ohms, 22 ohms, and 35 ohms connected in delta. What would be the resistances of the equivalent wye connected load?
2. A circuit consist of three resistors rated: 6 ohms, 4 ohms, and 11 ohms connected in delta. What would be the resistances of the equivalent wye connected load?
3. A circuit consist of three resistors rated: 6 ohms, 12 ohms, and 18 ohms connected in wye. What would be the resistances of the equivalent delta connected load?
4. A circuit consist of three resistors rated: 12 ohms, 15 ohms, and 18 ohms connected in wye. What would be the resistances of the equivalent delta connected load?
5. Three resistors of 11-ohm resistance are connected in delta. Inside of it, there is a wye connected resistors rated of 11 ohms each. Find the resistance between any two corners.
Activity 15
On a clean sheet of paper, create your own circuit and answer it. Send your work to your designated GDrive
60 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 12
Answer the following
1. A circuit consist of three resistors rated: 12 ohms, 22 ohms, and 35 ohms connected in delta. What would be the resistances of the equivalent wye connected load?
11.159 Ξ©, 6.087 Ξ©, 3.83 Ξ©
2. A circuit consist of three resistors rated: 6 ohms, 4 ohms, and 11 ohms connected in delta. What would be the resistances of the equivalent wye connected load?
2.1Ξ©, 3.14 Ξ©, 1.14 Ξ©
3. A circuit consist of three resistors rated: 6 ohms, 12 ohms, and 18 ohms connected in wye. What would be the resistances of the equivalent delta connected load?
66 Ξ©, 33 Ξ©, 22 Ξ©
4. A circuit consist of three resistors rated: 12 ohms, 15 ohms, and 18 ohms connected in wye. What would be the resistances of the equivalent delta connected load?
55.5 Ξ©, 44.4 Ξ©, 37 Ξ©
5. Three resistors of 11-ohm resistance are connected in delta. Inside of it, there is a wye connected resistors rated of 11 ohms each. Find the resistance between any two corners. 8.25 Ξ©, 8.25 Ξ©, 8.25 Ξ©
61 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
End of Module 4
62 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
Module 5: Batteries Table of Contents Lesson 1: Life of battery
Lesson 2: Series and Parallel Batteries
63 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 1: Life of battery Cells and Batteries
Cells and batteries are components composed of two different metals and a chemical solution such as acids or alkaline. The lifetime of a cell or battery depends on the amount of current it supplies. The greater the current, the shorter battery life. Mathematically, to compute for the life of a battery or cell, the following formula shall be used.
πΏπΏππππππ(π»π»πΏπΏπ»π»πππ»π») =π΄π΄ππππππππππ β π»π»ππππππ π π πΆπΆπΈπΈπππΈπΈπ π
π΄π΄πππππππππππΈπΈ ππππ πΈπΈπππππππππΈπΈπΈπΈ πππππππππππΈπΈππππ
Example 1. A device is connected to a battery rated 4500mAh. It is found that 250 mA is being consumed by the device. How long will the battery supply the device?
Solution.
πΏπΏππππππ(π»π»πΏπΏπ»π»πππ»π») =π΄π΄ππππππππππ β π»π»ππππππ π π πΆπΆπΈπΈπππΈπΈπ π
π΄π΄πππππππππππΈπΈ ππππ πΈπΈπππππππππΈπΈπΈπΈ πππππππππππΈπΈππππ
πΏπΏππππππ(π»π»πΏπΏπ»π»πππ»π») =4500π₯π₯10β3
250π₯π₯10β3
πΏπΏππππππ(π»π»πΏπΏπ»π»πππ»π») = ππππ π―π―πππ΅π΅π΅π΅ππ
64 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 13
Answer the following
1. A device is connected to a battery rated 4000mAh. It is found that 400 mA is being consumed by the device. How long will the battery can supply the device?
2. An LED module is connected to a battery rated 4400mAh. It if the battery can supply the device for 8 hours, how much current is the device drawn?
3. A certain building is suddenly de energized. An emergency light was energized by its internal power source that can light the building for 3 hours. the emergency light has two lamps are drawing 0.625A each. What is the Ampere-Hour rating of the internal power source?
Activity 16
On a clean sheet of paper, create your own battery problem and answer it. Send your work to your designated GDrive
65 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 13
Answer the following
1. A device is connected to a battery rated 4000mAh. It is found that 400 mA is being consumed by the device. How long will the battery can supply the device?
ππππ π―π―πππ΅π΅π΅π΅ππ 2. An LED module is connected to a battery rated 4400mAh. It if the battery can
supply the device for 8 hours, how much current is the device drawn? ππππ π΅π΅ππ
3. A certain building is suddenly de energized. An emergency light was energized by its internal power source that can light the building for 3 hours. the emergency light has two lamps are drawing 0.625A each. What is the Ampere-Hour rating of the internal power source?
ππππππππ π΅π΅ππππ
66 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Lesson 2: Series and Parallel Batteries
Series and Parallel Batteries When the batteries are connected in series, their voltages are added up and their
ampere-hour remains the same.
ππππ = ππ1 + ππ2 + β―+ ππππ π΄π΄βππ = π΄π΄β1 = π΄π΄β2 = β― = π΄π΄βππ
When the batteries are connected in parallel, their ampere-hour is added up and their voltages remain the same.
ππππ = ππ1 = ππ2 = β― = ππππ π΄π΄βππ = π΄π΄β1 + π΄π΄β2 + β―+ π΄π΄βππ
When the batteries are connected in combination, take consideration of its connection with respect whether it is a series combined with parallel or parallel combined with series.
Example 1. An electric bike has a motor rated 48 volts. How many 12 volts battery is needed for the electric bike to run where the number of 12 volt battery to be used is at minimum?
67 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Solution.
ππππ = ππ1 + ππ2 + β―+ ππππ
ππππ = πΈπΈ (ππ1)
48 = πΈπΈ (ππ1)
πΈπΈ = ππ π©π©πππππππ΅π΅π΅π΅πππ΅π΅ππ Example 2. An 12 volt motor rated 12 volts needed to run for 8 hours. If the 12 volt motor drawn 0.5A, how many 12 volt, 500 mAh battery is needed for the motor to run where the number of 12 volt battery to be used is at minimum?
Solution.
π΄π΄βππ = πΏπΏππππππ(π»π»πΏπΏπ»π»πππ»π»)[π΄π΄πππππππππππΈπΈ ππππ πΈπΈπππππππππΈπΈπΈπΈ πππππππππππΈπΈππππ]
π΄π΄βππ = [8β][0.5A]
π΄π΄βππ = 4 π΄π΄β
π΄π΄βππ = π΄π΄β1 + π΄π΄β2 + β―+ π΄π΄βππ
π΄π΄βππ = πΈπΈ (π΄π΄β1)
4 = πΈπΈ (500 mAh)
πΈπΈ = ππ π©π©πππππππ΅π΅π΅π΅πππ΅π΅ππ
Example 3. What will be the output for the battery connection given below.
Solution.
Finding for the Voltage Rating,
ππππ = ππ1 + ππ2
ππππ = 12 + 12
68 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 ππππ = ππππππ
Finding for the Ah Rating,
π΄π΄βππ = π΄π΄β1 + π΄π΄β2 + π΄π΄β3
π΄π΄βππ = 60 + 60 + 60
π΄π΄βππ = ππππππ ππππ
69 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Self-Assessment Questions 14
Answer the following
1. A remote controller needed a two AAA battery for it to energize. If the AAA battery is rated 1.5 volts, what is the voltage needed by the remote controller to be energized?
2. An amplifier is connected to a 12 volt source. It draws 8.33 Amperes and needed to be run for 8 hours. how many 12 volt, 3500 mAh battery is needed for the amplifier to run where the number of 12 volt battery to be used is at minimum?
3.
Activity 17
On a clean sheet of paper, create your own battery circuits and answer it. Send your work to your designated GDrive
70 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1 Answers to Self-Assessment Questions 14
Answer the following
1. A remote controller needed a two AAA battery for it to energize. If the AAA battery is rated 1.5 volts, what is the voltage needed by the remote controller to be energized?
3 Volts 2. An amplifier is connected to a 12 volt source. It draws 8.33 Amperes and needed
to be run for 8 hours. how many 12 volt, 3500 mAh battery is needed for the amplifier to run where the number of 12 volt battery to be used is at minimum?
19 Batteries
3.
36V, 180A-hr
71 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
End of Module 5
72 | P a g e URS-IM-AA-CI-0465 Rev 00 Effective Date: August 24, 2020
BASIC ELECTRICAL ENGINEERING EE 8 UNIT
1
End of Unit 1 Basics of Electrical
Engineering Circuits
REFERENCE BOOKS: Available at University of Rizal System Morong