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3091561100307

SECOND EDITION

First Printing, July 2003

Copyright March, 2003 Lab-Volt Systems, Inc.

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i

Table of Contents

Section 1 – Workstation Inventory and Installation............................................................... 1-1

Inventory of Workstation ........................................................................................................ 1-1

Minimum Computer Requirements.................................................................................... 1-1

Equipment and Supplies..................................................................................................... 1-1

Equipment Installation ............................................................................................................ 1-1

Software Installation ............................................................................................................... 1-1

Section 2 – Introduction to F.A.C.E.T. Curriculum............................................................... 2-1

Getting Started ........................................................................................................................ 2-2

Screen Buttons ........................................................................................................................ 2-3

F.A.C.E.T. Help Screens and Resources................................................................................. 2-4

Internet Access ........................................................................................................................ 2-5

Instructor Annotation Tool...................................................................................................... 2-5

Student Journal........................................................................................................................ 2-5

Assessing Progress .................................................................................................................. 2-6

Real-Number Questions and Answers .................................................................................... 2-8

Recall Values in Text ............................................................................................................ 2-10

Safety .................................................................................................................................... 2-11

Section 3 – Courseware ............................................................................................................. 3-1

Unit 1 – DC Network Theorems ............................................................................................... 3-1

Exercise 1 – Component Location/Identification ................................................................... 3-2

Exercise 2 – Circuit Board Operation ..................................................................................... 3-6

Unit 2 – Kirchhoff’s Current Law.......................................................................................... 3-13

Exercise 1 – Current in a Branch Circuit .............................................................................. 3-15

Exercise 2 – Node Currents in a Branch Circuit ................................................................... 3-21

Unit 3 – Kirchhoff’s Voltage Law........................................................................................... 3-29

Exercise 1 – 3-Element Series Voltages ............................................................................... 3-31

Exercise 2 – Algebraic Sum of Series Voltages.................................................................... 3-38

Unit 4 – Kirchhoff’s Loop Equations ..................................................................................... 3-45

Exercise 1 – Loop Equations................................................................................................. 3-46

Exercise 2 – Node Equations ................................................................................................ 3-53

ii

Unit 5 – Kirchhoff’s Solution with 2 Sources ........................................................................ 3-63

Exercise 1 – Kirchhoff's Voltage Law/2 Sources ................................................................. 3-65

Exercise 2 – Kirchhoff's Current Law/2 Sources.................................................................. 3-71

Exercise 3 – Mesh Solution With 2 Sources......................................................................... 3-78

Unit 6 – Superposition And Millman's Theorems ................................................................ 3-87

Exercise 1 – Superposition Theorem .................................................................................... 3-88

Exercise 2 – Millman's Theorem .......................................................................................... 3-92

Unit 7 – Thevenin Circuits ...................................................................................................... 3-99

Exercise 1 – Thevenizing a Single Source Network........................................................... 3-100

Exercise 2 – Thevenizing a Dual Source Network ............................................................. 3-104

Unit 8 – Thevenizing a Bridge Circuit ................................................................................. 3-113

Exercise 1 – Bridge Circuit Resistance............................................................................... 3-114

Exercise 2 – Thevenizing Bridge Circuit Voltage .............................................................. 3-117

Unit 9 – Thevenin/Norton Conversion ................................................................................. 3-125

Exercise 1 – Thevenin to Norton Conversion ..................................................................... 3-127

Exercise 2 – Norton to Thevenin Conversion ..................................................................... 3-131

Unit 10 – Delta and Wye Networks ...................................................................................... 3-139

Exercise 1 – Tee/Wye and Pi/Delta Networks.................................................................... 3-141

Exercise 2 – Delta and Wye Transformations..................................................................... 3-144

Appendix A – Pretest and Posttest Questions and Answers ................................................. A-1

Appendix B – Faults and Circuit Modifications (CMs) .........................................................B-1

Appendix C – Board and Courseware Troubleshooting....................................................... C-1

iii

Introduction

This Instructor Guide is divided into three sections and the appendices. It provides a unit-by-unit

outline of the Fault Assisted Circuits for Electronics Training (F.A.C.E.T.) curriculum.

Section 1 – Workstation Inventory and Installation contains a list and description of

equipment and materials required for all units in this course of study as well as installation

instructions.

Section 2 – Introduction to F.A.C.E.T. Curriculum provides a description of the courseware

structure, instructions on getting started with the multimedia presentation, and an explanation of

student-progress assessment methods.

Section 3 – Courseware includes information that enables the instructor to gain a general

understanding of the units within the course.

♦ The unit objective

♦ Unit Fundamentals questions and answers

♦ A list of new terms and words for the unit

♦ Equipment required for the unit

♦ The exercise objectives

♦ Exercise Discussion questions and answers

♦ Exercise Procedure questions and answers

♦ Review questions and answers

♦ CMs and Faults available

♦ Unit Test questions and answers

♦ Troubleshooting questions and answers (where applicable)

Appendices include the questions and answers to the Pretest and Posttest plus additional specific

information on faults and circuit modifications (CMs).

Please complete and return the OWNER REGISTRATION CARD included with the CD-

ROM. This will assist Lab-Volt in ensuring that our customers receive maximum support.

iv

THIS

SECTION 1 – WORKSTATION INVENTORY

AND INSTALLATION

DC Network Theorems Section 1 – Workstation Inventory and Installation

1-1

SECTION 1 – WORKSTATION INVENTORY AND INSTALLATION

Inventory of Workstation

Use this section to identify and inventory the items needed.

Minimum Computer Requirements 100% compatible Windows

®PC with Windows98 second edition or newer, NT, 2000, Me or XP;

Pentium class CPU, (Pentium II or newer); 126 MB RAM; 10 GB HDD; CD-ROM drive; SVGA

monitor and video card capable of 32-bit color display at 1024 x 768 resolution and sound

capabilities.

Equipment and Supplies The following equipment and supplies are needed for DC Network Theorems:

Quantity Description

1 F.A.C.E.T. base unit

1 DC NETWORK THEOREMS circuit board

1 Multimeter

1 Student Workbook

1 Instructor Guide

Equipment Installation

To install the hardware, refer to the Tech-Lab (minimum version 6.x) Installation Guide.

Software Installation

Third Party Application Installation

All applications and files that the courseware launches, or that are required for the course should

be installed before the courseware. Load all third party software according to the manufacturers'

directions. Install this software to the default location and note that location. (Alternatively, you

can install this software to a different location that you designate.) Remember to register all

software as required.

No third-party software is required for this course.

Installation of Courseware and Resources

To install the courseware and resources, refer to the Tech-Lab (minimum version 6.x) and

Gradepoint 2020 (minimum version 6.x) Installation Guide.

DC Network Theorems Section 1 – Workstation Inventory and Installation

1-2

SECTION 2 – INTRODUCTION TO F.A.C.E.T.

CURRICULUM

DC Network Theorems Section 2 – Introduction to F.A.C.E.T. Curriculum

2-1

SECTION 2 – INTRODUCTION TO F.A.C.E.T. CURRICULUM

Overview F.A.C.E.T. curriculum is multimedia-based courseware. The curriculum gives students hands-on

experience using equipment and software closely associated with industry standards. It provides

students with opportunities for instruction in academic and technical skills.

All courses are activity-driven curricula. Each course consists of several units containing two or

more exercises. Each unit begins with a statement explaining the overall goal of the unit (Unit

Objective). This is followed by Unit Fundamentals. Next is a list of new terms and words then

the equipment required for the unit. The exercises follow the unit material. When students

complete all the exercises, they complete the Troubleshooting section and take the Unit Test.

The exercises consist of an exercise objective, exercise discussion, and exercise procedures. The

Exercise Conclusions section provides the students with a list of their achievements. Every

exercise concludes with Review Questions. Available circuit modifications (CMs) and faults are

listed after the review questions. Additional specific information on CMs and faults is available

in Appendix B.


2-2

Getting Started

Desktop

After the Tech-Lab System is installed, the TechLab icon appears on the desktop.

1. Click on the TechLab icon.

2. The student clicks on LOGON and selects his or her name.

3. The student enters his or her password and clicks on OK. (If he or she is creating a password,

four alphanumeric characters must be entered. The system will ask for the password to be

entered again for verification. Keep a record of the students' passwords.)

4. The previous two steps are repeated until all members of the student team have logged on.

Click on Complete and then Yes.

5. When the Available Courses menu appears, students click on the course name.

6. A window with the name of the course and a list of units for that course appears. Students

click on the unit name. The unit title page appears and the students are ready to begin.

Selecting Other Courses and Exiting the Courseware

1. Clicking on Exit when in a unit returns the student to the list of units for that course.

2. If students wish to select another unit, they click on it.

3. If students wish to exit F.A.C.E.T., they click on the X symbol in the upper right corner.

4. If students wish to select another course, they click on the Course Menu button. The

Available Courses menu screen appears. They may also exit F.A.C.E.T. from this screen by

clicking on the LOGOFF button.


2-3

Screen Buttons

If you click on the F.A.C.E.T. logo on the top right of the unit title page the About screen

appears. It acknowledges the copyright holder(s) of video and/or screen-capture material used in

the topic.

The Menu button calls these menus:

when on an exercise menu screen, it calls the Unit Menu.

when on an exercise screen, it calls the Exercise Menu.

when on a unit screen, it calls the Unit Menu.

The Bookmark button marks the current screen. A student can click on the button at any time in

the lesson. The second time the student clicks on the button, the page displayed when the button

was first clicked will return to the screen. Any bookmarks used during a lesson are not saved

when the student logs out of the lesson.

The Application Launch button opens third-party software.

Click on the Resources button to view a pop-up menu. The pop-up menu includes access to a

calculator, a student journal, new terms and words, a print current screen option, the Lab-Volt

authored Internet Website, and a variety of F.A.C.E.T. help screens.

The Help button aids students with system information. On certain screens the Help button

appears to be depressed. On these screens, clicking on the Help button will access Screen Help

windows (context-sensitive help).

The Internet button opens an Internet browser. Students will have unrestricted access to all

search engines and web sites unless the school administration has restricted this usage.

Use the Exit button to exit the course.

The right arrow ⇒ button moves you forward to the next screen.

The left arrow ⇐ button moves you backward to the previous screen.


2-4

F.A.C.E.T. Help Screens and Resources

There are three ways to access F.A.C.E.T. help screens and other resources.

System Help Students access System Help by clicking on the Help button at the bottom of the screen when the

button does not appear to be depressed. The menu selections access a variety of system help,

navigation, and information windows.

Screen Help On certain screens, the Help button appears to be depressed. On these screens, clicking on the

Help button will access Screen Help windows. This is information specific to the content of that

particular screen.

Resources Students click on the Resources button to access the following windows.

Calculator

F.A.C.E.T. 32-Bit Microprocessor Help

F.A.C.E.T. Analog Communications Setup Procedure

F.A.C.E.T. Digital Communications Help

F.A.C.E.T. Electronics and Troubleshooting Help

F.A.C.E.T. Fiber Optic Communications Help

F.A.C.E.T. Math Help

Internet Link

New Terms and Words

Print Current Page

Student Journal


2-5

Internet Access

There are two ways for students to access the Internet:

The Internet button opens an Internet browser. Students have unrestricted access to all search

engines and websites unless the school administration has restricted this usage.

The Resources button pops up a menu that includes access to the Lab-Volt authored Internet

website. If students wish to access this site when they are not in the lesson, then they must go to

http://learning.labvolt.com.

NOTE: The Lab-Volt Internet site does not have content-filtering

software to block access to objectionable or inappropriate

websites.

Instructor Annotation Tool

The annotation tool gives the instructor the ability to add comments or additional information

onscreen. Refer to the Tech-Lab and GradePoint 2020 Installation Guide for detailed

information.

Student Journal

The student journal is an online notebook that each student can access while they are logged into

TechLab. The journal allows students to share notes with other students in their workgroups.

When used in conjunction with GradePoint 2020, the instructor may post messages, review, edit,

or delete any journal note.


2-6

Assessing Progress

Assessment Tools

Student assessment is achieved in several ways:

♦ Exercise questions

♦ Unit tests

♦ Pretest and Posttest

♦ Troubleshooting questions

Exercise and Troubleshooting Questions

Throughout the unit material, exercise discussion, exercise procedure, and troubleshooting

sections there are several types of questions with instant feedback. These questions occur in the

following formats:

♦ Multiple choice

♦ True-false

♦ Real-number entry

In most cases, when your students encounter a question set, they must answer these questions

before continuing. However, there are cases where students may progress to the next screen

without answering the questions. Lab-Volt recommends that you encourage your students to

complete all questions. In this way, students reinforce the material that's presented, verify that

they understand this material, and are empowered to decide if a review of this material is

required.

Review Questions

At the end of each exercise, there are review questions. The student receives feedback with each

entry. Feedback guides the student toward the correct answer.

Unit Tests

A unit test appears at the end of each unit. The test consists of 10 multiple-choice questions with

the option of having feedback. The Tech-Lab System defaults to no feedback, but the instructor

can configure the test so that students receive feedback after taking the test. You can randomize

questions in the unit test. Use the Tech-Lab Global Configurator to make feedback available,

randomize questions, and select other configuration options if desired. Refer to the Tech Lab

Quick-Start Guide for detailed information.


2-7

Pretest and Posttest

Every course includes a pretest and a posttest. These are multiple choice tests. Refer to the Tech

Lab Quick-Start Guide for detailed information on how to record student competency gains.

Grading

Student grades are based on exercise questions, troubleshooting questions, a unit test, and a

posttest. The default weighting value of the unit test and the threshold for passing the unit test

can be adjusted by using the Global Configurator of the Tech-Lab System. Refer to the Tech Lab

Quick-Start Guide for detailed information.

Student Progress and Instructor Feedback

Unit progress is available through the Unit menu. The Progress window allows the instructor and

student to view the percentage of the unit completed, number of sessions, and time spent on that

unit. The Progress window shows whether the Unit Test was completed. If the test was

completed, it indicates whether the student passed based on the scoring criteria.


2-8

Real-Number Questions and Answers

Throughout F.A.C.E.T. courses students may encounter real-number questions such as the one

shown below. Answers to real-number questions are graded correct if they fall within an

acceptable tolerance range.

The answer to the question posed in the illustration above does not involve a recall value from a

previous question. It appears in the Instructor Guide (IG) as shown in the box below.

The information in the IG tells you where the question is located and the range of acceptable

answers. In this case, the acceptable answers fall within the range of the nominal answer plus or

minus 5 percent tolerance: (15 ± 5%).

Location: Exercise Procedure page:

se1p1, Question ID: e1p1a

VS = Vdc

Recall Label for this Question: V1

Nominal Answer: 15.0

Min/Max Value: (14.25) to (15.75)

Value Calculation: 15.000

Correct Tolerance Percent = true

Correct Minus Tolerance = 5

Correct Plus Tolerance = 5

This is the name the computer uses internally

to identify the input value. In this case, 14.5

will be stored under the name V1.

NOTE: The recall value V1 is not the same as

the voltage V1. The recall label does not

appear onscreen.

In this case, the answer to this question is not

based on a value recalled from a previous

question. Therefore, the Value Calculation is

equal to the Nominal Answer.

The word "true" tells you that the tolerance is

calculated as a percent.

e1p1 stands for

Exercise 1 Procedure screen 1

The computer

saves this input

value so that it can

be recalled for use

in later questions.


2-9

A second example (shown below) illustrates an answer that the computer grades using a value

recalled from a previous question.

When a real-number question is based on a recall value from a previous question, the Min/Max

Value shown in the Instructor Guide is based upon a calculation using the lowest and highest

possible recall value. It represents the theoretical range of answers that could be accepted by the

computer. (It is not the nominal answer plus or minus the tolerance.)

To find the actual range of answers that the computer will accept onscreen, you must use the

actual recall value (14.5 in this example) in your calculations; see below.

NOTE: After four incorrect answers, students will be prompted to press <Ins> to insert the

correct answer if this feature has been enabled in the configuration settings. When the question is

based on a value recalled from a previous question, answers obtained using the Insert key may

not match the nominal answers in this guide.

Location: Exercise Procedure page:

se1p5, Question ID: e1p5c

IT = mA

Recall Label for this Question: I1

Nominal Answer: 9.091 *Min/Max Value: (6.477) to (11.93)

Value Calculation: #V1#/1650*1000




Since the value for #V1# is 14.5, the

computer will accept answers in the

following range as correct:

14.5/1650*1000 ± 25% or

8.79 ± 25% or

6.59 to 10.99

This calculated range is different from the

Min/Max Value shown in the IG, which

was based upon a calculation using the

lowest and highest possible recall value.

Any letter enclosed in "#" signs refers to a

recall value from a previous question.


2-10

Recall Values in Text

Sometimes numbers displayed on screen are values recalled from input on previous screens.

Because these numbers are recall values, they will change for each student.

The Instructor Guide lists the recall label in place of a number in this question.

The value of 10

was recalled

from a previous

screen.

Location:Exercise Procedure page: se1p11, Question ID: e1p11c

IR2 = VR2/R2

= #V4#/3.3 kΩ

= mA



Min/Max Value: (2.489) to (3.164)

Value Calculation: #V4#/3.3




This is a

recall label

for a value

recorded in a

previous

question.

The correct

answer will

depend on the

value the student

recorded in the

previous question.


2-11

Safety

Safety is everyone’s responsibility. All must cooperate to create the safest possible working

environment. Students must be reminded of the potential for harm, given common sense safety

rules, and instructed to follow the electrical safety rules.

Any environment can be hazardous when it is unfamiliar. The F.A.C.E.T. computer-based

laboratory may be a new environment to some students. Instruct students in the proper use of the

F.A.C.E.T. equipment and explain what behavior is expected of them in this laboratory. It is up

to the instructor to provide the necessary introduction to the learning environment and the

equipment. This task will prevent injury to both student and equipment.

The voltage and current used in the F.A.C.E.T. Computer-Based Laboratory are, in themselves,

harmless to the normal, healthy person. However, an electrical shock coming as a surprise will

be uncomfortable and may cause a reaction that could create injury. The students should be made

aware of the following electrical safety rules.

1. Turn off the power before working on a circuit.

2. Always confirm that the circuit is wired correctly before turning on the power. If required,

have your instructor check your circuit wiring.

3. Perform the experiments as you are instructed: do not deviate from the documentation.

4. Never touch “live” wires with your bare hands or with tools.

5. Always hold test leads by their insulated areas.

6. Be aware that some components can become very hot during operation. (However, this is not

a normal condition for your F.A.C.E.T. course equipment.) Always allow time for the

components to cool before proceeding to touch or remove them from the circuit.

7. Do not work without supervision. Be sure someone is nearby to shut off the power and

provide first aid in case of an accident.

8. Remove power cords by the plug, not by pulling on the cord. Check for cracked or broken

insulation on the cord.


2-12

SECTION 3 – COURSEWARE

SECTION 3 – COURSEWARE

DC Network Theorems Unit 1 – DC Network Theorems

3-1

UNIT 1 – DC NETWORK THEOREMS

UNIT OBJECTIVE

Locate and identify the major components on the DC NETWORK THEOREMS circuit board.

UNIT FUNDAMENTALS

Location: Unit Fundamentals page: sf3, Question ID: f3a

On what circuit block is the current source used?

a. THEVENIN CIRCUITS circuit block

b. THEVENIN/NORTON CONVERSION circuit block

c. SUPERPOSITION circuit block

CMS AVAILABLE

None

FAULTS AVAILABLE

None

NEW TERMS AND WORDS

constant current source - a circuit designed to provide a fixed current that does not vary with

changes in load.

theorems - statements or methods that propose verifiable solutions of voltage and/or current

within a network.

networks - groups of components that form interrelated circuits.

EQUIPMENT REQUIRED

F.A.C.E.T. base unit

DC NETWORK THEOREMS circuit board

Multimeter


3-2

Exercise 1 – Component Location/Identification

EXERCISE OBJECTIVE

Locate the major circuit blocks of the DC NETWORK THEOREMS circuit board. Verify results

by correctly identifying circuits and components.

EXERCISE DISCUSSION

Location: Exercise Discussion page: se1d3, Question ID: e1d3a

Find the ∆ TO Y or Y TO ∆ (DELTA TO WYE or WYE TO DELTA) circuit block on the DC

NETWORK THEOREMS circuit board. Is power required for this block?

a. yes

b. no

EXERCISE PROCEDURE

Location: Exercise Procedure page: se1p1, Question ID: e1p1a

1. Locate the KIRCHHOFF'S CURRENT LAW circuit block. The resistors in this circuit can be

configured in

a. series.

b. parallel.

c. series/parallel.


R1 = kΩ

Recall Label for this Question: None

Nominal Answer: 1.8

Min/Max Value: (1.8) to (1.8)






3-3


3. The resistors used on the KIRCHHOFF'S VOLTAGE LAW circuit block are connected in

a. series.

b. parallel.

c. series/parallel.


4. Which circuit block is configured with resistors connected as shown?

a. KIRCHHOFF'S VOLTAGE LAW circuit block

b. KIRCHHOFF'S CUR RENT LAW circuit block

c. THEVENIZING A BRIDGE CIRCUIT circuit block


5. How many circuit blocks use fixed voltage sources?

a. 3

b. 4

c. 5

d. All of the circuit blocks use a fixed voltage source.


6. Locate the THEVENIZING A BRIDGE CIRCUIT circuit block. What multimeter

measurements can you make for R5?

a. current

b. voltage

c. resistance

d. Any of the above.


7. How many different types of networks are there in the ∆ TO Y or Y TO ∆ (DELTA TO WYE

or WYE TO DELTA) circuit block?

a. 2

b. 3

c. 4


8. What does this symbol on the THEVENIN/NORTON CONVERSION circuit block represent?

a. a current source

b. a voltage source

c. total resistance


3-4


9. This resistor configuration is a

a. T network.

b. Y network.

c. π network.

d. DELTA network.


10. What F.A.C.E.T. component must you use to connect R3 of the SUPERPOSITION circuit

block to its power sources?

a. a terminal post

b. an interconnecting lead

c. a two-post connector

REVIEW QUESTIONS

Location: Review Questions page: se1r1, Question ID: e1r1

1. How many Kirchhoff's circuit blocks are on the circuit board?

a. 2

b. 3

c. 4

d. 5


2. The symbol similar to this one on the THEVENIN/NORTON CONVERSION circuit block

represents a

a. constant current source.

b. constant voltage source.

c. variable current source.

d. None of the above.


3. With two-post connectors inserted as shown here,

a. both power sources supply power to the network.

b. V2 is the only power source in the network.

c. V1 can be used to cancel the effect of V2.

d. current does not flow in the network.


3-5


4. This circuit is located in the

a. SUPERPOSITION circuit block.

b. KIRCHHOFF'S CURRENT LAW circuit block.

c. THEVENIN CIRCUITS circuit block.

d. THEVENIN/NORTON CONVERSION circuit block.


5. If you connect a multimeter across points A and D of the T NETWORK circuit block, what

are you measuring?

a. resistance of R1 and R2

b. voltage drop of R1 and R2

c. current through R1 and R2

d. resistance or voltage drop of R1 and R2

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-6

Exercise 2 – Circuit Board Operation

EXERCISE OBJECTIVE

Connect the various circuit blocks on the circuit board by using the KIRCHHOFF'S CURRENT

LAW circuit block as an example. Verify results with a multimeter.

EXERCISE DISCUSSION


What determines the circuit configuration of the KIRCHHOFF'S CURRENT LAW circuit block

with respect to R1, R2, and the power supply?

a. test leads

b. terminal posts

c. two-post connectors

EXERCISE PROCEDURE


VS = Vdc



Min/Max Value: (14.55) to (15.45)





Location: Exercise Procedure page: se2p2, Question ID: e2p2c

R1 = Ω



Min/Max Value: (1440) to (2160)






3-7

Location: Exercise Procedure page: se2p2, Question ID: e2p2e

R2 = Ω









4. What should the voltage drop across R1 or R2 be?

a. the same as VS

b. 0V


VR1 or VR2 = Vdc


Nominal Answer: 0.0







6. Do your measurements indicate an open path to R1 or R2?

a. yes

b. no


IR1 = mA


Nominal Answer: 8.3

Min/Max Value: (6.225) to (10.38)






3-8

Location: Exercise Procedure page: se2p4, Question ID: e2p4g

8. Why does current flow through R1?

a. because a two-post connector was added at VS

b. because a current meter was added at R1

Location: Exercise Procedure page: se2p4, Question ID: e2p4i

9. With the present test circuit connections, does current flow through R2?

a. yes

b. no


10. How can you cause current to flow through R2?

a. Place a two-post connector at the top of R2.

b. Connect a current meter at the top of R2.

c. Either of the above.

REVIEW QUESTIONS


1. Measure total circuit current by removing the two-post connector and replacing it with a meter

in position

a. A.

b. B.

c. C.

d. D.


2. Measure total circuit voltage by placing a meter in position

a. A.

b. B.

c. C.

d. D.


3. The meter in position C (with the two-post connector removed) indicates

a. maximum circuit current.

b. R1 current.

c. R2 current.

d. the combined current of R1 and R2.


3-9


4. Measure the voltage drop of R1 or R2 with a meter placed in position

a. A.

b. B.

c. C.

d. D.


5. For this circuit, how many two-post connectors are required to obtain maximum circuit

current?

a. 4

b. 3

c. 2

d. 1

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-10

UNIT TEST

Depending on configurator settings, these questions may be randomized onscreen.

Location: Unit Test Question page: sut1, Question ID: ut1

The measurement(s) required on the DC NETWORK THEOREMS circuit board is (are)

a. voltage.

b. voltage and current.

c. voltage, current, or resistance.

d. resistance.


The current source required in the THEVENIN/NORTON CONVERSION circuit block

a. must be externally supplied.

b. is available on the circuit board.

c. is student adjustable.

d. generates a constant voltage.


A network is a group of components that

a. are not related.

b. are exactly the same.

c. share a common circuit.

d. are in series.


Constant current sources

a. have very low output impedances.

b. vary the amount of current generated when the load changes.

c. cannot be operated into open circuits.

d. are load independent.


Network theorems are required because

a. Ohm's law cannot easily be applied to all circuits.

b. Ohms law can easily be applied to all circuits.

c. circuits will not operate without them.

d. Ohm's law cannot provide reliable results in series/parallel circuits.


3-11


The 3 resistor types on the circuit board

a. have equal tolerances.

b. can be distinguished by color code values.

c. are carbon composition, carbon film, and metal film types.

d. have equal power dissipation ratings.


On the DC NETWORK THEOREMS circuit board, which type of power source is used?

a. fixed voltage source

b. variable voltage source

c. fixed and variable voltage sources

d. no voltage sources


Which of the following should be used to configure branches within the circuit blocks of the DC

NETWORK THEOREMS circuit board?

a. two-post connectors

b. solid wire jumpers

c. terminal posts



When you measure resistance on the DC NETWORK THEOREMS circuit board,

a. circuit power should be maximum.

b. circuit power should be disconnected.

c. circuit power should be minimum.

d. meter polarity is important.


When you measure voltage or current on the DC NETWORK THEOREMS circuit board,

a. meter polarity does not matter.

b. voltage polarity is the same for any meter connection.

c. current flow through a circuit changes direction with an improper meter connection.

d. meter polarity determines the "correctness" of the indication.


3-12

DC Network Theorems Unit 2 – Kirchhoff’s Current Law

3-13

UNIT 2 – KIRCHHOFF’S CURRENT LAW

UNIT OBJECTIVE

Analyze dc circuits by using Kirchhoff's current law.

UNIT FUNDAMENTALS


What does the total circuit current equal?

a. sum of both branch currents (CURRENT 1 + CURRENT 2)

b. current through either branch (CURRENT 1 or CURRENT 2)


Total circuit current is the current through branch

a. R1.

b. R2.

c. R1 and branch R2.


How many branches are there at each node in this parallel branch circuit?

a. 1

b. 2

c. 3

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-14

NEW TERMS AND WORDS

Kirchhoff's current law - the algebraic sum of the currents at any node must equal zero.

junction - a circuit point where components are joined.

parallel branch - a circuit loop through which a part of the total circuit current flows.

nodes - circuit points where Kirchhoff's current law can be applied; also called junctions.

junction - a circuit point where components are joined.

algebraic sum - a combination of positive and negative values based on the rules of algebra.

EQUIPMENT REQUIRED



Multimeter


3-15

Exercise 1 – Current in a Branch Circuit

EXERCISE OBJECTIVE

Calculate total and individual branch currents in a two-element parallel circuit by using

Kirchhoff's current law. Verify results by measuring the circuit currents

EXERCISE DISCUSSION

No Questions

EXERCISE PROCEDURE


VS = Vdc

Recall Label for this Question: v1


Min/Max Value: (14.55) to (15.45)






R1 = Ω









3-16


R2 = Ω









IR1 = mA

Recall Label for this Question: i1

Nominal Answer: 8.333 ∗Min/Max Value: (7.275) to (9.442)

Value Calculation: (#v1#/1800)*1000





IR2 = mA







∗ NOTE: Min/Max Values shown are based upon a calculation using the absolute

lowest and highest recall value. By using the actual input in your calculations, you

will determine the correct value.


3-17


IT = mA


Nominal Answer: 15.15 ∗Min/Max Value: (11.9 ) to (18.88)

Value Calculation: #i1#+#i2#





IR1 = mA



Min/Max Value: (6.664) to (9.996)






IR2 = mA



Min/Max Value: (5.456) to (8.184)









3-18


IT = mA








11. Do your calculated and measured values agree within tolerance?

a. yes

b. no


IR1 = mA


Nominal Answer: 8.332 *Min/Max Value: (4.05 ) to (13.32)

Value Calculation: (#i3#–#i2#)





13. Does Kirchhoff's current law support the results you obtained from Ohm's law?

a. no

b. yes





3-19

REVIEW QUESTIONS

Location: Review Questions page: se1r1, Question ID: e1r1a

IT = mA

Recall Label for this Question: r1i1








If IR2 is 6.8 mA, what is the value of IR1?

a. 25.8 mA

b. # r1i1 – 6.8 # mA

c. 6.8 mA

d. 1.22 mA


2. If IR1 is # r1i1 – 6.8 # mA (with CM 1 activated) and the source voltage (VS) is 15.00 Vdc,

what is the present value of R1 in this circuit?

a. approximately 12.0 kΩ b. 15 / # ( r1i1 – 6.8 )# Ω c. approximately 12Ω

d. cannot be determined


3. If the CM switch decreases the value of R1, total circuit current

a. changes, but the branch currents remain the same.

b. and both branch currents change.

c. decreases while IR2 does not change.

d. increases while IR2 does not change.


3-20


4. The branch currents of this circuit

a. should be added to determine total current.

b. should be subtracted to determine total current.

c. are not correct because of the circuit modification.

d. do not equal the total circuit current.


5. If a third branch (R3) were added to the circuit, what would be the total circuit current?

a. IR1 + IR2 – IR3

b. IR1 + IR2 + IT

c. IR1 + IR2 + IR3


CMS AVAILABLE

CM 1

CM 1 TOGGLE

FAULTS AVAILABLE

None


3-21

Exercise 2 – Node Currents in a Branch Circuit

EXERCISE OBJECTIVE

Determine the magnitude and direction (sign) of node currents by using a two-element branch

circuit. Verify results by measuring the circuit currents.

EXERCISE DISCUSSION


Another way to state Kirchhoff's current law is that when all of the node currents are combined,

the total positive current must equal

a. zero.

b. half the negative current.

c. the total negative current.


How much more current must flow out of the node to satisfy Kirchhoff's current law?

a. 1.0A

b. 1.5A

c. 2.5A


3-22

EXERCISE PROCEDURE


VS = Vdc



Min/Max Value: (14.25) to (15.75)






IR1 = mA








IR2 = mA











3-23


IT (Kirchhoff's) = mA








6. Based on your results, is the current entering the circuit node equal to the current leaving the

circuit node?

a. yes

b. no


IT (calculated) = mA


Nominal Answer: 15.15 *Min/Max Value: (13.67) to (16.7 )

Value Calculation: (.00101*#v2#)*1000





8. Does the answer you calculated agree with the total current determined by Kirchhoff's current

law?

a. yes

b. no





3-24

REVIEW QUESTIONS


IR2 = mA


Nominal Answer: 6.8







The current out of the node

a. increases.

b. remains the same.

c. decreases.



2. With CM 2 still activated, the value of R2 is

a. 1.1 kΩ.

b. 2.2 kΩ.

c. 4.4 kΩ.

d. cannot be determined.


3. Total circuit current (IT) is 11.7 mA, and IR1 is 8.32 mA. What is the value of IR2?

a. 20.02 mA

b. 3.38 mA

c. 8.32 mA



4. When the resistance of R2 decreases, the node current

a. increases.

b. remains the same.

c. decreases.



3-25


5. Kirchhoff's current law, as applied to parallel circuits such as this one, states that

a. IT, IR1, and IR2 are not related because of a common power source.

b. VS must not change if either VR1 or VR2 changes.

c. the currents of NODE 1 and NODE 2 need not be equal.

d. the currents of NODE 1 and NODE 2 must be equal.

CMS AVAILABLE

CM 2 TOGGLE

CM 2

FAULTS AVAILABLE

None


3-26

UNIT TEST



In this circuit, total circuit current (IT)

a. cannot be determined.

b. equals the current of either circuit node.

c. equals the sum of the branch currents.

d. does not change if node current changes.


Which statement defines the current out of NODE 1?

a. IR1 + IR2 + IR3

b. IR2 + IR3

c. IT – (IR2 + IR3)

d. IT + (IR2 + IR3)


Which statement defines the current into NODE 2?

a. IR1 + IR2 + IR3

b. IT – IR1

c. IT – (IR2 + IR3)

d. IT + (IR2 + IR3)


Which statement defines the current out of NODE 2?

a. IR1 + IR2 + IR3

b. IR2 + IR3

c. IT – (IR2 + IR3)

d. IT + (IR2 + IR3)


In this circuit, IT enters NODE 1. What part of IT does not go through NODE 2?

a. IR3

b. IR2

c. IR1



3-27


The current through NODE 2 is

a. greater than the current through NODE 1.

b. less than the current through NODE 1.

c. equal to the current through NODE 1.

d. equal to the current from the power source.


In this circuit, the respective branch currents are

a. 10 mA, 5 mA, and 5 mA.

b. 5 mA, 10 mA, and 10 mA.

c. 10 mA, 5 mA, and 10 mA.

d. 10 mA, 10 mA, and 10 mA.


If R2 in this circuit increases in value, IR2 decreases and NODE 1 current

a. increases.

b. does not change.

c. decreases.

d. cannot be determined unless the amount of increase in R2 is specified.


Using Ohm's law and/or Kirchhoff's current law for parallel circuits, IT in this circuit


b. is 5 mA.

c. is 10 mA.

d. is 20 mA.


The current into NODE 2 is 10 mA; therefore, current out of NODE 2

a. must be less than 10 mA.

b. must be greater than 10 mA.

c. must be 10 mA.



3-28

TROUBLESHOOTING

Location: Troubleshooting page: ttrba2, Question ID: trba2a

IT = mA

Recall Label for this Question: it


Min/Max Value: (13.64) to (16.67)






3. Does the total current (#it# mA) equal the sum of the branch currents?

a. yes

b. no


4. Does the voltage across each branch equal the source voltage?

a. no

b. yes

Location: Troubleshooting page: ttrba5, Question ID: trba5

6. The faulty component is

a. VS1 (out of specification).

b. R1 (lower than specified minimum value).

c. R2 (lower than specified minimum value).

d. R1 (open).

CMS AVAILABLE

None

FAULTS AVAILABLE

Fault 1

DC Network Theorems Unit 3 – Kirchhoff’s Voltage Law

3-29

UNIT 3 – KIRCHHOFF’S VOLTAGE LAW

UNIT OBJECTIVE

Analyze dc circuits by using Kirchhoff's voltage law.

UNIT FUNDAMENTALS


The circuit current (IT) in this closed series circuit is

a. different in each circuit element.

b. common to each circuit element.


How may Kirchhoff's voltage law be stated?

a. The sum of all the voltage drops in a series circuit equals the circuit applied (source) voltage.

b. The algebraic sum of the voltage source(s) and voltage drops in a series circuit equals zero.

c. Both of the above.


In this circuit, if the source voltage is 9V and two of the voltage drops are 4V and 3V, what is the

third drop?

a. 1V

b. 2V

c. 7V

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-30

NEW TERMS AND WORDS

Kirchhoff's voltage law - The algebraic sum of the voltages around a closed loop must equal

zero. The sum of the voltage drops around a closed loop must equal the source voltage.

closed loop - A complete path or circuit for current flow.

EQUIPMENT REQUIRED



Multimeter


3-31

Exercise 1 – 3-Element Series Voltages

EXERCISE OBJECTIVE

Calculate total voltage and individual voltage drops by using a 3-element series circuit. Verify

results with a multimeter.

EXERCISE DISCUSSION


Can you use Kirchhoff's voltage law for any number of elements in a series circuit?

a. yes

b. no

EXERCISE PROCEDURE


VS = Vdc



Min/Max Value: (14.25) to (15.75)






3-32


IT = mA



Value Calculation: # ( V1 / 1480 ) * 1000 #





VR1 = Vdc



Value Calculation: # ( I1 * 220 ) / 1000 #





VR2 = Vdc











3-33


VR3 = Vdc








Do your results prove that the sum of the voltage drops about equals the source voltage

(VS #V1# Vdc)?

a. yes

b. no


8. Do your results indicate that Ohm's law and Kirchhoff's voltage law can be applied for a

circuit solution?

a. no

b. yes


Based on this equation, which formula can you use to calculate the value of VR2?

a. VR2 = VS – VR1 – VR3

b. VR2 = VS – (VR1 + VR3)






3-34


VR2 (calculated) = Vdc


Nominal Answer: 5.164 ∗Min/Max Value: (2.933) to (7.5 )

Value Calculation: # V1 – V2 – V4 #





VR2 (measured) = Vdc



Value Calculation: #V3#





12. Does your measured value agree with your calculated results, within tolerance?

a. no

b. yes


VR1 = Vdc











3-35


VR2 = Vdc








VR3 = Vdc



Value Calculation: # ( I1 * 750) / 1000 #





14. Does the sum of your measured voltage drops equal the value of your circuit voltage source?

a. no

b. yes





3-36

REVIEW QUESTIONS


Based on Kirchhoff's voltage law, the sum of the voltage drops

a. is greater than the source voltage.

b. does not change because the source voltage does not change.

c. is less than the source voltage.

d. can no longer be determined.


Based on Kirchhoff's law, the sum of the voltage drops

a. is greater than the source voltage.

b. does not change because the source voltage does not change.

c. is less than the source voltage.

d. can no longer be determined.


3. When you change the value of R3, the sum of the voltage drops does not change because the

source voltage

a. increases.

b. does not change.

c. decreases.



4. Using Kirchhoff's law, what is the voltage drop across R2 (VR2)?

a. 15V

b. 10V

c. 5V



5. Which statement correctly uses Kirchhoff's voltage law to explain this circuit?

a. VS = VR1 – VR2 + VR3 + VR4

b. VS = VR2 – (VR1 + VR3 + VR4)

c. VS = VS + VR2 – (VR1 + VR3 + VR4)

d. VS = VR1 + VR2 + VR3 + VR4


3-37

CMS AVAILABLE

CM 4 TOGGLE

CM 3 TOGGLE

FAULTS AVAILABLE

None


3-38

Exercise 2 – Algebraic Sum of Series Voltages

EXERCISE OBJECTIVE

Calculate the algebraic sum of voltage drops by using a 3-element series circuit. Verify results

with a multimeter.

EXERCISE DISCUSSION


In this circuit, which equation is correct for determining VR1?

a. VR1 = VS – VR2 – VR3

b. VR1 = VS – (VR2 + VR3)

c. Neither a. nor b.

d. Both a. and b.

EXERCISE PROCEDURE


VS = Vdc



Min/Max Value: (14.55) to (15.45)






3-39


VR1 = Vdc


Nominal Answer: –2.23 ∗Min/Max Value: (–2.53) to (–1.94)

Value Calculation: –# ( V21 / 1480 ) * 220 #





VR2 = Vdc


Nominal Answer: –5.17 *Min/Max Value: (–5.86) to (–4.51)






VR3 = Vdc











3-40


VR1 + VR2 + VR3 = Vdc


Nominal Answer: –15.0 ∗Min/Max Value: (–17. ) to (–13.01)

Value Calculation: # V21 * –1 #





Your result is closest to

a. 0.0 Vdc.

b. 15.00 Vdc.

c. 30.00 Vdc.

REVIEW QUESTIONS


CM 3 is now activated to decrease the resistance of R2. What is the sum of the circuit voltage

drops?

a. 20V

b. 15V

c. 10V



2. By applying Ohm's law and Kirchhoff's voltage law to this circuit, you determine that the

approximate value of R2 is

a. 44,200Ω.

b. 4420Ω.

c. 442Ω.

d. not changed by the circuit modification.





3-41


3. The polarity of the voltage source in your circuit

a. should be the same as that of the voltage drops.

b. cannot be determined.

c. should be opposite to that of the voltage drops.

d. is not needed for an algebraic summation.


4. In this circuit, what is the value of R1?

a. 1 kΩ b. 10 kΩ c. 3 kΩ d. Cannot be determined.


5. In this circuit, what is the voltage drop of R2?

a. 50 Vdc

b. 25 Vdc

c. 15 Vdc

d. 10 Vdc

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-42

UNIT TEST



In a closed loop such as this one, Kirchhoff's voltage law states that the sum of the voltage drops

a. must be greater than the circuit source voltage.

b. must equal the circuit source voltage.

c. must be less than the circuit source voltage.

d. cannot be determined unless circuit current is known.


In a closed loop such as this one, Kirchhoff's voltage law states that the circuit source voltage

a. must be greater than the sum of the voltage drops.

b. must equal the sum of the voltage drops.

c. must be less than the sum of the voltage drops.

d. cannot be determined unless circuit current is known.


In a closed loop, the algebraic sum of the circuit voltages

a. cannot be determined without circuit current.

b. must not equal zero if current flows in the loop.

c. varies depending on the source voltage.

d. equals zero for any value of source voltage.


Which equation defines Kirchhoff's voltage law?

a. VS = VR1 + VR2

b. 0 = VS – (VR1 + VR2)




A series circuit consists of 3 elements and a voltage source. If the source voltage and the voltage

drops of 2 elements are known, the voltage drop of the third element


b. is zero.

c. can be determined from Kirchhoff's voltage law.

d. must equal the voltage drop of the other elements.


3-43


Kirchhoff's voltage law proves that

a. Ohm's law is not accurate for series circuits.

b. Ohm's law can define the operation of a series circuit.

c. current and resistance cannot be used to determine a voltage drop.



If your calculations indicate that the algebraic sum of the voltages in your circuit is greater or

less than zero,

a. modify the circuit.

b. increase the voltage source.

c. decrease the voltage source.

d. check your calculations.


In order for you to apply Kirchhoff's voltage law to a circuit, the source voltage

a. must be zero.

b. must be positive.

c. must be negative.

d. may be positive or negative.


What is the value of each element?

a. 0.5Ω b. 1Ω c. 1.5Ω d. None of the above.


In this circuit, the source voltage is doubled. Based on Kirchhoff's voltage law,

a. the sum of the voltage drops must increase.

b. the sum of the voltage drops does not change.

c. the sum of the voltage drops must decrease.

d. more resistance must be added to the circuit.


3-44

TROUBLESHOOTING


IT = mA



Min/Max Value: (9.126) to (11.15)






3. Does the sum of the voltage drops equal VS?

a. yes

b. no


4. Does the algebraic sum of the voltages equal zero?

a. yes

b. no



a. R1 (increased).

b. R2 (increased).

c. R2 (decreased).

d. R3 (decreased).

CMS AVAILABLE

None

FAULTS AVAILABLE

Fault 2

DC Network Theorems Unit 4 – Kirchhoff’s Loop Equations

3-45

UNIT 4 – KIRCHHOFF’S LOOP EQUATIONS

UNIT OBJECTIVE

Use loop equations by applying Kirchhoff's laws to a series/parallel circuit.

UNIT FUNDAMENTALS


What is the loop equation for this loop?

a. VR1 + VRS = VS

b. VR2 + VRS = VS


For Kirchhoff's current law, which basic node equation is correct?

a. Inode in = Inode out

b. Inode out – Inode in = 0


CMS AVAILABLE

None

FAULTS AVAILABLE

None

NEW TERMS AND WORDS

None

EQUIPMENT REQUIRED



Multimeter


3-46

Exercise 1 – Loop Equations

EXERCISE OBJECTIVE

Use loop equations for a series/parallel circuit. Verify results by measuring voltage drops and

calculating equations.

EXERCISE DISCUSSION


Do the values show that Kirchhoff's voltage law for each loop equation is satisfied?

a. yes

b. no


Do the voltage values applied to the loop equations still result in zero?

a. no

b. yes

EXERCISE PROCEDURE


VS = Vdc



Min/Max Value: (14.25) to (15.75)






The first loop includes

a. R3, R2, and R1.

b. R6, R5, and R4.

c. R3, R2, R1, and VS.


3-47


5. The second loop includes

a. R3, R2, and R1.

b. R6, R5, R4, and VS.

c. R6, R5, R4, and R2.


7. The third loop includes

a. R3, R6, R5, R4, R1, and VS.

b. R3, R6, R5, R4, R2, and VS.

c. R3, R2, R5, and R1.


9. All current from the voltage source goes out through R3 and returns through

a. R2.

b. R5.

c. R1.


IT = mA



Value Calculation: #V1#/1650*1000








3-48


VR1 = Vdc



Value Calculation: #I1#*270/1000





VR3 = Vdc



Value Calculation: #I1#*680/1000





13. Which loop equation can be used to determine VR2, based on Kirchhoff's law and the known

loop values?

a. VR2 = VS + VR1 + VR3

b. VR2 = VS – (VR1 + VR3)

c. VR2 = VS – (VR6 + VR4)





3-49


VR2 = VS – (VR1 + VR3)

= Vdc



Value Calculation: # V1 – ( V2 + V3 ) #





VR2 = Vdc








16. Are the calculated and measured values of VR2 the same within tolerance?

a. no

b. yes





3-50

REVIEW QUESTIONS


VS = Vdc

Recall Label for this Question: VR1


Min/Max Value: (14.25) to (15.75)





Location: Review Questions page: se1r1, Question ID: e1r1c

VR1 = Vdc



Value Calculation: (#VR1#/2090)*270




Location: Review Questions page: se1r1, Question ID: e1r1e

VR2 = Vdc


Nominal Answer: 5.3










3-51


1. What is the new value of VR3 based on your measurements and the loop equation?

a. # VR1 – ( VR2 + VR3 )#V

b. #VR3#V

c. #VR2#V



What is the voltage across R5?

a. 2.5V

b. 3V

c. 7V

d. 8V


Therefore, the voltage drops of R1 and R2

a. are not affected by the change in R3.

b. remain the same.

c. cannot be determined.

d. must change.


4. What law(s) may you use to analyze the voltages within the loop composed of VS, R1, R2,

and R3?

a. Ohm's law

b. Kirchhoff's law




What is the polarity of R2?

a. negative at point A and positive at point B

b. positive at point A and negative at point B

c. negative at point A and at point B

d. positive at point A and at point B


3-52

CMS AVAILABLE

CM 8 TOGGLE

FAULTS AVAILABLE

None


3-53

Exercise 2 – Node Equations

EXERCISE OBJECTIVE

Generate node equations for a series/parallel circuit. Verify results by measuring voltage drops

and ensuring that the loop equations equal zero.

EXERCISE DISCUSSION


In this circuit, if you know IT and I1, can you calculate I2?

a. yes

b. no

EXERCISE PROCEDURE


VS = Vdc



Min/Max Value: (14.25) to (15.75)






3-54


VR3 = Vdc



Value Calculation: (#V21#/1702)*680





IT = mA


Nominal Answer: 8.813 *Min/Max Value: (6.782) to (11.2 )






VR1 = Vdc



Value Calculation: (#I21#*270)/1000








3-55


VR2 = Vdc



Value Calculation: # V21 – ( V22 + V23 ) #





5. Does the current flowing through R2 move into or out of NODE 2?

a. into NODE 2

b. out of NODE 2


IR2 = mA








IR6 = mA


Nominal Answer: 4.395 *Min/Max Value: ( –.14) to (9.365)

Value Calculation: #I21#–#I22#








3-56


8. Knowing IR6, can you use Ohm's law to determine the voltage drops of R6, R5, and R4?

a. no

b. yes


VR6 = Vdc


Nominal Answer: 3.604 ∗Min/Max Value: ( –.13) to (8.447)






VR5 = Vdc








VR4 = Vdc











3-57


10. Does the sum of the voltages and VR2 result in 0V for the loop?

a. yes

b. no


11. Based on your observation, can Kirchhoff's laws be combined with Ohm's law to solve for

unknowns in a series/parallel circuit?

a. no

b. yes

REVIEW QUESTIONS


1. In this circuit, I1

a. moves into NODE 1.

b. moves out of NODE 1.

c. must be zero.

d. equals IT + I1.


2. The current into NODE 2 equals

a. IT – I2.

b. IT + I1.

c. I1 + I2.

d. I2 + IT.


VR5 = Vdc



Min/Max Value: (1.863) to (2.277)






3-58


3. The I2 current out of NODE 1

a. increases.

b. decreases.

c. remains the same.



4. Since activating CM 9 increases I2, the I1 current out of NODE 1

a. increases.

b. does not change.

c. decreases.



5. If the current flowing into a node is 180 mA, all of the current flowing out of the node, based

on Kirchhoff's law, is

a. less than 180 mA.

b. greater than 180 mA.

c. less or greater than 180 mA.

d. equal to 180 mA.

CMS AVAILABLE

CM 9 TOGGLE

FAULTS AVAILABLE

None


3-59

UNIT TEST



Which diagram correctly shows node current?

a. A

b. B

c. C

d. D


A loop can be defined as

a. any circuit path, closed or opened.

b. a closed circuit path.

c. an open circuit path.

d. a voltage source.


A node represents a circuit point where

a. voltages are combined.

b. resistances are combined.

c. currents are combined.

d. charge must accumulate.


When you use Kirchhoff's laws, algebraic signs are

a. required.

b. not required.

c. required for voltage only.

d. required for current only.


In this circuit, the

a. voltage drops are greater than the voltage source.

b. voltage drops are less than the voltage source.

c. given equation does not specify the circuit.

d. given equation specifies the circuit.


3-60


In this circuit, IB

a. flows out of NODE 1.

b. flows into NODE 1.

c. equals IT.

d. does not flow into NODE 2.


In this circuit, IC

a. equals IB.

b. equals IA.

c. equals IT.

d. flows into NODE 2.


The value of IB equals

a. IT + IA.

b. IT – IA.

c. IT.

d. IB + IA.


The missing voltage is

a. 10V.

b. 5V.

c. 1V.



The current through R3

a. can flow in either direction.

b. can flow in only one direction.

c. is zero because the circuit loops cancel.

d. is zero because the circuit loops combine.


3-61

TROUBLESHOOTING


IT = mA

Recall Label for this Question: TSIT1


Min/Max Value: (7.929) to (9.691)





Location: Troubleshooting page: ttrba2, Question ID: trba2c

VR2 = V

Recall Label for this Question: TSV1


Min/Max Value: (5.967) to (7.293)






3. Does the total circuit current (#TSIT1# mA) flow through R2?

a. yes

b. no


4. Does the sum of VR3, VR2, and VR1 equal VS?

a. yes

b. no



a. R1 (shorted).

b. R2 (open).

c. R4 (shorted).

d. R6 (increased).


3-62

Location: Troubleshooting page: ttrbb2, Question ID: trbb2a

IT = mA

Recall Label for this Question: TSIT2


Min/Max Value: (7.929) to (9.691)





Location: Troubleshooting page: ttrbb2, Question ID: trbb2c

VR2 = V

Recall Label for this Question: TSV2


Min/Max Value: (5.967) to (7.293)





Location: Troubleshooting page: ttrbb3, Question ID: trbb3


a. R1 (shorted).

b. R2 (open).

c. R4 (shorted).

d. R6 (increased).

CMS AVAILABLE

None

FAULTS AVAILABLE

Fault 4

Fault 6

DC Network Theorems Unit 5 – Kirchhoff’s Solution with 2 Sources

3-63

UNIT 5 – KIRCHHOFF’S SOLUTION WITH 2 SOURCES

UNIT OBJECTIVE

Find voltage and current in circuits with two voltage sources by using Kirchhoff's laws. Verify

results by comparing measured and calculated values.

UNIT FUNDAMENTALS


If you make an incorrect assumption, what can you do to make the circuit solution correct?

a. Recalculate the currents.

b. Reverse the direction of assumed current flow through R3.


How many nodes are in this circuit?

a. 1

b. 2

c. 3


Can you check the solutions generated by these methods by ensuring that the voltage drops

and/or currents follow Kirchhoff's laws?

a. no

b. yes

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-64

NEW TERMS AND WORDS

nodes - common connections for two or more components.

mesh - a single closed path without any branches.

mesh equations - equations that define the current within a mesh

loop equations - equations that define the voltage drops around a closed loop.

EQUIPMENT REQUIRED



Multimeter


3-65

Exercise 1 – Kirchhoff's Voltage Law/2 Sources

EXERCISE OBJECTIVE

Apply Kirchhoff's voltage law to a circuit having two voltage sources. Verify results by using

measured data.

EXERCISE DISCUSSION


What is the third loop composed of?

a. VS1, R3, and R1

b. VS2, R3, and R2

c. VS1, R1, R2, and VS2


What is the LOOP 2 equation?

a. VS1 – VR3 – VR1 = 0

b. VS2 – VR2 + VR3 = 0


3-66

EXERCISE PROCEDURE


VS1 = Vdc









VS2 = Vdc









4. VS1, R1, and R3 form which loop in this circuit?

a. LOOP 1

b. LOOP 2


5. VS2, R2, and R3 form which loop in this circuit?

a. LOOP 1

b. LOOP 2


6. The third loop is composed of

a. LOOP 1 and LOOP 2.

b. VS1, R1, R2, and VS2.


3-67


VR1 = Vdc









VR2 = Vdc



Min/Max Value: (12.84) to (19.26)






VR3 = Vdc









3-68


VLOOP 1 = Vdc


Nominal Answer: 0.0 ∗Min/Max Value: (–2.53) to (2.53)

Value Calculation: #v1#–#v5#–#v3#





VLOOP 2 = Vdc


Nominal Answer: 0.0 *Min/Max Value: (–5.19) to (5.19)

Value Calculation: # v4 – v2 – v5 #





13. Do your calculations agree with Kirchhoff's voltage law?

a. no

b. yes


14. Does Kirchhoff's voltage law apply to a circuit with two voltage sources?

a. no

b. yes





3-69

REVIEW QUESTIONS


How many loops are in this circuit?

a. 4

b. 3

c. 2

d. 1


2. CM 17 is now activated to change the value of R1. Using the VS2, R2, and R3 circuit loop,

with VS2 = 10V and VR2 = 15.22 Vdc, what is VR3?

a. +5.22V

b. –5.22V




3. Measure the voltage drops of your circuit. With respect to circuit common, the voltage drop of

R3

a. does not depend on the circuit values.

b. is negative.

c. is positive.



4. Which figure represents the polarities of each voltage drop on the KIRCHHOFF SOLUTION

WITH 2 SOURCES circuit block?

a. A

b. B

c. C

d. D


5. With respect to circuit common, the voltage drop of R3 in this circuit

a. is positive.

b. is negative.

c. depends on the resistor values.



3-70

CMS AVAILABLE

CM 17

FAULTS AVAILABLE

None


3-71

Exercise 2 – Kirchhoff's Current Law/2 Sources

EXERCISE OBJECTIVE

Apply Kirchhoff's current law to a circuit having two voltage sources. Verify results by using

measured data.

EXERCISE DISCUSSION


Which equation is correct?

a. IR1 = VR1 /R1

b. IR2 = VR2 /R2

c. IR3 = VR3 /R3

d. All of the above.


With what Kirchhoff's law(s) can you check your solutions?

a. The sum of the voltages in any circuit loop equals zero.

b. The current into any circuit node equals the current out of the same node.



3-72

EXERCISE PROCEDURE


VS1 = Vdc









VS2 = Vdc









3. Based on the assumed current direction given in this circuit, what is the current formula for

NODE 1?

a. IR1 = IR3 + IR2

b. IR3 = IR1 + IR2

c. IR3 = IR1 – IR2


4. In this circuit, the voltage drop across which resistor allows for a complete circuit solution?

a. R1

b. R2

c. R3


3-73


VR3 = Vdc









6. Based on your measurement, is the voltage at NODE 1 positive or negative with respect to

circuit common?

a. positive

b. negative


7. Based on your measurement and polarity of VR3, is the assumed current flow correct?

a. no

b. yes


IR3 = mA


Nominal Answer: 0.807 ∗Min/Max Value: ( .581) to (1.065)









3-74


IR1 = mA



Value Calculation: ((#v21#–#v23#)/750)*1000





VR1 = Vdc



Value Calculation: (#i22#/1000)*750





IR2 = mA



Value Calculation: ((#v22#+#v23#)/3600)*1000








3-75


VR2 = Vdc








13. Do the NODE 1 currents agree with Kirchhoff's current law?

a. no

b. yes


14. Do the voltages agree with Kirchhoff's voltage law for each loop?

a. no

b. yes





3-76

REVIEW QUESTIONS


1. What is the equation for I3 with current direction as indicated?

a. I3 = I1 + I2

b. I3 = I1 – I2

c. I3 = I2 – I1

d. I3 + I1 + I1 = 0


2. With respect to circuit common, the voltage across R3

a. cannot be measured.

b. is about –4.69V.

c. is about +4.69V.

d. is about +6.05V.


3. Based on this circuit, what is the value of VR2?

a. VS1 – VR1

b. VS2 + VR3

c. VR3 + VR1



4. With CM 18 active, about what is the value of R2?

a. cannot be determined

b. 3600Ω c. 2278Ω d. 956Ω


5. What is the value of I3?

a. cannot be determined

b. 5.26 mA

c. 6.07 mA

d. 7.07 mA


3-77

CMS AVAILABLE

CM 18

FAULTS AVAILABLE

None


3-78

Exercise 3 – Mesh Solution With 2 Sources

EXERCISE OBJECTIVE

Apply a mesh solution to a circuit having two voltage sources. Verify results by using measured

data.

EXERCISE DISCUSSION


For MESH 2,

a. VR1 and VR2 are positive.

b. VR2 and VR3 are negative.

c. VR2 and VR3 are positive.


The common resistor, R3, has two

a. opposing voltage drops.

b. aiding voltage drops.

Location: Exercise Discussion page: se3d4, Question ID: e3d4c

MESH 2 current flows into the negative side of voltage source VS2; therefore, VS2 is considered

a. positive (+).

b. negative (–).


3-79

EXERCISE PROCEDURE


What is the MESH 1 equation for this circuit?

a. (I1 x R1) + (I1 x R3) – (I2 x R3) = VS1

b. (I2 x R2) + (I2 x R3) – (I1 x R3) = VS2


5. What is the MESH 2 equation for this circuit?

a. (I1 x R1) + (I1 x R3) – (I2 x R3) = VS1

b. (I2 x R2) + (I2 x R3) – (I1 x R3) = VS2


6. Do the mesh currents through R3 flow in the same or in opposite directions?

a. same

b. opposite


You can determine the actual current through R3 by

a. subtracting I1 and I2.

b. adding I1 and I2.


IR3 = mA



Min/Max Value: ( .769) to ( .851)






3-80


VR3 (calculated) = Vdc








VR3 (measured) = Vdc


Nominal Answer: 6.075 *Min/Max Value: (3.98 ) to (8.361)






11. Do your calculated and measured values agree?

a. no

b. yes


12. With VR3 known, can you determine the voltage drops of each circuit resistor?

a. no

b. yes


13. With respect to branch currents, what is the advantage of the mesh method of circuit

analysis?

a. Branch currents are required for a mesh solution.

b. Branch currents are not required for a mesh solution.





3-81

REVIEW QUESTIONS


1. When you assign the direction of mesh currents flowing through a common circuit resistor, the

currents

a. must flow in the same direction.

b. must flow in opposite directions.

c. may flow in either direction.



2. If a mesh current flows into the negative terminal of a power source, then its assigned polarity

a. is positive.

b. is negative.

c. cannot be determined without magnitude.

d. depends on the multimeter connection.


3. When you apply a mesh analysis to a circuit,

a. Kirchhoff's rules are suspended.

b. Ohm's law does not apply to the voltage drops.

c. Either of the above, depending on the loop selected.

d. None of the above because Kirchhoff's and Ohm's laws define circuit relationships.


4. If the solution of a set of mesh equations yields a negative current,

a. the current value is correct, but its initial direction was incorrect.

b. the current value is incorrect, but its initial direction was correct.

c. both its value and direction are correct.

d. neither its value nor its direction is correct.


5. If R1 is a common circuit resistance between two meshes, and if I1 and I2 are the mesh

currents, then which equation is true?

a. R2 x I2 = VR1

b. R3 x I1 = VR1

c. (R1 x I1) + (R1 x I2) = VR1

d. (R1 x I1) – (R1 x I2) = VR1


3-82

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-83

UNIT TEST



How many possible loops does this circuit have?

a. 4

b. 3

c. 2

d. 1


How many nodes does this circuit have?

a. 4

b. 3

c. 2

d. 1


In this circuit, according to Kirchhoff's law,

a. VS – VR3 – VR1 – VR2 = 0.

b. VS – VR3 – VR1 + VR2 = 0.

c. VS + VR3 + VR1 + VR2 = 0.

d. VS + VR3 + VR1 + VR2 = 20V.


Based on Kirchhoff's voltage law and on this circuit, the combined R1 and R2 voltage drop must

equal

a. 15V.

b. 10V.

c. 5V.

d. 2.5V.


Based on Kirchhoff's current law and on this circuit, the combined R2 and R3 current equals

a. 0.

b. IT + IR1.

c. IT – IR2.

d. IR1.


3-84


In this circuit,

a. IT = IR2 + IR3.

b. IT – IR2 – IR3 = 0.




Which statement applies to this circuit?

a. (VS1 – VA)/R1 = (VA – VS2)/R2 + (VA/R3)

b. The sum of the currents of each node must equal zero.

c. Both Ohm's law and Kirchhoff's current law can be applied to the circuit.



This circuit has

a. 3 loops, 3 nodes, and 3 mesh paths.

b. 3 loops, 2 nodes, and 2 mesh paths.

c. 2 loops, 2 nodes, and 2 mesh paths.

d. 2 loops, 2 nodes, and 1 mesh path.


In this circuit, VS1 equals VS2, and R1, R2, and R3 are equal in value. As a result,

a. VR3 and IR3 each equal zero.

b. VR3 = VS1 + VS2.

c. VR3 = VS1 or VS2, but not both.



If the two mesh current paths were shown for this circuit,

a. MESH 1 would be CW and MESH 2 would be CCW.

b. MESH 1 would be CCW and MESH 2 would be CW.

c. MESH 1 and MESH 2 would be either CW or CCW.



3-85

TROUBLESHOOTING


VR3 = Vdc



Min/Max Value: (5.445) to (6.655)







a. R3 (decreased).

b. R3 (increased).

c. R2 (shorted).

d. R1 (open).


VR3 = Vdc



Min/Max Value: (5.445) to (6.655)







a. R3 (decreased).

b. R3 (increased).

c. R2 (shorted).

d. R1 (open).


3-86

CMS AVAILABLE

None

FAULTS AVAILABLE

Fault 9

Fault 10

DC Network Theorems Unit 6 – Superposition and Millman's Theorems

3-87

UNIT 6 – SUPERPOSITION AND MILLMAN'S THEOREMS

UNIT OBJECTIVE

Determine voltages and currents by using the superposition theorem and Millman's theorem.

UNIT FUNDAMENTALS


Is VR3 measured with respect to circuit common?

a. yes

b. no


In this circuit, do the voltage sources cause a current flow through R3?

a. yes

b. no

CMS AVAILABLE

None

FAULTS AVAILABLE

None

NEW TERMS AND WORDS

superposition theorem - an analysis technique where the effects of multiple voltage sources are

considered individually and then added algebraically to determine the combined result.

Millman's theorem - a method for finding the voltage at the common point in a circuit with

multiple branches. To find the common point voltage, add the branch currents algebraically, and

then divide by the sum of the branch conductances.

EQUIPMENT REQUIRED



Multimeter


3-88

Exercise 1 – Superposition Theorem

EXERCISE OBJECTIVE

Apply the superposition method of circuit analysis. Verify results with a multimeter.

EXERCISE DISCUSSION


When you determine the effect of VS2 on VR3, which resistor is placed in parallel with R3?

a. R1

b. R2

c. R3

EXERCISE PROCEDURE


RA = Ω

Recall Label for this Question: ra


Min/Max Value: (259.7) to (270.3)






RB = Ω

Recall Label for this Question: rb


Min/Max Value: (331.2) to (344.8)






3-89


VRA = Vdc

Recall Label for this Question: vra


Value Calculation: (10*#ra#)/(510+#ra#)





VRB = Vdc

Recall Label for this Question: vrb


Value Calculation: (–10*#rb#)/(360+#rb#)





VR3 = Vdc

Recall Label for this Question: vr3


Value Calculation: #vra#+#vrb#





7. Measure the voltage drop across R3. Is the measured value the same as the calculated value of

#vr3#V?

a. yes

b. no





3-90


8. Does the superposition circuit solution conform to Kirchhoff's voltage law?

a. yes

b. no


9. Is the current into the node formed by R1, R2, and R3 essentially equal to the current out of

the same node?

a. yes

b. no


10. Based on the circuit information, is the superposition theorem required to calculate circuit

voltage drops and current distribution?

a. yes

b. no

REVIEW QUESTIONS


1. The superposition method of circuit analysis requires

a. mesh equations.

b. node equations.

c. Kirchhoff's equations.

d. Ohm's law.


2. Two voltages are developed across the common element of a two-source circuit. To determine

the actual voltage drop,

a. multiply both voltages.

b. directly subtract both voltages.

c. algebraically add both voltages.

d. add the two voltage sources.


3-91


3. Results from the superposition method of circuit solution

a. must conform to Kirchhoff's laws.

b. need not conform to Kirchhoff's laws.

c. cannot be verified without your measuring the circuit.

d. are valid only for two-source circuits.


4. In which position must you set S1 to determine the effect of VS2 on R3?

a. position A

b. position B

c. either position

d. neither (the switch must be removed from the circuit)


5. When S1 is placed in position B,

a. VS2 and R1 are in parallel.

b. R1 and R2 are in series.

c. R2 and R3 are in series.

d. R1 and R3 are in parallel.

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-92

Exercise 2 – Millman's Theorem

EXERCISE OBJECTIVE

Solve a circuit by applying Millman's theorem. Verify results by comparing calculated and

measured data.

EXERCISE DISCUSSION


Which parameter defines the voltage across BRANCH 1 of the circuit?

a. VS2 + VR2

b. VS1 + VR1

c. VR3


Location: Exercise Discussion page: se2d4, Question ID: e2d4c

Are the branch voltages equal?

a. yes

b. no

EXERCISE PROCEDURE


GT = millisiemens

Recall Label for this Question: GT


Min/Max Value: (5.624) to (5.853)

Value Calculation: ((1/360)+(1/1000)+(1/510))*1000





3-93


IR1 = mA

Recall Label for this Question: IR1

Nominal Answer: –27.8

Min/Max Value: (–28.6) to (–26.9)

Value Calculation: (10/360)*(–1000)





IR3 = mA


Nominal Answer: 0.0







IR2 = mA

Recall Label for this Question: IR2


Min/Max Value: (19.02) to (20.2 )

Value Calculation: (10/510)*1000





3-94


VR3 = Vdc

Recall Label for this Question: VR3A

Nominal Answer: –1.43 ∗Min/Max Value: (–1.72) to (–1.2)

Value Calculation: (#IR1#+#IR2#)/#GT#





8. Based on the Millman solution for VR3, can you determine the actual circuit currents and

voltage drops?

a. yes

b. no


9. Use your voltmeter to measure VR3. Are your results consistent with Millman's theorem?

a. yes

b. no


10. Measure one or several resistive voltage drops, and calculate the respective current flow. Are

your results consistent with the Millman solution?

a. yes

b. no





3-95

REVIEW QUESTIONS


1. Based on Millman's theorem, what is sum of the branch currents?

a. 4.08 mA

b. –4.08 mA

c. ± 4.08 mA



2. Based on Millman's theorem, what is the sum of the branch conductances?

a. 5.74 mS

b. –5.74 mS

c. > 5.74 mS



3. With respect to circuit common, what is the voltage drop across R3?

a. 0.7V

b. –0.7V




4. The sum of the conductances

a. increases as the source voltage is increased.

b. does not change with changes in source voltage.

c. decreases as the source voltage is decreased.

d. equals zero when the source voltage is zero.


5. For the circuit shown,

a. Millman's theorem cannot be applied because common is not in the proper place.

b. VS1 is negative when applied to Millman's theorem.

c. VS2 is positive when applied to Millman's theorem.

d. Millman's theorem does not affect the polarity of VS1 or VS2 when they are measured

with respect to circuit common.


3-96

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-97

UNIT TEST



The superposition method of circuit analysis requires

a. mesh equations.

b. node equations.

c. Kirchhoff equations.

d. Ohm's law.


When you use the superposition method for a circuit solution, the results

a. must conform to Kirchhoff's laws.

b. need not conform to Kirchhoff's laws.

c. cannot be verified without your measuring the circuit.

d. are valid only for two-source circuits.


When you apply superposition analysis to a circuit,

a. simultaneously remove both voltage sources.

b. remove each source in turn.

c. Either of the above if the sources are added.

d. Either of the above if the sources are subtracted.


Which resistors are in parallel?

a. R1 and R2

b. R1 and R3

c. R2 and R3

d. All 3 resistors are in parallel.


What is the value of VR2?

a. 20V

b. 10V

c. 0V

d. –10V


3-98


What is the total conductance of the circuit?

a. 2.01 mS

b. 3 mS

c. 50 mS



Based on a Millman configuration, how many branch circuits are present?

a. 4

b. 3

c. 2

d. 1


What is the effect on V1 if R3 and R4 are removed from the circuit?

a. V1 doubles.

b. V1 is halved.

c. There is no effect.

d. All current flow stops.


What is the value of V1?

a. 20V

b. –20V

c. 10V

d. 0V


Total circuit conductance

a. cannot be determined because there are 2 resistances in the common branch.

b. need not include R3 and R4.

c. must include the difference between R3 and R4.

d. must include the sum of R3 and R4.

DC Network Theorems Unit 7 – Thevenin Circuits

3-99

UNIT 7 – THEVENIN CIRCUITS

UNIT OBJECTIVE

Simplify one- and two-source circuits by using Thevenin's theorem.

UNIT FUNDAMENTALS


For a specific load, do both circuits provide the same load voltage and load current?

a. yes

b. no


Should VTH be greater than, equal to, or less than the network source voltage?

a. greater than

b. equal to

c. less than

CMS AVAILABLE

None

FAULTS AVAILABLE

None

NEW TERMS AND WORDS

Thevenin's theorem - a network can be represented by an equivalent VTH and a series RTH

circuit with respect to a selected pair of output terminals.

VTH - the Thevenin equivalent voltage of a network without a load.

RTH - the Thevenin equivalent resistance of a network without its source voltage.

Thevenizing - applying Thevenin's theorem to a network.

EQUIPMENT REQUIRED



Multimeter


3-100

Exercise 1 – Thevenizing a Single Source Network

EXERCISE OBJECTIVE

Simplify a single-source network by applying Thevenin's theorem. Verify results by comparing

calculated and measured values.

EXERCISE DISCUSSION

No Questions

EXERCISE PROCEDURE


2. Which component(s) makes up the network to be thevenized?

a. R3

b. VS and R2

c. VS, R2, and R1

d. VS and R3


RTH = Ω

Recall Label for this Question: rth


Min/Max Value: (970.2) to ( 1010)






4. Measure RTH with an ohmmeter. Are the measured and calculated values (#rth#Ω) about the

same?

a. yes

b. no


3-101


VTH = Vdc

Recall Label for this Question: vth

Nominal Answer: 5.5







6. Measure VTH of the network. Does the measured value agree with the calculated value (#vth#

Vdc)?

a. yes

b. no


IRL = µA

Recall Label for this Question: ir3


Value Calculation: (((#vth#*6800)/(#rth#+6800))/6800)*1000000





8. Measure VR3. Based on R3 (6800Ω), does the load current agree with the current supplied by

the thevenized circuit (#ir3# µA)? IR3 = VR3 /R3

a. yes

b. no





3-102


IRL = µA

Recall Label for this Question: ilcm19


Min/Max Value: ( 1051) to ( 1285)






10. CM 19 is activated to change the load resistor. Measure VRL and calculate the load current.

Is the value about the same as that provided by the Thevenin equivalent circuit (#ilcm19# µA)?

a. yes

b. no


11. Are the polarities of the load voltage and VTH identical?

a. yes

b. no

REVIEW QUESTIONS


1. In this circuit, RTH


b. cannot be measured.

c. equals R1 + (R1 x R2)/(R1 + R2).

d. equals R1, R2, and R3 in parallel.


2. CM 20 is activated to change R3 to 10.1 kΩ. With respect to B, what is the value of VTH?

a. 10V

b. +5.5V

c. –5.5V

d. VTH cannot be determined.


3-103


3. What is the value of RTH?

a. –990Ω b. 990Ω c. 902Ω d. RTH cannot be determined.


4. In this network, the polarity of VTH

a. has no effect on the current flow through RTH.

b. is opposite to the polarity of the network source voltage.

c. depends on the difference between VR2 and VR3.

d. is the same as the polarity of the network source voltage.


5. If R2 is removed from this circuit,

a. VTH changes but RTH does not.

b. VTH does not change but RTH does.

c. Both VTH and RTH change.

d. neither VTH nor RTH changes.

CMS AVAILABLE

CM 19

CM 20

FAULTS AVAILABLE

None


3-104

Exercise 2 – Thevenizing a Dual Source Network

EXERCISE OBJECTIVE

Simplify a dual source network by applying Thevenin's theorem. Verify results by comparing

calculated and measured values.

EXERCISE DISCUSSION

No Questions

EXERCISE PROCEDURE


2. Based on this circuit schematic, where is a load resistor connected?

a. across VS1

b. across VS2

c. between A and B

d. between B and circuit common


RTH = Ω

Recall Label for this Question: rth2


Min/Max Value: (488. ) to (508. )






4. Use two-post connectors to remove and short both voltage sources. Measure RTH. Is your

measured value about the same as the calculated value of 498Ω?

a. yes

b. no


3-105


VTH = Vdc

Recall Label for this Question: vth2


Min/Max Value: (–2.25) to (–2.17)

Value Calculation: –2.210





6. Place VS1 and VS2 back into your circuit. Measure VR2, or VTH. Are the measured and

calculated (#vth2# Vdc) values about the same?

a. yes

b. no


7. Based on the Thevenin equivalent circuit shown, what is the expected voltage drop across a

6800Ω resistor?

a. 2.06 Vdc

b. –2.06 Vdc

c. 2.21 Vdc

d. –2.21 Vdc


8. Is VR3 about the same as VTH (#vth2# Vdc)?

a. yes

b. no


9. What is the advantage of a Thevenin equivalent circuit?

a. It minimizes power dissipation in the network load.

b. The effects of load change can easily be determined.

c. Network circuit calculations are no longer required.

d. Both (b) and (c).


3-106

REVIEW QUESTIONS


1. CM 20 is activated to modify the value of R3. Based on this circuit, a change in the load

resistance

a. produces a large change in RTH.

b. produces no change in RTH.

c. produces a small change in RTH.

d. must be offset by a change in R2.


2. For you to determine RTH,

a. R1 and R2 must be in parallel.

b. R2 and R4 must be in parallel.

c. R1, R3, and R4 must be in parallel.

d. R1, R2, and R4 must be in parallel.


3. To find the Thevenin voltage of this circuit, you can use

a. the superposition theorem.

b. Ohm's law.

c. Norton's current law.

d. Kirchhoff's voltage law.


4. For the circuit shown, VTH and RTH respectively are

a. 2.22V and 498Ω.

b. –2.22V and 498Ω.

c. 2.22V and 10.1 kΩ.

d. –2.22V and 10.1 kΩ.


5. CM 20 is deactivated. A change in RL

a. produces a large change in VTH.

b. produces no change in VTH.

c. produces a small change in VTH.

d. must be offset by a change within the network.


3-107

CMS AVAILABLE

CM 20

FAULTS AVAILABLE

None


3-108

UNIT TEST



Thevenizing a circuit creates an equivalent

a. series circuit.

b. series/parallel circuit.

c. parallel circuit.



In a Thevenin circuit, VTH

a. equals the voltage across the circuit load.

b. equals the voltage across RTH.

c. equals the voltage across the open circuit terminals of the network.

d. cannot be determined without RTH.


In a Thevenin circuit, RTH

a. equals the resistance of the circuit load.

b. equals the resistance across VTH.

c. equals the resistance across the open circuit terminals of the network.

d. cannot be determined without VTH.


Thevenizing a circuit

a. does not provide an advantage.

b. requires a new load to be inserted into the network.

c. reduces the load's power consumption.

d. makes the effect of load changes easier to calculate.


To determine VTH in a single source network,

a. remove the load but keep the source.

b. remove the load and the source.

c. keep the load and the source.

d. keep the load but remove the source.


3-109


To determine RTH in a single source circuit,

a. remove the load but keep the source.

b. remove the load and the source.

c. keep the load and the source.

d. keep the load but remove the source.


When thevenizing a multisource network,

a. use only the most positive voltage source.

b. use only the most negative voltage source.

c. you must determine the effects of all voltage sources.

d. you can directly subtract source voltages of opposite polarities.


With respect to the network load, a thevenized circuit

a. generates large differences in load current.

b. generates no difference in load current.

c. is accurate because it generates a load current difference.

d. is valid only for a constant load.


In this circuit, RTH

a. is greater than 1 kΩ.

b. is less than 1 kΩ.

c. equals 1 kΩ.



In this circuit, VTH

a. is 10V.

b. is 8V.

c. is 2V.

d. changes when a load is connected.


3-110

TROUBLESHOOTING


VR3 = Vdc



Min/Max Value: (–2.27) to (–1.85)






RTH = Ω



Min/Max Value: (447.3) to (546.7)

Value Calculation: 497




Location: Troubleshooting page: ttrba3, Question ID: trba3c

VTH = Vdc



Min/Max Value: (–2.39) to (–1.95)







a. VTH and RTH (out of specification).

b. R1 (open).

c. R1 (increased).

d. R3 (increased).


3-111


VR3 = Vdc



Min/Max Value: (–2.27) to (–1.85)






3. Based on the circuit values, does a change in load voltage generate a change in RTH or VTH?

a. yes

b. no



a. VTH and RTH (out of specification).

b. R1 (open).

c. R1 (increased).

d. R3 (increased).

CMS AVAILABLE

None

FAULTS AVAILABLE

Fault 11

Fault 12


3-112

DC Network Theorems Unit 8 – Thevenizing a Bridge Circuit

3-113

UNIT 8 – THEVENIZING A BRIDGE CIRCUIT

UNIT OBJECTIVE

Thevenize a resistive bridge circuit by using the resistor divider equation.

UNIT FUNDAMENTALS


If the load is removed from the bridge, can the bridge circuit be thevenized?

a. yes

b. no

CMS AVAILABLE

None

FAULTS AVAILABLE

None

NEW TERMS AND WORDS

bridge circuit - A circuit configuration of 4 elements and having 4 terminals. The source voltage

is applied across 2 opposing terminals, and the output is taken across the remaining 2 terminals.

EQUIPMENT REQUIRED



Multimeter


3-114

Exercise 1 – Bridge Circuit Resistance

EXERCISE OBJECTIVE

Calculate the Thevenin resistance (RTH) of a bridge circuit. Verify results by comparing

calculated and measured data.

EXERCISE DISCUSSION

No Questions

EXERCISE PROCEDURE


2. Which part of the bridge circuit is its input side?

a. the load side

b. the voltage source side


3. Is RTH determined with respect to the input or output side of a bridge circuit?

a. input

b. output


4. When making an RTH calculation, which resistor pairs are in parallel?

a. All resistors are in parallel.

b. No resistors are in parallel.

c. R1 R3 and R2 R4

d. R1 R2 and R3 R4


3-115


RTH = Ω

Recall Label for this Question: rth


Min/Max Value: (419.4) to (436.6)






6. Remove all two-post connectors. Short the input terminals of the bridge circuit, and measure

RTH. Is the measured value about the same as the calculated value of #rth0#Ω?

a. yes

b. no

REVIEW QUESTIONS


1. The ohmmeter is measuring

a. VTH.

b. R1.

c. RTH.

d. R4.


2. RTH is

a. 1250Ω.

b. 750Ω.

c. 500Ω.

d. 1333Ω


3-116


3. Placing a load at the output terminals of a thevenized bridge circuit

a. increases the value of RTH.

b. does not change the value of RTH.

c. decreases the value of RTH.

d. requires a new source voltage.


4. What are the output terminals of the circuit?

a. A and C

b. D and A

c. D and B

d. B and C


5. The source voltage is applied

a. to the output terminals of a bridge.

b. between the input and output terminals of a bridge.

c. to the input terminals of a bridge.

d. to the load circuit of a bridge.

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-117

Exercise 2 – Thevenizing Bridge Circuit Voltage

EXERCISE OBJECTIVE

Calculate the Thevenin equivalent voltage (VTH) of a bridge circuit. Verify results by comparing

calculated and measured data.

EXERCISE DISCUSSION


VTH = Vdc

Recall Label for this Question: vth


Min/Max Value: (–3.97) to (–3.81)





EXERCISE PROCEDURE


VS = Vdc









3. What action is required before you can measure VTH?

a. The bridge must be loaded.

b. The bridge source voltage must be removed.

c. The bridge source voltage must be shorted.



3-118


VTH = Vdc

Recall Label for this Question: vth2


Min/Max Value: (7.722) to (9.438)






5. Which output terminal of the bridge is more negative with respect to common?

a. A

b. B


6. Based on the circuit shown, what is the value of VRL?

a. #vth2# Vdc

b. –#vth2# Vdc

c. 2.9 Vdc

d. –2.9 Vdc


VRL = Vdc

Recall Label for this Question: vrl








3-119


RL = Ω

Recall Label for this Question: rl5








9. Based on this circuit, do the calculated (#rl5#Ω) and measured values of RL agree?

a. yes

b. no

REVIEW QUESTIONS


1. In a Thevenin model of a bridge circuit, VTH and RTH are not affected when the load value

changes because

a. Thevenin calculations are performed with the load in the circuit.

b. Thevenin calculations are performed with no load in the circuit.

c. the network source voltage compensates the Thevenin model after the load is connected.

d. the Thevenin model represents a series circuit.


2. Changing the network voltage source of a bridge changes

a. VTH but not RTH.

b. RTH but not VTH.

c. VTH and RTH.



3. Changing the value of one resistor in a bridge circuit changes

a. VTH but not RTH.

b. VTH and RTH.

c. RTH but not VTH.



3-120


4. The Thevenin model and load resistor form a

a. series circuit.

b. parallel circuit.

c. series/parallel circuit.

d. parallel/series circuit.


5. Which formula defines the load voltage for a complete thevenized circuit?

a. VRL = (VTH x RL)/(RTH + RL)

b. VRL = (VTH x RL) x (RTH + RL)

c. VRL = (VTH x RL) – (RTH + RL)

d. VRL = (VTH x RL) + (RTH + RL)

CMS AVAILABLE

CM 5

FAULTS AVAILABLE

None


3-121

UNIT TEST



What is the Thevenin resistance between terminals B and D?

a. 200Ωb. 150Ωc. 100Ωd. 36Ω


After a bridge circuit has been thevenized, what can you easily find given any value of RL?

a. RTH

b. VTH

c. VRL



Thevenizing a bridge circuit means to reduce it to an equivalent

a. series circuit.



d. parallel/series circuit.


With the load removed from a bridge circuit and a voltage source applied, the voltage measured

across the output is called the

a. Thevenin voltage.

b. Thevenin resistance.

c. Kirchhoff voltage.

d. source voltage.


With terminals A and C shorted, what is the resistance between terminals D and B?

a. 57.48Ωb. 48.57Ωc. 97.26Ωd. 194.52Ω


3-122


The load is connected across terminals

a. A and B

b. B and C.

c. A and C.

d. B and D.


The open circuit voltage (VTH) is measured across

a. the load.

b. R5.

c. the source voltage.

d. terminals B and D.


To measure RTH, remove the

a. source voltage and load, short terminals A and C, and measure across terminals D and

B.

b. source voltage, short terminals A and C, and measure across the load.

c. load, and measure across terminals B and D.

d. load, and measure across terminals A and C.


What does the voltmeter indicate?

a. VR5

b. VR1

c. VS



Thevenin's theorem is used to

a. convert a series circuit into an equivalent network.

b. convert a network into an equivalent series circuit.

c. replace a circuit load with an equivalent network.

d. replace a network with one load resistor.


3-123

TROUBLESHOOTING


VRL = Vdc



Min/Max Value: (2.619) to (3.201)






3. Does a change in load resistance affect the Thevenin equivalent circuit?

a. yes

b. no


4. Does the open load output voltage of the thevenized circuit equal the value of VTH?

a. yes

b. no


5. If the load is connected, is VRL greater than, less than, or equal to VTH?

a. greater than

b. less than

c. equal to



a. R5 (decreased in value).

b. R5 (no change).

c. R5 (increased in value).

d. R5 (shorted).


3-124

CMS AVAILABLE

None

FAULTS AVAILABLE

Fault 3

DC Network Theorems Unit 9 – Thevenin/Norton Conversion

3-125

UNIT 9 – THEVENIN/NORTON CONVERSION

UNIT OBJECTIVE

Convert networks into equivalent voltage and current sources by using Thevenin's and Norton's

theorems.

UNIT FUNDAMENTALS


What is the output voltage across the load of this circuit?

a. 10V

b. 9.09V

c. 5V



Based on the circuit shown, what is the value of load current?

a. 1A

b. 0.0909A

c. 0.909A


CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-126

NEW TERMS AND WORDS

voltage source - a circuit that provides a constant voltage at its output terminals.

Norton's theorem - a network can be represented by an equivalent current source and parallel

resistor with respect to a pair of output terminals.

current source - a circuit that provides a constant current at its output terminals.

EQUIPMENT REQUIRED



Multimeter


3-127

Exercise 1 – Thevenin to Norton Conversion

EXERCISE OBJECTIVE

Convert a voltage source to a current source. Verify results by comparing calculated and

measured data.

EXERCISE DISCUSSION

No Questions

EXERCISE PROCEDURE


VO(NL) = Vdc

Recall Label for this Question: vtonl


Min/Max Value: (7.553) to (8.348)






VRL = Vdc

Recall Label for this Question: vtol


Min/Max Value: (3.762) to (4.158)






3-128


4. Why are the unloaded (VO(NL)) and loaded (VO(L)) circuit output voltages different?

a. The load forms a voltage divider with RTH.

b. Current does not flow through RTH when the load is removed.

c. The load causes a voltage drop across RTH.



5. What does the output voltage of a Thevenin equivalent circuit equal if its output terminals are

shorted together?

a. VTH

b. VRTH

c. VRL



Based on your readings, does VTH equal VRTH, and does the Thevenin output terminal equal 0?

a. yes

b. no


IN = mA



Min/Max Value: (16.06) to (17.75)






3-129


IN = mA



Min/Max Value: (16.06) to (17.75)






Does the value of IN change?

a. yes

b. no


11. Are these circuits equivalent in terms of their effect on the load resistor?

a. yes

b. no

REVIEW QUESTIONS


1. The open circuit (no-load) current of a Norton current source (IN) equals

a. the maximum current of a Thevenin equivalent circuit.

b. VTH /RTH.

c. All of the above.



2. In a Thevenin equivalent circuit, RTH is 1000Ω. Therefore,

a. the series resistance of the Norton equivalent circuit is 1000Ω.

b. the shunt resistance of the Norton equivalent circuit is 1000Ω.

c. the series/parallel resistance of the Norton equivalent circuit is 1000Ω.



3-130


3. When a Thevenin equivalent circuit is converted to its Norton equivalent, the current direction

of IN

a. does not matter.

b. should be opposite to the direction of the current caused by VTH.

c. depends on how the load is connected to the circuit output terminals.

d. should be the same as the direction of current caused by VTH .


4. If the load is removed from the output terminals of a Thevenin equivalent circuit, the circuit

output voltage

a. increases to VTH.

b. does not change.

c. decreases.

d. reduces to zero.


5. If the output voltage of a Thevenin equivalent circuit is 0V, the

a. load is open.

b. load current is properly connected.

c. load is shorted.

d. network represented by the Thevenin circuit is improperly configured.

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-131

Exercise 2 – Norton to Thevenin Conversion

EXERCISE OBJECTIVE

Convert a current source to a voltage source. Verify results by comparing calculated and

measured data.

EXERCISE DISCUSSION


Are the load current and load voltage identical for each circuit?

a. yes

b. no

EXERCISE PROCEDURE


VO(NL) = Vdc

Recall Label for this Question: v2nl


Min/Max Value: (7.791) to (8.109)






IO(SC) = mA

Recall Label for this Question: i2sc


Min/Max Value: (16.58) to (17.26)






3-132


VRL = Vdc

Recall Label for this Question: v2rl


Min/Max Value: (3.781) to (4.179)






IRL = mA

Recall Label for this Question: i2rl


Value Calculation: (#v2rl#/470)*1000





6. Based on your calculations, what is the current (IN) required for an equivalent constant current

source?

a. #v2nl# Vdc

b. #i2sc# mA

c. #v2rl# Vdc

d. #i2rl# mA


7. What is the current distribution between RN and RL?

a. #v2nl# Vdc

b. #i2sc# mA

c. #v2rl# Vdc

d. #i2rl# mA





3-133


8. What is the load voltage generated by the constant current source?

a. #v2nl# Vdc

b. #i2sc# mA

c. #v2rl# Vdc

d. #i2rl# mA


9. Measure the no-load output current of the constant current source. Is the current approximately

the same as the calculated short circuit current (#i2sc# mA) of the network?

a. yes

b. no


10. Place RL into your constant current circuit. Measure the load voltage and calculate the load

current. Is this current approximately equal to the load current (#i2rl# mA) generated by the

network?

a. yes

b. no


11. Based on your calculated and measured data, does the constant current source duplicate the

effects of the network?

a. yes

b. no


12. Compare the unloaded and loaded output voltages of the Thevenin and Norton equivalent

circuits. Are the voltages about the same?

a. yes

b. no


3-134

REVIEW QUESTIONS


1. In a Norton to Thevenin conversion, the value of RTH equals

a. VTH/RN.

b. RL.

c. RN.



2. When you calculate the value of VTH,

a. open the constant current source.

b. remove RN from the circuit.

c. remove RL.

d. remove RN and RL.


3. If the load is removed from a Norton equivalent circuit,

a. all of the current flows through RN.

b. IN is reduced to zero.

c. IN increases.

d. IN decreases.


4. When the load placed across the output terminals of a Norton equivalent circuit increases, IN

a. increases to maintain constant load current.

b. does not change, but IRN decreases.

c. decreases to maintain constant load current.

d. does not change, but decreases.


5. With respect to current distribution, the operation of a Norton equivalent circuit (with a load)

follows

a. series circuit rules.

b. series/parallel circuit rules.

c. parallel circuit rules.



3-135

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-136

UNIT TEST



Maximum current flows when

a. the load is open.

b. the load is shorted.

c. VTH is shorted.

d. the values of RTH and RL are equal.


In order to measure the Thevenin voltage of this Thevenin equivalent circuit,

a. remove the load (RL).

b. increase RL.

c. decrease RL.

d. short RL.


The load voltage equals

a. (VTH x RL)/(RTH + RL).

b. IRTH + RTH.

c. VTH + RTH.



The value of RL is doubled; therefore, VTH

a. doubles in value.

b. does not change.

c. is halved.

d. does not change, but RTH is halved.


Which of the following must be true in order for the circuit to be converted into a Norton

equivalent circuit?

a. VTH = IN, and RTH = (RTH + RL)/(RTH + RL)

b. VTH = IN, and RTH = RN

c. VTH/RTH = IN, and RTH = RN

d. VTH/RTH = IN, and RTH = RN + RTH


3-137


In order to "kill" the current source, a. remove RN from the circuit.

b. remove RL from the circuit.

c. place a short circuit across RL.

d. remove RN and RL from the circuit.


When RL is removed from the Norton equivalent circuit, IN

a. increases.

b. does not change.

c. decreases.

d. does not change, but RN increases.


IN is 1A and RN is 100Ω. Proper circuit operation requires that RL

a. be greater than 100Ω.

b. equal 100Ω.

c. be less than 100Ω.

d. None of the above applies because RL can be any value.


Each resistance can be converted to its equivalent conductance. Based on conductance, IN

a. divides directly.

b. divides inversely.

c. does not divide.

d. must change with load conductance variation.


Which of the following must be true in order for the circuit to be converted into a Thevenin

equivalent circuit?

a. You must know the component values of the initial network.

b. VTH = IN/RN, and RTH = RTH – RN

c. VTH = IN x RN, and RTH = RN

d. VTH = IN x RN, and RTH = (RTH x RN)/(RTH + RN)


3-138

DC Network Theorems Unit 10 – Delta and Wye Networks

3-139

UNIT 10 – DELTA AND WYE NETWORKS

UNIT OBJECTIVE

Simplify a resistive bridge network by using delta and wye transformations.

UNIT FUNDAMENTALS


R1, R2, and R3 of each network are identical. Is the resistance between identical terminals of

each network identical?

a. yes

b. no


Based on these circuits, what is the relationship between the resistors?

a. All resistors are in parallel.

b. RB and RC are in series.

c. The sum of RB and RC is in parallel with RA.

d. Both b. and c.


A wye-delta conversion results in the networks shown. Are the networks electrically identical?

a. yes

b. no

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-140

NEW TERMS AND WORDS

wye - a resistor configuration in the shape of a Y. Tee and wye are different names for the same

network.

tee - a resistor configuration in the shape of a T. Tee and wye are different names for the same

network.

delta - Greek letter that refers to a resistor configuration in the shape of a triangle. Pi and delta

are different names for the same network.

pi - Greek letter that refers to a resistor configuration in the shape of the symbol for pi . Pi and

delta are different names for the same network.

cross products - multiplication of each pair of resistors in a Y network.

EQUIPMENT REQUIRED



Multimeter


3-141

Exercise 1 – Tee/Wye and Pi/Delta Networks

EXERCISE OBJECTIVE

Compare tee, wye, delta, and pi networks. Verify results by using measured data.

EXERCISE DISCUSSION

No Questions

EXERCISE PROCEDURE


Are the readings approximately the same?

a. yes

b. no


3. CM 15 is activated to increase the value of R2 (Y network) to 2050Ω. Which terminal pairs of

the T and Y networks differ?

a. A/C

b. A/B

c. A/D, B/D, AND C/D

d. A/B, A/C, AND B/C


Are the readings approximately the same?

a. yes

b. no


3-142


5. CM 12 is activated to increase the value of RB to 3740Ω. Which terminal resistances of the

delta network are affected?

a. all

b. only A/D

c. A/D or C/D

d. None


6. With CM 12 activated, are the pi and delta networks equivalent?

a. yes

b. no

REVIEW QUESTIONS


1. Which networks are electrically identical?

a. A and B

b. A and C

c. A and D

d. B and C


2. An ohmmeter placed across any two circuit terminals of a 3-resistor delta circuit sees a

a. series circuit.





3. An ohmmeter placed between any two circuit terminals of a 3-resistor wye circuit sees a

a. series circuit.





3-143


4. The resistor values in a typical Y configuration are 100Ω, 200Ω, and 300Ω. The equivalent

a. pi network resistors are identical.

b. delta network resistors are identical.

c. tee network resistors are identical.

d. network must be another wye network because the resistors are unbalanced.


5. With respect to VS,

a. all resistors are in parallel.

b. all resistors are in series.

c. R1, R2, and R3 are in series.

d. R2 and R3 are in series with each other and in parallel with R1.

CMS AVAILABLE

CM 15

CM 12 TOGGLE

FAULTS AVAILABLE

None


3-144

Exercise 2 – Delta and Wye Transformations

EXERCISE OBJECTIVE

Convert between delta and wye circuits. Verify results by comparing calculated and measured

values.

EXERCISE DISCUSSION

No Questions

EXERCISE PROCEDURE


YR1 = Ω

Recall Label for this Question: yr1








YR2 = Ω









3-145


YR3 = Ω









DRB = Ω

Recall Label for this Question: drb


Value Calculation: ((#yr1#*#yr2#)+(#yr1#*#yr3#)+(#yr2#*#yr3#))/#yr2#





DRA = Ω

Recall Label for this Question: dra










3-146


DRC = Ω

Recall Label for this Question: drc







Do your measured values and calculated values agree within tolerance?

a. yes

b. no


5. Use your ohmmeter to compare the terminal resistances between the Y NETWORK and the

∆ NETWORK. Is the delta network equivalent to the wye network?

a. yes

b. no


6. Based on your Y to ∆ conversion results, can you convert a delta network into an equivalent Y

network?

a. yes

b. no





3-147

REVIEW QUESTIONS


1. In a delta network to wye network conversion, the denominator of the conversion formula is

the

a. sum of the products of all resistors.

b. difference of the products of all resistors.

c. sum of all resistors.



2. In a delta network to wye network conversion, the numerator of the conversion formula is the

a. sum of two adjacent pairs.

b. difference of two adjacent pairs.

c. product of two adjacent pairs.

d. sum of the products of two adjacent pairs.


3. Which formula can be used to convert one leg of a wye network into a delta value?

a. (R1 x R2) + (R2 x R3) + (R3 x R1)

RC = –––––––––––––––––––––––––––––––––––

R1

b. RA x RB

R1 = ––––––––––––––––

RA + RB + RC




4. Simplifying a resistive bridge network requires a

a. wye to delta conversion.

b. wye to wye conversion.

c. delta to delta conversion.

d. delta to wye conversion.


3-148


5. The circuits

a. draw identical current from the voltage source.

b. have identical component voltage drops.

c. are not equivalent to each other.

d. draw different current from the voltage source.

CMS AVAILABLE

None

FAULTS AVAILABLE

None


3-149

UNIT TEST



A tee network is identical to a

a. pi network.

b. wye network.

c. delta network.

d. bridge network.


A pi network is identical to a

a. tee network.

b. wye network.

c. delta network.

d. bridge network.


A wye network can be converted to an equivalent

a. series network.

b. tee network.

c. delta network.



A delta network can be converted to an equivalent

a. pi network.

b. wye network.

c. parallel network.



An ohmmeter placed across any two circuit terminals of a 3-resistor delta circuit sees a

a. series circuit.





3-150


An ohmmeter placed across any two circuit terminals of a 3-resistor wye circuit sees a

a. series circuit.





The resistor values of a typical Y configuration are 100Ω, 200Ω, and 300Ω. The

a. pi network resistors are identical.

b. delta network resistors are identical.

c. tee network resistors are identical.

d. network must be another wye network because the resistors are unbalanced.


In a delta network to wye network conversion, the denominator of the conversion formula is the

a. sum of the products of all resistors.

b. difference of the products of all resistors.

c. sum of all resistors.



What is the total circuit current?

a. 100 mA

b. 10 mA

c. 1 mA



Based on the given circuit values,

a. the loaded delta draws greater total current.

b. total current is identical.

c. the loaded delta draws less total current.

d. total currents cannot be compared because the circuits are not alike.


3-151

TROUBLESHOOTING


Are the resistive values equal to the given nominal vales?

a. yes

b. no


3. Do the measured values of the T NETWORK match those of the Y NETWORK?

a. yes

b. no


4. Does a change in the Y NETWORK circuit block affect the T NETWORK circuit block?

a. yes

b. no



a. R1 (increased).

b. R2 (increased).

c. R3 (increased).

d. R1 and R2 (increased).

CMS AVAILABLE

None

FAULTS AVAILABLE

Fault 8


3-152

DC Network Theorems Appendix A – Pretest and Posttest Questions and Answers

A-1

APPENDIX A – PRETEST AND POSTTEST QUESTIONS AND ANSWERS


Pretest Questions

1. Based on Kirchhoff's current law, the total current (IT) in a circuit with a voltage source and

two resistors in parallel is specified as

a. IT = IR1 - IR2

b. IT = IR2 - IR1

c. 0 = IT + IR1 + IR2

d. 0 = IT - IR1 - IR2

2. Based on Kirchhoff's current law, the total current into a node

a. has no relationship to the current out of that node.

b. maybe greater than the current out of that node.

c. maybe less than the current out of that node.

d. should be equal to the current out of that node.

3. Kirchhoff's current law states that the algebraic sum of the node currents

a. should equal zero.

b. should equal one.

c. should equal infinity.

d. lies between zero and infinity.

4. You can combine Kirchhoff's current law with Ohm's law to solve for

a. pi.

b. total circuit current.

c. a resistive wye circuit


5. Kirchhoff's current law supports the rule that in a parallel circuit, total circuit current equals

the sum of

a. the current through each resistor.

b. the first branch current only.

c. the branch currents.

d. There is not enough information to answer this question.

6. In a closed loop, the sum of the voltage drop equals

a. zero.

b. a maximum circuit voltage.

c. a minimum voltage drop.

d. an intermediate voltage.


A-2

7. Three series resistors drop voltages of 10V, 5V, and 2.5V. Based on Kirchhoff's voltage law,

the circuit battery voltage is

a. 0V.

b. 17.5V.

c. 15V.

d. 10V.

8. Which equation defines Kirchhoff's voltage law?

a. VS = V1 + V2 + VN

b. 0 = VS - (V1 + V2 + VN)



9. Proving Kirchhoff's voltage law requires that

a. all voltage drops in the loop be equal.

b. negative and positive polarities be assigned to the voltages in the loop.

c. negative polarities be assigned to the voltages in the loop.

d. positive polarities be assigned to the voltages in the loop.

10. A series circuit consists of 3 elements and a voltage source. If the source voltage and the

voltage drops of 2 elements are known, the voltage drop of the third element


b. is zero.



11. A circuit loop is

a. an open circuit path.

b. a short circuit path.

c. a multiple circuit path.

d. a closed circuit path.

12. A circuit with a voltage source and three resistors in parallel has

a. four current loops.

b. three current loops.

c. two current loops.

d. one current loop.

13. Applying Kirchhoff's laws, a circuit with two loops has current flowing

a. only through LOOP1.

b. only through LOOP2.

c. through both LOOP 1 AND LOOP2.



A-3

14. A circuit with a voltage source, two resistors in series, in parallel with one resistor has

a. one current loop.

b. two current loops.

c. three current loops.

d. four current loops.


a. one node.

b. two nodes.

c. three nodes.

d. four nodes.

16. Nodes are

a. special resistors.

b. common connections for two or more components.

c. special voltage sources.


17. Loop equations are

a. equations that define the voltage drops around a closed loop.

b. equations that define the voltage drops around an open loop.

c. equations that are used very rarely.

d. equations with no solution.

18. After you know the voltage of the element that is common to both loops,

a. apply Kirchhoff's current law to determine each circuit current.

b. use mesh equations to determine circuit current.

c. apply Ohm's law to determine each circuit current.


19. With the mesh method, branch currents

a. must be determined.

b. need not be determined.

c. are predetermined.


20. A mesh is

a. any current path with parallel branches.

b. two or more current loops that share a common circuit.

c. an open circuit current path.

d. the simplest possible closed current path within a circuit.


A-4

21. The superposition theorem

a. is applied primarily to high frequency dc circuits.

b. is applied primarily to low frequency dc circuits.

c. extends the use of Ohm's law to single voltage source circuits.

d. extends the use of Ohm's law to circuits having more than one voltage source.

22. Based on the superposition theorem,

a. multiple circuit voltages affect a common element of the circuit

b. multiple circuit voltages do not affect one another.

c. circuit voltages must have like polarities.

d. circuit voltages must have unlike polarities.

23. To implement a superposition solution, you must determine the effect of each voltage source

on

a. the common circuit element.

b. all circuit elements.

c. only a few circuit elements.


24. Millman's theorem uses the sum of the branch currents and the sum of the conductances to

help you determine the

a. current of the common element.

b. current through each mesh.

c. voltage across the branches.


25. Millman's theorem takes the form of current divided by

a. resistance.

b. conductance.

c. voltage.


26. A thevenized circuit requires

a. an equivalent current (ITH) in series with an equivalent resistance (RTH).

b. an equivalent voltage (VTH) and an equivalent resistance (RTH) in parallel with (VTH).

c. an equivalent voltage (VTH) and an equivalent resistance (RTH) in series with

(VTH).


27. VTH is the network output terminal voltage. VTH is determined with the network load

a. in series.

b. connected.

c. disconnected.



A-5

28. RTH is the total no-load network resistance. The network source voltage is replaced with a

a. short circuit.

b. multimeter.

c. a battery.


29. Thevenin's theorem allows for the reduction of a network into an equivalent circuit called a

a. current source.

b. voltage source.

c. source current.

d. voltage regulator.

30. The voltage across a load and the current through a load produced by a thevenin equivalent

circuit will be

a. higher to that generated by the original network.

b. identical to that generated by the original network.

c. lower to that generated by the original network.

d. opposite to that generated by the original network.

31. A resistive bridge circuit has

a. one terminal.

b. two terminals.

c. three terminals.

d. four terminals.

32. If the load is removed from a resistive bridge, the bridge circuit

a. cannot be thevenized.

b. can be thevenized.

c. can be dangerous.


33. Calculated and measured values of RTH should be approximately

a. 2:1 respectively.

b. 1:2 respectively.

c. the same.


34. To determine VTH of a bridge circuit, remove the

a. source voltage.

b. the voltage divider.

c. load resistor from the network.

d. all resistance.


A-6

35. A Thevenin model of a bridge circuit simplifies

a. load voltage calculations only.

b. load current calculations only.

c. load voltage and load current calculations.


36. A current source is a circuit

a. that provides a constant voltage at its output terminals.

b. that has a high internal resistance.

c. with a load dependent current output.

d. with a voltage dependent output current.

37. A voltage source is defined as a circuit

a. with a current dependent output voltage.

b. that provides a constant current at its output terminals.

c. with a load dependent voltage output.

d. that provides a constant voltage at its output terminals.

38. Norton's theorem allows for the reduction of a network into an equivalent circuit called a

a. voltage source.

b. source voltage.

c. current source.

d. current regulator.

39. A current source is

a. a circuit that provides an alternating current at its output terminals.

b. a circuit that provides a constant current at its output terminals.

c. a circuit that provides no current at its output terminals.


40. In the conversion process between Thevenin and Norton circuits,

a. RN equals R

TH.

b. RN equals V

TH.

c. RTH equals V

TH.


41. A resistive wye network is identical to

a. a delta network.

b. a pi network.

c. a tee network.



A-7

42. A resistive delta network is identical to

a. a delta network.

b. a pi network.

c. a tee network.


43. The resistor values of a Y configuration are 100 ohms, 200 ohms, and 300 ohms. The

equivalent

a. delta network resistors are identical.

b. tee network resistors are identical.

c. network must be another Y configuration since the specified resistors are not balanced.

d. pi network resistors are identical.

44. Cross products are product of each pair of resistors in a

a. delta network.

b. tee network.

c. Y network.

d. pi network.

45. In a delta-to-wye or wye-to-delta transformation, the

a. individual resistors of each network need not be equal.

b. individual resistors of each network are made equal.

c. resistors of the wye network are twice as large as the resistors of the delta network.

d. resistors of the wye network are half as large as the resistors of the delta network.

46. In troubleshooting a circuit,

a. take all resistance readings first.

b. insert an ammeter into all possible circuit paths.

c. check the circuit source voltage first.

d. network theorems are useless since they do not account for component tolerance.

47. When you troubleshoot an electrical circuit, the first and least troublesome step to perform

is a

a. complete and detailed circuit calibration.

b. 4-hour burn-in to ensure that a defective component fails.

c. diagnostic performance check.

d. thorough visual inspection.

48. With respect to network theorems, a closed loop represents

a. a complete single current path.

b. an open current path.

c. a partial current path.



A-8

49. A voltage source

a. ideally has a very low source resistance.

b. should have a 50 ohm output resistance.

c. generates maximum output voltage when connected across a short circuit.

d. requires a high internal series resistor.

50. When a troubleshooting procedure requires a mathematical analysis,

a. use the most complicated theorem that you can apply.

b. find another way to solve your problem.

c. you are better off guessing.

d. use the simplest technique that applies.


A-9

Posttest Questions

1. Proving Kirchhoff's voltage law requires that

a. all voltage drops in the loop be equal.

b. negative and positive polarities be assigned to the voltages in the loop.

c. negative polarities be assigned to the voltages in the loop.

d. positive polarities be assigned to the voltages in the loop.

2. In a closed loop, the sum of the voltage drop equals

a. zero.

b. a maximum circuit voltage.

c. a minimum voltage drop.

d. an intermediate voltage.

3. Three series resistors drop voltages of 10V, 5V, and 2.5V. Based on Kirchhoff's voltage law,

the circuit battery voltage is

a. 0V.

b. 17.5V.

c. 15V.

d. 10V.

4. A series circuit consists of 3 elements and a voltage source. If the source voltage and the

voltage drops of 2 elements are known, the voltage drop of the third element


b. is zero.



5. Which equation defines Kirchhoff's voltage law?

a. VS = V1 + V2 + VN

b. 0 = VS - (V1 + V2 + VN)



6. Applying Kirchhoff's laws, a circuit with two loops has current flowing

a. only through LOOP1.

b. only through LOOP2.

c. through both LOOP 1 AND LOOP2.


7. Loop equations are

a. equations that define the voltage drops around a closed loop.

b. equations that define the voltage drops around an open loop.

c. equations that are used very rarely.

d. equations with no solution.


A-10

8. A circuit with a voltage source and three resistors in parallel has

a. four current loops.

b. three current loops.

c. two current loops.

d. one current loop.

9. After you know the voltage of the element that is common to both loops,

a. apply Kirchhoff's current law to determine each circuit current.

b. use mesh equations to determine circuit current.

c. apply Ohm's law to determine each circuit current.

d. None of the above

10. Nodes are

a. special resistors.

b. common connections for two or more components.

c. special voltage sources.


11. A circuit loop is

a. an open circuit path.

b. a short circuit path.

c. a multiple circuit path.

d. a closed circuit path.


a. one node.

b. two nodes.

c. three nodes.

d. four nodes.


a. one current loop.

b. two current loops.

c. three current loops.

d. four current loops.

14. Kirchhoff's current law supports the rule that in a parallel circuit, total circuit current equals

the sum of

a. the current through each resistor.

b. the first branch current only.

c. the branch currents.

d. There is not enough information to answer this question.


A-11

15. You can combine Kirchhoff's current law with Ohm's law to solve for

a. pi.

b. total circuit current.

c. a resistive wye circuit.


16. Kirchhoff's current law states that the algebraic sum of the node currents

a. should equal zero.

b. should equal one.

c. should equal infinity.

d. lies between zero and infinity.

17. Based on Kirchhoff's current law, the total current into a node

a. has no relationship to the current out of that node.

b. maybe greater than the current out of that node.

c. maybe less than the current out of that node.

d. should be equal to the current out of that node.

18. Based on Kirchhoff's current law, the total current (IT) in a circuit with a voltage source and

two resistors in parallel is specified as

a. IT = IR1 - IR2

b. IT = IR2 - IR1

c. 0 = IT + IR1 + IR2

d. 0 = IT - IR1 - IR2

19. To implement a superposition solution, you must determine the effect of each voltage source

on

a. the common circuit element.

b. all circuit elements.

c. only a few circuit elements.


20. Based on the superposition theorem,

a. multiple circuit voltages affect a common element of the circuit.

b. multiple circuit voltages do not affect one another.

c. circuit voltages must have like polarities.

d. circuit voltages must have unlike polarities.

21. The superposition theorem

a. is applied primarily to high frequency dc circuits.

b. is applied primarily to low frequency dc circuits.

c. extends the use of Ohm's law to single voltage source circuits.

d. extends the use of Ohm's law to circuits having more than one voltage source.


A-12

22. The voltage across a load and the current through a load produced by a thevenin equivalent

circuit will be

a. higher to that generated by the original network.

b. identical to that generated by the original network.

c. lower to that generated by the original network.

d. opposite to that generated by the original network.

23. Thevenin's theorem allows for the reduction of a network into an equivalent circuit called a

a. current source.

b. voltage source.

c. source current.

d. voltage regulator.

24. A thevenized circuit requires

a. an equivalent current (ITH) in series with an equivalent resistance (RTH).

b. an equivalent voltage (VTH) and an equivalent resistance (RTH) in parallel with (VTH).

c. an equivalent voltage (VTH) and an equivalent resistance (RTH) in series with

(VTH).


25. A mesh is

a. any current path with parallel branches.

b. two or more current loops that share a common circuit.

c. an open circuit current path.

d. the simplest possible closed current path within a circuit.

26. With the mesh method, branch currents

a. must be determined.

b. need not be determined.

c. are predetermined.


27. RTH is the total no-load network resistance. The network source voltage is replaced with a

a. short circuit.

b. multimeter.

c. a battery.


28. VTH is the network output terminal voltage. VTH is determined with the network load

a. in series.

b. connected.

c. disconnected.



A-13

29. Millman's theorem takes the form of current divided by

a. resistance.

b. conductance.

c. voltage.


30. Millman's theorem uses the sum of the branch currents and the sum of the conductances to

help you determine the

a. current of the common element.

b. current through each mesh.

c. voltage across the branches.


31. A Thevenin model of a bridge circuit simplifies

a. load voltage calculations only.

b. load current calculations only.

c. load voltage and load current calculations.


32. To determine VTH of a bridge circuit, remove

a. the source voltage.

b. the voltage divider.

c. the load resistor from the network.

d. all resistance.

33. A current source is a circuit

a. that provides a constant voltage at its output terminals.

b. that has a high internal resistance.

c. with a load dependent current output.

d. with a voltage dependent output current.

34. In the conversion process between Thevenin and Norton circuits,

a. RN equals R

TH.

b. RN equals V

TH.

c. RTH equals V

TH.


35. Cross products are product of each pair of resistors in a

a. delta network.

b. tee network.

c. Y network.

d. pi network.


A-14

36. A current source is

a. a circuit that provides an alternating current at its output terminals.

b. a circuit that provides a constant current at its output terminals.

c. a circuit that provides no current at its output terminals.


37. A resistive delta network is identical to

a. a delta network.

b. a pi network.

c. a tee network.


38. Norton's theorem allows for the reduction of a network into an equivalent circuit called a

a. voltage source.

b. source voltage.

c. current source.

d. current regulator.

39. In a delta-to-wye or wye-to-delta transformation, the

a. individual resistors of each network need not be equal.

b. individual resistors of each network are made equal.

c. resistors of the wye network are twice as large as the resistors of the delta network.

d. resistors of the wye network are half as large as the resistors of the delta network.

40. The resistor values of a Y configuration are 100 ohms, 200 ohms, and 300 ohms. The

equivalent

a. delta network resistors are identical.

b. tee network resistors are identical.

c. network must be another Y configuration since the specified resistors are not balanced.

d. pi network resistors are identical.

41. In troubleshooting a circuit,

a. take all resistance readings first.

b. insert an ammeter into all possible circuit paths.

c. check the circuit source voltage first.

d. net

42. Calculated and measured values of RTH should be approximately

a. 2:1 respectively.

b. 1:2 respectively.

c. the same.



A-15

43. A resistive wye network is identical to

a. a delta network.

b. a pi network.

c. a tee network.


44. A resistive bridge circuit has

a. one terminal.

b. two terminals.

c. three terminals.

d. four terminals.

45. A voltage source

a. ideally has a very low source resistance.

b. should have a 50 ohm output resistance.

c. generates maximum output voltage when connected across a short circuit.

d. requires a high internal series resistor.

46. If the load is removed from a resistive bridge, the bridge circuit

a. cannot be thevenized.

b. can be thevinized.

c. can be dangerous.


47. When you troubleshoot an electrical circuit, the first and least troublesome step to perform

is a

a. complete and detailed circuit calibration.

b. 4-hour burn-in to ensure that a defective component fails.

c. diagnostic performance check.

d. a thorough visual inspection.

48. When a troubleshooting procedure requires a mathematical analysis,

a. use the most complicated theorem that you can apply.

b. find another way to solve your problem.

c. you are better off guessing.

d. use the simplest technique that applies.


A-16

49. A voltage source is defined as a circuit

a. with a current dependent output voltage.

b. that provides a constant current at its output terminals.

c. with a load dependent voltage output.

d. that provides a constant voltage at its output terminals.

50. With respect to network theorems, a closed loop represents

a. a complete single current path.

b. an open current path.

c. a partial current path.


DC Network Theorems Appendix B – Faults and Circuit Modifications (CMs)

B-1

APPENDIX B – FAULTS AND CIRCUIT MODIFICATIONS (CMS)

CM SCHEMATIC

SWITCH NO.

FAULT ACTION

– 21 1 places 910Ω in parallel

with 1.8-kΩ R1

– 22 2 R1 = 900Ω

– 23 3 R5 = 730Ω

– 24 4 shorts R1

– 26 6 R6 = 1500Ω

– 28 8 R3 = 2300Ω

– 29 9 R3 = 9700Ω

– 30 10 shorts R2

– 31 11 R1 = 2270Ω

– 32 12 R3 = 9200Ω

1 1 – places 3.9 kΩ in parallel

with 1.8-kΩ R1

2 2 – R2 = 4.4 kΩ


with 510Ω R2

4 4 – R3 = 1080Ω

5 5 – R5 = 440Ω

8 8 – R3 = 1070Ω

9 9 – places 47Ω in parallel

with 470Ω R5

12 12 – RB = 3740Ω

15 15 – R2 = 2050Ω

17 17 – R1 = 970Ω


with 3.6-kΩ R2


with 2.2-kΩ R2

20 20 – R3 = 10.1 kΩ

DC Network Theorems Appendix B – Faults and Circuit Modifications (CMs)

B-2

DC Network Theorems Appendix C – Board and Courseware Troubleshooting

C-1

APPENDIX C – BOARD AND COURSEWARE TROUBLESHOOTING

Circuit Board Problems

The F.A.C.E.T. equipment is carefully designed, manufactured, and tested to assure long,

reliable life. If you suspect a genuine failure in the equipment, the following steps should be

followed to trace a problem.

A. ALWAYS insert the board into a base unit before attempting to use an ohmmeter for

troubleshooting. The schematic diagrams imprinted on the boards are modified by the

absence of base unit switch connections; therefore, ohmmeter checks will produce erroneous

results with disconnected boards. Do not apply power to the base unit when you perform

resistance checks.

B. Information describing fault switch functions is provided in Appendix B in this instructor

guide.

Courseware Problems

The F.A.C.E.T. courseware has been written to meet carefully selected objectives. All exercises

have been tested for accuracy, and information presented in discussions has been reviewed for

technical content. Tolerances have been computed for all procedure and review question answers

to assure that responses are not invalidated by component or instrument errors.

Nevertheless, you or your students may discover mistakes or experience difficulty in using our

publications. We appreciate your comments and assure you that we will weigh them carefully in

our ongoing product improvement efforts.

As we address courseware problems, we will post corrections for download from our web site,

www.labvolt.com. Select the customer support tab, and then choose product line: F.A.C.E.T..

Select a course, select from a list of symptoms that have been addressed, and follow the

instructions.

DC Network Theorems Appendix C – Board and Courseware Troubleshooting

C-2

We will do our best to help you resolve problems if you call the number below. However, for

best results, and to avoid confusion, we prefer that you write with a description of the problem.

If you write, please include the following information:

• Your name, title, mailing address, and telephone number (please include the best time to

reach you).

• Publication title and number.

• Page number(s), and step and/or figure number(s) of affected material.

• Complete description of the problem encountered and any additional information that may

help us solve the problem.

Send your courseware comments to:

[email protected]

Lab-Volt Systems

P.O. Box 686

Farmingdale, NJ 07727

ATTN: Technical Support

If you prefer to telephone regarding hardware or courseware problems, call us between 9:00 AM

and 4:30 PM (Eastern time) at: (800) 522-4436 or (888)-LAB-VOLT.

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DC Network Theorems

DC Network Theorems

DC Network Theorems

Instructor Guide

Instructor Guide

Instructor Guide

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Binder Spine Labels

dc networks theorems

Documents

labvolt license agreement

labvolt systems

labvolt product

trademarks of lab

infringement of lab

cdrom software

trade secrets of lab

volts cdrom