DC Networks Theorems

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Instructor’s Guide

Edition 2 91561-10

SECOND EDITION

First Printing, July 2003

Copyright March, 2003 Lab-Volt Systems, Inc.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, photocopied, recorded, or otherwise, without prior written permission from Lab-Volt Systems, Inc. Information in this document is subject to change without notice and does not represent a ® ® commitment on the part of Lab-Volt Systems, Inc. The Lab-Volt F.A.C.E.T. software and other materials described in this document are furnished under a license agreement or a nondisclosure agreement. The software may be used or copied only in accordance with the terms of the agreement. ISBN 0-86657-226-0

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Table of Contents

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

Inventory of Workstation ............................................... .................................................... ......................................................... ..... 1-1 Minimum Computer Requirements.......... ............................................... ........................... 1-1 Equipment and Supplies................................................... Supplies ................................................... .................................................. 1-1 Equipment Installation .............................................. .................................................... .............................................................. .......... 1-1 Software Installation ................................................... .................................................... ............................................................ ........ 1-1 Section 2 – Introduction Introduction to F.A.C.E.T. Curriculum 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..................................................... 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 Courseware ............................................... .................................................... .............................................................. .......... 3-1 Unit 1 – DC Network Network Theorems ................................................... ............................................ 3-1

Exercise 1 – Component Location/Identification ................................................... ................ 3-2 Exercise 2 – Circuit Board Operation .......................................... ........................................... 3-6 Unit 2 – Kirchhoff’s Kirchhoff’s Current Current Law............................... Law............................................................................... ................................................ ........... 3-13

Exercise 1 – Current in a Branch Circuit Circuit .............................................. ................................ 3-15 Exercise 2 – Node Currents in a Branch Circuit .................................................. ................. 3-21 Unit 3 – Kirchhoff’s 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 Kirchhoff’s Loop Loop Equations. Equations..................................................... .................................................................................... ................................ 3-45

Exercise 1 – Loop Equations........................................... ............................................... ....... 3-46 Exercise 2 – Node Equations .......................................... ............................................... ....... 3-53

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Unit 5 – Kirchhoff’s Kirchhoff’s Solution Solution with 2 Sources................................................ 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 With 2 Sources ................................................ ......................... 3-78 Unit 6 – Superposition Superposition And Millman's Millman's Theorems 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............................................. Network ............................................. .............. 3-100 Exercise 2 – Thevenizing a Dual Source Network Network ....................................... ...................... 3-104 Unit 8 – Thevenizing Thevenizing a Bridge Bridge Circuit Circuit ................................................ ................................. 3-113

Exercise 1 – Bridge Circuit Resistance ............................................ ................................... 3-114 Exercise 2 – Thevenizing Bridge Circuit Voltage ............................................. ................. 3-117 Unit 9 – Thevenin/Nort Thevenin/Norton on Conversion Conversion............................................ ............................................ ..................................... 3-125

Exercise 1 – Thevenin to Norton Conversion............................................. Conversion ............................................. ........................ 3-127 Exercise 2 – Norton to Thevenin Conversion .............................................. ....................... 3-131 Unit 10 – Delta Delta and Wye Networks Networks ........................................... ........................................... 3-139

Exercise 1 – Tee/Wye Tee/Wye and Pi/Delta Networks Networks ........................................... ......................... 3-141 Exercise 2 – Delta and Wye Transformations...................... ............................................... 3-144 Appendix A – Pretest Pretest and Posttest Posttest Questions Questions and and Answers Answers ........................................... ...... A-1 Appendix B – Faults and Circuit Circuit Modifications Modifications (CMs) (CMs) ......................................... ................B-1 Appendix C – Board and Courseware Courseware Troubleshooting Troubleshooting.................................................. .................................................. ..... C-1

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

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SECTION 1 – WORKSTATION INVENTORY AND INSTALLATION

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DC Network Theorems

Section 1 – Workstation Inventory and Installation

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 1 1 1 1 1

Description

F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter Student Workbook 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. Lo ad all third party software according to the manufactur ers' 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 f or 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.

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Section 1 – Workstation Inventory and Installation

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

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

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.

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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.

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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 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 include s 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.

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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. depres sed. The menu selections access a va riety 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

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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.

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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 a re cases where students may progress progr ess 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.

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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 thresho ld for passing the unit test can be adjusted by using the Global Configurator of the Tech-Lab System. 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.

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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 computer saves this input value so that it can be recalled for use in later questions.

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%). e1p1 stands for Exercise 1 Procedure screen 1 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 fr om 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.

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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 repres ents the theoretical range of answers that could be ac cepted 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. Any letter enclosed in "#" signs refers to a recall value from a previous question.

Location: Exercise Procedure page: se1p5, Question ID: e1p5c

IT =

Since the value for #V1# is 14.5, the computer will accept answers in the following range as correct:

mA

Recall Label for this Question: I1 Nominal Answer: 9.091 * Min/Max Value: (6.477) to (11.93) Value Calculation: #V1#/1650*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 25 Correct Plus Tolerance = 25

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.

NOTE: After four incorrect answers, students will be prompted to press 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 fro m a previous question, answers obtained using the In sert key may not match the nominal answers in this guide.

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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 value of 10 was recalled from a previous screen.

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

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.

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

IR2 = VR2/R2 = #V4#/3.3 kΩ = mA Recall Label for this Question: I1 Nominal Answer: 2.818 Min/Max Value: (2.489) to (3.164) Value Calculation: #V4#/3.3 Correct Tolerance Percent = true Correct Minus Tolerance = 4 Correct Plus Tolerance = 4

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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.

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SECTION 3 – COURSEWARE

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Unit 1 – DC Network Theorems

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

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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. Location: Exercise Procedure page: se1p2, Question ID: e1p2a

R1 =

k Ω

Recall Label for this Question: None Nominal Answer: 1.8 Min/Max Value: (1.8) to (1.8) Value Calculation: 1.800 Correct Tolerance Percent = true Correct Minus Tolerance = 0 Correct Plus Tolerance = 0

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Location: Exercise Procedure page: se1p3, Question ID: e1p3a

3. The resistors used on the KIRCHHOFF'S VOLTAGE LAW circuit block are connected in a. series. b. parallel. c. series/parallel. Location: Exercise Procedure page: se1p4, Question ID: e1p4a

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 Location: Exercise Procedure page: se1p5, Question ID: e1p5a

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. Location: Exercise Procedure page: se1p6, Question ID: e1p6a

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. Location: Exercise Procedure page: se1p7, Question ID: e1p7a

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 Location: Exercise Procedure page: se1p8, Question ID: e1p8a

8. What does this symbol on the THEVENIN/NORTON CONVERSION circuit block represent? a. a current source b. a voltage source c. total resistance

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9. This resistor configuration is a a. T network. b. Y network. c. network. d. DELTA network. Location: Exercise Procedure page: se1p10, Question ID: e1p10a

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 Location: Review Questions page: se1r2, Question ID: e1r2

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. Location: Review Questions page: se1r3, Question ID: e1r3

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.

3-4

DC Network Theorems


Location: Review Questions page: se1r4, Question ID: e1r4

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. Location: Review Questions page: se1r5, Question ID: e1r5

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

3-5

DC Network Theorems


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 Location: Exercise Discussion page: se2d2, Question ID: e2d2a

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


VS =

Vdc

Recall Label for this Question: None Nominal Answer: 15.0 Min/Max Value: (14.55) to (15.45) Value Calculation: 15.000 Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se2p2, Question ID: e2p2c

R1 =

Ω

Recall Label for this Question: None Nominal Answer: 1800.0 Min/Max Value: (1440) to (2160) Value Calculation: 1800.000 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20

3-6

DC Network Theorems


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

R2 =

Ω

Recall Label for this Question: None Nominal Answer: 2200.0 Min/Max Value: (1760) to (2640) Value Calculation: 2200.000 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20 Location: Exercise Procedure page: se2p3, Question ID: e2p3a

4. What should the voltage drop across R1 or R2 be? a. the same as VS b. 0V Location: Exercise Procedure page: se2p4, Question ID: e2p4a

VR1 or VR2 =

Vdc

Recall Label for this Question: None Nominal Answer: 0.0 Min/Max Value: (0) to (0) Value Calculation: 0.000 Correct Tolerance Percent = true Correct Minus Tolerance = 0 Correct Plus Tolerance = 0 Location: Exercise Procedure page: se2p4, Question ID: e2p4c

6. Do your measurements indicate an open path to R1 or R2? a. yes b. no Location: Exercise Procedure page: se2p4, Question ID: e2p4e

IR1 =

mA


3-7

DC Network Theorems


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 Location: Exercise Procedure page: se2p5, Question ID: e2p5a

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.


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. Location: Review Questions page: se2r2, Question ID: e2r2

2. Measure total circuit voltage by placing a meter in position a. A. b. B. c. C. d. D. Location: Review Questions page: se2r3, Question ID: e2r3

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.

3-8

DC Network Theorems



4. Measure the voltage drop of R1 or R2 with a meter placed in position a. A. b. B. c. C. d. D. Location: Review Questions page: se2r5, Question ID: e2r5

5. For this circuit, how many two-post connectors are required to obtain maximum circuit current? a. 4 b. 3 c. 2 d. 1


3-9

DC Network Theorems


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. Location: Unit Test Question page: sut2, Question ID: ut2

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. Location: Unit Test Question page: sut3, Question ID: ut3

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. Location: Unit Test Question page: sut4, Question ID: ut4

Constant current sources a. have very low output impedances. b. vary the amount of current gener ated when the load changes. c. cannot be operated into open circuits. d. are load independent. Location: Unit Test Question page: sut5, Question ID: ut5

Network theorems are required because bec ause 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.

3-10

DC Network Theorems


Location: Unit Test Question page: sut6, Question ID: ut6

The 3 resistor types on the circuit board a. have equal tolerances. b. can be distinguished by color code va lues. c. are carbon composition, carbon film, and metal film types. d. have equal power dissipation ratings. Location: Unit Test Question page: sut7, Question ID: ut7

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 Location: Unit Test Question page: sut8, Question ID: ut8

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 d. None of the above. Location: Unit Test Question page: sut9, Question ID: ut9

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. Location: Unit Test Question page: sut10, Question ID: ut10

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.

3-11

DC Network Theorems


3-12

DC Network Theorems

Unit 2 – Kirchhoff’s Current Law

UNIT 2 – KIRCHHOFF’S CURRENT LAW

UNIT OBJECTIVE Analyze dc circuits by using Kirchhoff's current law. UNIT FUNDAMENTALS Location: Unit Fundamentals page: sf2, Question ID: f2a

What does the total circuit current equal? a. sum of both branch currents currents (CURRENT 1 + CURRENT 2) b. current through either branch bran ch (CURRENT 1 or CURRENT 2) Location: Unit Fundamentals page: sf3, Question ID: f3a

Total circuit current is the current through branch a. R1. b. R2. c. R1 and branch R2. Location: Unit Fundamentals page: sf4, Question ID: f4a

How many branches are there at each node in this parallel branch circuit? a. 1 b. 2 c. 3


3-13

DC Network Theorems


NEW TERMS AND WORDS Kirchhoff's current curr ent 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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-14

DC Network Theorems


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

VS =

Vdc

Recall Label for this Question: v1 Nominal Answer: 15.0 Min/Max Value: (14.55) to (15.45) Value Calculation: 15.000 Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p2, Question ID: e1p2a

R1 =

Ω

Recall Label for this Question: None Nominal Answer: 1800.0 Min/Max Value: (1800) to (1800) Value Calculation: 1800.000 Correct Tolerance Percent = true Correct Minus Tolerance = 0 Correct Plus Tolerance = 0

3-15

DC Network Theorems



R2 =

Ω

Recall Label for this Question: None Nominal Answer: 2200.0 Min/Max Value: (2200) to (2200) Value Calculation: 2200.000 Correct Tolerance Percent = true Correct Minus Tolerance = 0 Correct Plus Tolerance = 0 Location: Exercise Procedure page: se1p3, Question ID: e1p3a

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 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p3, Question ID: e1p3c

IR2 =

mA

Recall Label for this Question: i2 Nominal Answer: 6.818 * Min/Max Value: (5.952) to (7.725) Value Calculation: (#v1#/2200)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗

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. 3-16

DC Network Theorems



IT =

mA

Recall Label for this Question: i3 Nominal Answer: 15.15 ∗ Min/Max Value: (11.9 ) to (18.88) Value Calculation: #i1#+#i2# Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p5, Question ID: e1p5a

IR1 =

mA

Recall Label for this Question: i4 Nominal Answer: 8.33 Min/Max Value: (6.664) to (9.996) Value Calculation: 8.330 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20 Location: Exercise Procedure page: se1p5, Question ID: e1p5c

IR2 =

mA

Recall Label for this Question: i5 Nominal Answer: 6.82 Min/Max Value: (5.456) to (8.184) Value Calculation: 6.820 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20

∗


DC Network Theorems



IT =

mA

Recall Label for this Question: i6 Nominal Answer: 15.15 ∗ Min/Max Value: (11.51) to (19.09) Value Calculation: #i4#+#i5# Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se1p6, Question ID: e1p6a

11. Do your calculated and measured values agree within tolerance? a. yes b. no Location: Exercise Procedure page: se1p7, Question ID: e1p7a

IR1 =

mA

Recall Label for this Question: None Nominal Answer: 8.332 * Min/Max Value: (4.05 ) to (13.32) Value Calculation: (#i3#–#i2#) Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p8, Question ID: e1p8a

13. Does Kirchhoff's current law support the results you obtained from Ohm's law? a. no b. yes

∗


DC Network Theorems


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

IT =

mA

Recall Label for this Question: r1i1 Nominal Answer: 19.0 Min/Max Value: (15.2) to (22.8) Value Calculation: 19.000 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20 Location: Review Questions page: se1r1, Question ID: e1r1

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 Location: Review Questions page: se1r2, Question ID: e1r2

2. If IR1 is # r1i1 – 6.8 # mA (with CM 1 activated) and the source voltage (V S) is 15.00 Vdc, what is the present value of R1 in this circuit? a. approximately 12.0 k Ω b. 15 / # ( r1i1 – 6.8 )# c. approximately 12Ω 12Ω d. cannot be determined Location: Review Questions page: se1r3, Question ID: e1r3

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 I R2 does not change.

3-19

DC Network Theorems



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. Location: Review Questions page: se1r5, Question ID: e1r5

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

d. cannot be determined

CMS AVAILABLE CM 1 CM 1 TOGGLE FAULTS AVAILABLE None

3-20

DC Network Theorems


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 Location: Exercise Discussion page: se2d1, Question ID: e2d1a

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. Location: Exercise Discussion page: se2d2, Question ID: e2d2a

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

3-21

DC Network Theorems



VS =

Vdc


IR1 =

mA

Recall Label for this Question: i7 Nominal Answer: 8.333 ∗ Min/Max Value: (7.521) to (9.188) Value Calculation: (#v2#/1800)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se2p2, Question ID: e2p2c

IR2 =

mA

Recall Label for this Question: i8 Nominal Answer: 6.818 * Min/Max Value: (6.153) to (7.517) Value Calculation: (#v2#/2200)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5

∗


DC Network Theorems



IT (Kirchhoff's) =

mA

Recall Label for this Question: i9 Nominal Answer: 15.15 ∗ Min/Max Value: (12.99) to (17.54) Value Calculation: #i7#+#i8# Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se2p2, Question ID: e2p2g

6. Based on your results, is the current entering the circuit node equal to the current leaving the circuit node? a. yes b. no Location: Exercise Procedure page: se2p3, Question ID: e2p3a

IT (calculated) =

mA

Recall Label for this Question: i10 Nominal Answer: 15.15 * Min/Max Value: (13.67) to (16.7 ) Value Calculation: (.00101*#v2#)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se2p4, Question ID: e2p4a

8. Does the answer you calculated agree with the total current determined by Kirchhoff's current law? a. yes b. no

∗


DC Network Theorems



IR2 =

mA

Recall Label for this Question: None Nominal Answer: 6.8 Min/Max Value: (6.12) to (7.48) Value Calculation: 6.800 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Review Questions page: se2r1, Question ID: e2r1

The current out of the node a. increases. b. remains the same. c. decreases. d. None of the above. Location: Review Questions page: se2r2, Question ID: e2r2

2. With CM 2 still activated, the value of R2 is a. 1.1 k Ω. b. 2.2 k Ω. c. 4.4 k . d. cannot be determined. Location: Review Questions page: se2r3, Question ID: e2r3

3. Total circuit current (IT) is 11.7 mA, and I R1 is 8.32 mA. What is the value of I R2? a. 20.02 mA b. 3.38 mA c. 8.32 mA d. cannot be determined Location: Review Questions page: se2r4, Question ID: e2r4

4. When the resistance of R2 decreases, the node current a. increases. increases. b. remains the same. c. decreases. d. None of the above.

3-24

DC Network Theorems



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

3-25

DC Network Theorems



In this circuit, total circuit current (I T) 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. Location: Unit Test Question page: sut2, Question ID: ut2

Which statement defines the current out of NODE 1? a. IR1 + IR2 + IR3 b. IR2 + IR3 c. IT – (IR2 + IR3) d. IT + (IR2 + IR3) Location: Unit Test Question page: sut3, Question ID: ut3

Which statement defines the current into NODE 2? a. IR1 + IR2 + IR3 b. IT – IR1

c. IT – (IR2 + IR3) d. IT + (IR2 + IR3) Location: Unit Test Question page: sut4, Question ID: ut4

Which statement defines the current out of NODE 2? a. IR1 + IR2 + IR3 b. IR2 + IR3

c. IT – (IR2 + IR3) d. IT + (IR2 + IR3) Location: Unit Test Question page: sut5, Question ID: ut5

In this circuit, I T enters NODE 1. What part of IT does not go through NODE 2? a. IR3 b. IR2 c. IR1

d. None of the above.

3-26

DC Network Theorems



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. Location: Unit Test Question page: sut7, Question ID: ut7

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. Location: Unit Test Question page: sut8, Question ID: ut8

If R2 in this circuit increases in value, I R2 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. Location: Unit Test Question page: sut9, Question ID: ut9

Using Ohm's law and/or Kirchhoff's current law for parallel circuits, I T in this circuit a. cannot be determined. b. is 5 mA. c. is 10 mA. d. is 20 mA. Location: Unit Test Question page: sut10, Question ID: ut10

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. d. cannot be determined.

3-27

DC Network Theorems


TROUBLESHOOTING Location: Troubleshooting page: ttrba2, Question ID: trba2a

IT =

mA

Recall Label for this Question: it Nominal Answer: 15.15 Min/Max Value: (13.64) to (16.67) Value Calculation: 15.150 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba3, Question ID: trba3a

3. Does the total current (#it# mA) equal the sum of the branch currents? a. yes b. no Location: Troubleshooting page: ttrba4, Question ID: trba4a

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

3-28

DC Network Theorems

Unit 3 – Kirchhoff’s Voltage Law

UNIT 3 – KIRCHHOFF’S VOLTAGE LAW

UNIT OBJECTIVE Analyze dc circuits by using Kirchhoff's voltage law. UNIT FUNDAMENTALS Location: Unit Fundamentals page: sf2, Question ID: f2a

The circuit current (IT) in this closed series circuit is a. different in each circuit element. b. common to each circuit element. Location: Unit Fundamentals page: sf5, Question ID: f5a

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 sour ce(s) and voltage drops in a series circuit equals zero. c. Both of the above. Location: Unit Fundamentals page: sf7, Question ID: f7a

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


3-29

DC Network Theorems


NEW TERMS AND WORDS Kirchhoff's voltage vol tage 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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-30

DC Network Theorems


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 Location: Exercise Discussion page: se1d5, Question ID: e1d5a

Can you use Kirchhoff's voltage law for any number of elements in a series circuit? a. yes b. no


VS =

Vdc


3-31

DC Network Theorems



IT =

mA

Recall Label for this Question: I1 Nominal Answer: 10.14 ∗ Min/Max Value: (9.34 ) to (10.96) Value Calculation: # ( V1 / 1480 ) * 1000 # Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p2, Question ID: e1p2a

VR1 =

Vdc

Recall Label for this Question: V2 Nominal Answer: 2.231 * Min/Max Value: (1.952) to (2.532) Value Calculation: # ( I1 * 220 ) / 1000 # Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se1p2, Question ID: e1p2c

VR2 =

Vdc

Recall Label for this Question: V3 Nominal Answer: 5.171 * Min/Max Value: (4.525) to (5.869) Value Calculation: # ( I1 * 510 ) / 1000 # Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5

∗


DC Network Theorems



VR3 =

Vdc

Recall Label for this Question: V4 Nominal Answer: 7.605 ∗ Min/Max Value: (6.655) to (8.631) Value Calculation: # ( I1 * 750 ) / 1000 # Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se1p3, Question ID: e1p3a

Do your results prove that the sum of the voltage drops about equals the source voltage (VS #V1# Vdc)? a. yes b. no Location: Exercise Procedure page: se1p3, Question ID: e1p3c

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 Location: Exercise Procedure page: se1p4, Question ID: e1p4a

Based on this equation, which formula can you use to calculate the value of V R2? a. VR2 = VS – VR1 – VR3 b. VR2 = VS – (VR1 + VR3) c. Either of the above.

∗


DC Network Theorems



VR2 (calculated) =

Vdc

Recall Label for this Question: V5 Nominal Answer: 5.164 ∗ Min/Max Value: (2.933) to (7.5 ) Value Calculation: # V1 – V2 – V4 # Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se1p5, Question ID: e1p5a

VR2 (measured) =

Vdc

Recall Label for this Question: V6 Nominal Answer: 5.171 * Min/Max Value: (4.073) to (6.456) Value Calculation: #V3# Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p6, Question ID: e1p6a

12. Does your measured value agree with your calculated results, within tolerance? a. no b. yes Location: Exercise Procedure page: se1p7, Question ID: e1p7a

VR1 =

Vdc

Recall Label for this Question: V7 Nominal Answer: 2.231 * Min/Max Value: (1.849) to (2.652) Value Calculation: # ( I1 * 220 ) / 1000 # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗


DC Network Theorems



VR2 =

Vdc

Recall Label for this Question: None Nominal Answer: 5.171 ∗ Min/Max Value: (3.666) to (7.102) Value Calculation: #V6# Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p7, Question ID: e1p7e

VR3 =

Vdc

Recall Label for this Question: V8 Nominal Answer: 7.605 * Min/Max Value: (6.305) to (9.042) Value Calculation: # ( I1 * 750) / 1000 # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p8, Question ID: e1p8a

14. Does the sum of your measured voltage drops equal the value of your circuit voltage source? a. no b. yes

∗


DC Network Theorems



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. Location: Review Questions page: se1r2, Question ID: e1r2

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. Location: Review Questions page: se1r3, Question ID: e1r3

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. d. None of the above. Location: Review Questions page: se1r4, Question ID: e1r4

4. Using Kirchhoff's law, what is the voltage drop across R2 (V R2)? a. 15V b. 10V c. 5V d. cannot be determined Location: Review Questions page: se1r5, Question ID: e1r5

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

3-36

DC Network Theorems


CMS AVAILABLE CM 4 TOGGLE CM 3 TOGGLE FAULTS AVAILABLE None

3-37

DC Network Theorems


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 Location: Exercise Discussion page: se2d4, Question ID: e2d4a

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.


VS =

Vdc


3-38

DC Network Theorems



VR1 =

Vdc

Recall Label for this Question: V22 Nominal Answer: –2.23 ∗ Min/Max Value: (–2.53) to (–1.94) Value Calculation: –# ( V21 / 1480 ) * 220 # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p2, Question ID: e2p2c

VR2 =

Vdc

Recall Label for this Question: V23 Nominal Answer: –5.17 * Min/Max Value: (–5.86) to (–4.51) Value Calculation: –# ( V21 / 1480 ) * 510 # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p2, Question ID: e2p2e

VR3 =

Vdc

Recall Label for this Question: V24 Nominal Answer: –7.601 * Min/Max Value: (–8.61) to (–6.64) Value Calculation: –# ( V21 / 1480 ) * 750 # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗


DC Network Theorems



VR1 + VR2 + VR3 =

Vdc

Recall Label for this Question: V25 Nominal Answer: –15.0 ∗ Min/Max Value: (–17. ) to (–13.01) Value Calculation: # V21 * –1 # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p4, Question ID: e2p4a

Your result is closest to a. 0.0 Vdc. b. 15.00 Vdc. c. 30.00 Vdc.


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 d. None of the above. Location: Review Questions page: se2r2, Question ID: e2r2

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 44,200Ω. b. 4420Ω 4420Ω. c. 442 . d. not changed by the circuit modification.

∗


DC Network Theorems



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. Location: Review Questions page: se2r4, Question ID: e2r4

4. In this circuit, what is the value of R1? a. 1 k b. 10 k Ω c. 3 k Ω d. Cannot be determined. Location: Review Questions page: se2r5, Question ID: e2r5

5. In this circuit, what is the voltage drop of R2? a. 50 Vdc b. 25 Vdc c. 15 Vdc d. 10 Vdc


3-41

DC Network Theorems



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. Location: Unit Test Question page: sut2, Question ID: ut2

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. Location: Unit Test Question page: sut3, Question ID: ut3

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. Location: Unit Test Question page: sut4, Question ID: ut4

Which equation defines Kirchhoff's voltage law? a. VS = VR1 + VR2 b. 0 = VS – (VR1 + VR2) c. Both of the above. d. None of the above. Location: Unit Test Question page: sut5, Question ID: ut5

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 a. cannot be determined. b. is zero. c. can be determined from Kirchhoff's voltage law. d. must equal the voltage drop of the other elements.

3-42

DC Network Theorems



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. d. None of the above. Location: Unit Test Question page: sut7, Question ID: ut7

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. Location: Unit Test Question page: sut8, Question ID: ut8

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. Location: Unit Test Question page: sut9, Question ID: ut9

What is the value of each element? a. 0.5Ω 0.5Ω b. 1 c. 1.5Ω 1.5Ω d. None of the above. Location: Unit Test Question page: sut10, Question ID: ut10

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 n ot change. c. the sum of the voltage drops must decrease. d. more resistance must be added to the circuit.

3-43

DC Network Theorems



IT =

mA

Recall Label for this Question: None Nominal Answer: 10.14 Min/Max Value: (9.126) to (11.15) Value Calculation: 10.140 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba3, Question ID: trba3a

3. Does the sum of the voltage drops equal VS? a. yes b. no Location: Troubleshooting page: ttrba4, Question ID: trba4a

4. Does the algebraic sum of the voltages equal zero? a. yes b. no Location: Troubleshooting page: ttrba5, Question ID: trba5

6. The faulty component is a. R1 (increased). b. R2 (increased). c. R2 (decreased). d. R3 (decreased).


3-44

DC Network Theorems

Unit 4 – Kirchhoff’s Loop Equations

UNIT 4 – KIRCHHOFF’S LOOP EQUATIONS

UNIT OBJECTIVE Use loop equations by applying Kirchhoff's laws to a series/parallel circuit. UNIT FUNDAMENTALS Location: Unit Fundamentals page: sf2, Question ID: f2a

What is the loop equation for this loop? a. VR1 + VRS = VS b. VR2 + VRS = VS Location: Unit Fundamentals page: sf3, Question ID: f3a

For Kirchhoff's current law, which basic node equation is correct? a. Inode in = Inode out b. Inode out – Inode in = 0 c. Both of the above.

CMS AVAILABLE None FAULTS AVAILABLE None NEW TERMS AND WORDS None EQUIPMENT REQUIRED F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-45

DC Network Theorems


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 Location: Exercise Discussion page: se1d6, Question ID: e1d6a

Do the values show that Kirchhoff's voltage law for each loop equation is satisfied? a. yes b. no Location: Exercise Discussion page: se1d7, Question ID: e1d7a

Do the voltage values applied to the loop equations still result in zero? a. no b. yes


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 Location: Exercise Procedure page: se1p2, Question ID: e1p2a

The first loop includes a. R3, R2, and R1. b. R6, R5, and R4. c. R3, R2, R1, and VS.

3-46

DC Network Theorems



5. The second loop includes a. R3, R2, and R1. b. R6, R5, R4, and VS. c. R6, R5, R4, and R2. Location: Exercise Procedure page: se1p4, Question ID: e1p4a

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. Location: Exercise Procedure page: se1p5, Question ID: e1p5a

9. All current from the voltage source goes out through R3 and returns through a. R2. b. R5. c. R1. 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 Correct Tolerance Percent = true Correct Minus Tolerance = 25 Correct Plus Tolerance = 25

∗


DC Network Theorems



VR1 =

Vdc

Recall Label for this Question: V2 Nominal Answer: 2.455 ∗ Min/Max Value: (1.574) to (3.543) Value Calculation: #I1#*270/1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p6, Question ID: e1p6c

VR3 =

Vdc

Recall Label for this Question: V3 Nominal Answer: 6.182 * Min/Max Value: (3.964) to (8.924) Value Calculation: #I1#*680/1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p6, Question ID: e1p6e

13. Which loop equation can be used to determine V R2, 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)

∗


DC Network Theorems



VR2 = VS – (VR1 + VR3) =

Vdc

Recall Label for this Question: V4 Nominal Answer: 6.363 ∗ Min/Max Value: (1.605) to (11.23) Value Calculation: # V1 – ( V2 + V3 ) # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p7, Question ID: e1p7a

VR2 =

Vdc

Recall Label for this Question: V5 Nominal Answer: 6.363 * Min/Max Value: (1.445) to (12.35) Value Calculation: #V4# Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p7, Question ID: e1p7c

16. Are the calculated and measured values of V R2 the same within tolerance? a. no b. yes

∗


DC Network Theorems



VS =

Vdc

Recall Label for this Question: VR1 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 Location: Review Questions page: se1r1, Question ID: e1r1c

VR1 =

Vdc

Recall Label for this Question: VR2 Nominal Answer: 1.9378 ∗ Min/Max Value: (1.6568) to (2.2382) Value Calculation: (#VR1#/2090)*270 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Review Questions page: se1r1, Question ID: e1r1e

VR2 =

Vdc

Recall Label for this Question: VR3 Nominal Answer: 5.3 Min/Max Value: (4.77) to (5.83) Value Calculation: 5.3 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗


DC Network Theorems



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 d. cannot be determined Location: Review Questions page: se1r2, Question ID: e1r2

What is the voltage across R5? a. 2.5V b. 3V c. 7V d. 8V Location: Review Questions page: se1r3, Question ID: e1r3

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. Location: Review Questions page: se1r4, Question ID: e1r4

4. What law(s) may you use to analyze the voltages within the loop composed of V S, R1, R2, and R3? a. Ohm's law b. Kirchhoff's law c. Both of the above. d. None of the above. Location: Review Questions page: se1r5, Question ID: e1r5

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

3-51

DC Network Theorems


CMS AVAILABLE CM 8 TOGGLE FAULTS AVAILABLE None

3-52

DC Network Theorems


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 Location: Exercise Discussion page: se2d5, Question ID: e2d5a

In this circuit, if you know IT and I1, can you calculate I 2? a. yes b. no


VS =

Vdc


3-53

DC Network Theorems



VR3 =

Vdc

Recall Label for this Question: V22 Nominal Answer: 5.993 ∗ Min/Max Value: (5.124) to (6.922) Value Calculation: (#V21#/1702)*680 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p1, Question ID: e2p1e

IT =

mA

Recall Label for this Question: I21 Nominal Answer: 8.813 * Min/Max Value: (6.782) to (11.2 ) Value Calculation: (#V22#/680)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p2, Question ID: e2p2a

VR1 =

Vdc

Recall Label for this Question: V23 Nominal Answer: 2.38 * Min/Max Value: (1.648) to (3.326) Value Calculation: (#I21#*270)/1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗


DC Network Theorems



VR2 =

Vdc

Recall Label for this Question: V24 Nominal Answer: 6.627 ∗ Min/Max Value: (3.802) to (9.427) Value Calculation: # V21 – ( V22 + V23 ) # Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se2p3, Question ID: e2p3a

5. Does the current flowing through R2 move into or out of NODE 2? a. into NODE 2 b. out of NODE 2 Location: Exercise Procedure page: se2p4, Question ID: e2p4a

IR2 =

mA

Recall Label for this Question: I22 Nominal Answer: 4.418 * Min/Max Value: (2.281) to (6.913) Value Calculation: (#V24#/1500)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p4, Question ID: e2p4c

IR6 =

mA

Recall Label for this Question: I23 Nominal Answer: 4.395 * Min/Max Value: ( –.14) to (9.365) Value Calculation: #I21#–#I22# Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5

∗


DC Network Theorems



8. Knowing IR6, can you use Ohm's law to determine the voltage drops of R6, R5, and R4? a. no b. yes Location: Exercise Procedure page: se2p6, Question ID: e2p6a

VR6 =

Vdc

Recall Label for this Question: V25 Nominal Answer: 3.604 ∗ Min/Max Value: ( –.13) to (8.447) Value Calculation: (#I23#*820)/1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p6, Question ID: e2p6c

VR5 =

Vdc

Recall Label for this Question: V26 Nominal Answer: 2.066 * Min/Max Value: ( –.07) to (4.842) Value Calculation: (#I23#*470)/1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p6, Question ID: e2p6e

VR4 =

Vdc

Recall Label for this Question: V27 Nominal Answer: 0.967 * Min/Max Value: ( –.03) to (2.266) Value Calculation: (#I23#*220)/1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗


DC Network Theorems



10. Does the sum of the voltages and VR2 result in 0V for the loop? a. yes b. no Location: Exercise Procedure page: se2p8, Question ID: e2p8a

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


1. In this circuit, I 1 a. moves into NODE 1. b. moves out of NODE 1. c. must be zero. d. equals IT + I1. Location: Review Questions page: se2r2, Question ID: e2r2

2. The current into NODE 2 equals a. IT – I2. b. IT + I1. c. I1 + I2.

d. I2 + IT. Location: Review Questions page: se2r3, Question ID: e2r3a

VR5 =

Vdc

Recall Label for this Question: VR21 Nominal Answer: 2.07 Min/Max Value: (1.863) to (2.277) Value Calculation: 2.070 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

3-57

DC Network Theorems



3. The I2 current out of NODE 1 a. increases. increases. b. decreases. c. remains the same. d. None of the above. Location: Review Questions page: se2r4, Question ID: e2r4

4. Since activating CM 9 increases I 2, the I1 current out of NODE 1 a. increases. b. does not change. c. decreases. d. None of the above. Location: Review Questions page: se2r5, Question ID: e2r5

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

3-58

DC Network Theorems



Which diagram correctly shows node current? a. A b. B c. C d. D Location: Unit Test Question page: sut2, Question ID: ut2

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. Location: Unit Test Question page: sut3, Question ID: ut3

A node represents a circuit point where a. voltages are combined. b. resistances are combined. c. currents are combined. d. charge must accumulate. Location: Unit Test Question page: sut4, Question ID: ut4

When you use Kirchhoff's laws, algebraic signs are a. required. b. not required. c. required for voltage only. d. required for current only. Location: Unit Test Question page: sut5, Question ID: ut5

In this circuit, the a. voltage drops are greater than the voltage source. b. voltage drops are less than the voltage s ource. c. given equation does not specify the circuit. d. given equation specifies the circuit.

3-59

DC Network Theorems



In this circuit, I B a. flows out of NODE 1. b. flows into NODE 1. c. equals IT.

d. does not flow into NODE 2. Location: Unit Test Question page: sut7, Question ID: ut7

In this circuit, I C a. equals IB. b. equals I A. c. equals IT.

d. flows into NODE 2. Location: Unit Test Question page: sut8, Question ID: ut8

The value of IB equals a. IT + IA. b. IT – IA.

c. IT. d. IB + IA. Location: Unit Test Question page: sut9, Question ID: ut9

The missing voltage is a. 10V. b. 5V. c. 1V. d. None of the above. Location: Unit Test Question page: sut10, Question ID: ut10

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.

3-60

DC Network Theorems



IT =

mA

Recall Label for this Question: TSIT1 Nominal Answer: 8.81 Min/Max Value: (7.929) to (9.691) Value Calculation: 8.810 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba2, Question ID: trba2c

VR2 =

V

Recall Label for this Question: TSV1 Nominal Answer: 6.63 Min/Max Value: (5.967) to (7.293) Value Calculation: 6.63 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba3, Question ID: trba3a

3. Does the total circuit current (#TSIT1# mA) flow through R2? a. yes b. no Location: Troubleshooting page: ttrba4, Question ID: trba4a

4. Does the sum of VR3, VR2, and VR1 equal VS? a. yes b. no Location: Troubleshooting page: ttrba5, Question ID: trba5

6. The faulty component is a. R1 (shorted). b. R2 (open). c. R4 (shorted). d. R6 (increased).

3-61

DC Network Theorems


Location: Troubleshooting page: ttrbb2, Question ID: trbb2a

IT =

mA

Recall Label for this Question: TSIT2 Nominal Answer: 8.81 Min/Max Value: (7.929) to (9.691) Value Calculation: 8.810 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrbb2, Question ID: trbb2c

VR2 =

V

Recall Label for this Question: TSV2 Nominal Answer: 6.63 Min/Max Value: (5.967) to (7.293) Value Calculation: 6.63 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrbb3, Question ID: trbb3

4. The faulty component is a. R1 (shorted). b. R2 (open). c. R4 (shorted). d. R6 (increased).

CMS AVAILABLE None FAULTS AVAILABLE Fault 4 Fault 6

3-62

DC Network Theorems

Unit 5 – Kirchhoff’s Solution with 2 Sources

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 Location: Unit Fundamentals page: sf2, Question ID: f2a

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

How many nodes are in this circuit? a. 1 b. 2 c. 3 Location: Unit Fundamentals page: sf8, Question ID: f8a

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


3-63

DC Network Theorems


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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-64

DC Network Theorems


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 Location: Exercise Discussion page: se1d2, Question ID: e1d2a

What is the third loop composed of? a. VS1, R3, and R1 b. VS2, R3, and R2 c. VS1, R1, R2, and VS2 Location: Exercise Discussion page: se1d3, Question ID: e1d3a

What is the LOOP 2 equation? a. VS1 – VR3 – VR1 = 0 b. VS2 – VR2 + VR3 = 0

3-65

DC Network Theorems



VS1 =

Vdc

Recall Label for this Question: v1 Nominal Answer: 10.0 Min/Max Value: (9.7) to (10.3) Value Calculation: 10.000 Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p1, Question ID: e1p1c

VS2 =

Vdc


4. VS1, R1, and R3 form which loop in this circuit? a. LOOP 1 b. LOOP 2 Location: Exercise Procedure page: se1p2, Question ID: e1p2c

5. VS2, R2, and R3 form which loop in this circuit? a. LOOP 1 b. LOOP 2 Location: Exercise Procedure page: se1p2, Question ID: e1p2e

6. The third loop is composed of a. LOOP 1 and LOOP 2. b. VS1, R1, R2, and VS2.

3-66

DC Network Theorems



VR1 =

Vdc


VR2 =

Vdc

Recall Label for this Question: v4 Nominal Answer: 16.05 Min/Max Value: (12.84) to (19.26) Value Calculation: 16.050 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20 Location: Exercise Procedure page: se1p3, Question ID: e1p3e

VR3 =

Vdc

Recall Label for this Question: v5 Nominal Answer: 6.05 Min/Max Value: (4.84) to (7.26) Value Calculation: 6.050 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20

3-67

DC Network Theorems



VLOOP 1 =

Vdc

Recall Label for this Question: None Nominal Answer: 0.0 ∗ Min/Max Value: (–2.53) to (2.53) Value Calculation: #v1#–#v5#–#v3# Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p5, Question ID: e1p5c

VLOOP 2 =

Vdc

Recall Label for this Question: None Nominal Answer: 0.0 * Min/Max Value: (–5.19) to (5.19) Value Calculation: # v4 – v2 – v5 # Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p6, Question ID: e1p6a

13. Do your calculations agree with Kirchhoff's voltage law? a. no b. yes Location: Exercise Procedure page: se1p6, Question ID: e1p6c

14. Does Kirchhoff's voltage law apply to a circuit with two voltage sources? a. no b. yes

∗


DC Network Theorems



How many loops are in this circuit? a. 4 b. 3 c. 2 d. 1 Location: Review Questions page: se1r2, Question ID: e1r2

2. CM 17 is now activated to change the value of R1. Using the V S2, R2, and R3 circuit loop, with VS2 = 10V and VR2 = 15.22 Vdc, what is VR3? a. +5.22V b. –5.22V c. Either of the above. d. None of the above. Location: Review Questions page: se1r3, Question ID: e1r3

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. d. cannot be determined. Location: Review Questions page: se1r4, Question ID: e1r4

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 Location: Review Questions page: se1r5, Question ID: e1r5

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. d. cannot be determined.

3-69

DC Network Theorems


CMS AVAILABLE CM 17 FAULTS AVAILABLE None

3-70

DC Network Theorems


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 Location: Exercise Discussion page: se2d2, Question ID: e2d2a

Which equation is correct? a. IR1 = VR1 /R1 b. IR2 = VR2 /R2 c. IR3 = VR3 /R3 d. All of the above. Location: Exercise Discussion page: se2d4, Question ID: e2d4a

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. c. Both of the above.

3-71

DC Network Theorems



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 Location: Exercise Procedure page: se2p3, Question ID: e2p3a

4. In this circuit, the voltage drop across which resistor allows for a complete circuit solution? a. R1 b. R2 c. R3

3-72

DC Network Theorems



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 Location: Exercise Procedure page: se2p4, Question ID: e2p4e

7. Based on your measurement and polarity of VR3, is the assumed current flow correct? a. no b. yes Location: Exercise Procedure page: se2p5, Question ID: e2p5a

IR3 =

mA

Recall Label for this Question: i21 Nominal Answer: 0.807 ∗ Min/Max Value: ( .581) to (1.065) Value Calculation: (#v23#/7500)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗


DC Network Theorems



IR1 =

mA

Recall Label for this Question: i22 Nominal Answer: 5.267 ∗ Min/Max Value: (2.928) to (8.008) Value Calculation: ((#v21#–#v23#)/750)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p6, Question ID: e2p6a

VR1 =

Vdc

Recall Label for this Question: v24 Nominal Answer: 3.95 * Min/Max Value: (1.713) to (7.327) Value Calculation: (#i22#/1000)*750 Correct Tolerance Percent = true Correct Minus Tolerance = 22 Correct Plus Tolerance = 22 Location: Exercise Procedure page: se2p6, Question ID: e2p6c

IR2 =

mA

Recall Label for this Question: i23 Nominal Answer: 4.458 * Min/Max Value: (3.635) to (5.366) Value Calculation: ((#v22#+#v23#)/3600)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10

∗


DC Network Theorems



VR2 =

Vdc

Recall Label for this Question: v25 Nominal Answer: 16.05 ∗ Min/Max Value: (10.08) to (23.76) Value Calculation: (#i23#/1000)*3600 Correct Tolerance Percent = true Correct Minus Tolerance = 23 Correct Plus Tolerance = 23 Location: Exercise Procedure page: se2p7, Question ID: e2p7a

13. Do the NODE 1 currents agree with Kirchhoff's current law? a. no b. yes Location: Exercise Procedure page: se2p7, Question ID: e2p7c

14. Do the voltages agree with Kirchhoff's voltage law for each loop? a. no b. yes

∗


DC Network Theorems



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 Location: Review Questions page: se2r2, Question ID: e2r2

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. Location: Review Questions page: se2r3, Question ID: e2r3

3. Based on this circuit, what is the value of V R2? a. VS1 – VR1 b. VS2 + VR3

c. VR3 + VR1 d. None of the above. Location: Review Questions page: se2r4, Question ID: e2r4

4. With CM 18 active, about what is the value of R2? a. cannot be determined b. 3600Ω 3600Ω c. 2278 d. 956Ω 956Ω Location: Review Questions page: se2r5, Question ID: e2r5

5. What is the value of I 3? a. cannot be determined b. 5.26 mA c. 6.07 mA d. 7.07 mA

3-76

DC Network Theorems



3-77

DC Network Theorems


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 Location: Exercise Discussion page: se3d3, Question ID: e3d3a

For MESH 2, a. VR1 and VR2 are positive. b. VR2 and VR3 are negative. c. VR2 and VR3 are positive. Location: Exercise Discussion page: se3d4, Question ID: e3d4a

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 V S2; therefore, VS2 is considered a. positive (+). b. negative (–).

3-78

DC Network Theorems



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 Location: Exercise Procedure page: se3p2, Question ID: e3p2c

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) – (I 1 x R3) = VS2 Location: Exercise Procedure page: se3p3, Question ID: e3p3a

6. Do the mesh currents through R3 flow in the same or in opposite directions? a. same b. opposite Location: Exercise Procedure page: se3p3, Question ID: e3p3c

You can determine the actual current through R3 by a. subtracting I 1 and I2. b. adding I1 and I2. Location: Exercise Procedure page: se3p3, Question ID: e3p3e

IR3 =

mA

Recall Label for this Question: i31 Nominal Answer: 0.81 Min/Max Value: ( .769) to ( .851) Value Calculation: 0.810 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5

3-79

DC Network Theorems



VR3 (calculated) =

Vdc

Recall Label for this Question: v31 Nominal Answer: 6.075 ∗ Min/Max Value: (3.98 ) to (8.361) Value Calculation: (#i31#/1000)*7500 Correct Tolerance Percent = true Correct Minus Tolerance = 31 Correct Plus Tolerance = 31 Location: Exercise Procedure page: se3p4, Question ID: e3p4a

VR3 (measured) =

Vdc

Recall Label for this Question: v32 Nominal Answer: 6.075 * Min/Max Value: (3.98 ) to (8.361) Value Calculation: (#i31#/1000)*7500 Correct Tolerance Percent = true Correct Minus Tolerance = 31 Correct Plus Tolerance = 31 Location: Exercise Procedure page: se3p4, Question ID: e3p4c

11. Do your calculated and measured values agree? a. no b. yes Location: Exercise Procedure page: se3p4, Question ID: e3p4e

12. With VR3 known, can you determine the voltage drops of each circuit resistor? a. no b. yes Location: Exercise Procedure page: se3p5, Question ID: e3p5a

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.

∗


DC Network Theorems



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. d. None of the above. Location: Review Questions page: se3r2, Question ID: e3r2

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. Location: Review Questions page: se3r3, Question ID: e3r3

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. Location: Review Questions page: se3r4, Question ID: e3r4

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 corre ct. c. both its value and direction are correct. d. neither its value nor its direction is correct. Location: Review Questions page: se3r5, Question ID: e3r5

5. If R1 is a common circuit resistance between two meshes, and if I 1 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 I 2) = VR1

3-81

DC Network Theorems



3-82

DC Network Theorems



How many possible loops does this circuit have? a. 4 b. 3 c. 2 d. 1 Location: Unit Test Question page: sut2, Question ID: ut2

How many nodes does this circuit have? a. 4 b. 3 c. 2 d. 1 Location: Unit Test Question page: sut3, Question ID: ut3

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. Location: Unit Test Question page: sut4, Question ID: ut4

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. Location: Unit Test Question page: sut5, Question ID: ut5

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.

3-83

DC Network Theorems



In this circuit, a. IT = IR2 + IR3. b. IT – IR2 – IR3 = 0. c. Both of the above. d. None of the above. Location: Unit Test Question page: sut7, Question ID: ut7

Which statement applies to this circuit? a. (VS1 – VA)/R1 = (VA – VS2)/R2 + (VA/R3) b. The sum of the currents of each e ach node must equal zero. c. Both Ohm's law and Kirchhoff's current law can be applied to the circuit. d. All of the above. Location: Unit Test Question page: sut8, Question ID: ut8

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. Location: Unit Test Question page: sut9, Question ID: ut9

In this circuit, VS1 equals VS2, and R1, R2, and R3 are equal in value. As a result, a. VR3 and I R3 each equal zero.

b. VR3 = VS1 + VS2. c. VR3 = VS1 or VS2, but not both. d. None of the above. Location: Unit Test Question page: sut10, Question ID: ut10

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. d. None of the above.

3-84

DC Network Theorems



VR3 =

Vdc

Recall Label for this Question: None Nominal Answer: 6.05 Min/Max Value: (5.445) to (6.655) Value Calculation: 6.050 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba3, Question ID: trba3

4. The faulty component is a. R3 (decreased). b. R3 (increased). c. R2 (shorted). d. R1 (open). Location: Troubleshooting page: ttrbb2, Question ID: trbb2a

VR3 =

Vdc

Recall Label for this Question: None Nominal Answer: 6.05 Min/Max Value: (5.445) to (6.655) Value Calculation: 6.050 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrbb3, Question ID: trbb3

4. The faulty component is a. R3 (decreased). b. R3 (increased). c. R2 (shorted). d. R1 (open).

3-85

DC Network Theorems



3-86

DC Network Theorems

Unit 6 – Superposition and Millman's Theorems

UNIT 6 – SUPERPOSITION AND MILLMAN'S THEOREMS

UNIT OBJECTIVE Determine voltages and currents by using the superposition theorem and Millman's theorem. UNIT FUNDAMENTALS Location: Unit Fundamentals page: sf2, Question ID: f2a

Is VR3 measured with respect to circuit common? a. yes b. no Location: Unit Fundamentals page: sf5, Question ID: f5a

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 theo rem - 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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-87

DC Network Theorems


Exercise 1 – Superposition Theorem

EXERCISE OBJECTIVE Apply the superposition method of circuit analysis. Verify results with a multimeter. EXERCISE DISCUSSION Location: Exercise Discussion page: se1d3, Question ID: e1d3a

When you determine the effect of VS2 on VR3, which resistor is placed in parallel with R3? a. R1 b. R2 c. R3


R A =

Ω

Recall Label for this Question: ra Nominal Answer: 265.0 Min/Max Value: (259.7) to (270.3) Value Calculation: 265.000 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2 Location: Exercise Procedure page: se1p2, Question ID: e1p2c

R B =

Ω

Recall Label for this Question: rb Nominal Answer: 338.0 Min/Max Value: (331.2) to (344.8) Value Calculation: 338.000 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2

3-88

DC Network Theorems



VRA =

Vdc

Recall Label for this Question: vra Nominal Answer: 3.419 ∗ Min/Max Value: (3.273) to (3.568) Value Calculation: (10*#ra#)/(510+#ra#) Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p4, Question ID: e1p4a

VRB =

Vdc

Recall Label for this Question: vrb Nominal Answer: –4.84 * Min/Max Value: (–4.93) to (–4.74) Value Calculation: (–10*#rb#)/(360+#rb#) Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p5, Question ID: e1p5a

VR3 =

Vdc

Recall Label for this Question: vr3 Nominal Answer: –1.42 * Min/Max Value: (–1.71) to (–1.14) Value Calculation: #vra#+#vrb# Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p5, Question ID: e1p5c

7. Measure the voltage drop across R3. Is the measured value the same as the calculated value of #vr3#V? a. yes b. no

∗


DC Network Theorems



8. Does the superposition circuit solution conform to Kirchhoff's voltage law? a. yes b. no Location: Exercise Procedure page: se1p6, Question ID: e1p6c

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 Location: Exercise Procedure page: se1p7, Question ID: e1p7a

10. Based on the circuit information, is the superposition theorem required to calculate circuit voltage drops and current distribution? a. yes b. no


1. The superposition method of circuit analysis requires a. mesh equations. b. node equations. c. Kirchhoff's equations. d. Ohm's law. Location: Review Questions page: se1r2, Question ID: e1r2

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.

3-90

DC Network Theorems



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. Location: Review Questions page: se1r4, Question ID: e1r4

4. In which position must you set S1 to determine the effect of V S2 on R3? a. position A b. position B c. either position d. neither (the switch must be removed from the circuit) Location: Review Questions page: se1r5, Question ID: e1r5

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.


3-91

DC Network Theorems


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 Location: Exercise Discussion page: se2d4, Question ID: e2d4a

Which parameter defines the voltage across BRANCH 1 of the circuit? a. VS2 + VR2 b. VS1 + VR1 c. VR3 d. All of the above. Location: Exercise Discussion page: se2d4, Question ID: e2d4c

Are the branch voltages equal? a. yes b. no


GT =

millisiemens

Recall Label for this Question: GT Nominal Answer: 5.739 Min/Max Value: (5.624) to (5.853) Value Calculation: ((1/360)+(1/1000)+(1/510))*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2

3-92

DC Network Theorems



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) Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se2p3, Question ID: e2p3e

IR3 =

mA

Recall Label for this Question: None Nominal Answer: 0.0 Min/Max Value: (0) to (0) Value Calculation: 0.000 Correct Tolerance Percent = true Correct Minus Tolerance = 0 Correct Plus Tolerance = 0 Location: Exercise Procedure page: se2p3, Question ID: e2p3g

IR2 =

mA

Recall Label for this Question: IR2 Nominal Answer: 19.61 Min/Max Value: (19.02) to (20.2 ) Value Calculation: (10/510)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3

3-93

DC Network Theorems



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# Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se2p5, Question ID: e2p5a

8. Based on the Millman solution for VR3, can you determine the actual circuit currents and voltage drops? a. yes b. no Location: Exercise Procedure page: se2p6, Question ID: e2p6a

9. Use your voltmeter to measure VR3. Are your results consistent with Millman's theorem? a. yes b. no Location: Exercise Procedure page: se2p7, Question ID: e2p7a

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

∗


DC Network Theorems



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 d. None of the above. Location: Review Questions page: se2r2, Question ID: e2r2

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 d. All of the above. Location: Review Questions page: se2r3, Question ID: e2r3

3. With respect to circuit common, what is the voltage drop across R3? a. 0.7V b. –0.7V c. Either of the above. d. None of the above. Location: Review Questions page: se2r4, Question ID: e2r4

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. Location: Review Questions page: se2r5, Question ID: e2r5

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 V S1 or VS2 when they are measured with respect to circuit common.

3-95

DC Network Theorems



3-96

DC Network Theorems



The superposition method of circuit analysis requires a. mesh equations. b. node equations. c. Kirchhoff equations. d. Ohm's law. Location: Unit Test Question page: sut2, Question ID: ut2

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. Location: Unit Test Question page: sut3, Question ID: ut3

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. Location: Unit Test Question page: sut4, Question ID: ut4

Which resistors are in parallel? a. R1 and R2 b. R1 and R3 c. R2 and R3 d. All 3 resistors are in parallel. Location: Unit Test Question page: sut5, Question ID: ut5

What is the value of VR2? a. 20V b. 10V c. 0V d. –10V

3-97

DC Network Theorems



What is the total conductance of the circuit? a. 2.01 mS b. 3 mS c. 50 mS d. None of the above. Location: Unit Test Question page: sut7, Question ID: ut7

Based on a Millman configuration, how many branch circuits are present? a. 4 b. 3 c. 2 d. 1 Location: Unit Test Question page: sut8, Question ID: ut8

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. Location: Unit Test Question page: sut9, Question ID: ut9

What is the value of V1? a. 20V b. –20V c. 10V d. 0V Location: Unit Test Question page: sut10, Question ID: ut10

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.

3-98

DC Network Theorems

Unit 7 – Thevenin Circuits

UNIT 7 – THEVENIN CIRCUITS

UNIT OBJECTIVE Simplify one- and two-source circuits by using Thevenin's theorem. UNIT FUNDAMENTALS Location: Unit Fundamentals page: sf3, Question ID: f3a

For a specific load, do both circuits provide the same load voltage and load current? a. yes b. no Location: Unit Fundamentals page: sf6, Question ID: f6a

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. V TH TH - 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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-99

DC Network Theorems


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 Location: Exercise Procedure page: se1p2, Question ID: e1p2a

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 Location: Exercise Procedure page: se1p2, Question ID: e1p2c

R TH =

Ω

Recall Label for this Question: rth Nominal Answer: 990.0 Min/Max Value: (970.2) to ( 1010) Value Calculation: 990.000 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2 Location: Exercise Procedure page: se1p3, Question ID: e1p3a

4. Measure R TH with an ohmmeter. Are the measured and calculated values (#rth#Ω (#rth# Ω) about the same? a. yes b. no

3-100

DC Network Theorems



VTH =

Vdc

Recall Label for this Question: vth Nominal Answer: 5.5 Min/Max Value: (5.39) to (5.61) Value Calculation: 5.500 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2 Location: Exercise Procedure page: se1p4, Question ID: e1p4c

6. Measure VTH of the network. Does the measured value agree with the calculated value (#vth# Vdc)? a. yes b. no Location: Exercise Procedure page: se1p5, Question ID: e1p5a

IRL =

µA

Recall Label for this Question: ir3 Nominal Answer: 706.0 ∗ Min/Max Value: (669.4) to (743.6) Value Calculation: (((#vth#*6800)/(#rth#+6800))/6800)*1000000 Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se1p6, Question ID: e1p6a

8. Measure VR3. Based on R3 (6800Ω (6800Ω), does the load current agree with the current supplied by the thevenized circuit (#ir3# µA)? IR3 = VR3 /R3 a. yes b. no

∗


DC Network Theorems



IRL =

µA

Recall Label for this Question: ilcm19 Nominal Answer: 1168.0 Min/Max Value: ( 1051) to ( 1285) Value Calculation: 1168.000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se1p8, Question ID: e1p8a

10. CM 19 is activated to change the load resistor. Measure V RL 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 Location: Exercise Procedure page: se1p9, Question ID: e1p9a

11. Are the polarities of the load voltage and V TH identical? a. yes b. no


1. In this circuit, R TH a. cannot be determined. b. cannot be measured. c. equals R1 + (R1 x R2)/(R1 + R2). d. equals R1, R2, and R3 in parallel. Location: Review Questions page: se1r2, Question ID: e1r2

2. CM 20 is activated to change R3 to 10.1 k Ω. With respect to B, what is the value of VTH? a. 10V b. +5.5V c. –5.5V d. VTH cannot be determined.

3-102

DC Network Theorems



3. What is the value of R TH? a. –990Ω –990Ω b. 990 c. 902Ω 902Ω d. R TH cannot be determined. Location: Review Questions page: se1r4, Question ID: e1r4

4. In this network, the polarity of VTH a. has no effect on the current flow through R TH. 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. Location: Review Questions page: se1r5, Question ID: e1r5

5. If R2 is removed from this circuit, a. VTH changes but R TH does not. b. VTH does not change but R TH does. c. Both VTH and R TH change.

d. neither VTH nor R TH changes.

CMS AVAILABLE CM 19 CM 20 FAULTS AVAILABLE None

3-103

DC Network Theorems


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 Location: Exercise Procedure page: se2p2, Question ID: e2p2a

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 Location: Exercise Procedure page: se2p3, Question ID: e2p3a

R TH =

Ω

Recall Label for this Question: rth2 Nominal Answer: 498.0 Min/Max Value: (488. ) to (508. ) Value Calculation: 498.000 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2 Location: Exercise Procedure page: se2p4, Question ID: e2p4a

4. Use two-post connectors to remove and short both voltage sources. Measure R TH. Is your measured value about the same as the calculated value of 498Ω 498 Ω? a. yes b. no

3-104

DC Network Theorems



VTH =

Vdc

Recall Label for this Question: vth2 Nominal Answer: –2.21 Min/Max Value: (–2.25) to (–2.17) Value Calculation: –2.210 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2 Location: Exercise Procedure page: se2p6, Question ID: e2p6a

6. Place VS1 and VS2 back into your circuit. Measure V R2, or VTH. Are the measured and calculated (#vth2# Vdc) values about the same? a. yes b. no Location: Exercise Procedure page: se2p7, Question ID: e2p7a

7. Based on the Thevenin equivalent circuit shown, what is the expected voltage drop across a 6800Ω 6800Ω resistor? a. 2.06 Vdc b. –2.06 Vdc c. 2.21 Vdc d. –2.21 Vdc Location: Exercise Procedure page: se2p8, Question ID: e2p8a

8. Is VR3 about the same as V TH (#vth2# Vdc)? a. yes b. no Location: Exercise Procedure page: se2p9, Question ID: e2p9a

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).

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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 R TH. b. produces no change in R TH.

c. produces a small change in R TH. d. must be offset by a change in R2. Location: Review Questions page: se2r2, Question ID: e2r2

2. For you to determine R TH, 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. Location: Review Questions page: se2r3, Question ID: e2r3

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. Location: Review Questions page: se2r4, Question ID: e2r4

4. For the circuit shown, VTH and R TH respectively are a. 2.22V and 498Ω 498Ω. b. –2.22V and 498 . c. 2.22V and 10.1 k Ω. d. –2.22V and 10.1 k Ω. Location: Review Questions page: se2r5, Question ID: e2r5

5. CM 20 is deactivated. A change in R L a. produces a large change in VTH. b. produces no change in V TH.

c. produces a small change in V TH. d. must be offset by a change within the network.

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Thevenizing a circuit creates an equivalent a. series circuit. b. series/parallel circuit. c. parallel circuit. d. None of the above. Location: Unit Test Question page: sut2, Question ID: ut2

In a Thevenin circuit, VTH a. equals the voltage across the circuit load. b. equals the voltage across R TH. c. equals the voltage across the open circuit terminals of the network. d. cannot be determined without R TH. Location: Unit Test Question page: sut3, Question ID: ut3

In a Thevenin circuit, R TH 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. Location: Unit Test Question page: sut4, Question ID: ut4

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. Location: Unit Test Question page: sut5, Question ID: ut5

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.

3-108

DC Network Theorems



To determine R TH 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. Location: Unit Test Question page: sut7, Question ID: ut7

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. Location: Unit Test Question page: sut8, Question ID: ut8

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. Location: Unit Test Question page: sut9, Question ID: ut9

In this circuit, R TH a. is greater than 1 k Ω. b. is less than 1 k . c. equals 1 k Ω. d. cannot be determined. Location: Unit Test Question page: sut10, Question ID: ut10

In this circuit, VTH a. is 10V. b. is 8V. c. is 2V. d. changes when a load is connected.

3-109

DC Network Theorems



VR3 =

Vdc

Recall Label for this Question: None Nominal Answer: –2.06 Min/Max Value: (–2.27) to (–1.85) Value Calculation: –2.060 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba3, Question ID: trba3a

R TH =

Ω

Recall Label for this Question: None Nominal Answer: 497.0 Min/Max Value: (447.3) to (546.7) Value Calculation: 497 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba3, Question ID: trba3c

VTH =

Vdc

Recall Label for this Question: None Nominal Answer: –2.17 Min/Max Value: (–2.39) to (–1.95) Value Calculation: –2.170 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba4, Question ID: trba4

6. The faulty component is a. VTH and R TH (out of specification). b. R1 (open). c. R1 (increased). (increased). d. R3 (increased).

3-110

DC Network Theorems


Location: Troubleshooting page: ttrbb2, Question ID: trbb2a

VR3 =

Vdc

Recall Label for this Question: None Nominal Answer: –2.06 Min/Max Value: (–2.27) to (–1.85) Value Calculation: –2.060 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrbb3, Question ID: trbb3a

3. Based on the circuit values, does a change in load voltage generate a change in R TH or VTH? a. yes b. no Location: Troubleshooting page: ttrbb4, Question ID: trbb4

6. The faulty component is a. VTH and R TH (out of specification). b. R1 (open). c. R1 (increased). d. R3 (increased).


3-111

DC Network Theorems


3-112

DC Network Theorems

Unit 8 – Thevenizing a Bridge Circuit

UNIT 8 – THEVENIZING A BRIDGE CIRCUIT

UNIT OBJECTIVE Thevenize a resistive bridge circuit by using the resistor divider equation. UNIT FUNDAMENTALS Location: Unit Fundamentals page: sf2, Question ID: f2a

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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-113

DC Network Theorems


Exercise 1 – Bridge Circuit Resistance

EXERCISE OBJECTIVE Calculate the Thevenin resistance (R TH) of a bridge circuit. Verify results by comparing calculated and measured data. EXERCISE DISCUSSION No Questions EXERCISE PROCEDURE Location: Exercise Procedure page: se1p1, Question ID: e1p1a

2. Which part of the bridge circuit is its input side? a. the load side b. the voltage source side Location: Exercise Procedure page: se1p1, Question ID: e1p1c

3. Is R TH determined with respect to the input or output side of a bridge circuit? a. input b. output Location: Exercise Procedure page: se1p2, Question ID: e1p2a

4. When making an R TH 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

3-114

DC Network Theorems



R TH =

Ω

Recall Label for this Question: rth Nominal Answer: 428.0 Min/Max Value: (419.4) to (436.6) Value Calculation: 428.000 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2 Location: Exercise Procedure page: se1p3, Question ID: e1p3a

6. Remove all two-post connectors. Short the input terminals of the bridge circuit, and measure R TH. Is the measured value about the same as the calculated value of #rth0#Ω #rth0# Ω? a. yes b. no


1. The ohmmeter is measuring a. VTH. b. R1. c. R TH. d. R4. Location: Review Questions page: se1r2, Question ID: e1r2

2. R TH is a. 1250 . b. 750Ω 750Ω. c. 500Ω 500Ω. d. 1333Ω 1333Ω

3-115

DC Network Theorems



3. Placing a load at the output terminals of a thevenized bridge circuit a. increases the value of R TH. b. does not change the value of R TH.

c. decreases the value of R TH. d. requires a new source voltage. Location: Review Questions page: se1r4, Question ID: e1r4

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 Location: Review Questions page: se1r5, Question ID: e1r5

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.


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DC Network Theorems


Exercise 2 – Thevenizing Bridge Circuit Voltage

EXERCISE OBJECTIVE Calculate the Thevenin equivalent voltage (V TH) of a bridge circuit. Verify results by comparing calculated and measured data. EXERCISE DISCUSSION Location: Exercise Discussion page: se2d2, Question ID: e2d2a

VTH =

Vdc

Recall Label for this Question: vth Nominal Answer: –3.89 Min/Max Value: (–3.97) to (–3.81) Value Calculation: –3.890 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2


VS =

Vdc

Recall Label for this Question: None Nominal Answer: 15.0 Min/Max Value: (13.5) to (16.5) Value Calculation: 15.000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p3, Question ID: e2p3a

3. What action is required before you can measure V TH? a. The bridge must be loaded. b. The bridge source voltage must be r emoved. c. The bridge source voltage must be shorted. d. None of the above.

3-117

DC Network Theorems



VTH =

Vdc

Recall Label for this Question: vth2 Nominal Answer: 8.58 Min/Max Value: (7.722) to (9.438) Value Calculation: 8.580 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p5, Question ID: e2p5a

5. Which output terminal of the bridge is more negative with respect to common? a. A b. B Location: Exercise Procedure page: se2p6, Question ID: e2p6a

6. Based on the circuit shown, what is the value of V RL? a. #vth2# Vdc b. –#vth2# Vdc c. 2.9 Vdc d. –2.9 Vdc Location: Exercise Procedure page: se2p7, Question ID: e2p7a

VRL =

Vdc

Recall Label for this Question: vrl Nominal Answer: 4.35 Min/Max Value: (3.48) to (5.22) Value Calculation: 4.350 Correct Tolerance Percent = true Correct Minus Tolerance = 20 Correct Plus Tolerance = 20

3-118

DC Network Theorems



R L =

Ω

Recall Label for this Question: rl5 Nominal Answer: 440.0 Min/Max Value: (396) to (484) Value Calculation: 440.000 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Exercise Procedure page: se2p8, Question ID: e2p8a

9. Based on this circuit, do the calculated (#rl5#Ω (#rl5# Ω) and measured values of R L agree? a. yes b. no


1. In a Thevenin model of a bridge circuit, V TH and R TH 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. Location: Review Questions page: se2r2, Question ID: e2r2

2. Changing the network voltage source of a bridge changes a. VTH but not R TH. b. R TH but not VTH. c. VTH and R TH. d. None of the above. Location: Review Questions page: se2r3, Question ID: e2r3

3. Changing the value of one resistor in a bridge circuit changes a. VTH but not R TH. b. VTH and R TH.

c. R TH but not VTH. d. None of the above.

3-119

DC Network Theorems



4. The Thevenin model and load resistor form a a. series circuit. b. parallel circuit. c. series/parallel circuit. d. parallel/series circuit. Location: Review Questions page: se2r5, Question ID: e2r5

5. Which formula defines the load voltage for a complete thevenized circuit? a. VRL = (VTH x R L)/(R TH + R L) b. VRL = (VTH x R L) x (R TH + R L) c. VRL = (VTH x R L) – (R TH + R L) d. VRL = (VTH x R L) + (R TH + R L)


3-120

DC Network Theorems



What is the Thevenin resistance between terminals B and D? a. 200Ω 200Ω b. 150Ω 150Ω c. 100 d. 36Ω 36Ω Location: Unit Test Question page: sut2, Question ID: ut2

After a bridge circuit has been thevenized, what can you easily find given any value of R L? a. R TH b. VTH c. VRL

d. All of the above. Location: Unit Test Question page: sut3, Question ID: ut3

Thevenizing a bridge circuit means to reduce it to an equivalent a. series circuit. b. parallel circuit. c. series/parallel circuit. d. parallel/series circuit. Location: Unit Test Question page: sut4, Question ID: ut4

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. Location: Unit Test Question page: sut5, Question ID: ut5

With terminals A and C shorted, what is the resistance between terminals D and B? a. 57.48Ω 57.48Ω b. 48.57 c. 97.26Ω 97.26Ω d. 194.52Ω 194.52Ω

3-121

DC Network Theorems



The load is connected across terminals a. A and B b. B and C. c. A and C. d. B and D. Location: Unit Test Question page: sut7, Question ID: ut7

The open circuit voltage (VTH) is measured across a. the load. b. R5. c. the source voltage. d. terminals B and D. Location: Unit Test Question page: sut8, Question ID: ut8

To measure R TH, 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, an d measure across the load. c. load, and measure across terminals B and D. d. load, and measure across terminals A and C. Location: Unit Test Question page: sut9, Question ID: ut9

What does the voltmeter indicate? a. VR5 b. VR1 c. VS

d. None of the above. Location: Unit Test Question page: sut10, Question ID: ut10

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.

3-122

DC Network Theorems



VRL =

Vdc

Recall Label for this Question: None Nominal Answer: 2.91 Min/Max Value: (2.619) to (3.201) Value Calculation: 2.910 Correct Tolerance Percent = true Correct Minus Tolerance = 10 Correct Plus Tolerance = 10 Location: Troubleshooting page: ttrba3, Question ID: trba3a

3. Does a change in load resistance affect the Thevenin equivalent circuit? a. yes b. no Location: Troubleshooting page: ttrba4, Question ID: trba4a

4. Does the open load output voltage of the thevenized circuit equal the value of V TH? a. yes b. no Location: Troubleshooting page: ttrba5, Question ID: trba5a

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 Location: Troubleshooting page: ttrba6, Question ID: trba6

7. The faulty component is a. R5 (decreased in value). b. R5 (no change). c. R5 (increased in value). d. R5 (shorted).

3-123

DC Network Theorems



3-124

DC Network Theorems

Unit 9 – Thevenin/Norton Conversion

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

What is the output voltage across the load of this circuit? a. 10V b. 9.09V c. 5V d. None of the above. Location: Unit Fundamentals page: sf6, Question ID: f6a

Based on the circuit shown, what is the value of load current? a. 1A b. 0.0909A c. 0.909A d. None of the above.


3-125

DC Network Theorems


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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-126

DC Network Theorems


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 Location: Exercise Procedure page: se1p3, Question ID: e1p3a

VO(NL) =

Vdc

Recall Label for this Question: vtonl Nominal Answer: 7.95 Min/Max Value: (7.553) to (8.348) Value Calculation: 7.950 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se1p4, Question ID: e1p4a

VRL =

Vdc

Recall Label for this Question: vtol Nominal Answer: 3.96 Min/Max Value: (3.762) to (4.158) Value Calculation: 3.960 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5

3-127

DC Network Theorems



4. Why are the unloaded (VO(NL)) and loaded (VO(L)) circuit output voltages different? a. The load forms a voltage divider with R TH. b. Current does not flow through R TH when the load is removed. c. The load causes a voltage drop across R TH. d. All of the above. Location: Exercise Procedure page: se1p6, Question ID: e1p6a

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 d. None of the above. Location: Exercise Procedure page: se1p7, Question ID: e1p7a

Based on your readings, does VTH equal VRTH, and does the Thevenin output terminal equal 0? a. yes b. no Location: Exercise Procedure page: se1p8, Question ID: e1p8a

I N =

mA


3-128

DC Network Theorems



I N =

mA

Recall Label for this Question: None Nominal Answer: 16.9 Min/Max Value: (16.06) to (17.75) Value Calculation: 16.900 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se1p11, Question ID: e1p11a

Does the value of I N change? a. yes b. no Location: Exercise Procedure page: se1p12, Question ID: e1p12a

11. Are these circuits equivalent in terms of their effect on the load resistor? a. yes b. no


1. The open circuit (no-load) current of a Norton current source (I N) equals a. the maximum current of a Thevenin equivalent circuit. b. VTH /R TH. c. All of the above. d. None of the above. Location: Review Questions page: se1r2, Question ID: e1r2

2. In a Thevenin equivalent circuit, R TH is 1000Ω 1000Ω. Therefore, a. the series resistance of the Norton equivalent circuit is 1000Ω 1000 Ω. b. the shunt resistance of the Norton equivalent circuit is 1000 . c. the series/parallel resistance of the Norton equivalent circuit is 1000Ω 1000 Ω. d. None of the above.

3-129

DC Network Theorems



3. When a Thevenin equivalent circuit is converted to its Norton equivalent, the current direction of I N a. does not matter. b. should be opposite to the direction of the cur rent 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 V TH . Location: Review Questions page: se1r4, Question ID: e1r4

4. If the load is removed from the output terminals of a Thevenin equivalent circuit, the circuit output voltage a. increases to V TH. b. does not change. c. decreases. d. reduces to zero. Location: Review Questions page: se1r5, Question ID: e1r5

5. If the output voltage of a Thevenin equivalent circuit is 0V, the a. load is open. b. load current is properly connected. conne cted. c. load is shorted. d. network represented by the Thevenin circuit is improperly configured.


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DC Network Theorems


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 Location: Exercise Discussion page: se2d2, Question ID: e2d2a

Are the load current and load voltage identical for each circuit? a. yes b. no


VO(NL) =

Vdc

Recall Label for this Question: v2nl Nominal Answer: 7.95 Min/Max Value: (7.791) to (8.109) Value Calculation: 7.950 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2 Location: Exercise Procedure page: se2p2, Question ID: e2p2c

IO(SC) =

mA

Recall Label for this Question: i2sc Nominal Answer: 16.92 Min/Max Value: (16.58) to (17.26) Value Calculation: 16.920 Correct Tolerance Percent = true Correct Minus Tolerance = 2 Correct Plus Tolerance = 2

3-131

DC Network Theorems



VRL =

Vdc

Recall Label for this Question: v2rl Nominal Answer: 3.98 Min/Max Value: (3.781) to (4.179) Value Calculation: 3.980 Correct Tolerance Percent = true Correct Minus Tolerance = 5 Correct Plus Tolerance = 5 Location: Exercise Procedure page: se2p2, Question ID: e2p2g

IRL =

mA

Recall Label for this Question: i2rl Nominal Answer: 8.468 ∗ Min/Max Value: (7.803) to (9.158) Value Calculation: (#v2rl#/470)*1000 Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se2p3, Question ID: e2p3a

6. Based on your calculations, what is the current (I N) required for an equivalent constant current source? a. #v2nl# Vdc b. #i2sc# mA c. #v2rl# Vdc d. #i2rl# mA Location: Exercise Procedure page: se2p4, Question ID: e2p4a

7. What is the current distribution between R N and R L? a. #v2nl# Vdc b. #i2sc# mA c. #v2rl# Vdc d. #i2rl# mA

∗


DC Network Theorems



8. What is the load voltage generated by the constant current source? a. #v2nl# Vdc b. #i2sc# mA c. #v2rl# Vdc d. #i2rl# mA Location: Exercise Procedure page: se2p6, Question ID: e2p6a

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 Location: Exercise Procedure page: se2p7, Question ID: e2p7a

10. Place R L 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 Location: Exercise Procedure page: se2p8, Question ID: e2p8a

11. Based on your calculated and measured data, does the constant current source duplicate the effects of the network? a. yes b. no Location: Exercise Procedure page: se2p9, Question ID: e2p9a

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

3-133

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1. In a Norton to Thevenin conversion, the value of R TH equals a. VTH/R N. b. R L. c. R N.

d. None of the above. Location: Review Questions page: se2r2, Question ID: e2r2

2. When you calculate the value of VTH, a. open the constant current source. b. remove R N from the circuit. c. remove R L.

d. remove R N and R L. Location: Review Questions page: se2r3, Question ID: e2r3

3. If the load is removed from a Norton equivalent circuit, a. all of the current flows through R N. b. I N is reduced to zero. c. I N increases. d. I N decreases. Location: Review Questions page: se2r4, Question ID: e2r4

4. When the load placed across the output terminals of a Norton equivalent circuit increases, I N a. increases to maintain constant load current. b. does not change, but I RN decreases. c. decreases to maintain constant load current. d. does not change, but decreases. Location: Review Questions page: se2r5, Question ID: e2r5

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. d. All of the above.

3-134

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3-135

DC Network Theorems



Maximum current flows when a. the load is open. b. the load is shorted. c. VTH is shorted. d. the values of R TH and R L are equal. Location: Unit Test Question page: sut2, Question ID: ut2

In order to measure the Thevenin voltage of this Thevenin equivalent circuit, a. remove the load (R L). b. increase R L. c. decrease R L. d. short R L. Location: Unit Test Question page: sut3, Question ID: ut3

The load voltage equals a. (VTH x R L)/(R TH + R L). b. IRTH + R TH. c. VTH + R TH. d. None of the above. Location: Unit Test Question page: sut4, Question ID: ut4

The value of R L is doubled; therefore, VTH a. doubles in value. b. does not change. c. is halved. d. does not change, but R TH is halved. Location: Unit Test Question page: sut5, Question ID: ut5

Which of the following must be true in order for the circuit to be converted into a Norton equivalent circuit? a. VTH = I N, and R TH = (R TH + R L)/(R TH + R L) b. VTH = I N, and R TH = R N c. VTH/R TH = IN, and R TH = R N

d. VTH/R TH = I N, and R TH = R N + R TH

3-136

DC Network Theorems



In order to "kill" the current source, a. remove R N from the circuit. b. remove R L from the circuit. c. place a short circuit across R L. d. remove R N and R L from the circuit. Location: Unit Test Question page: sut7, Question ID: ut7

When R L is removed from the Norton equivalent circuit, I N a. increases. b. does not change. c. decreases. d. does not change, but R N increases. Location: Unit Test Question page: sut8, Question ID: ut8

I N is 1A and R 100Ω. Proper circuit operation requires that R L N is 100Ω a. be greater than 100Ω 100Ω. b. equal 100Ω 100Ω. c. be less than 100Ω 100Ω. d. None of the above applies because R L can be any value. Location: Unit Test Question page: sut9, Question ID: ut9

Each resistance can be converted to its equivalent conductance. Based on conductance, I N a. divides directly. b. divides inversely. c. does not divide. d. must change with load conductance variation. Location: Unit Test Question page: sut10, Question ID: ut10

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 = I N/R N, and R TH = R TH – R N c. VTH = IN x R N, and R TH = R N

d. VTH = I N x R N, and R TH = (R TH x R N)/(R TH + R N)

3-137

DC Network Theorems


3-138

DC Network Theorems

Unit 10 – Delta and Wye Networks

UNIT 10 – 10 – DELTA AND W YE NETWORKS

UNIT OBJECTIVE Simplify a resistive bridge network by using delta and wye transformations. UNIT FUNDAMENTALS Location: Unit Fundamentals page: sf3, Question ID: f3a

R1, R2, and R3 of each network are identical. Is the resistance between identical terminals of each network identical? a. yes b. no Location: Unit Fundamentals page: sf6, Question ID: f6a

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. Location: Unit Fundamentals page: sf9, Question ID: f9a

A wye-delta conversion results in the networks shown. Are the networks electrically identical? a. yes b. no


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DC Network Theorems


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 F.A.C.E.T. base unit DC NETWORK THEOREMS circuit board Multimeter

3-140

DC Network Theorems


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 Location: Exercise Procedure page: se1p2, Question ID: e1p2a

Are the readings approximately the same? a. yes b. no Location: Exercise Procedure page: se1p3, Question ID: e1p3a

3. CM 15 is activated to increase the value of R2 (Y network) to 2050Ω 2050 Ω. 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 Location: Exercise Procedure page: se1p4, Question ID: e1p4a

Are the readings approximately the same? a. yes b. no

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DC Network Theorems



5. CM 12 is activated to increase the value of RB to 3740Ω 3740 Ω. Which terminal resistances of the delta network are affected? a. all b. only A/D c. A/D or C/D d. None Location: Exercise Procedure page: se1p6, Question ID: e1p6a

6. With CM 12 activated, are the pi and delta networks equivalent? a. yes b. no


1. Which networks are electrically identical? a. A and B b. A and C c. A and D d. B and C Location: Review Questions page: se1r2, Question ID: e1r2

2. An ohmmeter placed across any two circuit terminals of a 3-resistor delta circuit sees a a. series circuit. b. parallel circuit. c. series/parallel circuit. d. None of the above. Location: Review Questions page: se1r3, Question ID: e1r3

3. An ohmmeter placed between any two circuit terminals of a 3-resistor wye circuit sees a a. series circuit. b. parallel circuit. c. series/parallel circuit. d. None of the above.

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4. The resistor values in a typical Y configuration are 100Ω 100 Ω, 200Ω 200Ω, and 300Ω 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. Location: Review Questions page: se1r5, Question ID: e1r5

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

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DC Network Theorems


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 Location: Exercise Procedure page: se2p2, Question ID: e2p2a

YR1 =

Ω

Recall Label for this Question: yr1 Nominal Answer: 1100.0 Min/Max Value: (935) to (1265) Value Calculation: 1100 Correct Tolerance Percent = true Correct Minus Tolerance = 15 Correct Plus Tolerance = 15 Location: Exercise Procedure page: se2p2, Question ID: e2p2c

YR2 =

Ω

Recall Label for this Question: yr2 Nominal Answer: 1580.0 Min/Max Value: (1343) to (1817) Value Calculation: 1580 Correct Tolerance Percent = true Correct Minus Tolerance = 15 Correct Plus Tolerance = 15

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DC Network Theorems



YR3 =

Ω

Recall Label for this Question: yr3 Nominal Answer: 1000.0 Min/Max Value: (850) to (1150) Value Calculation: 1000 Correct Tolerance Percent = true Correct Minus Tolerance = 15 Correct Plus Tolerance = 15 Location: Exercise Procedure page: se2p3, Question ID: e2p3a

DRB =

Ω

Recall Label for this Question: drb Nominal Answer: 2796.2 ∗ Min/Max Value: (2305.5) to (3312.1) Value Calculation: ((#yr1#*#yr2#)+(#yr1#*#yr3#)+(#yr2#*#yr3#))/#yr2# Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se2p3, Question ID: e2p3c

DRA =

Ω

Recall Label for this Question: dra Nominal Answer: 4418.0 * Min/Max Value: (3642.6) to (5233.1) Value Calculation: ((#yr1#*#yr2#)+(#yr1#*#yr3#)+(#yr2#*#yr3#))/#yr3# Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3

∗


DC Network Theorems



DRC =

Ω

Recall Label for this Question: drc Nominal Answer: 4016.4 ∗ Min/Max Value: (3002.5) to (5357.9) Value Calculation: ((#yr1#*#yr2#)+(#yr1#*#yr3#)+(#yr2#*#yr3#))/#yr1# Correct Tolerance Percent = true Correct Minus Tolerance = 3 Correct Plus Tolerance = 3 Location: Exercise Procedure page: se2p4, Question ID: e2p4a

Do your measured values and calculated values agree within tolerance? a. yes b. no Location: Exercise Procedure page: se2p5, Question ID: e2p5a

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 Location: Exercise Procedure page: se2p6, Question ID: e2p6a

6. Based on your Y to ∆ conversion results, can you convert a delta network into an equivalent Y network? a. yes b. no

∗


DC Network Theorems



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 produc ts of all resistors. c. sum of all resistors. d. None of the above. Location: Review Questions page: se2r2, Question ID: e2r2

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. Location: Review Questions page: se2r3, Question ID: e2r3

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 c. Either of the above. d. None of the above. Location: Review Questions page: se2r4, Question ID: e2r4

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.

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DC Network Theorems



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.


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DC Network Theorems



A tee network is identical to a a. pi network. b. wye network. c. delta network. d. bridge network. Location: Unit Test Question page: sut2, Question ID: ut2

A pi network is identical to a a. tee network. b. wye network. c. delta network. d. bridge network. Location: Unit Test Question page: sut3, Question ID: ut3

A wye network can be converted to an equivalent a. series network. b. tee network. c. delta network. d. None of the above. Location: Unit Test Question page: sut4, Question ID: ut4

A delta network can be converted to an equivalent a. pi network. b. wye network. c. parallel network. d. None of the above. Location: Unit Test Question page: sut5, Question ID: ut5

An ohmmeter placed across any two circuit terminals of a 3-resistor delta circuit sees a a. series circuit. b. parallel circuit. c. series/parallel circuit. d. None of the above.

3-149

DC Network Theorems



An ohmmeter placed across any two circuit terminals of a 3-resistor wye circuit sees a a. series circuit. b. parallel circuit. c. series/parallel circuit. d. None of the above. Location: Unit Test Question page: sut7, Question ID: ut7

The resistor values of a typical Y configuration are 100Ω 100 Ω, 200Ω 200Ω, and 300Ω 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. Location: Unit Test Question page: sut8, Question ID: ut8

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 produc ts of all resistors. c. sum of all resistors. d. None of the above. Location: Unit Test Question page: sut9, Question ID: ut9

What is the total circuit current? a. 100 mA b. 10 mA c. 1 mA d. None of the above. Location: Unit Test Question page: sut10, Question ID: ut10

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.

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Are the resistive values equal to the given nominal vales? a. yes b. no Location: Troubleshooting page: ttrba3, Question ID: trba3a

3. Do the measured values of the T NETWORK match those of the Y NETWORK? a. yes b. no Location: Troubleshooting page: ttrba4, Question ID: trba4a

4. Does a change in the Y NETWORK circuit block affect the T NETWORK circuit block? a. yes b. no Location: Troubleshooting page: ttrba5, Question ID: trba5

6. The faulty component is a. R1 (increased). b. R2 (increased). c. R3 (increased). (increased). d. R1 and R2 (increased).


3-151

DC Network Theorems


3-152

DC Network Theorems

Appendix A – Pretest and Posttest Questions and Answers

APPENDIX A – PRETEST AND POSTTEST QUESTIONS AND ANSWERS Depending on configurator settings, these questions may be randomized onscreen.

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 no de. c. maybe less 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 d. None of the above. 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. b. c. d.

a closed loop, the sum of the voltage drop equals zero. a maximum circuit voltage. a minimum voltage drop. an intermediate voltage.

A-1

DC Network Theorems


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 + V N b. 0 = VS - (V1 + V2 + V N) c. Either of the above. d. None of the above. 9. Proving Kirchhoff's voltage 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 a. cannot be determined. b. is zero. c. can be determined from Kirchhoff's voltage law. d. must equal the voltage drop of the other elements. 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. d. None of the above.

A-2

DC Network Theorems


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. 15. A circuit with a voltage source, two resistors in series, in parallel with one resistor has 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. d. None of the above. 17. Loop equations are a. equations that define the voltage drops around a closed loop. b. equations that define the voltage drops around an op en 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. d. None of the above. 19. With the mesh method, branch currents a. must be determined. b. need not be determined. c. are predetermined. d. None of the above. 20. A mesh is a. any current path with parallel branches. b. two or more current loops that share a common c ircuit. c. an open circuit current path. d. the simplest possible closed current path within a circuit.

A-3

DC Network Theorems


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. d. None of the above. 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. d. None of the above. 25. Millman's theorem takes the form of current divided by a. resistance. b. conductance. c. voltage. d. All of the above. 26. A thevenized circuit requires a. an equivalent current (ITH) in series with an equivalent resistance (R TH TH). b. an equivalent voltage (VTH) and an equivalent resistance (R TH TH) in parallel with (V TH). c. an equivalent voltage (V TH) and an equivalent resistance (R TH) in series with (VTH). d. None of the above. 27. VTH is the network output terminal voltage. V TH is determined with the network load a. b. c. d.

in series. connected. disconnected. None of the above.

A-4

DC Network Theorems


28. R TH is the total no-load network resistance. The network source voltage is replaced with a a. b. c. d.

short circuit. multimeter. a battery. None of the above.

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. d. None of the above. 33. Calculated and measured values of R TH should be approximately a. b. c. d.

2:1 respectively. 1:2 respectively. the same. None of the above.

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

source voltage. the voltage divider. load resistor from the network. all resistance.

A-5

DC Network Theorems


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. d. None of the above. 36. A current source is a circuit a. that provides a constant voltage at its output terminals. 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 its output terminals. d. None of the above. 40. In the conversion process between Thevenin and Norton circuits, a. R N equals R TH. b. R N equals VTH. c. R TH equals VTH. d. None of the above. 41. A resistive wye network is identical to a. a delta network. b. a pi network. c. a tee network. d. None of the above.

A-6

DC Network Theorems


42. A resistive delta network is identical to a. a delta network. b. a pi network. c. a tee network. d. None of the above. 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 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 defe ctive 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. d. None of the above.

A-7

DC Network Theorems


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-8

DC Network Theorems


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 a. cannot be determined. b. is zero. c. can be determined from Kirchhoff's voltage law. d. must equal the voltage drop of the other elements. 5. Which equation defines Kirchhoff's voltage law? a. VS = V1 + V2 + V N b. 0 = VS - (V1 + V2 + V N) c. Either of the above. d. None of the above. 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. d. None of the above. 7. Loop equations are a. equations that define the voltage drops around a closed loop. b. equations that define the voltage drops around an op en loop. c. equations that are used very rarely. d. equations with no solution.

A-9

DC Network Theorems


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 10. Nodes are a. special resistors. b. common connections for two or more components. c. special voltage sources. d. None of the above. 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, two resistors in series, in parallel with one resistor has a. one node. b. two nodes. c. three nodes. d. four nodes. 13. 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. 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-10

DC Network Theorems


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. d. None of the above. 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 no de. c. maybe less 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 (I T) 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. d. None of the above. 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-11

DC Network Theorems


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 (R TH TH). b. an equivalent voltage (VTH) and an equivalent resistance (R TH TH) in parallel with (V TH). c. an equivalent voltage (V TH) and an equivalent resistance (R TH) in series with (VTH). d. None of the above. 25. A mesh is a. any current path with parallel branches. b. two or more current loops that share a common c ircuit. 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. d. None of the above. 27. R TH is the total no-load network resistance. The network source voltage is replaced with a a. b. c. d.

short circuit. multimeter. a battery. None of the above.

28. VTH is the network output terminal voltage. V TH is determined with the network load a. b. c. d.

in series. connected. disconnected. None of the above.

A-12

DC Network Theorems


29. Millman's theorem takes the form of current divided by a. resistance. b. conductance. c. voltage. d. All of the above. 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. d. None of the above. 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. d. None of the above. 32. To determine VTH of a bridge circuit, remove a. b. c. d.

the source voltage. the voltage divider. the load resistor from the network. all resistance.

33. A current source is a circuit a. that provides a constant voltage at its output terminals. 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. R N equals R TH. b. R N equals VTH. c. R TH equals VTH. d. None of the above. 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-13

DC Network Theorems


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 its output terminals. d. None of the above. 37. A resistive delta network is identical to a. a delta network. b. a pi network. c. a tee network. d. None of the above. 38. Norton's 38. Norton's theorem allows for the reduction of a networ k 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 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. d. None of the above.

A-14

DC Network Theorems


43. A resistive wye network is identical to a. a delta network. b. a pi network. c. a tee network. d. None of the above. 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. d. None of the above. 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 defe ctive 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.

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DC Network Theorems


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. d. None of the above.

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DC Network Theorems

Appendix B – Faults and Circuit Modifications (CMs)

APPENDIX B – FAULTS AND CIRCUIT MODIFICATIONS (CMS) CM

FAULT

–

SCHEMATIC SWITCH NO. 21

– – – – – – – – – 1

22 23 24 26 28 29 30 31 32 1

2 3 4 6 8 9 10 11 12 –

2 3

2 3

– –

4 5 8 9

4 5 8 9

– – – –

12 15 17 18

12 15 17 18

– – – –

19

19

–

20

20

–

1

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ACTION

places 910Ω in parallel with 1.8-kΩ R1 R1 = 900Ω R5 = 730Ω shorts R1 R6 = 1500Ω R3 = 2300Ω R3 = 9700Ω shorts R2 R1 = 2270Ω R3 = 9200Ω places 3.9 kΩ in parallel with 1.8-kΩ R1 R2 = 4.4 kΩ places 3.3 kΩ in parallel with 510Ω R2 R3 = 1080Ω R5 = 440Ω R3 = 1070Ω places 47Ω in parallel with 470Ω R5 RB = 3740Ω R2 = 2050Ω R1 = 970Ω places 6.2 kΩ in parallel with 3.6-kΩ R2 places 8.2 kΩ in parallel with 2.2-kΩ R2 R3 = 10.1 kΩ

DC Network Theorems

Appendix B – Faults and Circuit Modifications (CMs)

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DC Network Theorems

Appendix C – Board and Courseware Troubleshooting

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 stude nts may discover mistakes or experience diff iculty in using our publications. We appreciate your comments and as sure 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.. www.labvolt.com Select a course, select from a list of symptoms that have been addressed, and follow the instructions.

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DC Network Theorems

Appendix C – Board and Courseware Troubleshooting

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 pr efer 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.

C-2

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Binder Spine Labels

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DC Network Theorems

Instructor Guide

DC Network Theorems

Instructor Guide

DC Network Theorems

Instructor Guide

DC Networks Theorems

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