1 Chapter 4 Circuit Theorems 1. Linearity and Proportionality. Source Transformation 3. Superposition Theorem 4. Thevenin s Theorem and Norton s Theorem 5. Maximum Power Transfer Theorem Mazita Sem BEL10103
2 Learning Outcomes... At the end of this topic, students should be able to: Simplify the circuit s complexity by using Thevenin-Norton equivalent networks and/or source transformation Analyse the circuits by using the superposition theorem, etc.
3 Linearity and Proportionality Motivation: Engineering combines the study of mathematics and natural and social sciences to direct the forces of nature for the benefit of humankind. An engineer, in the accomplishment of a task, 1. Analyses the problem. Synthesises a solution 3. Evaluates the results and possibly re-synthesises a solution use models to represent the electric circuit element Source: Richard C. Dorf and James A. Svoboda
4 Linearity and Proportionality (cont.) A device or element is said to be linear if its excitation and response satisfy the properties of superposition and homogeneity. Mathematically: Superposition: then i 1 + i i i 1 v v v v Homogeneity: then i v ki kv
5 Example Consider the element represented by the relationship between current and voltage as v = Ri. Determine whether this device is linear. Solution: then v 1 + v v v 1 = = = = Ri Ri 1 Ri1 + R i ( + i ) 1 Ri satisfy the superposition property i v v then = = = = ki1 Ri Rki kv 1 1 This device is linear as it satisfies both superposition and homogeneity properties. satisfy the homogeneity property
6 Source Transformation A source transformation is a procedure for transforming one source into another while retaining the terminal characteristics of the original source. Based on the concept of equivalence, i.e. terminal characteristics still remain identical to those of the origin.
7 Source Transformation (cont.) Consider two extreme values of R L R L = 0 Ω R L = Ω Fig. i: Fig. ii: i = v R i = i s s s Fig. i: Fig. ii: v ab = v s v = i For both circuits to be equivalent, v ab must be equal. R S = R p ab s R P
9 Example Find the source transformation for the circuits shown below.
10 Solution For circuit i; R i P S = = R v R S S S = 7 Ω 8 = = 7 4 A
11 Solution (cont.) For circuit ii; S S = RP = 1 Ω = i R = 1 Current A is flowing down reverse the terminal polarity for voltage source R v S P = 4 V
12 Exercise Using source transformation, determine the current i for the circuit shown below. (Answer: 1.15 A)
13 Superposition Theorem Linear element holds superposition theorem, i.e. then i 1 i i + i 1 v v v The superposition principle requires that the total effect of several causes acting simultaneously is equal to the sum of the effects of the individual causes acting one at a time v
14 How to apply the principle of Superposition Theorem? The principle of superposition is only applicable for linear circuits consisting of linear elements and independent sources. Steps in applying the superposition theorem: 1. Activate only one independent source at one time and deactivate the rest of independent sources. If the dependent source is available, it should remain active.. Determine the current or voltage where necessary. 3. Repeat steps 1- until the effects of all the independent sources in the network have been analysed. 4. Add the total currents or voltages.
15 Example 1 Find the current in the 6 Ω resistor using the principle of superposition for the circuit shown below.
16 Solution Consider the effect of 6 V voltage source: i v = = = R T 6 3 A Note: 1. Set the current source to zero appears as an open circuit.. Label portion of current due to excitation by 6V source as i Do circuit analysis.
17 Solution (cont.) Consider the effect of A current source: Apply current divider: R3Ω 3 i = A = = R + R Ω 6Ω 3 A Note: 1. Set the voltage source to zero appears as a short circuit.. Label portion of current due to excitation by A source as i. 3. Do circuit analysis.
18 Solution (cont.) The total current, i = i 1 + i : i = i1 + i = = A 3 Note: 1. Check whether all the independent sources have been analysed.. If yes, total up the current value.
19 Example Find the current i using the principle of superposition for the circuit shown below.
20 Solution Consider the effect of 4 V voltage source: Apply KVL (follow the direction of current, i 1 ) 4 + 3i 1 + i 1 + 3i1 8i i 1 1 = 0 = 4 = 3 A Note: 1. Set the current source to zero appears as an open circuit. A dependent source should remain active.. Label current as i 1. Dependent source is now referred to i Do circuit analysis.
21 Solution (cont.) Consider the effect of 7 A current source: Apply KCL at node a; va 3i = i + 7 va 3i = i + 14 v = 5i + 14Lequation (1) a Apply Ohm s Law across 3 Ω resistor; v a = i 3 Lequation () Note: 1. Set the voltage source to zero appears as a short circuit. A dependent source should remain active.. Label current as i. Dependent source is now referred to i. 3. Do circuit analysis.
22 Solution (cont.) Solve equations (1) & () to get i ; i Finally, the total current, i: i 14 = 8 = = i1 + i 7 = = A A Note: 1. Check whether all the independent sources have been analysed.. If yes, total up the current value.
23 Exercise Using the principle of superposition, find the voltage v of the circuit shown below. (Answer: 4 V)
24 Thevénin s Theorem Motivation: To reduce the complexity of circuits. How? Reduce some portion of the circuit to an equivalent source and a single element Thevenin equivalent circuit
25 Thevénin s Theorem (cont.) Thevenin s theorem requires that, for any circuit of resistance elements and energy sources with an identified terminal pair, the circuit can be replaced by a series combination of an ideal source, v TH and a resistance, R TH. v TH is the open-circuit voltage at the two terminals R TH is the input/equivalent resistance at the terminals when the independent sources are turned off. Source: Richard C. Dorf & James A. Svoboda and Charles K. Alexander & Matthew N.O. Sadiku
26 Thevénin s Theorem (cont.) Summary of Thevenin Circuit Approach 1) Identify circuit A and circuit B ) Separate circuit A and circuit B 3) Replace circuit A with its Thevenin equivalent 4) Reconnect circuit B and determine the variable of interest
27 Example 1 Find the Thevenin equivalent circuit between the output terminals A and B of the circuit shown below.
28 Solution Determine the voltage, V TH Note: 1. Since there is no current flowing through R 4, therefore no voltage drop across it. ( Ignore R 4 ) V TH = = V 10. Use voltage divider rule to determine the V TH = V AB.
29 Solution (cont.) Determine the resistance, R TH Note: 1. Turn off the independent source, i.e. replace the voltage source with short circuit. R TH ( R //( R + )) = R4 + 1 R3 1 1 = = 1.41kΩ 0 1. Determine the total equivalent resistance across terminals A-B.
30 Solution (cont.) The Thevenin equivalent circuit is
31 Exercise 1 For the circuit shown below, determine the Thevenin equivalent circuit as viewed from the output terminals A and B. (Answer: R TH = kω, V TH = 3.06 V)
32 Exercise Find the Thevenin equivalent of the circuit shown below. (Answer: R TH = 8 Ω, V TH = 3 V)
33 Thevenin Theorem (cont.) Please take note that: Thevenin Equivalency Depends on the Viewpoint
34 Norton s Theorem Motivation: To reduce the complexity of circuits. How? Reduce some portion of the circuit to an equivalent source and a single element Norton equivalent circuit
35 Norton s Theorem Norton and Thevenin equivalent circuits are related by a source transformation. To determine Thevenin or Norton equivalent circuit, we need to find i N, Norton current equals to the short-circuit current at the terminals of interest R N, Norton resistance equals to the Thevenin resistance, i.e. resistance at terminals of interest when all the independent sources are off. v TH, Thevenin voltage equals to the open-circuit voltage across the terminals of interest.
36 Example Determine the Norton equivalent circuit as seen by the R L for the circuit shown below.
37 Solution Determine the current, I N Note: 1. Short circuit terminals A-B.. To determine the I N, use current divider rule. R T I T = 47 + = = = 1.05 A Ω 47 Therefore, I N I = A = T
38 Solution (cont.) Determine the resistance, R N Note: 1. Turn off the independent source, i.e. replace the voltage source with short circuit. R N ( R ) = R3 + 1 // R 47 = = 13.5 Ω. Determine the total equivalent resistance across terminals A-B.
39 Solution (cont.) The Norton equivalent circuit is
40 Exercise Find the Norton equivalent of the circuit shown below. (Answer: R N = 8 Ω, I N = 4 A)
41 Maximum Power Transfer Many applications of circuits require maximum power available from a source be transferred to a load resistor, R L. General problem of power transfer deals with its efficiency and effectiveness issues. Example: power utility systems to transport the power to the load with greatest efficiency by reducing the losses on the power lines Signal transmission (communication): difficulty in attaining the maximum signal strength at the load (e.g. FM radio, mobile telephone).
42 Maximum Power Transfer (cont.) It is known that a complex circuitry could be reduced to its Thevenin equivalent: Current, I is given by I = R L V + TH R TH Hence, the power to the load is P = R L V + TH R TH R L
43 Maximum Power Transfer (cont.) To obtain maximum power transfer, dp R L + RTH RL RL + R = VTH 4 drl ( RL + RTH ) Solving this: ( ) ( ) R L = R TH TH = 0 Note: Use differentiation : d dx u v = du v dx u v dv dx Power delivered to the load varies with the changes of R L values. To confirm the point is maximum: d dr L P < 0
44 Maximum Power Transfer (cont.) Hence Maximum power transfer theorem states that the maximum power delivered by a source represented by its Thevenin equivalent circuit is attained when the load R L is equal to the Thevenin resistance R TH. P V TH max = RL = R L TH V 4R L
45 Maximum Power Transfer (cont.) The efficiency of power transfer is defined as the ratio of the power delivered to the load P OUT to the power supplied by the source P IN. We know that Efficiency is η = P P IN = V OUTMAX P IN TH = I η = = V VTH 4R VTH R OUT Therefore, the efficiency obtained at maximum power condition is only ½ i.e. 50%. L TH L P P IN VTH R = 1 L V = R TH L
46 Example Find the load R L that will result in maximum power delivered to the load for the circuit shown below. Also determine the P max and its efficiency.
47 Solution First, determine the Thevenin equivalent circuit. Determine V TH Determine R TH VTH 150 = 180 = 150V R TH = = 5Ω Therefore, maximum power transfer is obtained when R L = R TH = 5 Ω.
48 Solution (cont.) Then, determine maximum power transfer and power transfer efficiency at R L = 5 Ω. P max = = VTH = 4R L W Total power delivered by the Thevenin source is P IN 150 = 150 = = 450 W The power transferred efficiency is P 5 η % = max 100 = 100 = 50% 450 P IN Note: The actual source of the circuit is 180 V and it delivers a power p = 180i 1 where i 1 is the current through 5 Ω, i.e. 3.5 A. Actual source delivers 630 W resulting in an efficiency of 35.7 %.
49 Exercise Find the load R L that will result in maximum power delivered to the load of the circuit shown below. Determine the maximum power delivered to the load. (Answer: R L = 1 Ω, P max = 3 W)
50 References Alexander Sadiku, Fundamentals of Electric Circuits, 4 th edition, McGraw-Hill, 009 Richard C. Dorf and James A. Svoboda, Introduction to Electric Circuits, 3 rd edition, John Wiley, 1996 Thomas L. Floyd and David M. Buchla, Electric Circuits Fundamentals, 8 th edition, Pearson, 010 James W. Nilsson & Susan A. Riedel, Electric Circuits, 9 th edition, Pearson-Prentice Hall, 011
ECE2262 Electric Circuits Chapter 5: Circuit Theorems 1 Equivalence Linearity Superposition Thevenin s and Norton s Theorems Maximum Power Transfer Analysis of Circuits Using Circuit Theorems 2 5. 1 Equivalence
ECE2262 Electric Circuits Equivalence Chapter 5: Circuit Theorems Linearity Superposition Thevenin s and Norton s Theorems Maximum Power Transfer Analysis of Circuits Using Circuit Theorems 1 5. 1 Equivalence
Many electric circuits are complex, but it is an engineer s goal to reduce their complexity to analyze them easily. In the previous chapters, we have mastered the ability to solve networks containing independent
Chapter 2 Basic Laws. Ohm s Law 2. Branches, loops and nodes definition 3. Kirchhoff s Law 4. Series resistors circuit and voltage division. 5. Equivalent parallel circuit and current division. 6. Wye-Delta
POLYTECHNIC UNIVERSITY Electrical Engineering Department EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems Modified for Physics 18, Brooklyn College I. Overview of Experiment In this
Chapter 5: Circuit Theorems This chapter provides a new powerful technique of solving complicated circuits that are more conceptual in nature than node/mesh analysis. Conceptually, the method is fairly
Sinusoidal Steady State Analysis (AC Analysis) Part I Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University firstname.lastname@example.org http://scholar.cu.edu.eg/refky/
Notes for course EE1.1 Circuit Analysis 2004-05 TOPIC 3 CIRCUIT ANALYSIS USING SUB-CIRCUITS OBJECTIVES 1) To introduce the Source Transformation 2) To consider the concepts of Linearity and Superposition
EE-201, Review Probs Test 1 page-1 Spring 98 EE-201 Review Exam I Multiple Choice (5 points each, no partial credit.) 1. The voltage Vx in the circuit below is: (1) 3V (2) 2V (3) -2V (4) 1V (5) -1V (6)
Transient Analysis of First-Order Circuits: Approaches and Recommendations Khalid Al-Olimat Heath LeBlanc ECCS Department ECCS Department Ohio Northern University Ohio Northern University Ada, OH 45810
UNIVERSITY F P RTLAND Sch l f Engineering EE271-Electrical Circuits Laboratory Spring 2004 Dr. Aziz S. Inan & Dr. Joseph P. Hoffbeck Lab Experiment #4: Electrical Circuit Theorems - p. 1 of 5 - Electrical
CHAPTER 4 Circuit Theorems The growth in areas of application of electrical circuits has led to an evolution from simple to complex circuits. To handle such complexity, engineers over the years have developed
MAE140 - Linear Circuits - Fall 14 Midterm, November 6 Instructions (i) This exam is open book. You may use whatever written materials you choose, including your class notes and textbook. You may use a
The equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A = 10 10 4. Section Break Difficulty: Easy Learning Objective: Understand how real operational
Chapter 2 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 2 Objectives Understand symbols and behavior of the following circuit elements: Independent voltage and current sources; Dependent voltage and
Thevenin equivalent circuits We have seen the idea of equivalency used in several instances already. 1 2 1 2 same as 1 2 same as 1 2 R 3 same as = 0 V same as 0 A same as same as = EE 201 Thevenin 1 The
UNIT-1 D C Circuit Analysis and Network Theorems: Circuit Concepts: Concepts of network, Active and passive elements, voltage and current sources, source transformation, unilateral and bilateral elements,
Thevenin Norton Equivalencies - GATE Study Material in PDF In these GATE 2018 Notes, we explain the Thevenin Norton Equivalencies. Thevenin s and Norton s Theorems are two equally valid methods of reducing
CHAPTER16 Two-Port Networks THE LEARNING GOALS FOR THIS CHAPTER ARE THAT STUDENTS SHOULD BE ABLE TO: Calculate the admittance, impedance, hybrid, and transmission parameter for two-port networks. Convert
Chapter 5 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 5 Objectives State and apply the property of linearity State and apply the property of superposition Investigate source transformations Define
Sinusoidal Steady State Analysis (AC Analysis) Part II Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University email@example.com http://scholar.cu.edu.eg/refky/
Experiment 2: Analysis and Measurement of Resistive Circuit Parameters Report Due In-class on Wed., Mar. 28, 2018 Pre-lab must be completed prior to lab. 1.0 PURPOSE To (i) verify Kirchhoff's laws experimentally;
The University of Toledo Section number s5ms_elci7.fm - Electric Circuits I Midterm # Problems Points. 3 2. 7 3. 5 Total 5 Was the exam fair? yes no The University of Toledo Section number s5ms_elci7.fm
EECE251 Circuit Analysis I Lecture Integrated Program Set 3: Circuit Theorems Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia firstname.lastname@example.org 1 Linearity
Chapter 10 Sinusoidal Steady State Analysis Chapter Objectives: Apply previously learn circuit techniques to sinusoidal steady-state analysis. Learn how to apply nodal and mesh analysis in the frequency
BME/ISE 3511 Bioelectronics - Test Three Course Notes Fall 2016 Delta & Y Configurations, Principles of Superposition, esistor Voltage Divider Designs Use following techniques to solve for current through
German University in Cairo Faculty of Information Engineering and Technology (IET) ELECTRIC CIRCUITS I (ELCT 301) LECTURE 1: BASIC CONCEPTS COURSE INSTRUCTOR Instructor: Prof. Dr. Eng. Yasser G. Hegazy
15EE103L ELECTRIC CIRCUITS LAB RECORD REGISTER NO: NAME OF THE STUDENT: SEMESTER: DEPARTMENT: INDEX SHEET S.No. Date of Experiment Name of the Experiment Date of submission Marks Staff Sign 1 Verification
University of California, Berkeley Spring 2010 EE 42/100 Prof. A. Niknejad Midterm Exam (closed book/notes) Tuesday, February 23, 2010 Guidelines: Closed book. You may use a calculator. Do not unstaple
EE 3120 Electric Energy Systems Study Guide for Prerequisite Test Wednesday, Jan 18, 2006 6-7 pm, Room TBA First retrieve your EE2110 final and other course papers and notes! The test will be closed book
Objectives: Introduction Notes for course EE1.1 Circuit Analysis 4-5 Re-examination of 1-port sub-circuits Admittance parameters for -port circuits TOPIC 1 -PORT CIRCUITS Gain and port impedance from -port
Chapter 07 Series-Parallel Circuits The Series-Parallel Network Complex circuits May be separated both series and/or parallel elements Combinations which are neither series nor parallel To analyze a circuit
1. Review of Circuit Theory Concepts Lecture notes: Section 1 ECE 65, Winter 2013, F. Najmabadi Circuit Theory is an pproximation to Maxwell s Electromagnetic Equations circuit is made of a bunch of elements
1 On the Application of Superposition to Dependent Sources in Circuit Analysis W Marshall Leach, Jr c Copyright 1994-009 All rights reserved Abstract Many introductory circuits texts state or imply that
Problem 1.24 The plot in Fig. P1.24 displays the cumulative charge q(t) that has entered a certain device up to time t. Sketch a plot of the corresponding current i(t). q 20 C 0 1 2 3 4 5 t (s) 20 C Figure
APPENDIX D SOME USEFUL NETWORK THEOREMS Introduction In this appendix we review three network theorems that are useful in simplifying the analysis of electronic circuits: Thévenin s theorem Norton s theorem
DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE NAME. Section 1 2 3 UNIVERSITY OF LAHORE Department of Computer engineering Linear Circuit Analysis Laboratory Manual 2 Compiled by Engr. Ahmad Bilal
S Electronic ircuits D ircuits 8.7 Delta-Star Transformation Fig..(a) shows three resistors R, R and R connected in a closed delta to three terminals, and, their numerical subscripts,, and, being opposite
SUPERPOSITION PRINCIPLE IN LINEAR NETWORKS WITH CONTROLLED SOURCES arxiv:64563v [csoh] 8 Jan 26 CIRO VISONE Abstract The manuscript discusses a well-known issue that, despite its fundamental role in basic
Module 2 DC Circuit esson 8 evenin s and Norton s theorems in the context of dc voltage and current sources acting in a resistive network Objectives To understand the basic philosophy behind the evenin
Questions on Thevenin Equivalent Circuits Fall 2004 2. Thevenin Circuits (25 points) Let V1=12V, R1=50 ohms, R2=10K ohms, R3=2K ohms, and R4=500 ohms. RL represents the load placed on the circuit between
Instructions MAE40 - Linear ircuits - Winter 09 Midterm, February 5 (i) This exam is open book. You may use whatever written materials you choose, including your class notes and textbook. You may use a
University of California, Berkeley Spring 2013 EE 42/100 Prof. K. Pister Homework 3 Solution Due Friday (5pm), Feb. 14, 2013 Please turn the homework in to the drop box located next to 125 Cory Hall (labeled
THERE MUST BE 50 WAYS TO FIND YOUR VALUES: AN EXPLORATION OF CIRCUIT ANALYSIS TECHNIQUES FROM OHM S LAW TO EQUIVALENT CIRCUITS Kristine McCarthy Josh Pratti Alexis Rodriguez-Carlson November 20, 2006 Table
Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University email@example.com http://scholar.cu.edu.eg/refky/
Kirchhoff's Laws and Circuit Analysis (EC ) Circuit analysis: solving for I and V at each element Linear circuits: involve resistors, capacitors, inductors Initial analysis uses only resistors Power sources,
- AC Power 11/17/2015 Reading: Chapter 11 1 Outline Instantaneous power Complex power Average (real) power Reactive power Apparent power Maximum power transfer Power factor correction 2 Power in AC Circuits
Module 2 DC Circuit Lesson 5 Node-voltage analysis of resistive circuit in the context of dc voltages and currents Objectives To provide a powerful but simple circuit analysis tool based on Kirchhoff s
EECE25 Circuit Analysis I Set 4: Capacitors, Inductors, and First-Order Linear Circuits Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia firstname.lastname@example.org
SCHOOL OF ENGINEERING AND APPLIED SCIENCE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 2115: ENGINEERING ELECTRONICS LABORATORY Tutorial #4: Bias Point Analysis in Multisim INTRODUCTION When BJTs
Lab Week 6 Quiz #3 Voltage Divider Homework P11, P12 Kirchhoff's Voltage Law (KVL) Kirchhoff's Current Law (KCL) KCL + KVL Module Report tips Quiz 3 Voltage Divider (20 pts.) Please clear desks and turn
Mesh Analysis 1 Objectives Meaning of circuit analysis; distinguish between the terms mesh and loop. To provide more general and powerful circuit analysis tool based on Kirchhoff s voltage law (KVL) only.
Preamble Circuit Analysis II Physics, 8 th Edition Custom Edition Cutnell & Johnson When circuits get really complex methods learned so far will still work, but they can take a long time to do. A particularly
Subject Code: 03EC0302 Subject Name: Circuits and Networks B. Tech. Year II (Semester III) Objective: After completion of this course, student will be able to: 1. To introduce electric circuits and its
Engr228 Lab #2 Voltage Dividers, Nodal, and Mesh Analysis Name Partner(s) Grade /10 Introduction This lab exercise is designed to further your understanding of the use of the lab equipment and to verify
Chapter 5 Parallel Circuits Topics Covered in Chapter 5 5-1: The Applied Voltage V A Is the Same Across Parallel Branches 5-2: Each Branch I Equals V A / R 5-3: Kirchhoff s Current Law (KCL) 5-4: Resistance
Chapter 5 Solution P5.2-2, 3, 6 P5.3-3, 5, 8, 15 P5.4-3, 6, 8, 16 P5.5-2, 4, 6, 11 P5.6-2, 4, 9 P 5.2-2 Consider the circuit of Figure P 5.2-2. Find i a by simplifying the circuit (using source transformations)
EECS 6A Designing Information Devices and Systems I Spring 08 Homework 7 This homework is due March, 08, at 3:59. Self-grades are due March 5, 08, at 3:59. Submission Format Your homework submission should
Physics 116A Notes Fall 2004 David E. Pellett Draft v.0.9 Notes Copyright 2004 David E. Pellett unless stated otherwise. References: Text for course: Fundamentals of Electrical Engineering, second edition,
BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING Alternating Current Circuits : Basic Law Ismail Mohd Khairuddin, Zulkifil Md Yusof Faculty of Manufacturing Engineering Universiti Malaysia Pahang Alternating
German Jordanian University (GJU) Electrical Circuits Laboratory Section Experiment Kirchhoff's Laws and Maximum Power Transfer Post lab Report Mahmood Hisham Shubbak / / 8 Objectives: To learn KVL and
EECE208 Intro to Electrical Engineering Lab Dr. Charles Kim 5. Circuit Theorems - Thevenin Theorem, Maximum Power Transfer, and Superposition Objectives: This experiment emphasizes e following ree circuit
Fundamental of Electrical circuits 1 Course Description: Electrical units and definitions: Voltage, current, power, energy, circuit elements: resistors, capacitors, inductors, independent and dependent
Electrical Engineering Technology 1 ECET 17700 - DAQ & Control Systems Lecture # 9 Loading, Thévenin Model & Norton Model Professors Robert Herrick & J. Michael Jacob Module 1 Circuit Loading Lecture 9
Ver 8 E. Analysis of Circuits (0) E. Circuit Analysis Problem Sheet - Solutions Note: In many of the solutions below I have written the voltage at node X as the variable X instead of V X in order to save
Electric Circuit Theory Nam Ki Min email@example.com 010-9419-2320 Chapter 18 Two-Port Circuits Nam Ki Min firstname.lastname@example.org 010-9419-2320 Contents and Objectives 3 Chapter Contents 18.1 The Terminal Equations
University of Alabama Department of Physics and Astronomy PH 26 LeClair Fall 20 Problem Set 4. A battery has an ideal voltage V and an internal resistance r. A variable load resistance R is connected to
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.2: Circuits & Electronics Problem Set # Solution Exercise. The three resistors form a series connection.
RevisionLecture 1: E1.1 Analysis of Circuits (2014-4530) Revision Lecture 1 1 / 13 Format Question 1 (40%): eight short parts covering the whole syllabus. Questions 2 and 3: single topic questions (answer
Study Notes on Network Theorems for GATE 2017 Network Theorems is a highly important and scoring topic in GATE. This topic carries a substantial weight age in GATE. Although the Theorems might appear to
Chapter 18 Direct Current Circuits Sources of emf The source that maintains the current in a closed circuit is called a source of emf Any devices that increase the potential energy of charges circulating