# Chapter 10 AC Analysis Using Phasors

Size: px
Start display at page:

Transcription

1 Chapter 10 AC Analysis Using Phasors 10.1 Introduction We would like to use our linear circuit theorems (Nodal analysis, Mesh analysis, Thevenin and Norton equivalent circuits, Superposition, etc.) to be able to solve for circuit parameters in phasor circuits. In this chapter we will show that all of these theorems hold, we just need to convert the circuit we are given to its phasor equivalent, and then use the complex domain versions of these theorems to solve for the circuit parameters we are interested in. - We need to remember though, that if we are asked for a time domain circuit parameter, then once we have the phasor solution we must convert the phasor back into its time domain equivalent Superposition We know from Chapter 3 that superposition is a property of ALL linear circuits. - Changing the circuit notation from time domain to phasor domain does not change the linearity of the circuit. S.W. Neville Page 291

2 - Therefore, superposition continues to hold for phasor circuits. Ex Find the current through the voltage source assuming I s = 5 25 A, and V s = 3 45 V ω = 4 rad/s 0.25H 0.5H I s 10Ω 1H 1/4F + - Vs Solution: S.W. Neville Page 292

3 10.3 Thevenin s Theorem From Chapter 3 we had that Thevenin s theorem states Any linear circuit can be represented at a given pair of nodes by an equivalent circuit consisting of a single voltage source and in series with a single resistor. Phasor equivalents circuits of linear circuits are still linear circuits so Thevenin s theorem holds. Where - But we need to write Thevenin s theorem in its complex form Any linear circuit can be represented at a given pair of nodes by an equivalent circuit consisting of a single voltage source in series with a single impedance. - = is the Thevenin voltage V T V oc - is the short-circuit current I sc - and = is the Thevenin impedance. Z T V oc I sc S.W. Neville Page 293

4 So everything is the same as before except that we are expressing the voltages and currents in terms of phasors and we now have complex impedances (instead of just the resistances we had in Chapter 3). The application of Thevenin s theorem has not changed. Ex Given the circuit below find its Thevenin equivalent with respect to nodes A and B A R L B Solution: S.W. Neville Page 294

5 Ex Given the following circuit find it Thevenin equivalent at the load inductor 0.5H 0.25H 10Ω 10cos( 8t + 25 ) + - 4Ω L L Solution: S.W. Neville Page 295

6 10.4 Norton s Theorem From Chapter 3 we had that Norton s theorem states Any linear circuit can be represented at a given pair of nodes by an equivalent circuit consisting of a single current source in parallel with a single resistor. Phasor equivalents circuits of linear circuits are still linear circuits so Norton s theorem holds. Where - But we do need to write Norton s theorem in its complex form - The complex form of Norton s theorem states that Any linear circuit can be represented at a given pair of nodes by an equivalent circuit consisting of a single current source in parallel with a single impedance. - = is the Norton current I N I sc - = is the open-circuit voltage V oc V T - and = = is the Norton impedance. Z N V oc Z T I sc S.W. Neville Page 296

7 So everything is the same as before except that we are expressing the voltages and currents in terms of phasors and we now have complex impedances (instead of just the resistances we had in Chapter 3). The application of Norton s theorem has not changed. Ex Given the circuit below find its Norton equivalent with respect to nodes A and B. 0.5H A 4sin( 4t) + - 4Ω 2H 1/4F 6cos( 4t 15 ) B Solution: S.W. Neville Page 297

8 10.5 Nodal Analysis Nodal analysis is just a systematic way of applying KCL to a circuit, based on the assumption that the law of conservation of charge holds (i.e. charge cannot accumulate at a node, hence sum of currents entering a node must equal the sum of currents leaving the node) Converting a circuit to complex impedances and phasor notation for the power sources does not change this assumption that the law of conservation of charge holds. Therefore, nodal analysis applies to phasor circuits S.W. Neville Page 298

9 Ex Find the node voltages for the following circuit 1/2F 1/4F sin( 2t 35 ) 4Ω + - 2i + 3 3H 2H i + - 2Ω 4cos( 2t + 30 ) Solution: S.W. Neville Page 299

10 10.6 Mesh Analysis Mesh analysis is just a systematic way of applying KVL to a circuit, based on the assumption that the law of conservation of energy holds (i.e. the energy gained around a closed loop must be zero hence the energy gained around a loop must equal the energy lost around the same loop) Converting a circuit to complex impedances and phasor notation for the power sources does not change this assumption that the law of conservation of energy holds. Therefore, mesh analysis applies to phasor circuits S.W. Neville Page 300

11 Ex Solve for the mesh currents in the following circuit and give the time domain voltage across the load capacitor assuming ω = 3 rad/s. 2Ω 4Ω 3H 2v L /6F + - v L + - 3Ω + - 3H 3H 1/3F 1/9F Solution: S.W. Neville Page 301

12 10.7 Sources with Different Frequencies How do we solve when circuits contain power sources at different frequencies? - Remember that phasor notation assumes that the frequency ω is constant throughout the circuit - But we also have linear circuits so we can use superposition to separate out the power sources at different frequencies. - We can then use phasor analysis to solve each of these new circuits - Once we have the phasor solutions we can convert them back to time domain - We can now combine the time domain solution to get the overall solution for the original circuit. - If the power sources are at different frequencies then we MUST solve for their effects independently (via superposition) and then combine the time domain results to get the complete circuit solution. - This is because phasors are defined for only singular frequencies. Hence, phasor analysis can only deal with one of the frequencies (sources) at a time. S.W. Neville Page 302

13 Ex Solve for the voltage across the load resistor in the following circuit. 2cos( 2t + 30 ) + - 4Ω 1/2F 1/6F 3H 2Ω 3sin( 6t 10 ) 6H - vl + Solution: S.W. Neville Page 303

14 Assignment #10 Refer to Elec 250 course web site for assigned problems. Due 1 week from 5pm in the Elec 250 Assignment Drop box. S.W. Neville Page 304

### Chapter 5. Department of Mechanical Engineering

Source Transformation By KVL: V s =ir s + v By KCL: i s =i + v/r p is=v s /R s R s =R p V s /R s =i + v/r s i s =i + v/r p Two circuits have the same terminal voltage and current Source Transformation

### Sinusoidal Steady State Analysis (AC Analysis) Part I

Sinusoidal Steady State Analysis (AC Analysis) Part I Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

### Chapter 10: Sinusoidal Steady-State Analysis

Chapter 10: Sinusoidal Steady-State Analysis 10.1 10.2 10.3 10.4 10.5 10.6 10.9 Basic Approach Nodal Analysis Mesh Analysis Superposition Theorem Source Transformation Thevenin & Norton Equivalent Circuits

### Electric Circuits II Sinusoidal Steady State Analysis. Dr. Firas Obeidat

Electric Circuits II Sinusoidal Steady State Analysis Dr. Firas Obeidat 1 Table of Contents 1 2 3 4 5 Nodal Analysis Mesh Analysis Superposition Theorem Source Transformation Thevenin and Norton Equivalent

### BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING. Alternating Current Circuits : Basic Law

BFF1303: ELECTRICAL / ELECTRONICS ENGINEERING Alternating Current Circuits : Basic Law Ismail Mohd Khairuddin, Zulkifil Md Yusof Faculty of Manufacturing Engineering Universiti Malaysia Pahang Alternating

### Chapter 10 Sinusoidal Steady State Analysis Chapter Objectives:

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

### 4/27 Friday. I have all the old homework if you need to collect them.

4/27 Friday Last HW: do not need to turn it. Solution will be posted on the web. I have all the old homework if you need to collect them. Final exam: 7-9pm, Monday, 4/30 at Lambert Fieldhouse F101 Calculator

### Chapter 10: Sinusoidal Steady-State Analysis

Chapter 10: Sinusoidal Steady-State Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques

### UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS

UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS 1.0 Kirchoff s Law Kirchoff s Current Law (KCL) states at any junction in an electric circuit the total current flowing towards that junction is equal

Network Topology-2 & Dual and Duality Choice of independent branch currents and voltages: The solution of a network involves solving of all branch currents and voltages. We know that the branch current

### ELEC 250: LINEAR CIRCUITS I COURSE OVERHEADS. These overheads are adapted from the Elec 250 Course Pack developed by Dr. Fayez Guibaly.

Elec 250: Linear Circuits I 5/4/08 ELEC 250: LINEAR CIRCUITS I COURSE OVERHEADS These overheads are adapted from the Elec 250 Course Pack developed by Dr. Fayez Guibaly. S.W. Neville Elec 250: Linear Circuits

### MAE140 - Linear Circuits - Fall 14 Midterm, November 6

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

### Sinusoidal Steady State Analysis (AC Analysis) Part II

Sinusoidal Steady State Analysis (AC Analysis) Part II Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

### EE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain.

Name If you have any questions ask them. Remember to include all units on your answers (V, A, etc). Clearly indicate your answers. All angles must be in the range 0 to +180 or 0 to 180 degrees. 1) [6 pts]

### Thevenin Norton Equivalencies - GATE Study Material in PDF

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

### EE 3120 Electric Energy Systems Study Guide for Prerequisite Test Wednesday, Jan 18, pm, Room TBA

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

### D C Circuit Analysis and Network Theorems:

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,

### POLYTECHNIC UNIVERSITY Electrical Engineering Department. EE SOPHOMORE LABORATORY Experiment 2 DC circuits and network theorems

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

### Midterm Exam (closed book/notes) Tuesday, February 23, 2010

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

### Electric Circuits I Final Examination

EECS:300 Electric Circuits I ffs_elci.fm - Electric Circuits I Final Examination Problems Points. 4. 3. Total 38 Was the exam fair? yes no //3 EECS:300 Electric Circuits I ffs_elci.fm - Problem 4 points

### Sinusoids and Phasors

CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are time-varying. In this chapter, we are particularly interested in sinusoidally time-varying

### Chapter 5 Steady-State Sinusoidal Analysis

Chapter 5 Steady-State Sinusoidal Analysis Chapter 5 Steady-State Sinusoidal Analysis 1. Identify the frequency, angular frequency, peak value, rms value, and phase of a sinusoidal signal. 2. Solve steady-state

### ECE2262 Electric Circuits

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

### Preamble. Circuit Analysis II. Mesh Analysis. When circuits get really complex methods learned so far will still work,

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

### DC STEADY STATE CIRCUIT ANALYSIS

DC STEADY STATE CIRCUIT ANALYSIS 1. Introduction The basic quantities in electric circuits are current, voltage and resistance. They are related with Ohm s law. For a passive branch the current is: I=

### Circuit Theorems Overview Linearity Superposition Source Transformation Thévenin and Norton Equivalents Maximum Power Transfer

Circuit Theorems Overview Linearity Superposition Source Transformation Thévenin and Norton Equivalents Maximum Power Transfer J. McNames Portland State University ECE 221 Circuit Theorems Ver. 1.36 1

### Chapter 1W Basic Electromagnetic Concepts

Chapter 1W Basic Electromagnetic Concepts 1W Basic Electromagnetic Concepts 1W.1 Examples and Problems on Electric Circuits 1W.2 Examples on Magnetic Concepts This chapter includes additional examples

### ECE2262 Electric Circuits. Chapter 5: Circuit Theorems

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

### Fall 2011 ME 2305 Network Analysis. Sinusoidal Steady State Analysis of RLC Circuits

Fall 2011 ME 2305 Network Analysis Chapter 4 Sinusoidal Steady State Analysis of RLC Circuits Engr. Humera Rafique Assistant Professor humera.rafique@szabist.edu.pk Faculty of Engineering (Mechatronics)

### MAE140 - Linear Circuits - Winter 09 Midterm, February 5

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

### Kirchhoff's Laws and Circuit Analysis (EC 2)

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,

### 3.1 Superposition theorem

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

### Series & Parallel Resistors 3/17/2015 1

Series & Parallel Resistors 3/17/2015 1 Series Resistors & Voltage Division Consider the single-loop circuit as shown in figure. The two resistors are in series, since the same current i flows in both

### Basics of Network Theory (Part-I)

Basics of Network Theory (PartI). A square waveform as shown in figure is applied across mh ideal inductor. The current through the inductor is a. wave of peak amplitude. V 0 0.5 t (m sec) [Gate 987: Marks]

### Study Notes on Network Theorems for GATE 2017

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

### Solution: Based on the slope of q(t): 20 A for 0 t 1 s dt = 0 for 3 t 4 s. 20 A for 4 t 5 s 0 for t 5 s 20 C. t (s) 20 C. i (A) Fig. P1.

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

### Delhi Noida Bhopal Hyderabad Jaipur Lucknow Indore Pune Bhubaneswar Kolkata Patna Web: Ph:

Serial : CH_EE_B_Network Theory_098 Delhi Noida Bhopal Hyderabad Jaipur Lucknow ndore Pune Bhubaneswar Kolkata Patna Web: E-mail: info@madeeasy.in Ph: 0-56 CLASS TEST 08-9 ELECTCAL ENGNEENG Subject : Network

### 1. Review of Circuit Theory Concepts

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

### Lecture Notes on DC Network Theory

Federal University, Ndufu-Alike, Ikwo Department of Electrical/Electronics and Computer Engineering (ECE) Faculty of Engineering and Technology Lecture Notes on DC Network Theory Harmattan Semester by

### Schedule. ECEN 301 Discussion #20 Exam 2 Review 1. Lab Due date. Title Chapters HW Due date. Date Day Class No. 10 Nov Mon 20 Exam Review.

Schedule Date Day lass No. 0 Nov Mon 0 Exam Review Nov Tue Title hapters HW Due date Nov Wed Boolean Algebra 3. 3.3 ab Due date AB 7 Exam EXAM 3 Nov Thu 4 Nov Fri Recitation 5 Nov Sat 6 Nov Sun 7 Nov Mon

### 11. AC Circuit Power Analysis

. AC Circuit Power Analysis Often an integral part of circuit analysis is the determination of either power delivered or power absorbed (or both). In this chapter First, we begin by considering instantaneous

### ELEC273 Lecture Notes Set 11 AC Circuit Theorems

ELEC273 Lecture Notes Set C Circuit Theorems The course web site is: http://users.encs.concordia.ca/~trueman/web_page_273.htm Final Exam (confirmed): Friday December 5, 207 from 9:00 to 2:00 (confirmed)

### SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS 1. Introduction A sinusoidal current has the following form: where I m is the amplitude value; ω=2 πf is the angular frequency; φ is the phase shift. i (t )=I m.sin

### Thevenin equivalent circuits

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

### QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34)

QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34) NOTE: FOR NUMERICAL PROBLEMS FOR ALL UNITS EXCEPT UNIT 5 REFER THE E-BOOK ENGINEERING CIRCUIT ANALYSIS, 7 th EDITION HAYT AND KIMMERLY. PAGE NUMBERS OF

### Chapter 5 Objectives

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

### Electric Circuits I. Nodal Analysis. Dr. Firas Obeidat

Electric Circuits I Nodal Analysis Dr. Firas Obeidat 1 Nodal Analysis Without Voltage Source Nodal analysis, which is based on a systematic application of Kirchhoff s current law (KCL). A node is defined

### ECE2262 Electric Circuit

ECE2262 Electric Circuit Chapter 7: FIRST AND SECOND-ORDER RL AND RC CIRCUITS Response to First-Order RL and RC Circuits Response to Second-Order RL and RC Circuits 1 2 7.1. Introduction 3 4 In dc steady

### Notes for course EE1.1 Circuit Analysis TOPIC 10 2-PORT CIRCUITS

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

### Basic Electrical Circuits Analysis ECE 221

Basic Electrical Circuits Analysis ECE 221 PhD. Khodr Saaifan http://trsys.faculty.jacobs-university.de k.saaifan@jacobs-university.de 1 2 Reference: Electric Circuits, 8th Edition James W. Nilsson, and

### Chapter 10: Sinusoids and Phasors

Chapter 10: Sinusoids and Phasors 1. Motivation 2. Sinusoid Features 3. Phasors 4. Phasor Relationships for Circuit Elements 5. Impedance and Admittance 6. Kirchhoff s Laws in the Frequency Domain 7. Impedance

### Network Graphs and Tellegen s Theorem

Networ Graphs and Tellegen s Theorem The concepts of a graph Cut sets and Kirchhoff s current laws Loops and Kirchhoff s voltage laws Tellegen s Theorem The concepts of a graph The analysis of a complex

### Electric Circuits I FINAL EXAMINATION

EECS:300, Electric Circuits I s6fs_elci7.fm - Electric Circuits I FINAL EXAMINATION Problems Points.. 3. 0 Total 34 Was the exam fair? yes no 5//6 EECS:300, Electric Circuits I s6fs_elci7.fm - Problem

### Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1. Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω.

Homework 2 SJTU233 Problem 1 Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω. Express Zab in polar form. Enter your answer using polar notation. Express argument in degrees.

### AC Circuit Analysis and Measurement Lab Assignment 8

Electric Circuit Lab Assignments elcirc_lab87.fm - 1 AC Circuit Analysis and Measurement Lab Assignment 8 Introduction When analyzing an electric circuit that contains reactive components, inductors and

### Basic. Theory. ircuit. Charles A. Desoer. Ernest S. Kuh. and. McGraw-Hill Book Company

Basic C m ш ircuit Theory Charles A. Desoer and Ernest S. Kuh Department of Electrical Engineering and Computer Sciences University of California, Berkeley McGraw-Hill Book Company New York St. Louis San

### Chapter 4. Techniques of Circuit Analysis

Chapter 4. Techniques of Circuit Analysis By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology http://wp.kntu.ac.ir/faradji/electriccircuits1.htm Reference:

### Electrical Circuits I Lecture 8

Electrical Circuits I Lecture 8 Thevenin and Norton theorems Thevenin theorem tells us that we can replace the entire network, exclusive of the load resistor, by an equivalent circuit

### ECE 201 Fall 2009 Final Exam

ECE 01 Fall 009 Final Exam December 16, 009 Division 0101: Tan (11:30am) Division 001: Clark (7:30 am) Division 0301: Elliott (1:30 pm) Instructions 1. DO NOT START UNTIL TOLD TO DO SO.. Write your Name,

### Notes for course EE1.1 Circuit Analysis TOPIC 3 CIRCUIT ANALYSIS USING SUB-CIRCUITS

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

### In this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents

In this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents around an electrical circuit. This is a short lecture,

### Lecture 6: Impedance (frequency dependent. resistance in the s- world), Admittance (frequency. dependent conductance in the s- world), and

Lecture 6: Impedance (frequency dependent resistance in the s- world), Admittance (frequency dependent conductance in the s- world), and Consequences Thereof. Professor Ray, what s an impedance? Answers:

### Chapter 9 Objectives

Chapter 9 Engr8 Circuit Analysis Dr Curtis Nelson Chapter 9 Objectives Understand the concept of a phasor; Be able to transform a circuit with a sinusoidal source into the frequency domain using phasor

### V x 4 V x. 2k = 5

Review Problem: d) Dependent sources R3 V V R Vx - R2 Vx V2 ) Determine the voltage V5 when VV Need to find voltage Vx then multiply by dependent source multiplier () Node analysis 2 V x V x R R 2 V x

### SOME USEFUL NETWORK THEOREMS

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

### Chapter 2. Engr228 Circuit Analysis. Dr Curtis Nelson

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

### Chapter 5: Circuit Theorems

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

### Lecture #3. Review: Power

Lecture #3 OUTLINE Power calculations Circuit elements Voltage and current sources Electrical resistance (Ohm s law) Kirchhoff s laws Reading Chapter 2 Lecture 3, Slide 1 Review: Power If an element is

### E2.2 Analogue Electronics

E2.2 Analogue Electronics Instructor : Christos Papavassiliou Office, email : EE 915, c.papavas@imperial.ac.uk Lectures : Monday 2pm, room 408 (weeks 2-11) Thursday 3pm, room 509 (weeks 4-11) Problem,

### CURRENT SOURCES EXAMPLE 1 Find the source voltage Vs and the current I1 for the circuit shown below SOURCE CONVERSIONS

CURRENT SOURCES EXAMPLE 1 Find the source voltage Vs and the current I1 for the circuit shown below EXAMPLE 2 Find the source voltage Vs and the current I1 for the circuit shown below SOURCE CONVERSIONS

### Lecture 8: 09/18/03 A.R. Neureuther Version Date 09/14/03 EECS 42 Introduction Digital Electronics Andrew R. Neureuther

EECS ntroduction Digital Electronics ndrew. Neureuther Lecture #8 Node Equations Systematic Node Equations Example: oltage and Current Dividers Example 5 Element Circuit Schwarz and Oldham 5-58,.5, &.6

### Outline. Week 5: Circuits. Course Notes: 3.5. Goals: Use linear algebra to determine voltage drops and branch currents.

Outline Week 5: Circuits Course Notes: 3.5 Goals: Use linear algebra to determine voltage drops and branch currents. Components in Resistor Networks voltage source current source resistor Components in

### Module 2. DC Circuit. Version 2 EE IIT, Kharagpur

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

### EIT Review. Electrical Circuits DC Circuits. Lecturer: Russ Tatro. Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1

EIT Review Electrical Circuits DC Circuits Lecturer: Russ Tatro Presented by Tau Beta Pi The Engineering Honor Society 10/3/2006 1 Session Outline Basic Concepts Basic Laws Methods of Analysis Circuit

### UNIVERSITY F P RTLAND Sch l f Engineering

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

### Introduction to AC Circuits (Capacitors and Inductors)

Introduction to AC Circuits (Capacitors and Inductors) Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

### E1.1 Analysis of Circuits ( ) Revision Lecture 1 1 / 13

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

### I. Impedance of an R-L circuit.

I. Impedance of an R-L circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the R-L circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC

### Electric Circuits I. Midterm #1

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

### EE40. Lec 3. Basic Circuit Analysis. Prof. Nathan Cheung. Reading: Hambley Chapter 2

EE40 Lec 3 Basic Circuit Analysis Prof. Nathan Cheung 09/03/009 eading: Hambley Chapter Slide Outline Chapter esistors in Series oltage Divider Conductances in Parallel Current Divider Node-oltage Analysis

### Physics 116A Notes Fall 2004

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,

### Electric Circuit Theory

Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 18 Two-Port Circuits Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 18.1 The Terminal Equations

### 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

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)

### CHAPTER FOUR CIRCUIT THEOREMS

4.1 INTRODUCTION CHAPTER FOUR CIRCUIT THEOREMS The growth in areas of application of electric circuits has led to an evolution from simple to complex circuits. To handle the complexity, engineers over

### EE-201 Review Exam I. 1. The voltage Vx in the circuit below is: (1) 3V (2) 2V (3) -2V (4) 1V (5) -1V (6) None of above

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)

### Basic RL and RC Circuits R-L TRANSIENTS: STORAGE CYCLE. Engineering Collage Electrical Engineering Dep. Dr. Ibrahim Aljubouri

st Class Basic RL and RC Circuits The RL circuit with D.C (steady state) The inductor is short time at Calculate the inductor current for circuits shown below. I L E R A I L E R R 3 R R 3 I L I L R 3 R

### = 32.0\cis{38.7} = j Ω. Zab = Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1

Homework 2 SJTU233 Problem 1 Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω. Express Zab in polar form. Enter your answer using polar notation. Express argument in degrees.

### Fundamentals of Electric Circuits, Second Edition - Alexander/Sadiku

Chapter 3, Problem 9(8). Find V x in the network shown in Fig. 3.78. Figure 3.78 Chapter 3, Solution 9(8). Consider the circuit below. 2 Ω 2 Ω -j 8 30 o I j 4 j 4 I 2 -j2v For loop, 8 30 = (2 j4)i ji 2

### Electrical Circuits Lab Series RC Circuit Phasor Diagram

Electrical Circuits Lab. 0903219 Series RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a series RC circuit without memorizing: * Start with the quantity (voltage or current) that is

### UC DAVIS. Circuits I Course Outline

UC DAVIS Circuits I Course Outline ENG 17 Professor Spencer Fall 2010 2041 Kemper Hall Lecture: MWF 4:10-5:00, 1003 Giedt Hall 752-6885 Discussion Section 1: W 1:10-2:00, 55 Roessler CRN: 61417 Discussion

### Chapter 3. Loop and Cut-set Analysis

Chapter 3. Loop and Cut-set Analysis By: FARHAD FARADJI, Ph.D. Assistant Professor, Electrical Engineering, K.N. Toosi University of Technology http://wp.kntu.ac.ir/faradji/electriccircuits2.htm References:

### To find the step response of an RC circuit

To find the step response of an RC circuit v( t) v( ) [ v( t) v( )] e tt The time constant = RC The final capacitor voltage v() The initial capacitor voltage v(t ) To find the step response of an RL circuit

### Voltage Dividers, Nodal, and Mesh Analysis

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

### Figure Circuit for Question 1. Figure Circuit for Question 2

Exercises 10.7 Exercises Multiple Choice 1. For the circuit of Figure 10.44 the time constant is A. 0.5 ms 71.43 µs 2, 000 s D. 0.2 ms 4 Ω 2 Ω 12 Ω 1 mh 12u 0 () t V Figure 10.44. Circuit for Question

### Notes for course EE1.1 Circuit Analysis TOPIC 4 NODAL ANALYSIS

Notes for course EE1.1 Circuit Analysis 2004-05 TOPIC 4 NODAL ANALYSIS OBJECTIVES 1) To develop Nodal Analysis of Circuits without Voltage Sources 2) To develop Nodal Analysis of Circuits with Voltage

### CHAPTER 4. Circuit Theorems

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

### ECE 205: Intro Elec & Electr Circuits

ECE 205: Intro Elec & Electr Circuits Final Exam Study Guide Version 1.00 Created by Charles Feng http://www.fenguin.net ECE 205: Intro Elec & Electr Circuits Final Exam Study Guide 1 Contents 1 Introductory

### Tutorial #4: Bias Point Analysis in Multisim

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