Sinusoidal Steady State Analysis (AC Analysis) Part I

Size: px
Start display at page:

Download "Sinusoidal Steady State Analysis (AC Analysis) Part I"

Transcription

1 Sinusoidal Steady State Analysis (AC Analysis) Part I Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com

2 OUTLINE Previously on ELCN102 Solution of AC Circuits Simplification Method Loop Analysis Method Node Analysis Method Superposition Method 2

3 Previously on ELCN102 Phasor Relationships for Circuit Elements Resistor Inductor Capacitor v R t = Ri R t v L t = L di L t dt i C t = C dv C t dt V R = R I R V L = ωli L 90 o = jωl I L I C = ωcv C 90o = jωc V C The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I, measured in Ω. Z R = R Z L = jωl Z C = 1 jωc = j ωc

4 Previously on ELCN102 Phasor Relationships for Circuit Elements Resistor Inductor Capacitor v R t = Ri R t v L t = L di L t dt i C t = C dv C t dt V R = R I R V L = ωli L 90 o = jωl I L I C = ωcv C 90o = jωc V C Y R = 1 R Y L = 1 jωl = j ωl Y C = jωc The admittance Y of a circuit is the ratio of the phasor current I to the phasor voltage V, measured in Ω 1.

5 Previously on ELCN102 Impedance and Admittance Impedance The impedance Z of a circuit is the ratio of the phasor voltage V to the phasor current I, measured in Ω. Z = R + jx R is the resistance & X is the reactance Z is inductive if X is +ve. Z is capacitive if X is ve. Z, R, and X are in units of Ω Z L = jωl Z C = 1 jωc = j ωc

6 Previously on ELCN102 Impedance and Admittance Admittance The admittance Y of a circuit is the ratio of the phasor current I to the phasor voltage V, measured in Ω 1. Y = G + jb G is the conductance & B is the susceptance. Y is inductive if B is ve. Y is capacitive if B is +ve. Y, G, and B are in units of Ω 1 Y L = 1 jωl = j ωl Y C = jωc

7 Previously on ELCN102 Impedance Combination Series Combination Z eq = Z 1 + Z Z N

8 Previously on ELCN102 Impedance Combination Parallel Combination 1 = Z eq Z 1 Z 2 Z N

9 Previously on ELCN102 Admittance Combination Series Combination 1 Y eq = 1 Y Y Y N

10 Previously on ELCN102 Admittance Combination Parallel Combination Y eq = Y 1 + Y Y N

11 Previously on ELCN102 Star-Delta Transformation Z A = Z AB Z BC Z B = Z AC + Z BC + Z AB Z AB Z AC Z AC + Z BC + Z AB Z C = Z BC Z AC Z AC + Z BC + Z AB Z AB = Z A + Z B + Z AZ B Z C Z AC = Z A + Z C + Z AZ C Z B Z BC = Z B + Z C + Z BZ C Z A

12 Definition Solution of AC Circuits A circuit is said to be solved when the voltage across and the current in every element have been determined due to input excitation (voltage and/or current sources).

13 Solution of AC Circuits Methods of Solution of AC Circuits To solve a AC circuit you can use one or more of the following methods: Simplification Method Loop Analysis Method Node Analysis Method Superposition Method Thevenin equivalent circuit Norton equivalent circuit

14 Solution of AC Circuits Simplification Method In step by step simplification we can use: Source transformation Combination of active elements Combination of series and parallel elements Star-delta & delta-star transformation

15 Simplification Method Source Transformation A voltage source V AC with a series impedance Z can be transformed into a current source I AC = V AC /Z and a parallel impedance Z A current source I AC with a parallel impedance Z can be transformed into a voltage source V AC = I AC Z and a series impedance Z

16 Example (1) Simplification Method Use simplification method to find V x for the circuit shown.

17 Example (2) Simplification Method Use simplification method to find I x for the circuit shown.

18 Definition Loop Analysis Method The Loop Analysis Method (Mesh Method) uses KVL to generate a set of simultaneous equations. 1) Convert the independent current sources into equivalent voltage sources 2) Identify the number of independent loop (L) on the circuit 3) Label a loop current on each loop. 4) Write an expression for the KVL around each loop. 5) Solve the simultaneous equations to get the loop currents.

19 Matrix Form Loop Analysis Method Z 11 Z 12 Z 1N Z 21 Z 22 Z 2N Z N1 Z N2 Z NN I 1 I 2 I N = V 1 V 2 V N Z ii = impedance in loop i Z ij = Common impedance between loops i and j = Z ji V i = voltage sources in loop i V is +ve if it supplies current in the direction of the loop current

20 Example (3) Loop Analysis Method Use loop analysis to find I x for the circuit shown.

21 Example (4) Loop Analysis Method Use loop analysis to find I x for the circuit shown.

22 Example (5) Loop Analysis Method Use loop analysis to find V x for the circuit shown.

23 Definition Node Analysis Method The Node Analysis Method (Nodal Analysis) uses KCL to generate a set of simultaneous equations. 1) Convert independent voltage sources into equivalent current sources. 2) Identify the number of non simple nodes (N) of the circuit. 3) Write an expression for the KCL at each N 1 Node (exclude the ground node). 4) Solve the resultant simultaneous equations to get the voltages. 23

24 Matrix Form Node Analysis Method Y 11 Y 12 Y 1N Y 21 Y 22 Y 2N Y N1 Y N2 Y NN V 1 V 2 V N = I 1 I 2 I N Y ii = admittance of node i Y ij = common admittance between node i and j = Y ji I i = current sources at node i I is +ve if it supply current into the node

25 Example (6) Node Analysis Method Use node analysis to find V 1 & V 2 for the circuit shown.

26 Definition Superposition Theorem For a linear circuit containing multiple independent sources, the voltage across (or current through) any of its elements is the algebraic sum of the voltages across (or currents through) that element due to each independent source acting alone o V 5 0 o A Total I a I b I = I a + I b

27 Example (7) Superposition Theorem Use superposition theorem to find I x for the circuit shown.

28 Definition Thevenin s Theorem A linear two-terminal circuit, can be replaced by an equivalent circuit consisting of a voltage source V th in series with a impedance Z th.

29 Solution Steps Thevenin s Theorem 1) Identify the load impedance and introduce two nodes a and b 2) Remove the load impedance between node a and b 3) Calculate the open circuit voltage between nodes a and b. This voltage is V th of the Thevenin equivalent circuit. 4) Set all the independent sources to zero (voltage sources are SC and current sources are OC) and calculate the impedance seen between nodes a and b. This impedance is Z th of the Thevenin equivalent circuit.

30 Example (8) Thevenin s Theorem Obtain the Thevenin equivalent at terminals a and b of the circuit shown.

31 Definition Norton s Theorem A linear two-terminal circuit can be replaced by equivalent circuit consisting of a current source I N in parallel with a impedance Z N

32 Solution Steps Norton s Theorem 1) Identify the load impedance and introduce two nodes a and b 2) Remove the load impedance between node a and b and set all the independent sources to zero (voltage sources are SC and current sources are OC) and calculate the impedance seen between nodes a and b. This resistance is Z N of the Norton equivalent circuit. 3) Replace the load impedance with a short circuit and calculate the short circuit current between nodes a and b. This current is I N of the Norton equivalent circuit.

33 Norton s Theorem Thevenin and Norton equivalent circuits Thevenin equivalent circuit must be equivalent to Norton equivalent circuit Z N = Z th, V th = I N Z N, I N = V th Z Z th = V th th I N

34 Example (9) Thevenin s Theorem Obtain the Norton equivalent at terminals a and b of the circuit shown.

Sinusoidal Steady State Analysis (AC Analysis) Part II

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/

More information

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

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

More information

Chapter 10: Sinusoidal Steady-State Analysis

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

More information

Chapter 10 AC Analysis Using Phasors

Chapter 10 AC Analysis Using Phasors 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

More information

Electric Circuit Theory

Electric Circuit Theory Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 11 Sinusoidal Steady-State Analysis Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 11.1

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis Sinusoidal Steady-State Analysis Mauro Forti October 27, 2018 Constitutive Relations in the Frequency Domain Consider a network with independent voltage and current sources at the same angular frequency

More information

Sinusoids and Phasors

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

More information

Chapter 5 Steady-State Sinusoidal Analysis

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

More information

Introduction to AC Circuits (Capacitors and Inductors)

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/

More information

Chapter 5. Department of Mechanical Engineering

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

More information

Chapter 10 Sinusoidal Steady State Analysis Chapter Objectives:

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

More information

EE292: Fundamentals of ECE

EE292: Fundamentals of ECE EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis

More information

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

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

More information

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

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

More information

Chapter 9 Objectives

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

More information

Three Phase Circuits

Three Phase Circuits Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/ OUTLINE Previously on ELCN102 Three Phase Circuits Balanced

More information

CIRCUIT ANALYSIS II. (AC Circuits)

CIRCUIT ANALYSIS II. (AC Circuits) Will Moore MT & MT CIRCUIT ANALYSIS II (AC Circuits) Syllabus Complex impedance, power factor, frequency response of AC networks including Bode diagrams, second-order and resonant circuits, damping and

More information

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, 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

More information

Chapter 10: Sinusoidal Steady-State Analysis

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

More information

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS

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

More information

Sinusoidal Steady State Analysis

Sinusoidal Steady State Analysis Sinusoidal Steady State Analysis 9 Assessment Problems AP 9. [a] V = 70/ 40 V [b] 0 sin(000t +20 ) = 0 cos(000t 70 ).. I = 0/ 70 A [c] I =5/36.87 + 0/ 53.3 =4+j3+6 j8 =0 j5 =.8/ 26.57 A [d] sin(20,000πt

More information

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 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

More information

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

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

More information

D C Circuit Analysis and Network Theorems:

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,

More information

UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS

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

More information

Thevenin Norton Equivalencies - GATE Study Material in PDF

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

More information

Single Phase Parallel AC Circuits

Single Phase Parallel AC Circuits Single Phase Parallel AC Circuits 1 Single Phase Parallel A.C. Circuits (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) n parallel a.c. circuits similar

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis Sinusoidal Steady-State Analysis Almost all electrical systems, whether signal or power, operate with alternating currents and voltages. We have seen that when any circuit is disturbed (switched on or

More information

Electric Circuits I FINAL EXAMINATION

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

More information

Chapter 10: Sinusoids and Phasors

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

More information

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 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:

More information

Sinusoidal Steady-State Analysis

Sinusoidal Steady-State Analysis Chapter 4 Sinusoidal Steady-State Analysis In this unit, we consider circuits in which the sources are sinusoidal in nature. The review section of this unit covers most of section 9.1 9.9 of the text.

More information

Electric Circuits I Final Examination

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

More information

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

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)

More information

Basics of Network Theory (Part-I)

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]

More information

Physics 116A Notes Fall 2004

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,

More information

ECE 205: Intro Elec & Electr Circuits

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

More information

Phasors: Impedance and Circuit Anlysis. Phasors

Phasors: Impedance and Circuit Anlysis. Phasors Phasors: Impedance and Circuit Anlysis Lecture 6, 0/07/05 OUTLINE Phasor ReCap Capacitor/Inductor Example Arithmetic with Complex Numbers Complex Impedance Circuit Analysis with Complex Impedance Phasor

More information

09/29/2009 Reading: Hambley Chapter 5 and Appendix A

09/29/2009 Reading: Hambley Chapter 5 and Appendix A EE40 Lec 10 Complex Numbers and Phasors Prof. Nathan Cheung 09/29/2009 Reading: Hambley Chapter 5 and Appendix A Slide 1 OUTLINE Phasors as notation for Sinusoids Arithmetic with Complex Numbers Complex

More information

P A R T 2 AC CIRCUITS. Chapter 9 Sinusoids and Phasors. Chapter 10 Sinusoidal Steady-State Analysis. Chapter 11 AC Power Analysis

P A R T 2 AC CIRCUITS. Chapter 9 Sinusoids and Phasors. Chapter 10 Sinusoidal Steady-State Analysis. Chapter 11 AC Power Analysis P A R T 2 AC CIRCUITS Chapter 9 Sinusoids and Phasors Chapter 10 Sinusoidal Steady-State Analysis Chapter 11 AC Power Analysis Chapter 12 Three-Phase Circuits Chapter 13 Magnetically Coupled Circuits Chapter

More information

QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34)

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

More information

EE 212 PASSIVE AC CIRCUITS

EE 212 PASSIVE AC CIRCUITS EE 212 PASSIVE AC CIRCUITS Condensed Text Prepared by: Rajesh Karki, Ph.D., P.Eng. Dept. of Electrical Engineering University of Saskatchewan About the EE 212 Condensed Text The major topics in the course

More information

EE292: Fundamentals of ECE

EE292: Fundamentals of ECE EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 20 121101 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Chapters 1-3 Circuit Analysis Techniques Chapter 10 Diodes Ideal Model

More information

EE 40: Introduction to Microelectronic Circuits Spring 2008: Midterm 2

EE 40: Introduction to Microelectronic Circuits Spring 2008: Midterm 2 EE 4: Introduction to Microelectronic Circuits Spring 8: Midterm Venkat Anantharam 3/9/8 Total Time Allotted : min Total Points:. This is a closed book exam. However, you are allowed to bring two pages

More information

MAE140 - Linear Circuits - Fall 14 Midterm, November 6

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

More information

AC Circuit Analysis and Measurement Lab Assignment 8

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

More information

ECE2262 Electric Circuits

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

More information

Transformer. Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.).

Transformer. Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.). . Transformers Transformer Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.). f the primary side is connected to an AC voltage source v (t), an AC flux (t) will be

More information

3.1 Superposition theorem

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

More information

ECE2262 Electric Circuit

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

More information

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. 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

More information

Chapter 10: Sinusoidal Steady-State Analysis

Chapter 10: Sinusoidal Steady-State Analysis Chapter 0: Sinusoidal Steady-State Analysis Sinusoidal Sources If a circuit is driven by a sinusoidal source, after 5 tie constants, the circuit reaches a steady-state (reeber the RC lab with t τ). Consequently,

More information

ECE2262 Electric Circuits. Chapter 5: Circuit Theorems

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

More information

Chapter 5 Objectives

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

More information

Announcements: Today: more AC circuits

Announcements: Today: more AC circuits Announcements: Today: more AC circuits I 0 I rms Current through a light bulb I 0 I rms I t = I 0 cos ωt I 0 Current through a LED I t = I 0 cos ωt Θ(cos ωt ) Theta function (is zero for a negative argument)

More information

Circuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18

Circuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18 Circuit Analysis-III Sinusoids Example #1 ü Find the amplitude, phase, period and frequency of the sinusoid: v (t ) =12cos(50t +10 ) Signal Conversion ü From sine to cosine and vice versa. ü sin (A ± B)

More information

Series & Parallel Resistors 3/17/2015 1

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

More information

Electrical Circuit & Network

Electrical Circuit & Network Electrical Circuit & Network January 1 2017 Website: www.electricaledu.com Electrical Engg.(MCQ) Question and Answer for the students of SSC(JE), PSC(JE), BSNL(JE), WBSEDCL, WBSETCL, WBPDCL, CPWD and State

More information

BASIC NETWORK ANALYSIS

BASIC NETWORK ANALYSIS SECTION 1 BASIC NETWORK ANALYSIS A. Wayne Galli, Ph.D. Project Engineer Newport News Shipbuilding Series-Parallel dc Network Analysis......................... 1.1 Branch-Current Analysis of a dc Network......................

More information

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 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

More information

REACTANCE. By: Enzo Paterno Date: 03/2013

REACTANCE. By: Enzo Paterno Date: 03/2013 REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE - R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or

More information

1 Phasors and Alternating Currents

1 Phasors and Alternating Currents Physics 4 Chapter : Alternating Current 0/5 Phasors and Alternating Currents alternating current: current that varies sinusoidally with time ac source: any device that supplies a sinusoidally varying potential

More information

Electrical Circuits Lab Series RC Circuit Phasor Diagram

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

More information

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

More information

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

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

More information

ELEC273 Lecture Notes Set 11 AC Circuit Theorems

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)

More information

11. AC Circuit Power Analysis

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

More information

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

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

More information

LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09

LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09 LINEAR CIRCUIT ANALYSIS (EED) U.E.T. TAXILA 09 ENGR. M. MANSOOR ASHRAF INTRODUCTION Thus far our analysis has been restricted for the most part to dc circuits: those circuits excited by constant or time-invariant

More information

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

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

More information

Network Graphs and Tellegen s Theorem

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

More information

E2.2 Analogue Electronics

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,

More information

Phasor Diagram. Figure 1: Phasor Diagram. A φ. Leading Direction. θ B. Lagging Direction. Imag. Axis Complex Plane. Real Axis

Phasor Diagram. Figure 1: Phasor Diagram. A φ. Leading Direction. θ B. Lagging Direction. Imag. Axis Complex Plane. Real Axis 1 16.202: PHASORS Consider sinusoidal source i(t) = Acos(ωt + φ) Using Eulers Notation: Acos(ωt + φ) = Re[Ae j(ωt+φ) ] Phasor Representation of i(t): = Ae jφ = A φ f v(t) = Bsin(ωt + ψ) First convert the

More information

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 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

More information

AC analysis - many examples

AC analysis - many examples AC analysis - many examples The basic method for AC analysis:. epresent the AC sources as complex numbers: ( ). Convert resistors, capacitors, and inductors into their respective impedances: resistor Z

More information

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.

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

More information

Chapter 1W Basic Electromagnetic Concepts

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

More information

Study Notes on Network Theorems for GATE 2017

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

More information

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

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

More information

1.7 Delta-Star Transformation

1.7 Delta-Star Transformation 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

More information

Electric Circuit Theory

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

More information

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.

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]

More information

NETWORK ANALYSIS WITH APPLICATIONS

NETWORK ANALYSIS WITH APPLICATIONS NETWORK ANALYSIS WITH APPLICATIONS Third Edition William D. Stanley Old Dominion University Prentice Hall Upper Saddle River, New Jersey I Columbus, Ohio CONTENTS 1 BASIC CIRCUIT LAWS 1 1-1 General Plan

More information

Sinusoidal Steady- State Circuit Analysis

Sinusoidal Steady- State Circuit Analysis Sinusoidal Steady- State Circuit Analysis 9. INTRODUCTION This chapter will concentrate on the steady-state response of circuits driven by sinusoidal sources. The response will also be sinusoidal. For

More information

GATE 20 Years. Contents. Chapters Topics Page No.

GATE 20 Years. Contents. Chapters Topics Page No. GATE 0 Years Contents Chapters Topics Page No. Chapter- Chapter- Chapter- Chapter-4 Chapter-5 GATE Syllabus for this Chapter Topic elated to Syllabus Previous 0-Years GATE Questions Previous 0-Years GATE

More information

To find the step response of an RC circuit

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

More information

An op amp consisting of a complex arrangement of resistors, transistors, capacitors, and diodes. Here, we ignore the details.

An op amp consisting of a complex arrangement of resistors, transistors, capacitors, and diodes. Here, we ignore the details. CHAPTER 5 Operational Amplifiers In this chapter, we learn how to use a new circuit element called op amp to build circuits that can perform various kinds of mathematical operations. Op amp is a building

More information

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 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:.

More information

Chapter 5: Circuit Theorems

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

More information

CHAPTER 4. Circuit Theorems

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

More information

EE292: Fundamentals of ECE

EE292: Fundamentals of ECE EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 14 121011 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review Steady-State Analysis RC Circuits RL Circuits 3 DC Steady-State

More information

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 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

More information

1. Review of Circuit Theory Concepts

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

More information

DC STEADY STATE CIRCUIT ANALYSIS

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=

More information

Sinusoidal Response of RLC Circuits

Sinusoidal Response of RLC Circuits Sinusoidal Response of RLC Circuits Series RL circuit Series RC circuit Series RLC circuit Parallel RL circuit Parallel RC circuit R-L Series Circuit R-L Series Circuit R-L Series Circuit Instantaneous

More information

Chapter 2 Circuit Elements

Chapter 2 Circuit Elements Chapter Circuit Elements Chapter Circuit Elements.... Introduction.... Circuit Element Construction....3 Resistor....4 Inductor...4.5 Capacitor...6.6 Element Basics...8.6. Element Reciprocals...8.6. Reactance...8.6.3

More information

Lecture #3. Review: Power

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

More information

Chapter 3. Loop and Cut-set Analysis

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:

More information

Lecture 11 - AC Power

Lecture 11 - AC Power - 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

More information

y(d) = j

y(d) = j Problem 2.66 A 0-Ω transmission line is to be matched to a computer terminal with Z L = ( j25) Ω by inserting an appropriate reactance in parallel with the line. If f = 800 MHz and ε r = 4, determine the

More information