# Chapter 5: Circuit Theorems

Size: px
Start display at page:

Transcription

1 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 straightforward to write down, however, they are complicated to apply in practice. One will find that the amount of work increases dramatically using these circuit theorems to solve a circuit. There are four theorems we will look at in this chapter: Source Transformations, Superposition Principle and Thévenin & Norton Equivalents, and Maimum Power Theorem. There are two useful ideas to take away from this chapter.. Thévenin-Norton source transformations. In certain situations, there is a way to convert a voltage source into a current source and vice-versa. Source transformations are going to change how you solve circuits and in some cases, a series of source transformations will have a dramatic affect in making the circuit calculation quite straight forward. Source transformations will become an additional technique in your arsenal in solving circuits regardless of the techniques one uses (T, Node, Mesh ).. Thévenin-Norton Equivalents. The techniques of Chapter 4 (Mesh and Node) are very powerful and fairly straight forward to use. When we start studying nonlinear circuits (circuits with capacitors and inductors), mesh/node techniques will not be applicable. The way we will solve these nonlinear circuits are similar to solving irreducible dependent source circuits with KVL and KCL equations. The Thévenin-Norton Equivalents will help us to simplify circuits as they get more and more challenging. Picture wise, we will break-up the circuit into two subcircuits: the (i) load circuit and (ii) subcircuit to be simplified via the Thévenin-Norton Equivalent. That is, we will rewrite it into an equivalent form that is either a simple series circuit or a simple parallel circuit. Thévenin Norton Source Transformation There are transformations that convert current sources into voltage sources (and vice versa). That is, there is an equivalent circuit transformation between a series resistor and voltage source into a parallel resistor and current source: In order for these two circuits to be equivalent, the two separate subcircuits must have the same terminal current i and the terminal voltage v. In order to have the same terminal current and voltage, certain conditions must be met. These are derived by applying KVL to the series circuit and KCL to the parallel circuit. Here is what we get: KVL: v = v ir v v v i = i = R = R and v = i R KCL: i = i v/r R R R Th Th solving for i Th N Th N Th N Th N N N Th Th necessary conditions for equivalance That is, a Thévenin-Norton Source Transformation converts a voltage source with a resistor in series into a current source and the same resistor in parallel: 5.

2 Eample 5. Use source transformations to solve for the current through the 3Ω-resistor. Solution There are several ways one can solve for the current in this circuit: simple circuits or mesh/node. With the help of source transformations, you will see how useful these can be in reducing the circuit down to one loop before you can change a baby s diaper. Important Point: do not apply a source transformation to the 3Ω element. If a source transformation changes the 3Ω resistor to a parallel one, that specific information on the current through that 3Ω resistor is lost. Leave it alone! Let s convert this circuit using three different source transformations: Applying KVL/Mesh to the last loop, (3 4) i 6 = 0 i =.9A 3Ω 3 3Ω Superposition Theorem In Chapter, we briefly addressed the issue of a linear circuit. We stated then that for a circuit to be linear it meant that () the elements of the circuit are linear themselves and () the total response of an element (the voltages or currents) can be determined by the sum of the individual responses from each independent source in the circuit. This last statement is the Superposition theorem. Analogy: Newton s nd law (F net = F F F n) Superposition Principle The current i R through an element is equal to the algebraic sum of the currents (i, i i n) produced independently by each individual source. That is, i = = R i in isource all sources current produce by source- current produce by source-n Solving Strategies Step : Isolate one source and deactivate all other independent sources. To deactivate an independent current and voltage sources replace a voltage source with a short circuit (a short has v short = 0) current source with an open circuit (an open has i open = 0) With only one active source in the circuit, calculate the current/voltage of the element of interest. Repeat this process for each independent source in the circuit. Step : If there are n-sources, then there are n-circuits to solve using superposition. Eample 5. Use superposition to find the current i through the 0kΩ-resistor. Solution Superposition states that to calculate the current i 0kΩ, this current is the sum of all of the individual currents produced by the V, 3mA and 9mA-sources: i = i i i i i i 0k V 3mA 9mA 3 5.

3 Response of the V-source Deactivate both current sources (replace them with opens), and calculate the current i produced by the V source using a KVL/Mesh loop: 36 i = i = ma 3 Response of the 3mA-source Deactivate the other sources (short V and open 9 ma sources), and calculate the current i produced by the 3mA source using CDR: 6 i 4 = (3mA) = ma = i Response of the 9mA-source Deactivate the other sources (short V and open 3 ma sources), and calculate the current i 3 produced by the 9mA source using CDR: i 3 = (9A) = 3 ma = i3 4 According to Superposition, the current i 0kΩ is the sum of all of these individual currents: i 4 0kΩ = i i i3 = 3 = ma = i 3 3 0kΩ Thévenin s Theorem History: this theorem was independently derived in 853 by Helmholtz and in 883 by Léon Charles Thévenin. Léon Charles Thévenin was a French telegraph engineer who etended Ohm's law to the analysis of comple electrical circuits. The goal of Thévenin s theorem is to identify and separate a portion of a comple circuit (called the subcircuit) and replace it with a Thévenin equivalent (series voltage source and resistor). In doing so, the solving of the circuit problem is greatly simplified. A typical application of a Thévenin theorem goes something like this: Step. Focus on a load and separate it out from the subcircuit to be replaced with a Thévenin equivalent. Step. Perform the necessary calculations to rewrite the subcircuit as a Thévenin equivalent circuit. Step 3. Reconnect the Thévenin equivalent circuit back onto the load circuit and now solve the simplified circuit. To accomplish this, one applies the Thévenin s Rules. Thévenin s Rules (Notation: v Th = v OC, R Th = R N, and i N = i Sc) a. Determine v oc with all sources activated If the open circuit contains sources about the open, apply KVL around the open circuit to determine v OC. 5.3

4 Use any method to solve for v OC b. Determine R Th. Method-: Independent Sources Only (Conceptual Approach) Deactivate all sources and determine R Th relative to the terminal points a-b. Method-: Independent & Dependent Sources (Calculational Approach) i. Place a short at the terminal points a-b and calculate i sc using any method. ii. Determine R Th by using R Th = v OC/i. c. Redraw the equivalent Thévenin circuit. If the Thévenin resistance is negative, subtract it from the load resistance. Dependent sources only the book does not give any problems related to only dependent sources. I will not cover them; however, if you are transferring to San Jose State and plan on majoring in EE, at the end of the semester I can teach you these in about 0-5 minutes. Independent Sources Only Because this eample circuit only has an independent source, I will not only demonstrate how a Thévenin equivalent is determine between points a-b, but also show that Method- and Method- are equivalent. Suppose the following circuit has its load identified and removed, so that we can determine the Thévenin equivalent between points a-b. Both Method- and Method- determine v oc eactly the same. Step : Determine v oc What does the voltage v oc mean? It is the effective voltage that the load sees between the points a and b with respect to the rest of the circuit. Identifying nodes and applying node analysis because one of the nodes is v oc, we get Node v oc : ( ) v 0 oc ( ) v 0 ( ) 8 = 0 v oc = vth = V Node v : ( ) v ( ) v ( ) 8 = oc 6 What differentiates Method- and Method- is in the way that the Thévenin resistance is determined. Step : Determine R Th Method : Deactivating Sources There is only an independent voltage source in the circuit, and because of this, we can use Method-. Method- is NOT applicable if there are dependent sources in the circuit. We start by deactivating the voltage source by shorting it out (replace the 8V-source with a wire) and place an Ohmmeter at the terminal points. Effectively, one way to envision how an Ohmmeter measures resistance is by sending out a calibrated current which is then compared to the returning current, and reads the resistance. The R Th resistance is (0 3 6) R Th = (0 3 6) = = 6Ω= What does this resistance physically mean? It is the effective resistance that the load sees between the points a and b with respect to the rest of the circuit. The Thévenin equivalent circuit has replaced a comple circuit with a Thévenin equivalent circuit with values of v Th = V and R Th = 6Ω: 5.4

5 Method : Determine i to calculate R Th = v OC/i Method- is applicable for both independent and dependent sources in the circuit. Place a short across the open and calculate current i. There are three loops in the circuit and will use mesh analysis to determine i. Loop - i : ( 0 6) i (6) i 0 i = i 0 matri = form i = i = 0 Loop - i : (6 3) i (6) i 3 i 8 Loop - i : (0 3) i (0) i (3) i 0 solution i = However, I think that the most efficient way is using node analysis since there is only one node plus a KCL to get i. Applying node to the v y, we get y y = 6 y Node v : ( ) v ( ) 8 0 v = 5V Now apply KCL at node a: Calculating R Th, we get : = 8Ω 0Ω KCL i i i = = A = i = v = V = Ω OC 6 i A This agrees with our previous calculation of R Th and therefore, both methods are equivalent. A Eample 5.3 Determine the current through the 4Ω-resistor using a Thévenin equivalent circuit (Methods and ). Solution First, remove the 4Ω-resistor and convert the circuit into a Thévenin equivalent. Step : Determine voc = v Th. Focus on the open circuit and see how voc is defined. Since the 4Ω resistor is connected to an open loop, there is no current flowing through it and therefore, has no voltage drop. Applying a KVL loop around the open circuit loop, the 0V-source will still contribute to voc and we have v = 0 v v = v 0 0 oc oc 0 5.5

6 So to determine voc, my real task is first to determine the voltage across the 0Ω resistor. Question: what is the most efficient way to determine v 0Ω? For Carlos, I d say a source transformation on the series 8V and 9Ω, converting them into a parallel current source and resistor, then add the current sources together. The circuit I get is Applying CDR to get the current of the 0Ω resistor and Ohm s law to get the voltage v 0Ω, we get 9 0 Ohm's CDR : i 0Ω = A = A v 5 law 0Ω = R0Ωi = 0 5 = 4V Using our KVL relation from above, we determine voc: v = v 0 = 4 0 = 4V = v = v oc 0Ω oc Th Step : Find R Th. Method : Deactivating Independent Sources Since the sources are all independent sources, we can use Method- and deactivate all of sources to determine the Thévenin resistance R Th at a-b. It is important to realize that in the previous voc-circuit, there was no 4Ω resistor; however, in the R Th-circuit the 4Ω resistor reappears and must be accounted for. 5 0 = 4 (6 9) 0 = 4 = 0Ω= 5 0 Now that we have both the Thévenin voltage and resistance, I can draw the equivalent Thévenin circuit, add back in the load 4Ω-resistor, and solve for the current i 4Ω. Using Ohm s law to determine the current i 4Ω, we see that the current flows from b to a, not a to b and therefore, I assign a negative value to this current: 4V i 4 Ω = = A = i Ω Interpretation of results. Effectively, when we calculate the Thévenin equivalent, the 4Ω resistor sees an effective voltage of -4V and an effective resistance of 6Ω from the view point of terminal points a-b. That is, regardless of the load (whether it s a 4Ω resistor or some complicated load circuit), this load feels -4V and 6Ω from the rest of the circuit. It does not see the individual 0V, 8V and A-sources but a combination of these that effectively reads the Thévenin voltage of -4V between a-b. It does not see some combination of all of the resistors in the circuit, but the effective Thévenin resistance of 6Ω between a-b. 5.6

7 . It clearly is a lot more work to calculate the current i 4Ω using Thévenin Equivalent circuits, whereas using Node or Mesh would have given us this current more efficiently. So what s all the fuss about learning these Thévenin equivalent techniques then if there are other techniques more efficient? To put this into prospective, resistive circuits are only half of this course, with the other have being capacitive and inductive circuits. Node and Mesh only apply to linear resistive circuits (as well as to ac phasor circuits). When we start capacitive and inductive circuits (nonlinear circuits), we will not be able to solve these circuits using Node or Mesh and we will be forced to use Simple Circuit Techniques (KVL & KCL) along with Thévenin equivalents to guide us. Thévenin equivalents are a powerful ally in solving these considerably tougher circuits. Method : Finding i to determine R Th = v OC/i When a short is placed across a-b to calculate i, note that i = i 4Ω. I epect that you are most likely thinking of calculating i using mesh analysis (3 loops = loop equations plus a ). Even though this is a different circuit, I already have reduced the left-hand portion circuit with a source transformation that combined the 8V-source with the A-source. I want to continue using this simplified circuit and make one more source transformation on the 0/9A-source to convert it into a voltage source. This is what I get: I immediately see that there is only one node voltage to solve for and a solver equation for i Node v : ( ) v ( ) ( 0) ( ) (0) = 0 v = 0.4V 0 v Solver : i = =.4A = i 4 4Ω Using a combination of voc and i, the Thévenin resistance is determined to be v 4V = = = Ω OC 0 i.4a Interpretation of results. Both methods ( & ) determine the Thévenin resistance, however, Method- is only valid if there are ONLY independent sources. If there are any dependent sources, Method- is NOT valid and ONLY Method- can be used.. The combination voc/i, is a measure of the effective resistance (R Th) that the load sees relative to the terminal points a-b. Norton Equivalent Circuits 5.7

8 Independent & Dependent Sources There are two important changes when dealing with independent and dependent sources in circuit where Thévenin s theorem is going to be applied:. Without dependent sources, zeroing all the independent sources leaves a resistive circuit so that the Thévenin resistance can be calculated directly. However, dependent sources typically alter the Thévenin resistance so those can't be zeroed. That is, Method- is NOT VALID whenever dependent sources are in the circuit and the only way to determine R Th is by using Medthod-; determine the ratio v OC/i = R Th.. Thévenin circuit with dependent sources can have positive and negative Thévenin resistance. It is not like there is an actual negative resistor that one can actual purchase at the store or something like that, but has implications that circuits have a impedance matching and can be resonated. Eample 5.4 Obtain the Thévenin equivalent for the following circuit. Solution The fact that there is a dependent source in the circuit immediately tells us that Method- cannot be applied to this circuit. Only Method- is valid. Step : Determine voc Focusing on the open circuit where voc is defined, the open immediately tells us that the kω resistor is a dead resistor since there is no current flowing through it and has no voltage drop. So the voltage across the 3kΩ resistor is equivalent to voc: v = v = 3i oc Clearly, to determine voc we shift our attention to first determining i. Thinking in terms of source transformations first, converting the.5ma source into a voltage source allows us to reduce the circuit to one loop. 3kΩ X : X X X oc X KVL (6 4 3)i = 5 i i = ma v = 3i = 3V Step : Determine i sc such that R Th = voc /isc. Since I ve already modified the left side of the circuit, I will continue using it. Placing the short across a-b, i sc is the current through the kω resistor. To determine i sc we can either use (i) mesh analysis which will produce 3 equations and 3 unknowns (i sc, i, i z), (ii) node analysis which also has 3 equations and 3 unknowns (i sc, i, v y) or (ii) simple circuits that has equations and unknowns (i sc, i ). Let s do simple circuits! 5.8

9 I will use VDR to determine the voltage 3i (and current i ) and use Ohm s law to get i sc: 3 VDR: v3kω = vkω = 3i = (5 i ) 3 0 solving for i i = 3 ma solving vkω for i i = = ma = i kω Applying R Th = v OC/i, we find that voc 3V R = Th 3kΩ i = ma = Step 3 Redraw the equivalent circuit: sc Eample 5.5 Determine the current through the Ω-resistor at a-b using a Thévenin equivalent circuit. Solution Step : Determine v oc The simplest way to determine v oc is by applying KVL around the top loop. Why? Because I immediately know the dependent current i since it is in series with the 4A-source. i= 4A voc 8 i 6i = 0 voc = 4V Step : Determine i sc such that R Th = v oc/i sc. Placing the short at a-b sets up three loops (i, i sc, i ). However, this short really sets up an unusual situation where the loop current-i (which also has a dependent source controlled by i) is directly connected to i sc via a constant 4Asource. Note that I have completely ignored i. The trick is to see that doing a mesh loop for loop-i and applying KCL between a-b, there are equations and unknowns (i sc, i) that quickly determines i sc: solving for i Loop - i : 6i i = 8 i = A KCL at a-b: i = 4 i = 6A Applying R Th = v OC/i, we find that v 4 V = = = Ω oc 4 isc 6 A Step 3: Redraw the equivalent circuit and solve the circuit problem. 5.9

12 4 loops sources = loops eqs ( regular (i ) & SL (i,i,i ) DC (i,v ) y Solver (i ) 3 6 eqs, 6 unknowns (i,i,i,i,v,i ) Writing out the equations, Loop : i i = 3i ( ) 3 y SL: i i 0 i = 3i : loop loop i 3 3 y y 3 i i = 9, i i = v DC : v = i i Solver : i = i i The matri and solutions are i 0 i = 3.58A i i =.6A i i A solutions = = i i 0 = 0.9A v v y 0 y =.65V i 0 i = 7.67A Step 3: Find R TH and solve the circuit problem Applying R Th = v OC/i, we find that v 79.3V = = = Ω oc 0.3 isc 7.67A R = 0.3 Ω v = 79.3V Th Th maimum power theorem v L (79.3 / ) R ma Th = RL = 0.3Ω P = = = 53 W = P R 0.3 L ma 5.

### 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 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### 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

### ENGG 225. David Ng. Winter January 9, Circuits, Currents, and Voltages... 5

ENGG 225 David Ng Winter 2017 Contents 1 January 9, 2017 5 1.1 Circuits, Currents, and Voltages.................... 5 2 January 11, 2017 6 2.1 Ideal Basic Circuit Elements....................... 6 3 January

### 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

### 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,

### Chapter 4 Circuit Theorems

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 1 111

### 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,

### EECE208 Intro to Electrical Engineering Lab. 5. Circuit Theorems - Thevenin Theorem, Maximum Power Transfer, and Superposition

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

### DEPARTMENT OF COMPUTER ENGINEERING UNIVERSITY OF LAHORE

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

### 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)

### EECE251 Circuit Analysis I Lecture Integrated Program Set 3: Circuit Theorems

EECE251 Circuit Analysis I Lecture Integrated Program Set 3: Circuit Theorems Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia shahriar@ece.ubc.ca 1 Linearity

### 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

### 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

### Experiment #6. Thevenin Equivalent Circuits and Power Transfer

Experiment #6 Thevenin Equivalent Circuits and Power Transfer Objective: In this lab you will confirm the equivalence between a complicated resistor circuit and its Thevenin equivalent. You will also learn

### 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

### 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/

### 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

### 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

### Review of Circuit Analysis

Review of Circuit Analysis Fundamental elements Wire Resistor Voltage Source Current Source Kirchhoff s Voltage and Current Laws Resistors in Series Voltage Division EE 42 Lecture 2 1 Voltage and 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

### 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

### Lecture # 2 Basic Circuit Laws

CPEN 206 Linear Circuits Lecture # 2 Basic Circuit Laws Dr. Godfrey A. Mills Email: gmills@ug.edu.gh Phone: 026907363 February 5, 206 Course TA David S. Tamakloe CPEN 206 Lecture 2 205_206 What is Electrical

### Notes on Electric Circuits (Dr. Ramakant Srivastava)

Notes on Electric ircuits (Dr. Ramakant Srivastava) Passive Sign onvention (PS) Passive sign convention deals with the designation of the polarity of the voltage and the direction of the current arrow

### 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:

### 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

### Electric Current. Note: Current has polarity. EECS 42, Spring 2005 Week 2a 1

Electric Current Definition: rate of positive charge flow Symbol: i Units: Coulombs per second Amperes (A) i = dq/dt where q = charge (in Coulombs), t = time (in seconds) Note: Current has polarity. EECS

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

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

### 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

### 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

### 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/

Chapter 1 : Resistors in Circuits - Practice â The Physics Hypertextbook In AC circuit analysis, if the circuit has sources operating at different frequencies, Superposition theorem can be used to solve

### 09-Circuit Theorems Text: , 4.8. ECEGR 210 Electric Circuits I

09Circuit Theorems Text: 4.1 4.3, 4.8 ECEGR 210 Electric Circuits I Overview Introduction Linearity Superposition Maximum Power Transfer Dr. Louie 2 Introduction Nodal and mesh analysis can be tedious

### LABORATORY MODULE ELECTRIC CIRCUIT

LABORATORY MODULE ELECTRIC CIRCUIT HIGH VOLTAGE AND ELECTRICAL MEASUREMENT LAB ELECTRICAL ENGINEERING DEPARTMENT FACULTY OF ENGINEERING UNIVERSITAS INDONESIA DEPOK 2018 MODULE 1 LABORATORY BRIEFING All

### COOKBOOK KVL AND KCL A COMPLETE GUIDE

1250 COOKBOOK KVL AND KCL A COMPLETE GUIDE Example circuit: 1) Label all source and component values with a voltage drop measurement (+,- ) and a current flow measurement (arrow): By the passive sign convention,

### Resonant Matching Networks

Chapter 1 Resonant Matching Networks 1.1 Introduction Frequently power from a linear source has to be transferred into a load. If the load impedance may be adjusted, the maximum power theorem states that

### 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

### OUTCOME 3 - TUTORIAL 2

Unit : Unit code: QCF evel: 4 Credit value: 15 SYABUS Engineering Science /601/1404 OUTCOME 3 - TUTORIA Be able to apply DC theory to solve electrical and electronic engineering problems DC electrical

### INTRODUCTION TO ELECTRONICS

INTRODUCTION TO ELECTRONICS Basic Quantities Voltage (symbol V) is the measure of electrical potential difference. It is measured in units of Volts, abbreviated V. The example below shows several ways

### Chapter 4: Methods of Analysis

Chapter 4: Methods of Analysis When SCT are not applicable, it s because the circuit is neither in series or parallel. There exist extremely powerful mathematical methods that use KVL & KCL as its basis

### 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

### 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=

### 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:

### Designing Information Devices and Systems I Fall 2018 Lecture Notes Note Introduction: Op-amps in Negative Feedback

EECS 16A Designing Information Devices and Systems I Fall 2018 Lecture Notes Note 18 18.1 Introduction: Op-amps in Negative Feedback In the last note, we saw that can use an op-amp as a comparator. However,

### Chapter 4: Techniques of Circuit Analysis

Chapter 4: Techniques of Circuit Analysis This chapter gies us many useful tools for soling and simplifying circuits. We saw a few simple tools in the last chapter (reduction of circuits ia series and

### 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

### Networks and Systems Prof. V. G. K. Murti Department of Electrical Engineering Indian Institute of Technology, Madras

Networks and Systems Prof. V. G. K. Murti Department of Electrical Engineering Indian Institute of Technology, Madras Lecture - 34 Network Theorems (1) Superposition Theorem Substitution Theorem The next

### 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

### University of Alabama Department of Physics and Astronomy. Problem Set 4

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

### Basic Laws. Bởi: Sy Hien Dinh

Basic Laws Bởi: Sy Hien Dinh INTRODUCTION Chapter 1 introduced basic concepts such as current, voltage, and power in an electric circuit. To actually determine the values of this variable in a given circuit

### Electronics. Basics & Applications. group talk Daniel Biesinger

Electronics Basics & Applications group talk 23.7.2010 by Daniel Biesinger 1 2 Contents Contents Basics Simple applications Equivalent circuit Impedance & Reactance More advanced applications - RC circuits

### Circuit Analysis. by John M. Santiago, Jr., PhD FOR. Professor of Electrical and Systems Engineering, Colonel (Ret) USAF. A Wiley Brand FOR-

Circuit Analysis FOR A Wiley Brand by John M. Santiago, Jr., PhD Professor of Electrical and Systems Engineering, Colonel (Ret) USAF FOR- A Wiley Brand Table of Contents. ' : '" '! " ' ' '... ',. 1 Introduction

### 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)

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

### LCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module. What you'll learn in Module 9. Module 9 Introduction

Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing

### 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,

### 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,

### 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

### ES250: Electrical Science. HW1: Electric Circuit Variables, Elements and Kirchhoff s Laws

ES250: Electrical Science HW1: Electric Circuit Variables, Elements and Kirchhoff s Laws Introduction Engineers use electric circuits to solve problems that are important to modern society, such as: 1.

### ECE 1311: Electric Circuits. Chapter 2: Basic laws

ECE 1311: Electric Circuits Chapter 2: Basic laws Basic Law Overview Ideal sources series and parallel Ohm s law Definitions open circuits, short circuits, conductance, nodes, branches, loops Kirchhoff's

### 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

### Homework 3 Solution. Due Friday (5pm), Feb. 14, 2013

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

### E40M Review - Part 1

E40M Review Part 1 Topics in Part 1 (Today): KCL, KVL, Power Devices: V and I sources, R Nodal Analysis. Superposition Devices: Diodes, C, L Time Domain Diode, C, L Circuits Topics in Part 2 (Wed): MOSFETs,

### 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

### NETWORK ANALYSIS AND NETWORK THEORMS

ASSIGNMENT NETWORK ANALYSIS AND NETWORK THEORMS VAIBHAV SHARMA Adm.no.-2012MS0044 Network Analysis and Theorems Generally speaking, network analysis is any structured technique used to mathematically analyze

### 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

### 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

### Series Parallel Analysis of AC Circuits

HAE 9 eries arallel Analysis of A ircuits hapter Outline 9. A eries ircuits 9.2 A arallel ircuits 9.3 A eries arallel ircuits 9.4 Analysis of Multiple-ource A ircuits Using uperposition 9. A EIE IUI In

### 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)

### Transient Analysis of First-Order Circuits: Approaches and Recommendations

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

### ENGR 2405 Class No Electric Circuits I

ENGR 2405 Class No. 48056 Electric Circuits I Dr. R. Williams Ph.D. rube.williams@hccs.edu Electric Circuit An electric circuit is an interconnec9on of electrical elements Charge Charge is an electrical

### Discussion Question 6A

Discussion Question 6 P212, Week 6 Two Methods for Circuit nalysis Method 1: Progressive collapsing of circuit elements In last week s discussion, we learned how to analyse circuits involving batteries

### 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

### Homework 2. Due Friday (5pm), Feb. 8, 2013

University of California, Berkeley Spring 2013 EE 42/100 Prof. K. Pister Homework 2 Due Friday (5pm), Feb. 8, 2013 Please turn the homework in to the drop box located next to 125 Cory Hall (labeled EE

### Electronics II. Final Examination

The University of Toledo f17fs_elct27.fm 1 Electronics II Final Examination Problems Points 1. 11 2. 14 3. 15 Total 40 Was the exam fair? yes no The University of Toledo f17fs_elct27.fm 2 Problem 1 11

### 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

### 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

### RC, RL, and LCR Circuits

RC, RL, and LCR Circuits EK307 Lab Note: This is a two week lab. Most students complete part A in week one and part B in week two. Introduction: Inductors and capacitors are energy storage devices. They

### 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

### 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

### (amperes) = (coulombs) (3.1) (seconds) Time varying current. (volts) =

3 Electrical Circuits 3. Basic Concepts Electric charge coulomb of negative change contains 624 0 8 electrons. Current ampere is a steady flow of coulomb of change pass a given point in a conductor in