# Thevenin Equivalent Circuits

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 hevenin Equivalent Circuits Introduction In each of these problems, we are shown a circuit and its hevenin or Norton equivalent circuit. he hevenin and Norton equivalent circuits are described using three parameters: V oc, the open circuit voltage of the circuit, I sc, the short circuit of the circuit and R th, the hevenin resistance of the circuit. Each problem, asks us to determine the value of asked to determine the value of V oc, I sc or R th. hevenin equivalent circuits are discussed in Section 5.5 of Introduction to Electric Circuits by R.C. Dorf and J.A Svoboda. Norton equivalent circuits are discussed in Section 5.6. Worked Examples Example 1: he circuit shown in Figure 1b is the hevenin equivalent circuit of the circuit shown in Figure 1a. Find the value of the open circuit voltage, V oc and hevenin resistance, R th. Figure 1 he circuit considered in Example 1. Solution: he circuit from Figure 1a can be reduced to its hevenin equivalent circuit in four steps shown in Figure 2a, b, c and d. A source transformation transforms the series voltage source and 20 Ω resistor in Figure 1a into the parallel current source and 20 Ω resistor in Figure 2a. he current source current is calculated from the voltage source voltage and resistance as 20 V = 1 A. After the source 20 Ω transformation, the 20 Ω resistor is parallel to the 80 Ω resistor. Replacing these parallel resistors with the equivalent 16 Ω resistor produces the circuit shown in Figure 2b. 2

2 A second source transformation transforms the parallel current source and 16 Ω resistor in Figure 2b into the series voltage source and 16 Ω resistor in Figure 2c. he voltage source 1 A 16 Ω = 16 V. After voltage is calculated from the current source current and resistance as ( )( ) the source transformation, the two16 Ω resistors are in series. Replacing these series resistors with the equivalent 32 Ω resistor produces the circuit shown in Figure 2d. Comparing Figure 2d to Figure 1b shows that the hevenin resistance is R th = 32 Ω and the open circuit voltage, V oc = -16 V. (a) (b) (c) (d) Figure 2 he circuit from Figure 1a can be reduced to its hevenin equivalent circuit in four steps shown here as (a), (b), (c), and (d). 3

3 Example 2: he circuit shown in Figure 3b is the hevenin equivalent circuit of the circuit shown in Figure 1a. Find the value of the open circuit voltage, V oc and hevenin resistance, R th. Figure 3 he circuit considered in Example 2. Solution: he circuit from Figure 3a can be reduced to its hevenin equivalent circuit in five steps shown in Figure 4a, b, c, d and e. A source transformation transforms the parallel current source and 3 Ω resistor in Figure 3a into the series voltage source and 3 Ω resistor in Figure 4a. he voltage source voltage is 2 A 3 Ω = 6 V. After the source calculated from the current source current and resistance as ( )( ) transformation, the 3 Ω and 6 Ω resistors are in series. Also, the 6V and 3 V voltage sources are in series. Replacing the series resistors with the equivalent 9 Ω resistor and the series voltage sources with the equivalent 8 V source produces the circuit shown in Figure 4b. A second source transformation transforms the series 8 V voltage source and 9 Ω resistor in Figure 4b into the parallel current source and 9 Ω resistor in Figure 4c. he current source current is calculated from the voltage source voltage and resistance as 8 V = 0.89 A. After the 9 Ω source transformation, the 9 Ω resistor is parallel to the 6 Ω resistor. Replacing these parallel resistors with the equivalent 3.6 Ω resistor produces the circuit shown in Figure 4d. A third source transformation transforms the parallel 0.89 A current source and 3.6 Ω resistor in Figure 4d into the series voltage source and 3.6 Ω resistor in Figure 4e. he voltage source voltage is calculated from the current source current and resistance as 0.89 A 3.6 Ω = 3.2 V. ( )( ) Comparing Figure 4e to Figure 3b shows that hevenin resistance is R th = 3.6 Ω and that the open circuit voltage, V oc = -3.2 V. 4

4 (a) (b) (c) (d) Figure 4 he circuit from Figure 3a can be reduced to its hevenin equivalent circuit in five steps shown here as (a), (b), (c), (d) and (e). (e) 5

5 Example 3: he circuit shown in Figure 5b is the hevenin equivalent circuit of the circuit shown in Figure 5a. Find the value of the open circuit voltage, V oc and hevenin resistance, R th. Figure 5 he circuit considered in Example 3. Solution: he circuit from Figure 5a can be reduced to its hevenin equivalent circuit in four steps shown in Figure 6a, b, c and d. A source transformation transforms the series 10 V voltage source and 5 Ω resistor in Figure 5a into the parallel current source and 5 Ω resistor in Figure 6a. he current source current is calculated from the voltage source voltage and resistance as 10 V = 2 A. After the 5 Ω source transformation, the 5 Ω resistor is parallel to the 20 Ω resistor. Also, the 2 A current source is parallel to the 1 A current source. Replacing these parallel resistors with the equivalent 4 Ω resistor and replacing the parallel current sources with the equivalent 1 A current source produces the circuit shown in Figure 6b. A second source transformation transforms the parallel 1 A current source and 4 Ω resistor in Figure 6b into the series voltage source and 4 Ω resistor in Figure 6c. he voltage 1 A 4 Ω = 4 V source voltage is calculated from the current source current and resistance as ( )( ). After the source transformation, the two 4 Ω resistors are in series. Replacing the series resistors with the equivalent 8 Ω produces the circuit shown in Figure 6d. Comparing Figure 6d to Figure 5b shows that hevenin resistance is R th = 8 Ω and that the open circuit voltage, V oc = 4 V. 6

6 (a) (b) (c) (d) Figure 6 he circuit from Figure 5a can be reduced to its hevenin equivalent circuit in four steps shown here as (a), (b), (c), and (d). Example 4: he circuit shown in Figure 7b is the hevenin equivalent circuit of the circuit shown in Figure 7a. Find the value of the open circuit voltage, V oc and hevenin resistance, R th. Also, determine the value of the short circuit current, I sc. Figure 7 he circuit considered in Example 4. 7

7 Solution: o determine the value of the open circuit voltage, V oc, we connect an open circuit across the terminals of the circuit and then calculate the value of the voltage across that open circuit. Figure 8 shows the circuit from Figure 7a after adding the open circuit and labeling the open circuit voltage. Also, the meshes have been identified and labeled in anticipation of writing mesh equations. Let i 1 and i 2 denote the mesh currents in meshes 1 and 2, respectively. In Figure 8, mesh current i 2 is equal to the current in the open circuit. Consequently, i 2 = 0 A. he controlling current of the CCVS is expressed in terms of the mesh currents as ia = i1 i2 = i1 0 = i 1 Apply KVL to mesh 1 to get ( ) ( ) ( ) ( ) 3i 2 i i + 6 i i 10= 0 3i 2 i i 0 10= Apply KVL to mesh 2 to get 10 i1 = = 1.43 A 7 ( ) oc ( ) ( ) 5 i + V 6 i i = 0 V = 6 i = = 8.58 V 2 oc Next, to determine the value of the short circuit current, I sc, we connect a short circuit across the terminals of the circuit and then calculate the value of the current in that short circuit. Figure 9 shows the circuit from Figure 7a after adding the short circuit and labeling the short circuit current. Also, the meshes have been identified and labeled in anticipation of writing mesh equations. Let i 1 and i 2 denote the mesh currents in meshes 1 and 2, respectively. In Figure 9, mesh current i 2 is equal to the current in the short circuit. Consequently, i = I. he controlling current of the CCVS is expressed in terms of the mesh currents as 2 sc ia = i1 i2 = i1 Is c Figure 8 Calculating the open circuit voltage, V oc, using mesh equations. Apply KVL to mesh 1 to get 8

8 ( ) ( ) 3i 2 i i + 6 i i 10= 0 7i 4i = 10 (1) Apply KVL to mesh 2 to get 11 5i2 6( i1 i2) = 0 6i1+ 11i2 = 0 i1 = i 2 6 Substituting into equation 1 gives 11 7 i2 4 i2 = 10 i2 = 1.13 A I sc = 1.13 A 6 Figure 9 Calculating the short circuit current, I sc, using mesh equations. Figure 10 Calculating the hevenin resistance, R th v i =, using mesh equations. o determine the value of the hevenin resistance, R th, first replace the 10 V voltage source by a 0 V voltage source, i.e. a short circuit. Next, connect a current source across the terminals of the circuit and then label the voltage across that current source as shown in Figure 10. he hevenin resistance will be calculated from the current and voltage of the current source as 9

9 R th v = i In Figure 10, the meshes have been identified and labeled in anticipation of writing mesh equations. Let i 1 and i 2 denote the mesh currents in meshes 1 and 2, respectively. In Figure 10, mesh current i 2 is equal to the negative of the current source current. Consequently, i = i. he controlling current of the CCVS is expressed in terms of the mesh currents as 2 Apply KVL to mesh 1 to get Apply KVL to mesh 2 to get i = i i = i + i a i1 2( i1 i2) + 6( i1 i2) = 0 7i1 4i2 = 0 i1 = i 2 (2) 7 ( ) Substituting for i 1 using equation 2 gives 5i + v 6 i i = 0 6i + 11i = v Finally, 4 6 i2 + 11i2 = v 7.57i2 = v 7 R th v v v = = = = 7.57 Ω i i i 2 As a check, notice that ( )( ) R I = = 8.55 V th sc oc 10

10 Example 5: he circuit shown in Figure 11b is the hevenin equivalent circuit of the circuit shown in Figure 11a. Find the value of the open circuit voltage, V oc and hevenin resistance, R th. Also, determine the value of the short circuit current, I sc. Figure 11 he circuit considered in Example 5. Solution: o determine the value of the open circuit voltage, V oc, we connect an open circuit across the terminals of the circuit and then calculate the value of the voltage across that open circuit. Figure 12 shows the circuit from Figure 11a after adding the open circuit and labeling the open circuit voltage. Also, the nodes have been identified and labeled in anticipation of writing node equations. Let v 1, v 2 and v 3 denote the node voltages at nodes 1, 2 and 3, respectively. In Figure 12, node voltage v 1 is equal to the negative of the voltage source voltage. Consequently, v 1 = 24 V. he controlling voltage of the VCCS, va, is equal to the node voltage at node 2, i.e. va = v2. he voltage at node 3 is equal to the open circuit voltage, i.e. v3 = Voc. Apply KCL at node 2 to get v1 v2 v2 v3 = 2v1+ v3 = 3v2 48+ Voc =3 v 3 6 a Figure 12 Calculating the open circuit voltage, V oc, using node equations. 11

11 Apply KCL at node 3 to get v v 4 + v2 = 0 9v2 v3 = 0 9va = V o c Combining these equations gives ( ) V = 9v = V V = 72 V oc a oc oc Next, to determine the value of the short circuit current, I sc, we connect a short circuit across the terminals of the circuit and then calculate the value of the current in that short circuit. Figure 13 shows the circuit from Figure 7a after adding the short circuit and labeling the short circuit current. Also, the nodes have been identified and labeled in anticipation of writing node equations. Let v 1, v 2 and v 3 denote the node voltages at nodes 1, 2 and 3, respectively. In Figure 13, node voltage v 1 is equal to the negative of the voltage source voltage. Consequently, v 1 = 24 V. he voltage at node 3 is equal to the voltage across a short, v 3 = 0. he controlling voltage of the VCCS, v a, is equal to the node voltage at node 2, i.e. v a = v 2. he voltage at node 3 is equal to the voltage across a short, i.e. v 3 = 0. Apply KCL at node 2 to get Apply KCL at node 3 to get v1 v2 v2 v3 = 2v1+ v3 = 3v2 48= 3va va = 16 V 3 6 v v v2 = Isc va = Isc Isc = ( 16) = 24 A Figure 13 Calculating the short circuit current, I sc, using mesh equations. 12

12 Figure 14 Calculating the hevenin resistance, R th v i =, using mesh equations. o determine the value of the hevenin resistance, R th, first replace the 24 V voltage source by a 0 V voltage source, i.e. a short circuit. Next, connect a current source circuit across the terminals of the circuit and then label the voltage across that current source as shown in Figure 14. he hevenin resistance will be calculated from the current and voltage of the current source as v Rth = i Also, the nodes have been identified and labeled in anticipation of writing node equations. Let v 1, v 2 and v 3 denote the node voltages at nodes 1, 2 and 3, respectively. In Figure 14, node voltage v 1 is equal to the across a short circuit, i.e. v 1 = 0. he controlling voltage of the VCCS, va, is equal to the node voltage at node 2, i.e. v a = v 2. he voltage at node 3 is equal to the voltage across the current source, i.e. v3 = v. Apply KCL at node 2 to get Apply KCL at node 3 to get Finally, v 2 3 As a check, notice that v1 v2 v2 v3 = 2v1+ v3 = 3v2 v =3 v 3 6 v 4 + v2 + i = 0 9v2 v3+ 6i = v v + 6i = 0 a 3v v + 6i = 0 2v = 6i R th v = = 3 Ω i a 13

### Series and Parallel Resistors

Series and Parallel Resistors 1 Objectives To calculate the equivalent resistance of series and parallel resistors. 2 Examples for resistors in parallel and series R 4 R 5 Series R 6 R 7 // R 8 R 4 //

### Example: Determine the power supplied by each of the sources, independent and dependent, in this circuit:

Example: Determine the power supplied by each of the sources, independent and dependent, in this circuit: Solution: We ll begin by choosing the bottom node to be the reference node. Next we ll label the

### Mesh-Current Method (Loop Analysis)

Mesh-Current Method (Loop Analysis) Nodal analysis was developed by applying KCL at each non-reference node. Mesh-Current method is developed by applying KVL around meshes in the circuit. A mesh is a loop

### Chapter 4: Techniques of Circuit Analysis

4.1 Terminology Example 4.1 a. Nodes: a, b, c, d, e, f, g b. Essential Nodes: b, c, e, g c. Branches: v 1, v 2, R 1, R 2, R 3, R 4, R 5, R 6, R 7, I d. Essential Branch: v 1 -R 1, R 2 -R 3, v 2 -R 4, R

### Chapter 4: Methods of Analysis

Chapter 4: Methods of Analysis 4.1 Motivation 4.2 Nodal Voltage Analysis 4.3 Simultaneous Eqs. & Matrix Inversion 4.4 Nodal Voltage Analysis with Voltage Sources 4.5 Mesh Current Analysis 4.6 Mesh Current

### Chapter 2. Circuit Analysis Techniques

Chapter 2 Circuit Analysis Techniques 1 Objectives To formulate the node-voltage equations. To solve electric circuits using the node voltage method. To introduce the mesh current method. To formulate

### Series and Parallel Resistive Circuits

Series and Parallel Resistive Circuits The configuration of circuit elements clearly affects the behaviour of a circuit. Resistors connected in series or in parallel are very common in a circuit and act

### 07-Nodal Analysis Text: ECEGR 210 Electric Circuits I

07Nodal Analysis Text: 3.1 3.4 ECEGR 210 Electric Circuits I Overview Introduction Nodal Analysis Nodal Analysis with Voltage Sources Dr. Louie 2 Basic Circuit Laws Ohm s Law Introduction Kirchhoff s Voltage

### Chapter 4 Objectives

Chapter 4 Engr228 Circuit Analysis Dr Curtis Nelson Chapter 4 Objectives Understand and be able to use the node-voltage method to solve a circuit; Understand and be able to use the mesh-current method

### 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

### Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Alexander-Sadiku Fundamentals of Electric Circuits Chapter 3 Methods of Analysis Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or display. 1 Methods of Analysis - Chapter

### EE 201 ELECTRIC CIRCUITS. Class Notes CLASS 8

EE 201 ELECTRIC CIRCUITS Class Notes CLASS 8 The material covered in this class will be as follows: Nodal Analysis in the Presence of Voltage Sources At the end of this class you should be able to: Apply

### SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING. Self Study Course

SCHOOL OF MATHEMATICS MATHEMATICS FOR PART I ENGINEERING Self Stud Course MODULE 27 FURTHER APPLICATIONS TO ELECTRICAL CIRCUITS Module Topics 1. Inverse of a matri using elimination 2. Mesh analsis of

### Problem set #5 EE 221, 09/26/ /03/2002 1

Chapter 3, Problem 42. Problem set #5 EE 221, 09/26/2002 10/03/2002 1 In the circuit of Fig. 3.75, choose v 1 to obtain a current i x of 2 A. Chapter 3, Solution 42. We first simplify as shown, making

### Basic Laws Circuit Theorems Methods of Network Analysis Non-Linear Devices and Simulation Models

EE Modul 1: Electric Circuits Theory Basic Laws Circuit Theorems Methods of Network Analysis Non-Linear Devices and Simulation Models EE Modul 1: Electric Circuits Theory Current, Voltage, Impedance Ohm

### How can we deal with a network branch which is part of two networks each with a source? R3 is carrying current supplied by each battery

Network nalysis ims: Consolidate use of KCL in circuit analysis. Use Principle of Superposition. Learn basics of Node Voltage nalysis (uses KCL) Learn basics of Mesh Current nalysis (uses KVL) Lecture

### ECE 211 WORKSHOP: NODAL AND LOOP ANALYSIS. Tutor: Asad Akram

ECE 211 WORKSHOP: NODAL AND LOOP ANALYSIS Tutor: Asad Akram 1 AGENDA Background: KCL and KVL. Nodal Analysis: Independent Sources and relating problems, Dependent Sources and relating problems. Loop (Mesh

### ADVANCED METHODS OF DC AND AC CIRCUIT

CHAPTER 11 ADVANCED METHODS OF DC AND AC CIRCUIT ANALYSIS Learning Objectives As a result of successfully completing this chapter, you should be able to: 1. Explain why more sophisticated methods of circuit

### 4. Basic Nodal and Mesh Analysis

1 4. Basic Nodal and Mesh Analysis This chapter introduces two basic circuit analysis techniques named nodal analysis and mesh analysis 4.1 Nodal Analysis For a simple circuit with two nodes, we often

### Nodal and Loop Analysis

Nodal and Loop Analysis The process of analyzing circuits can sometimes be a difficult task to do. Examining a circuit with the node or loop methods can reduce the amount of time required to get important

### Chapter 07. Series-Parallel Circuits

Chapter 07 Series-Parallel Circuits Source: Circuit Analysis: Theory and Practice Delmar Cengage Learning The Series-Parallel Network Complex circuits May be separated both series and/or parallel elements

### The node voltage method

The node voltage method Equivalent resistance Voltage / current dividers Source transformations Node voltages Mesh currents Superposition Not every circuit lends itself to short-cut methods. Sometimes

### Chapter 08. Methods of Analysis

Chapter 08 Methods of Analysis Source: Circuit Analysis: Theory and Practice Delmar Cengage Learning C-C Tsai Outline Source Conversion Mesh Analysis Nodal Analysis Delta-Wye ( -Y) Conversion Bridge Networks

### Circuits. Page The diagram below represents a series circuit containing three resistors.

Name: Circuits Date: 1. Which circuit segment has an equivalent resistance of 6 ohms? 4. The diagram below represents a series circuit containing three resistors. 2. Base your answer to the following question

### 120 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES SUMMARY PROBLEMS SECTION 3.1

IRWI03_082132v3 8/26/04 9:41 AM Page 120 120 CHAPTER 3 NODAL AND LOOP ANALYSIS TECHNIQUES SUMMARY Nodal analysis for an Nnode circuit Select one node in the Nnode circuit as the reference node. Assume

### Circuit Analysis using the Node and Mesh Methods

Circuit Analysis using the Node and Mesh Methods We have seen that using Kirchhoff s laws and Ohm s law we can analyze any circuit to determine the operating conditions (the currents and voltages). The

### Chapter 5: Circuit Theorems

Chapter 5: Circuit Theorems 5.1 Motivation 5.2 Source Transformation 5.3 Superposition (2.1 Linearity Property) 5.4 Thevenin s Theorem 5.5 Norton s Theorem 5.6 Maximum Power Transfer 5.7 Summary 1 5.1

### Exercise 3 (Resistive Network Analysis)

Circuit Analysis Exercise 0/0/08 Problem. (Hambley.49) Exercise (Resistive Network Analysis) Problem. (Hambley.5) Circuit Analysis Exercise 0/0/08 Problem. (Hambley.59) Problem 4. (Hambley.68) Circuit

### Chapter 2 Objectives

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

### First Order Transient Response

First Order Transient Response When non-linear elements such as inductors and capacitors are introduced into a circuit, the behaviour is not instantaneous as it would be with resistors. A change of state

### Node and Mesh Analysis

Node and Mesh Analysis 1 Copyright ODL Jan 2005 Open University Malaysia Circuit Terminology Name Definition Node Essential node Path Branch Essential Branch Loop Mesh A point where two ore more branches

### ELEC166 Tutorial Week 3 Solutions

ELEC166 Tutorial eek 3 Solutions Q1 n ideal voltmeter gives a reading of 9 when measuring between the terminals of a (real) battery n ideal ohmmeter gives a reading of 900Ω when measuring between the ends

### Series-Parallel Circuits. Objectives

Series-Parallel Circuits Objectives Identify series-parallel configuration Analyze series-parallel circuits Apply KVL and KCL to the series-parallel circuits Analyze loaded voltage dividers Determine the

### 30. Bode Plots. Introduction

0. Bode Plots Introduction Each of the circuits in this problem set is represented by a magnitude Bode plot. The network function provides a connection between the Bode plot and the circuit. To solve these

### Basic circuit analysis

EIE209 Basic Electronics Basic circuit analysis Analysis 1 Fundamental quantities Voltage potential difference bet. 2 points across quantity analogous to pressure between two points Current flow of charge

### ES250: Electrical Science. HW7: Energy Storage Elements

ES250: Electrical Science HW7: Energy Storage Elements Introduction This chapter introduces two more circuit elements, the capacitor and the inductor whose elements laws involve integration or differentiation;

### Equivalent Circuits and Transfer Functions

R eq isc Equialent Circuits and Transfer Functions Samantha R Summerson 14 September, 009 1 Equialent Circuits eq ± Figure 1: Théenin equialent circuit. i sc R eq oc Figure : Mayer-Norton equialent circuit.

### Preamble. Kirchoff Voltage Law (KVL) Series Resistors. In this section of my lectures we will be. resistor arrangements; series and

Preamble Series and Parallel Circuits Physics, 8th Edition Custom Edition Cutnell & Johnson Chapter 0.6-0.8, 0.0 Pages 60-68, 69-6 n this section of my lectures we will be developing the two common types

### Matrices & Their Applications: Nodal Analysis

Matrices & Their Applications: Nodal Analysis Introduction Nodal analysis is a method applied to electrical circuits to determine the nodal voltages. In electrical circuits nodes are points where two or

### EE301 - PARALLEL CIRCUITS AND KIRCHHOFF S CURRENT LAW

Objectives a. estate the definition of a node and demonstrate how to measure voltage and current in parallel circuits b. Solve for total circuit resistance of a parallel circuit c. State and apply KCL

### EECE251 Circuit Analysis Set 2: Methods of Circuit Analysis

EECE251 Circuit Analysis Set 2: Methods of Circuit Analysis Shahriar Mirabbasi Department of Electrical and Computer Engineering University of British Columbia shahriar@ece.ubc.ca 1 Reading Material Chapter

### 1.Find the Thévenin equivalent with respect to the 7k ohm resistor.

Tutorial questions 1.Find the Thévenin equivalent with respect to the 7k ohm resistor. Remove the 7k ohm, since it is not part of the circuit we wish to simplify. Keep the terminals open since we are finding

### Dependent Sources: Introduction and analysis of circuits containing dependent sources.

Dependent Sources: Introduction and analysis of circuits containing dependent sources. So far we have explored timeindependent (resistive) elements that are also linear. We have seen that two terminal

### DOKUZ EYLUL UNIVERSITY FACULTY OF ENGINEERING OFFICE OF THE DEAN COURSE / MODULE / BLOCK DETAILS ACADEMIC YEAR / SEMESTER. Course Code: EEE 2073

Offered by: Elektrik-Elektronik Mühendisliği Course Title: FUNDAMENTALS OF ELECTRIC AND ELECTRONICS Course Org. Title: FUNDAMENTALS OF ELECTRIC AND ELECTRONICS Course Level: Lisans Course Code: EEE 07

### Electric Circuits. Overview. Hani Mehrpouyan,

Electric Circuits Hani Mehrpouyan, Department of Electrical and Computer Engineering, Lecture 5 (Mesh Analysis) Sep 8 th, 205 Hani Mehrpouyan (hani.mehr@ieee.org) Boise State c 205 Overview With Ohm s

### Graph theory and systematic analysis

Electronic Circuits 1 Graph theory and systematic analysis Contents: Graph theory Tree and cotree Basic cutsets and loops Independent Kirchhoff s law equations Systematic analysis of resistive circuits

### Chapter 5. Parallel Circuits ISU EE. C.Y. Lee

Chapter 5 Parallel Circuits Objectives Identify a parallel circuit Determine the voltage across each parallel branch Apply Kirchhoff s current law Determine total parallel resistance Apply Ohm s law in

### Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law (KCL) I. Charge (current flow) conservation law (the Kirchhoff s Current law) Pipe Pipe Pipe 3 Total volume of water per second flowing through pipe = total volume of water per

### W03 Analysis of DC Circuits. Yrd. Doç. Dr. Aytaç Gören

W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören ELK 2018 - Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and

### Q1. (a) The diagram shows the voltage-current graphs for three different electrical components.

Q. (a) The diagram shows the voltage-current graphs for three different electrical components. Which one of the components A, B or C could be a 3 volt filament lamp? Explain the reason for your choice...................

### More Concepts. I = dq. Current is the rate of flow of charge around a circuit.

RC Circuits In this presentation, circuits with multiple batteries, resistors and capacitors will be reduced to an equivalent system with a single battery, a single resistor, and a single capacitor. Kirchoff's

### EXAMPLE 8: An Electrical System (Mechanical-Electrical Analogy)

EXAMPLE 8: An Electrical System (Mechanical-Electrical Analogy) A completely analogous procedure can be used to find the state equations of electrical systems (and, ultimately, electro-mechanical systems

### J. McNames Portland State University ECE 221 Basic Laws Ver

Basic Laws Overview Ideal sources: series & parallel Resistance & Ohm s Law Definitions: open circuit, short circuit, conductance Definitions: nodes, branches, & loops Kirchhoff s Laws Voltage dividers

### Parallel Circuits. Objectives

Parallel Circuits Objectives Identify a parallel circuit Determine the voltage across each parallel branch Apply Kirchhoff s Current Law Determine total parallel resistance Apply Ohm s law in a parallel

### Physics Worksheet Electric Circuits Section: Name: Series Circuits

Do Now: (1) What is electric circuit? (2) Convert the following picture into schematic diagram. Series Circuits 4. Label every component of the circuit; identify each of the voltage and current. 5. Relation

### 5: Thévenin and Norton Equivalents

E1.1 Analysis of (2015-7087) Thevenin and Norton: 5 1 / 12 Equivalent Networks From linearity theorem: V = ai +b. E1.1 Analysis of (2015-7087) Thevenin and Norton: 5 2 / 12 Equivalent Networks From linearity

### Reactance and Impedance

Reactance and Impedance Capacitance in AC Circuits Professor Andrew H. Andersen 1 Objectives Describe capacitive ac circuits Analyze inductive ac circuits Describe the relationship between current and

### Lecture 7 Circuit analysis via Laplace transform

S. Boyd EE12 Lecture 7 Circuit analysis via Laplace transform analysis of general LRC circuits impedance and admittance descriptions natural and forced response circuit analysis with impedances natural

### PHYS 343 Homework Set #3 Solutions

PHYS 343 Homework Set #3 Solutions 1. In the circuit shown, resistor C has a resistance R and the voltage across the battery is. The power delivered to resistor C is 3 times as great as the power delivered

### Verification of Ohm s Law, Kirchoff s Voltage Law and Kirchoff s Current Law Brad Peirson

Verification of Ohm s Law, Kirchoff s Voltage Law and Kirchoff s Current Law Brad Peirson 2-24-05 EGR 214 Circuit Analysis I Laboratory Section 04 Prof. Blauch Abstract The purpose of this report is to

### Nodal Analysis Objective: To analyze circuits using a systematic technique: the nodal analysis.

Circuits (MTE 20) (Spring 200) Nodal Analysis Objective: To analyze circuits using a systematic technique: the nodal analysis. http://pami.uwaterloo.ca/~akrem/ University of Waterloo, Electrical and Computer

### 2: Resistor Circuits. E1.1 Analysis of Circuits ( ) Resistor Circuits: 2 1 / 13. 2: Resistor Circuits

and E1.1 Analysis of Circuits (2016-8284) Resistor Circuits: 2 1 / 13 Kirchoff s Voltage Law and The five nodes are labelled A, B, C, D, E wheree is the reference node. Each component that links a pair

### A) The potential difference across the 6-ohm B) 2.0 A resistor is the same as the potential difference across the 3-ohm resistor. D) 4.

1. A 2.0-ohm resistor and a 4.0-ohm resistor are connected in series with a 12-volt battery. If the current through the 2.0-ohm resistor is 2.0 amperes, the current through the 4.0-ohm resistor is A) 1.0

### Chapter 21 Electric Current and Direct-Current Circuit

Chapter 21 Electric Current and Direct-Current Circuit Outline 21-1 Electric Current 21-2 Resistance and Ohm s Law 21-3 Energy and Power in Electric Circuit 21-4 Resistance in Series and Parallel 21-5

### Solving for Voltage and Current

Chapter 3 Solving for Voltage and Current Nodal Analysis If you know Ohm s Law, you can solve for all the voltages and currents in simple resistor circuits, like the one shown below. In this chapter, we

### = (0.400 A) (4.80 V) = 1.92 W = (0.400 A) (7.20 V) = 2.88 W

Physics 2220 Module 06 Homework 0. What are the magnitude and direction of the current in the 8 Ω resister in the figure? Assume the current is moving clockwise. Then use Kirchhoff's second rule: 3.00

### Series and Parallel Circuits

Series and Parallel Circuits Components in a circuit can be connected in series or parallel. A series arrangement of components is where they are inline with each other, i.e. connected end-to-end. A parallel

### Chapter 21 Electric Current and Direct-Current Circuit

Chapter 2 Electric Current and Direct-Current Circuit Outline 2- Electric Current 2-2 Resistance and Ohm s Law 2-3 Energy and Power in Electric Circuit 2-4 Resistance in Series and Parallel 2-5 Kirchhoff

### Application of Linear Algebra in. Electrical Circuits

Application of Linear Algebra in Electrical Circuits Seamleng Taing Math 308 Autumn 2001 December 2, 2001 Table of Contents Abstract..3 Applications of Linear Algebra in Electrical Circuits Explanation..

### Chapter 6. Series-Parallel Circuits. Objectives

Chapter 6 Series-Parallel Circuits Objectives Identify series-parallel relationships Analyze series-parallel circuits Analyze loaded voltage dividers Determine the loading effect of a voltmeter on a circuit

### Department of Electrical and Electronic Engineering, California State University, Sacramento

Department of Electrical and Electronic Engineering, California State University, Sacramento Engr 17 Introductory Circuit Analysis, graded, 3 units Instructor: Tatro - Spring 2016 Section 2, Call No. 30289,

### EMF and Terminal Voltage Resistors in Series and Parallel Kirchhoff s Rules EMFs in Series and Parallel; Charging a Battery Circuits with Capacitors

Chapter 19 DC Electrical Circuits Topics in Chapter 19 EMF and Terminal Voltage Resistors in Series and Parallel Kirchhoff s Rules EMFs in Series and Parallel; Charging a Battery Circuits with Capacitors

### EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67 - FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 1 TUTORIAL 1 - DIRECT CURRENT CIRCUIT THEOREMS

EDEXCE NATIONA CERTIFICATE/DIPOMA UNIT 67 - FURTHER EECTRICA PRINCIPES NQF EVE 3 OUTCOME 1 TUTORIA 1 - DIRECT CURRENT CIRCUIT THEOREMS Unit content 1 Be able to apply direct current (DC) circuit analysis

### Sirindhorn International Institute of Technology Thammasat University at Rangsit

Sirindhorn International Institute of Technology Thammasat University at angsit School of Information, Computer and Communication Technology COUSE : ECS 204 Basic Electrical Engineering Lab INSTUCTO :

### Circuits 1 M H Miller

Introduction to Graph Theory Introduction These notes are primarily a digression to provide general background remarks. The subject is an efficient procedure for the determination of voltages and currents

### Cornerstone Electronics Technology and Robotics I Week 15 Combination Circuits (Series-Parallel Circuits)

Cornerstone Electronics Technology and Robotics I Week 15 Combination Circuits (Series-Parallel Circuits) Administration: o Prayer o Turn in quiz Electricity and Electronics, Chapter 8, Introduction: o

### ch 18 practice Multiple Choice

ch 18 practice Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which of the following is the best description of a schematic diagram? a. uses pictures

### Small Signal Amplifier with Bipolar Junction Transistor

mall ignal Amplifier with Bipolar Junction Transistor This tutorial will teach you in very easy steps how to design class-a amplifiers tarting with the results of bias point design we get the following

### Circuits-Circuit Analysis

Base your answers to questions 1 through 3 on the information and diagram below. 4. A 9-volt battery is connected to a 4-ohm resistor and a 5-ohm resistor as shown in the diagram below. A 3.0-ohm resistor,

### 13.10: How Series and Parallel Circuits Differ pg. 571

13.10: How Series and Parallel Circuits Differ pg. 571 Key Concepts: 5. Connecting loads in series and parallel affects the current, potential difference, and total resistance. - Using your knowledge of

### Students will need about 30 minutes to complete these constructed response tasks.

Electric Title of Circuits Concept Constructed Response Teacher Guide Students will need about 30 minutes to complete these constructed response tasks. Objectives assessed: Understand the functions of

### EE101 - Lab 2: Resistive Circuits. Resistor Color Codes --- Note: carbon composition resistors will be used

EE101 - Lab 2: Resistive Circuits ALL PRELABS ARE TO BE COMPLETED ON SEPARATE PAPER AND TURNED IN AT THE BEGINNING OF THE LAB PERIOD (MAKE A COPY TO USE DURING THE LAB). ALL LAB EXERCISES MUST BE COMPLETED

### UNIVERSITY OF CALIFORNIA BERKELEY Engineering 7 Department of Civil and Environmental Engineering. Linear Equations: Engineering Supplement

UNIVERSITY OF CALIFORNIA BERKELEY Engineering 7 Department of Civil and Environmental Engineering Spring 203 Professor: S. Govindjee Linear Equations: Engineering Supplement Introduction The workhorse

### Electric Circuits II

Electric Circuits II Experiment 4: Resistances in Circuits Equipment needed: - AC/DC Electronic Lab Board: Resistors - Multimeter Purpose The purpose of this lab is to begin experimenting with the variables

### Student Exploration: Circuits

Name: Date: Student Exploration: Circuits Vocabulary: ammeter, circuit, current, ohmmeter, Ohm s law, parallel circuit, resistance, resistor, series circuit, voltage Prior Knowledge Questions (Do these

### 3. Introduction and Chapter Objectives

Real nalog Circuits Chapter 3: Nodal and Mesh nalysis 3. Introduction and Chapter Objectives In Chapters and 2, we introduced several tools used in circuit analysis: Ohm s law, Kirchoff s laws, and circuit

### Experiment 8 Series-Parallel Circuits

Experiment 8 Series-Parallel Circuits EL 111 - DC Fundamentals By: Walter Banzhaf, E.K. Smith, and Winfield Young University of Hartford Ward College of Technology Objectives: 1. For the student to measure

### THE BREADBOARD; DC POWER SUPPLY; RESISTANCE OF METERS; NODE VOLTAGES AND EQUIVALENT RESISTANCE; THÉVENIN EQUIVALENT CIRCUIT

THE BREADBOARD; DC POWER SUPPLY; RESISTANCE OF METERS; NODE VOLTAGES AND EQUIVALENT RESISTANCE; THÉVENIN EQUIVALENT CIRCUIT YOUR NAME LAB MEETING TIME Reference: C.W. Alexander and M.N.O Sadiku, Fundamentals

### Series and Parallel Circuits

Pre-Laboratory Assignment Series and Parallel Circuits ECE 2100 Circuit Analysis Laboratory updated 16 May 2011 1. Consider the following series circuit. Derive a formula to calculate voltages V 1, V 2,

### Basic Definitions and DC Circuits

Basic Definitions and DC Circuits 2 This chapter s main objective is to highlight some of the commonly used definitions and fundamental concepts in electric circuits, which are supported by a set of custom-written

### ECE EQUIVALENT CIRCUITS - INVESTIGATION 17 EQUIVALENT RESISTANCE

ECE 109 - EQUALET CRCUTS - ESTGATO 17 EQUALET RESSTACE FALL 2006 A.P. FELZER To do "well" on this investigation you must not only get the right answers but must also do neat, complete and concise writeups

### Chapter 28A - Direct Current Circuits. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University

Chapter 28A - Direct Current Circuits A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should

### Chapter 10. RC Circuits. Objectives

Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine

### LAB2 Resistors, Simple Resistive Circuits in Series and Parallel Objective:

LAB2 Resistors, Simple Resistive Circuits in Series and Parallel Objective: In this lab, you will become familiar with resistors and potentiometers and will learn how to measure resistance. You will also

### 8. Resistors in Parallel

8. Resistors in Parallel Resistors are said to be connected together in "Parallel" when both of their terminals are respectively connected to each terminal of the other resistor or resistors. Unlike the

### Section 20.7 Parallel Wiring

Here are a series of questions taken from the Cutnell & Johnson test bank. These are offered for practice purposes only. I will not grade your results and I do not want you to spend too much time on these.

### Kirchhoff s Laws. Kirchhoff's Law #1 - The sum of the currents entering a node must equal the sum of the currents exiting a node.

Kirchhoff s Laws There are two laws necessary for solving circuit problems. For simple circuits, you have been applying these equations almost instinctively. Kirchhoff's Law #1 - The sum of the currents

### Chapter 3 Nodal and Mesh Equations - Circuit Theorems

Chapter 3 Nodal and Mesh Equations - Circuit Theems 3.14 Exercises Multiple Choice 1. The oltage across the resist in the circuit of Figure 3.67 is A. B. C. D. E. 6 V 16 V 8 V 32 V none of the aboe 6 V