UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS


 Ross Lee
 3 years ago
 Views:
Transcription
1 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 to the total current flowing away from the junction, i.e. I = 0 Thus, referring to figure 1: I1 I2 I3 I5 I4 current towards = current flowing away I 1 + I 2 + I 3 = I 4 + I 5 I 1 + I 2 + ( I 3 ) + ( I 4 ) + (I 5 ) = 0 I = 0 Figure 1 Kirchoff s Voltage Law (KVL) states in any closed loop in a network, the algebraic sum Figure 2 of the voltage drops (i.e. products of current and resistance) taken around the loop is equal to the resultant e.m.f. acting in that loop. V E = I + I E = I( + ) E + ( I ) + ( I) = 0 Figure Mesh analysis Analysis using KVL to solve for the currents around each closed loop of the network and hence determine the currents through and voltages across each elements of the network. Mesh analysis procedure: 1. Assign a distinct current to each closed loop of the network. 2. Apply KVL around each closed loop of the network. 3. Solve the resulting simultaneous linear equation for the loop currents. MAIANA/JKE/POLISAS/ET101UNIT4 1
2 Example 1 Find the current flow through each resistor using mesh analysis for the circuit below. 20V Figure 3 Solution: Step 1: Assign a distinct current to each closed loop of the network. I1 I2 I13 I1 I2 20V Figure 4 Step 2: Apply KVL around each closed loop of the network. Loop 1: Loop 2: equation equation 2 Step 3: Solve the resulting simultaneous linear equation for the loop currents. Solve equation 1 and 2 using matrix Matrix form: From KCL : MAIANA/JKE/POLISAS/ET101UNIT4 2
3 Example 2 Find the current flow through each resistor using mesh analysis for the circuit below. 5kΩ 3kΩ 40V 6kΩ 55V Figure 5 Solution: Step 1: Assign a distinct current to each closed loop of the network. I1 I2 5kΩ I3 3kΩ 40V I1 6kΩ I2 55V Figure 6 Step 2: Apply KVL around each closed loop of the network. Loop 1: Loop 2: equation equation 2 Step 3: Solve the resulting simultaneous linear equation for the loop currents. Solve equation 1 and 2 using matrix Matrix form: From KCL : MAIANA/JKE/POLISAS/ET101UNIT4 3
4 1.2 Nodes analysis Analysis using KCL to solve for voltages at each common node of the network and hence determines the currents through and voltages across each elements of the network. Nodal analysis procedure: 1. Determine the number of common nodes and reference node within the network. 2. Assign current and its direction to each distinct branch of the nodes in the network. 3. Apply KCL at each of the common nodes in the network 4. Solve the resulting simultaneous linear equation for the nodal voltages. 5. Determine the currents through and voltages across each the elements in the network. Example 3 Find the current flow through each resistor using mesh analysis for the circuit below. 20V Solution: Figure 7 Step 1: Determine the number of common nodes and reference node within the network (Figure 8). 1 common node (Va), reference node C Step 2: Assign current and its direction to each distinct branch of the nodes in the network (Figure 8). I1 Va I2 I13 20V C Figure 8 Step 3: Apply KCL at each of the common nodes in the network KCL: MAIANA/JKE/POLISAS/ET101UNIT4 4
5 Step 4: Solve the resulting simultaneous linear equation for the nodal voltages. Step 5: Determine the currents through each elements Example 4 Find the current flow through each resistor using mesh analysis for the circuit below. 5kΩ 3kΩ 40V 6kΩ 55V Figure 9 Solution: Step 1: Determine the number of common nodes and reference node within the network (Figure 10). 1 common node (Va), reference node C Step 2: Assign current and its direction to each distinct branch of the nodes in the network (Figure 10). I1 Va I2 5kΩ I3 3kΩ 40V 6kΩ 55V C Figure 10 MAIANA/JKE/POLISAS/ET101UNIT4 5
6 Step 3: Apply KCL at each of the common nodes in the network KCL: Step 4: Solve the resulting simultaneous linear equation for the nodal voltages. Step 5: Determine the currents through each elements MAIANA/JKE/POLISAS/ET101UNIT4 6
7 TUTORIAL 1 Find the current through each resistor for the networking below using Mesh Analysis and Nodal Analysis. a) d) 4V b) 4Ω 8Ω 2Ω 6V 4Ω 3Ω 12V 12Ω e) 15Ω 15V 5.6kΩ 2.2kΩ 3.3kΩ V3 c) 20V 30V 4kΩ 3kΩ 30V 25V 2kΩ MAIANA/JKE/POLISAS/ET101UNIT4 7
8 2.0 Thevenin s Theorem Thevenins Theorem states: "Any linear circuit containing several energy source and resistances can be replaced by just a Single Voltage in series with a Single Resistor". Thevenins equivalent circuit. A Linear Network Containing Several Energy Source and Resistance A B VTH RTH Thevenin s Equivalent Circuit Figure 11 Thevenin s theorem procedure: 1. Open circuit R L and find Thevenin s voltage (V TH ). 2. Find Thevenin s resistance (R TH ) when voltage source is short circuit or current source is open circuit and R L is open circuit. 3. Draw the Thevenin s equivalent circuit such as in figure 11 with the value of V TH and R TH. Find the I L which current flow through the R L. Example 5 Find the current flow through equal to 30Ω for the circuit in Figure Ω Figure 12 MAIANA/JKE/POLISAS/ET101UNIT4 8
9 Solution: Step 1: Open circuit R L and find Thevenin s voltage (V TH ). Using VDR find V TH VTH Figure 13 Step 2: Find Thevenin s resistance (R TH ) when voltage source is short circuit RTH Figure 14 Step 3: Draw the Thevenin s equivalent circuit with the value of V TH and R TH RTH 28Ω VTH 8V 30Ω Figure 15 MAIANA/JKE/POLISAS/ET101UNIT4 9
10 Example 6 Find current flow through R 4. 60Ω Is 300mA R4 30Ω 90Ω 25Ω Solution : Figure 16 Step 1 : Open circuit R L and find Thevenin s voltage (V TH ). I1 60Ω I2 Using CDR, find I 2 Is 300mA 30Ω 90Ω VTH Figure 17 Step 2: Find Thevenin s resistance (R TH ) when current source,i S is open circuit. 60Ω 30Ω 90Ω RTH Figure 18 Step 3: Draw the Thevenin s equivalent circuit with the value of V TH and R TH RTH 45Ω VTH 4.5V 25Ω Figure 19 MAIANA/JKE/POLISAS/ET101UNIT4 10
11 TUTORIAL 2 1. Refer to figure 1, find the current flow through resistor 12Ω using Thevenin s Theorem. 3Ω 4Ω R4 36V 6Ω 12Ω 5. Calculate the current flow in 30Ω resistor for the circuit in figure 5 using Thevenin s Theorem. Is R4 2A 30Ω Figure 1 2. Find the current flow through resistor 15Ω for the circuit in figure 2 using Thevenin s Theorem. 15V 3Ω 2Ω 15Ω Figure 2 4Ω 6Ω 5Ω 3. Count value stream I L by using Thevenin s Theorem. 5kΩ 4kΩ 3kΩ 2kΩ 20V Figure 5 6. Refer to figure 6, find the current flow through 50Ω using Thevenin s Theorem. Is 200mA 30Ω 50Ω Figure 6 7. Use Thevenin s Theorem, find the current flow through resistor R=. 6V 8Ω 15Ω 1kΩ Figure 7 Figure 3 4. Use Thevenin s Theorem to find the current flowing in 5Ω resistor shown in figure 4. 15V 6Ω 4Ω 5Ω 8Ω 2Ω 8. Use Thevenin s Theorem, find the current flow through resistor R=. 6V 8Ω 15Ω Figure 4 Figure 8
12 3.0 Norton s Theorem Nortons Theorem states: "Any linear circuit containing several energy sources and resistances can be replaced by a single Constant Current generator in parallel with a Single Resistor". A Linear Network Containing Several Energy Source and Resistance A B IN RN Norton Equivalent Circuit Example 7 Figure 20 Norton s theorem procedure: 1. Remove R L from the circuit. Find I N by shorting links output terminal. 2. Find R N by shortcircuit voltage source or opencircuit current source. 3. Draw the Norton s equivalent circuit such as in figure 20 with the value of I N and R N. Find the I L which current flow through the R L. Find the current flow through equal to 30Ω for the circuit in Figure Ω Step 1: Figure 21 Remove R L from the circuit. Find I N by shorting links output terminal. IT I1 IN 30Ω Figure 22
13 Step 2: Find R N by shortcircuit voltage source. RN Figure 23 Step3: Draw the Norton s equivalent circuit with the value of I N and R N. Find the I L which current flow through the R L. Using CDR, find I L IN RN 0.286A 28Ω 30Ω Example 6 Figure 24 Find current flow through R 4. 60Ω Is 300mA R4 30Ω 90Ω 25Ω Figure 25 MAIANA/JKE/POLISAS/ET101UNIT4 13
14 Solution: Step 1: Remove R L from the circuit. Find I N by shorting links output terminal. Current flow at 90Ω is 0A, so. Is 300mA 60Ω IN R4 30Ω 90Ω 25Ω Step 2: Figure 26 Find R N by opencircuit current source. 30Ω 60Ω 90Ω RN Figure 27 Step3: Draw the Norton s equivalent circuit with the value of I N and R N. Find the I L which current flow through the R L. Using CDR, find I L IN RN 100mA 45Ω 25Ω Figure 28 MAIANA/JKE/POLISAS/ET101UNIT4 14
15 TUTORIAL 3 1. Refer to figure 1, find the current flow through resistor 12Ω using Norton s Theorem. 3Ω 4Ω R4 36V 6Ω 12Ω 5. Calculate the current flow in 30Ω resistor for the circuit in figure 5 using Norton Theorem. Is R4 2A 30Ω Figure 1 2. Find the current flow through resistor 15Ω for the circuit in figure 2 using Norton Theorem. Figure 5 6. Refer to figure 6, find the current flow through 50Ω using Norton Theorem. 15V 3Ω 2Ω 15Ω Figure 2 4Ω 6Ω 5Ω 3. Count value stream I L by using Norton Theorem. 5kΩ 4kΩ 3kΩ 2kΩ 20V Is 200mA 30Ω 50Ω Figure 6 7. Use Norton Theorem, find the current flow through resistor R=. 6V 8Ω 15Ω 1kΩ Figure 7 Figure 3 4. Use Norton Theorem to find the current flowing in 5Ω resistor shown in figure 4. 15V 6Ω 4Ω 5Ω 8Ω 2Ω 8. Use Norton Theorem, find the current flow through resistor R=. 6V 8Ω 15Ω Figure 4 Figure 8 MAIANA/JKE/POLISAS/ET101UNIT4 15
16 4.0 Maximum Power Transfer theorem The maximum power transfer theorem states: A load will receive maximum power from a linear bilateral dc network when its total resistive value equal to the Thevenin s or Norton resistance of the network as seen by the load. RTH VTH IN RN Thevenin Equivalent Circuit Norton Equivalent Circuit Figure 29 For the Thevenin equivalent circuit above, maximum power will be delivered to the load when: For the Norton equivalent circuit above, maximum power will be delivered to the load when: There are four conditions occur when maximum power transfer took place in a circuit: 1. Value of equal to R TH (R L =R TH ). 2. Value of current is half of the current when is short circuited. 3. Value of load voltage is half the Thevenin s voltage (V L = ½V TH ). 4. Percentage of efficiency, % = 50%. Where: Example 7 Refer to figure 30, determine the load power for each of the following value of the variable load resistance and sketch the graph load power versus load resistance. a) 25Ω b) 50Ω c) 75Ω d) 100Ω e) 125Ω RTH 75Ω VTH Figure 30
17 Load Power (W) UNIT 4 DC EQUIVALENT CIRCUIT AND NETWORK THEOREMS Solution: a) d) b) e) c) R TH R L I V TH VL=IR L % P L 75Ω A 0V 0% 0W 75Ω 25Ω 0.1A 2.5V 25% 0.25W 75Ω 50Ω 0.08A 4V 40% 0.32W 75Ω 75Ω 0.067A 5.0V 50% 0.336W 75Ω 100Ω 0.057A 5.7V 57% 0.325W 75Ω 125Ω 0.05A 6.5V 65% 0.312W Load Power (PL) vs Load Resistance() 0, 0 25, , , , , Load Resistance (Ω) Figure 31 MAIANA/JKE/POLISAS/ET101UNIT4 17
18 Example 8 For the network in figure 32, determine the value of R for maximum power transfer to R and hence calculate the maximum power using Thevenin s equivalent circuit. 6Ω 8Ω 12V 3Ω R Figure 32 Solution: Open circuit R and find Thevenin s voltage (V TH ). 6Ω 8Ω 12V 3Ω VTH Using VDR find V TH Figure 33 Find Thevenin s resistance (R TH ) when voltage source is short circuit 6Ω 8Ω 3Ω RTH Figure 34 Draw the Thevenin s equivalent circuit with the value of V TH and R TH RTH VTH 4V R Maximum power transfer occur when R=R TH. So, the value of R is. Figure 35 Maximum power transfer, MAIANA/JKE/POLISAS/ET101UNIT4 18
19 5.0 Superposition Theorem The superposition theorem states: In any network made up of linear resistances and containing more than one source of e.m.f, the resultant current flowing in any branch is the algebraic sum of the currents that would flow in that branch if each source was considered separately, all other sources being replaced at that time by their respective internal resistances. Removing the effect of voltage and current source Short circuit Open circuit Voltage source Current source Example 9 Determine the current through resistor =5Ω for the network in figure 36 using superposition theorem. V 15V 5Ω I 9A Figure 36 Solution: Step 1: V active, I inactive. So current source is open circuit. Ia V 15V 5Ω Figure 37
20 Step 2: V inactive, I active. So voltage source is short circuit. Ib Using CDR 5Ω I 9A Figure 38 Step 3: Total current through =5Ω. Ia 1A Ib 6A Example 10 Find the current flow through each resistor for the network in figure V Figure 39 Solution: Step 1: active, inactive I1' I2' I3' Figure 40 MAIANA/JKE/POLISAS/ET101UNIT4 20
21 Step 2: inactive, active I1' I2' I3' 20V Figure 41 Step 3: Total current flow through each resistor I I 1 =0.429A So I 1 =0.571A I I 2 =0.286A So I 2 =0.714A I I 3 =0.143A I 3 =0.143A So
22 TUTORIAL 4 Find the current through each resistor for the networking below using Superposition Theorem. b) d) 4V b) 4Ω 8Ω 2Ω 6V 4Ω 3Ω 12V 12Ω e) 15Ω 15V 5.6kΩ 2.2kΩ 3.3kΩ V3 c) 20V 30V 4kΩ 3kΩ 30V 25V 2kΩ MAIANA/JKE/POLISAS/ET101UNIT4 22
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 informationThevenin 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 informationPOLYTECHNIC 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
More informationCHAPTER 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
More informationD C Circuit Analysis and Network Theorems:
UNIT1 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 informationChapter 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 informationDC 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 informationModule 2. DC Circuit. Version 2 EE IIT, Kharagpur
Module 2 DC Circuit Lesson 5 Nodevoltage 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 informationCircuit 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 informationSinusoidal 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 informationChapter 10: Sinusoidal SteadyState Analysis
Chapter 10: Sinusoidal SteadyState 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 informationLecture Notes on DC Network Theory
Federal University, NdufuAlike, Ikwo Department of Electrical/Electronics and Computer Engineering (ECE) Faculty of Engineering and Technology Lecture Notes on DC Network Theory Harmattan Semester by
More informationSeries & Parallel Resistors 3/17/2015 1
Series & Parallel Resistors 3/17/2015 1 Series Resistors & Voltage Division Consider the singleloop circuit as shown in figure. The two resistors are in series, since the same current i flows in both
More informationCURRENT 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 informationElectric 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 informationEE201 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
EE201, Review Probs Test 1 page1 Spring 98 EE201 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)
More informationECE2262 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 informationECE2262 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 informationSolution: 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 informationVoltage 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
More informationPreamble. Circuit Analysis II. Mesh Analysis. When circuits get really complex methods learned so far will still work,
Preamble Circuit Analysis II Physics, 8 th Edition Custom Edition Cutnell & Johnson When circuits get really complex methods learned so far will still work, but they can take a long time to do. A particularly
More informationChapter 10 Sinusoidal Steady State Analysis Chapter Objectives:
Chapter 10 Sinusoidal Steady State Analysis Chapter Objectives: Apply previously learn circuit techniques to sinusoidal steadystate analysis. Learn how to apply nodal and mesh analysis in the frequency
More informationMAE140  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 informationSinusoidal 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/
More informationElectrical Engineering Technology
Electrical Engineering Technology 1 ECET 17700  DAQ & Control Systems Lecture # 9 Loading, Thévenin Model & Norton Model Professors Robert Herrick & J. Michael Jacob Module 1 Circuit Loading Lecture 9
More informationCHAPTER 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 informationBFF1303: 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 informationElectric Circuits I. Midterm #1
The University of Toledo Section number s5ms_elci7.fm  Electric Circuits I Midterm # Problems Points. 3 2. 7 3. 5 Total 5 Was the exam fair? yes no The University of Toledo Section number s5ms_elci7.fm
More informationChapter 7. Chapter 7
Chapter 7 Combination circuits Most practical circuits have combinations of series and parallel components. You can frequently simplify analysis by combining series and parallel components. An important
More informationChapter 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
More informationChapter 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 informationKirchhoff'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,
More informationTutorial #4: Bias Point Analysis in Multisim
SCHOOL OF ENGINEERING AND APPLIED SCIENCE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING ECE 2115: ENGINEERING ELECTRONICS LABORATORY Tutorial #4: Bias Point Analysis in Multisim INTRODUCTION When BJTs
More informationUNIVERSITY F P RTLAND Sch l f Engineering
UNIVERSITY F P RTLAND Sch l f Engineering EE271Electrical Circuits Laboratory Spring 2004 Dr. Aziz S. Inan & Dr. Joseph P. Hoffbeck Lab Experiment #4: Electrical Circuit Theorems  p. 1 of 5  Electrical
More informationMidterm 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 informationNetwork Topology2 & 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 informationElectric Circuits I. Nodal Analysis. Dr. Firas Obeidat
Electric Circuits I Nodal Analysis Dr. Firas Obeidat 1 Nodal Analysis Without Voltage Source Nodal analysis, which is based on a systematic application of Kirchhoff s current law (KCL). A node is defined
More information3.1 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 informationChapter 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
More informationChapter 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:
More informationmywbut.com Mesh Analysis
Mesh Analysis 1 Objectives Meaning of circuit analysis; distinguish between the terms mesh and loop. To provide more general and powerful circuit analysis tool based on Kirchhoff s voltage law (KVL) only.
More informationTHERE MUST BE 50 WAYS TO FIND YOUR VALUES: AN EXPLORATION OF CIRCUIT ANALYSIS TECHNIQUES FROM OHM S LAW TO EQUIVALENT CIRCUITS
THERE MUST BE 50 WAYS TO FIND YOUR VALUES: AN EXPLORATION OF CIRCUIT ANALYSIS TECHNIQUES FROM OHM S LAW TO EQUIVALENT CIRCUITS Kristine McCarthy Josh Pratti Alexis RodriguezCarlson November 20, 2006 Table
More informationDEPARTMENT 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
More informationStudy 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 informationKirchhoff's Laws and Maximum Power Transfer
German Jordanian University (GJU) Electrical Circuits Laboratory Section Experiment Kirchhoff's Laws and Maximum Power Transfer Post lab Report Mahmood Hisham Shubbak / / 8 Objectives: To learn KVL and
More informationChapter 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 informationQUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34)
QUESTION BANK SUBJECT: NETWORK ANALYSIS (10ES34) NOTE: FOR NUMERICAL PROBLEMS FOR ALL UNITS EXCEPT UNIT 5 REFER THE EBOOK ENGINEERING CIRCUIT ANALYSIS, 7 th EDITION HAYT AND KIMMERLY. PAGE NUMBERS OF
More informationEngineering Fundamentals and Problem Solving, 6e
Engineering Fundamentals and Problem Solving, 6e Chapter 17 Electrical Circuits Chapter Objectives Compute the equivalent resistance of resistors in series and in parallel Apply Ohm s law to a resistive
More informationMAE140  Linear Circuits  Winter 09 Midterm, February 5
Instructions MAE40  Linear ircuits  Winter 09 Midterm, February 5 (i) This exam is open book. You may use whatever written materials you choose, including your class notes and textbook. You may use a
More informationEE 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 67 pm, Room TBA First retrieve your EE2110 final and other course papers and notes! The test will be closed book
More informationChapter 5 Solution P5.22, 3, 6 P5.33, 5, 8, 15 P5.43, 6, 8, 16 P5.52, 4, 6, 11 P5.62, 4, 9
Chapter 5 Solution P5.22, 3, 6 P5.33, 5, 8, 15 P5.43, 6, 8, 16 P5.52, 4, 6, 11 P5.62, 4, 9 P 5.22 Consider the circuit of Figure P 5.22. Find i a by simplifying the circuit (using source transformations)
More informationE1.1 Analysis of Circuits ( ) Revision Lecture 1 1 / 13
RevisionLecture 1: E1.1 Analysis of Circuits (20144530) Revision Lecture 1 1 / 13 Format Question 1 (40%): eight short parts covering the whole syllabus. Questions 2 and 3: single topic questions (answer
More information1.7 DeltaStar Transformation
S Electronic ircuits D ircuits 8.7 DeltaStar 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 informationV 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
More informationModule 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
More informationErrors in Electrical Measurements
1 Errors in Electrical Measurements Systematic error every times you measure e.g. loading or insertion of the measurement instrument Meter error scaling (inaccurate marking), pointer bending, friction,
More informationOUTCOME 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
More informationModule 2. DC Circuit. Version 2 EE IIT, Kharagpur
Module DC Circuit Lesson 4 Loop Analysis of resistive circuit in the context of dc voltages and currents Objectives Meaning of circuit analysis; distinguish between the terms mesh and loop. To provide
More informationLet V1=12V, R1=50 ohms, R2=10K ohms, R3=2K ohms, and R4=500 ohms. RL represents the load placed on the circuit between points Aand B.
Questions on Thevenin Equivalent Circuits Fall 2004 2. Thevenin Circuits (25 points) Let V1=12V, R1=50 ohms, R2=10K ohms, R3=2K ohms, and R4=500 ohms. RL represents the load placed on the circuit between
More informationElectric 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 informationElectrical 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
More informationSeries/Parallel Circuit Simplification: Kirchoff, Thevenin & Norton
Series/Parallel Circuit Simplification: Kirchoff, Thevenin & Norton Session 1d of Basic Electricity A Fairfield University ECourse Powered by LearnLinc Basic Electricity Two Parts Electron Flow and Resistance
More informationIntroductory Circuit Analysis
Introductory Circuit Analysis CHAPTER 6 Parallel dc Circuits OBJECTIVES Become familiar with the characteristics of a parallel network and how to solve for the voltage, current, and power to each element.
More informationExperiment #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
More informationBasic Electrical Circuits Analysis ECE 221
Basic Electrical Circuits Analysis ECE 221 PhD. Khodr Saaifan http://trsys.faculty.jacobsuniversity.de k.saaifan@jacobsuniversity.de 1 2 Reference: Electric Circuits, 8th Edition James W. Nilsson, and
More informationHomework 1 solutions
Electric Circuits 1 Homework 1 solutions (Due date: 2014/3/3) This assignment covers Ch1 and Ch2 of the textbook. The full credit is 100 points. For each question, detailed derivation processes and accurate
More informationSOME USEFUL NETWORK THEOREMS
APPENDIX D SOME USEFUL NETWORK THEOREMS Introduction In this appendix we review three network theorems that are useful in simplifying the analysis of electronic circuits: Thévenin s theorem Norton s theorem
More informationBASIC NETWORK ANALYSIS
SECTION 1 BASIC NETWORK ANALYSIS A. Wayne Galli, Ph.D. Project Engineer Newport News Shipbuilding SeriesParallel dc Network Analysis......................... 1.1 BranchCurrent Analysis of a dc Network......................
More informationECE 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
More informationIn this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents
In this lecture, we will consider how to analyse an electrical circuit by applying KVL and KCL. As a result, we can predict the voltages and currents around an electrical circuit. This is a short lecture,
More informationEIT 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 informationDirect Current Circuits. February 18, 2014 Physics for Scientists & Engineers 2, Chapter 26 1
Direct Current Circuits February 18, 2014 Physics for Scientists & Engineers 2, Chapter 26 1 Kirchhoff s Junction Rule! The sum of the currents entering a junction must equal the sum of the currents leaving
More informationThe equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A =
The equivalent model of a certain op amp is shown in the figure given below, where R 1 = 2.8 MΩ, R 2 = 39 Ω, and A = 10 10 4. Section Break Difficulty: Easy Learning Objective: Understand how real operational
More informationFundamentals of Electric Circuits, Second Edition  Alexander/Sadiku
Chapter 3, Problem 9(8). Find V x in the network shown in Fig. 3.78. Figure 3.78 Chapter 3, Solution 9(8). Consider the circuit below. 2 Ω 2 Ω j 8 30 o I j 4 j 4 I 2 j2v For loop, 8 30 = (2 j4)i ji 2
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science : Circuits & Electronics Problem Set #1 Solution
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.2: Circuits & Electronics Problem Set # Solution Exercise. The three resistors form a series connection.
More information1. 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 informationBasics of Network Theory (PartI)
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 informationDelta & Y Configurations, Principles of Superposition, Resistor Voltage Divider Designs
BME/ISE 3511 Bioelectronics  Test Three Course Notes Fall 2016 Delta & Y Configurations, Principles of Superposition, esistor Voltage Divider Designs Use following techniques to solve for current through
More informationModule 2. DC Circuit. Version 2 EE IIT, Kharagpur
Module 2 DC Circuit Lesson 7 Superposition Theorem in the context of dc voltage and current sources acting in a resistive network Objectives Statement of superposition theorem and its application to a
More information15EE103L ELECTRIC CIRCUITS LAB RECORD
15EE103L ELECTRIC CIRCUITS LAB RECORD REGISTER NO: NAME OF THE STUDENT: SEMESTER: DEPARTMENT: INDEX SHEET S.No. Date of Experiment Name of the Experiment Date of submission Marks Staff Sign 1 Verification
More informationElectrical Technology (EE101F)
Electrical Technology (EE101F) Contents Series & Parallel Combinations KVL & KCL Introduction to Loop & Mesh Analysis Frequently Asked Questions NPTEL Link SeriesParallel esistances 1 V 3 2 There are
More information4/27 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: 79pm, Monday, 4/30 at Lambert Fieldhouse F101 Calculator
More informationChapter 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 informationThe CommonEmitter Amplifier
c Copyright 2009. W. Marshall Leach, Jr., Professor, Georgia Institute of Technology, School of Electrical and Computer Engineering. The CommonEmitter Amplifier Basic Circuit Fig. shows the circuit diagram
More informationBasic RL and RC Circuits RL TRANSIENTS: STORAGE CYCLE. Engineering Collage Electrical Engineering Dep. Dr. Ibrahim Aljubouri
st Class Basic RL and RC Circuits The RL circuit with D.C (steady state) The inductor is short time at Calculate the inductor current for circuits shown below. I L E R A I L E R R 3 R R 3 I L I L R 3 R
More informationDiscussion 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
More informationNotes for course EE1.1 Circuit Analysis TOPIC 10 2PORT CIRCUITS
Objectives: Introduction Notes for course EE1.1 Circuit Analysis 45 Reexamination of 1port subcircuits Admittance parameters for port circuits TOPIC 1 PORT CIRCUITS Gain and port impedance from port
More informationENGG 1203 Tutorial_05. Use of Multimeter. Lab 5 : SYSTEM. Office hours : Chow Yei Ching, CBLG205 Thu, Fri; 15:3017:30
ENGG 1203 Tutorial_05 Office hours : Chow Yei Ching, CBLG205 Thu, Fri; 15:3017:30 HW : 25%/day at least after 4 days, sample answer posted for study Lab 5 : Use of Multimeter The value showing is maximum
More informationLecture # 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
More informationOnePort Networks. OnePort. Network
TwoPort s Definitions Impedance Parameters dmittance Parameters Hybrid Parameters Transmission Parameters Cascaded TwoPort s Examples pplications OnePort s v i' 1 OnePort pair of terminals at which a signal
More informationR 2, R 3, and R 4 are in parallel, R T = R 1 + (R 2 //R 3 //R 4 ) + R 5. CC Tsai
Chapter 07 SeriesParallel Circuits The SeriesParallel Network Complex circuits May be separated both series and/or parallel elements Combinations which are neither series nor parallel To analyze a circuit
More informationChapter 10: Sinusoidal SteadyState Analysis
Chapter 10: Sinusoidal SteadyState Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques
More informationEECE251 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
More informationNotes for course EE1.1 Circuit Analysis TOPIC 3 CIRCUIT ANALYSIS USING SUBCIRCUITS
Notes for course EE1.1 Circuit Analysis 200405 TOPIC 3 CIRCUIT ANALYSIS USING SUBCIRCUITS OBJECTIVES 1) To introduce the Source Transformation 2) To consider the concepts of Linearity and Superposition
More informationChapter 2 Direct Current Circuits
Chapter 2 Direct Current Circuits 2.1 Introduction Nowadays, our lives are increasingly dependent upon the availability of devices that make extensive use of electric circuits. The knowledge of the electrical
More informationElectricity & Magnetism
Electricity & Magnetism D.C. Circuits Marline Kurishingal Note : This chapter includes only D.C. In AS syllabus A.C is not included. Recap... Electrical Circuit Symbols : Draw and interpret circuit diagrams
More informationQUIZ 1 SOLUTION. One way of labeling voltages and currents is shown below.
F 14 1250 QUIZ 1 SOLUTION EX: Find the numerical value of v 2 in the circuit below. Show all work. SOL'N: One method of solution is to use Kirchhoff's and Ohm's laws. The first step in this approach is
More informationLecture #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 informationThevenin 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
More informationChapter 2 Resistive Circuits
1. Sole circuits (i.e., find currents and oltages of interest) by combining resistances in series and parallel. 2. Apply the oltagediision and currentdiision principles. 3. Sole circuits by the nodeoltage
More information