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


 Anabel Stevens
 4 years ago
 Views:
Transcription
1 W03 Analysis of DC Circuits Yrd. Doç. Dr. Aytaç Gören
2 ELK Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits (self and condenser) W04 Transistors and Applications (HBridge) W05 Op Amps and Applications W06 Sensors and Measurement (1/2) W07 Sensors and Measurement (2/2) W08 Midterm W09 Basic Concepts in Digital Electronics (Boolean Algebra, Decimal to binary, gates) W10 Digital Logic Circuits (Gates and Flip Flops) W11 PLC s W12 Microprocessors W13 Data Acquisition, D/A and A/D Converters. 2 Yrd. Doç. Dr. Aytaç Gören
3 ELK 2018 W01 Contents 1. Kirchoffs Circuit Law 2. Basic definitions for circuit analysis 3. Circuit Analysis 1. Mesh Current Analysis 2. Nodal Voltage Analysis 4. Thevenins Theorem 5. Nortons Theorem 6. Transient Analysis 7. Transient Analysis Capacitor 8. Transient Analysis  Inductor Extra Reference for this week: 3 Yrd. Doç. Dr. Aytaç Gören
4 Reminder Yrd. Doç. Dr. Aytaç Gören
5 Reminder Parameter Symbol Measuring Unit Description Voltage Volt V or E Current Ampere I or i Resistance Ohm R or Ω Conductance Siemen G or Capacitance Farad C Charge Coulomb Q Inductance Henry L or H Power Watts W Impedance Ohm Z Frequency Hertz Hz Unit of Electrical Potential V = I R Unit of Electrical Current I = V R Unit of DC Resistance R = V I Reciprocal of Resistance G = 1 R Unit of Capacitance C = Q V Unit of Electrical Charge Q = C V Unit of Inductance V L = L(di/dt) Unit of Power P = V I or I 2 R Unit of AC Resistance Z 2 = R 2 + X 2 Unit of Frequency ƒ = 1 T Yrd. Doç. Dr. Aytaç Gören
6 Reminder Prefix Symbol Multiplier Power of Ten Terra T 1,000,000,000, Giga G 1,000,000, Mega M 1,000, kilo k 1, none none centi c 1/ milli m 1/1, micro µ 1/1,000, nano n 1/1,000,000, pico p 1/1,000,000,000, Yrd. Doç. Dr. Aytaç Gören
7 Yrd. Doç. Dr. Aytaç Gören Kirchoffs Circuit Law In complex circuits such as bridge or T networks, we can not simply use Ohm's Law alone to find the voltages or currents circulating within the circuit. Kirchoff developed a pair or set of rules which deal with the conservation of current and energy within electrical circuits. The rules are commonly known as: Kirchoffs Circuit Laws with one of these laws dealing with current flow around a closed circuit, Kirchoffs Current Law, (KCL) and the other which deals with the voltage around a closed circuit, Kirchoffs Voltage Law, (KVL).
8 Kirchoffs Circuit Law Kirchoffs Current Law or KCL, states that the "total current or charge entering a junction or node is exactly equal to the charge leaving the node as it has no other place to go except to leave, as no charge is lost within the node". (Conservation of Charge) The term Node in an electrical circuit generally refers to a connection or junction of two or more current carrying paths or elements such as cables and components
9 Kirchoffs Circuit Law Kirchoffs Voltage Law or KVL, states that "in any closed loop network, the total voltage around the loop is equal to the sum of all the voltage drops within the same loop" which is also equal to zero. In other words the algebraic sum of all voltages within the loop must be equal to zero.
10 Basic definitions for circuit analysis The terms, used frequently in circuit analysis: Path  a line of connecting elements or sources with no elements or sources included more than once. Node  a node is a junction, connection or terminal within a circuit were two or more circuit elements are connected or joined together giving a connection point between two or more branches. A node is indicated by a dot. Branch  a branch is a single or group of components such as resistors or a source which are connected between two nodes. Loop  a loop is a simple closed path in a circuit in which no circuit element or node is encountered more than once. Mesh  a mesh is a single open loop that does not have a closed path.
11 Example Using Kirchoffs Current Law (KCL) the equations are given as: At node A : I 1 + I 2 = I 3 At node B : I 3 = I 1 + I 2 Using Kirchoffs Voltage Law, KVL the equations are given as; Loop 1 is given as : 10 = R 1 x I 1 + R 3 x I 3 = 10I I 3 Loop 2 is given as : 20 = R 2 x I 2 + R3 x I3 = 20I I 3 Loop 3 is given as : = 10I 120I 2 As I 3 is the sum of I1 + I2 we can rewrite the equations as; 10 = 10I (I 1 + I 2 ) = 50I I 2 20 = 20I (I 1 + I 2 ) = 40I I 2
12 Example I 1 = Amps (Wrong Direction) I 2 = Amps I 3 = I 1 + I 2 At node B : I 3 = I 1 + I = Amps Using Kirchoff's Circuit Laws is as follows: 1. Assume all voltage sources and resistances are given. 2. Label each branch with a branch current. 3. Find Kirchoff's first law equations for each node. 4. Find Kirchoff's second law equations for each of the independent loops of the circuit. 5. Use Linear simultaneous equations as required to find the unknown currents.
13 Circuit Analysis While Kirchoff s Laws give us the basic method for analysing any complex electrical circuit, there are different ways of improving upon this method by using Mesh Current Analysis Nodal Voltage Analysis that results in a lessening of the math's involved and when large networks are involved this reduction in maths can be a big advantage.
14 Circuit Analysis One simple method of reducing the amount of math's involved is to analyse the circuit using Kirchoff's Current Law equations to determine the currents, I 1 and I 2 flowing in the two resistors. Then there is no need to calculate the current I 3 as its just the sum of I 1 and I 2. So Kirchoff's second voltage law simply becomes: Equation No 1 : 10 = 50I I 2 Equation No 2 : 20 = 40I I 2 therefore, one line of math's calculation have been saved.
15 Mesh Current Analysis A more easier method of solving the above circuit is by using Mesh Current Analysis or Loop Analysis which is also sometimes called Maxwell s Circulating Currents method. Instead of labelling the branch currents we need to label each "closed loop" with a circulating current. As a general rule of thumb, only label inside loops in a clockwise direction with circulating currents as the aim is to cover all the elements of the circuit at least once
16 Mesh Current Analysis Kirchoff's voltage law equation can be applied in the same way as before to solve them but the advantage of this method is that it ensures that the information obtained from the circuit equations is the minimum required to solve the circuit as the information is more general and can easily be put into a matrix form.
17 Mesh Current Analysis [ V ] gives the total battery voltage for loop 1 and then loop 2. [ I ] states the names of the loop currents [ R ] is called the resistance matrix.
18 Mesh Current Analysis The basic procedure for solving Mesh Current Analysis equations is as follows: 1. Label all the internal loops with circulating currents. (I 1, I 2,...I L etc) 2. Write the [ L x 1 ] column matrix [ V ] giving the sum of all voltage sources in each loop. 3. Write the [ L x L ] matrix, [ R ] for all the resistances in the circuit as follows; o R 11 = the total resistance in the first loop. o R nn = the total resistance in the nth loop.
19 Nodal Voltage Analysis Nodal Voltage Analysis uses the "Nodal" equations of Kirchoff's first law to find the voltage potentials around the circuit. By adding together all these nodal voltages the net result will be equal to zero. For each node we apply Kirchoff's first law equation, that is: "the currents entering a node are exactly equal in value to the currents leaving the node" then express each current in terms of the voltage across the branch.
20 As V a = 10v and V c = 20v Nodal Voltage Analysis
21 Thevenins Theorem Thevenins Theorem states that "Any linear circuit containing several voltages and resistances can be replaced by just a Single Voltage in series with a Single Resistor". it is possible to simplify any "Linear" circuit, to an equivalent circuit with just a single voltage source in series with a resistance connected to a load as shown below. Thevenins Theorem is especially useful in analyzing power or battery systems and other interconnected circuits where it will have an effect on the adjoining part of the circuit.
22 Thevenins Theorem Example the value of the voltage required Vs is the total voltage across terminals A and B with an open circuit and no load resistor Rs connected. The value of resistor Rs is found by calculating the total resistance at the terminals A and B with all the emf s removed
23 Thevenins Theorem Example The Equivalent Resistance (Rs) The Equivalent Voltage (Vs)
24 Thevenins Theorem Example Thevenins Equivalent circuit is shown below with the 40Ω resistor connected. The basic procedure for solving a circuit using Thevenins Theorem is as follows: 1. Remove the load resistor R L or component concerned. 2. Find R S by shorting all voltage sources or by open circuiting all the current sources. 3. Find V S by the usual circuit analysis methods. 4. Find the current flowing through the load resistor R L.
25 Nortons Theorem Nortons Theorem states that "Any linear circuit containing several energy sources and resistances can be replaced by a single Constant Current generator in parallel with a Single Resistor". The value of this "constant current" is one which would flow if the two output terminals where shorted together while the source resistance would be measured looking back into the terminals, (the same as Thevenin).
26 Nortons Theorem To find the Nortons equivalent of the above circuit we firstly have to remove the centre 40Ω load resistor and short out the terminals A and B to give us the following circuit.
27 Nortons Theorem When the terminals A and B are shorted together the two resistors are connected in parallel across their two respective voltage sources and the currents flowing through each resistor as well as the total short circuit current can now be calculated as:
28 Nortons Theorem The value of the internal resistor Rs is found by calculating the total resistance at the terminals A and B giving us the following circuit.
29 Nortons Theorem Nortons equivalent circuit. The basic procedure for solving a circuit using Nortons Theorem is as follows: 1. Remove the load resistor R L or component concerned. 2. Find R S by shorting all voltage sources or by open circuiting all the current sources. 3. Find I S by placing a shorting link on the output terminals A and B. 4. Find the current flowing through the load resistor R L.
30 Transient Analysis The time constant Electrical or Electronic circuits or systems suffer from some form of "timedelay" between its input and output, when a signal or voltage, either continuous, (DC) or alternating (AC) is firstly applied to it. This delay is generally known as the Time Constant of the circuit and it is the time response of the circuit when a step voltage or signal is firstly applied. The resultant time constant of any circuit or system will mainly depend upon the reactive components either capacitive or inductive.
31 Transient Analysis  Capacitor When an increasing DC voltage is applied to a discharged Capacitor the capacitor draws a charging current and "charges up", and when the voltage is reduced, the capacitor discharges in the opposite direction. Because capacitors are able to store electrical energy they act like small batteries and can store or release the energy as required. The charge on the plates of the capacitor is given as: Q = CV. This charging (storage) and discharging (release) of a capacitors energy is never instant but takes a certain amount of time to occur with the time taken for the capacitor to charge or discharge to within a certain percentage of its maximum supply value being known as its Time Constant (τ).
32 Transient Analysis  Capacitor RC Charging Circuit The figure below shows a capacitor, (C) in series with a resistor, (R) forming a RC Charging Circuitconnected across a DC battery supply (Vs) via a mechanical switch. When the switch is closed, the capacitor will gradually charge up through the resistor until the voltage across it reaches the supply voltage of the battery.
33 Transient Analysis  Capacitor RC Charging Circuit If C is fully "discharged" and the switch (S) is fully open, these are the initial conditions of the circuit, then t = 0, i = 0 and q = 0. When the switch is closed the time begins at t = 0 and current begins to flow into the capacitor via the resistor. Since the initial voltage across the capacitor is zero, (V c = 0) the capacitor appears to be a short circuit and the maximum current flows through the circuit restricted only by the resistor R.
34 Transient Analysis  Capacitor RC Charging Circuit The current no flowing around the circuit is called the Charging Current and is found by using Ohms law as:i = V R /R.
35 Transient Analysis  Capacitor RC Charging Circuit The capacitor now starts to charge up as shown, with the rise in the RC charging curve steeper at the beginning because the charging rate is fastest at the start and then slow down as the capacitor takes on additional charge at a slower rate. As the capacitor charges up, the voltage difference between Vs and Vc reduces, so to does the circuit current, i. Then at the final condition, t =, i = 0, q = Q = CV. Then at infinity the current diminishes to zero, the capacitor acts like an open circuit condition therefore, the voltage drop is entirely across the capacitor.
36 Transient Analysis  Capacitor RC Charging Circuit As the capacitor charges the potential difference across its plates increases with the actual time taken for the charge on the capacitor to reach 63% of its maximum possible voltage, in our curve 0.63Vs being known as the Time Constant, (T) of the circuit. V is related to charge on a capacitor given by the equation, Vc = Q/C, the voltage across the value of the voltage across the capacitor, (Vc) at any instant in time during the charging period is given as:
37 Transient Analysis  Capacitor RC Charging Circuit Vc is the voltage across the capacitor Vs is the supply voltage RC is the time constant of the RC charging circuit After a period equivalent to 4 time constants, (4T) the capacitor in this RC charging circuit is virtually fully charged and the voltage across the capacitor is approx 0.99Vs. The time period taken for the capacitor to reach this 4T point is known as the Transient Period. As the capacitor is fully charged no more current flows in the circuit. The time period after this 5T point is known as the Steady State Period.
38 Transient Analysis  Inductor An inductor could not change instantaneously, but would increase at a constant rate determined by the selfinduced emf in the inductor. In other words, an inductor in a circuit opposes the flow of current, ( i ) through it. An LR Series Circuit consists basically of an inductor of inductance L connected in series with a resistor of resistance R. The resistance R is the DC resistive value of the wire turns or loops that goes into making up the inductors coil.
39 Transient Analysis  Inductor The above LR series circuit is connected across a constant voltage source, (the battery) and a switch. Assume that the switch, S is open until it is closed at a time t = 0, and then remains permanently closed producing a "step response" type voltage input. The current, i begins to flow through the circuit but does not rise rapidly to its maximum value of I max as determined by the ratio of V / R (Ohms Law). This limiting factor is due to the presence of the self induced emf within the inductor as a result of the growth of magnetic flux, (Lenz's Law).
40 Transient Analysis  Inductor After a time the voltage source neutralizes the effect of the self induced emf, the current flow becomes constant and the induced current and field are reduced to zero. Kirchoffs Voltage Law, (KVL) to define the individual voltage drops:
41 Transient Analysis  Inductor Expression for the Current in an LR Series Circuit Since the voltage drop across the resistor, V R is equal to IxR (Ohms Law), it will have the same exponential growth and shape as the current. However, the voltage drop across the inductor, V L will have a value equal to: Ve (Rt/L).
42 Ref for this week: 42 Yrd. Doç. Dr. Aytaç Gören
Yrd. Doç. Dr. Aytaç Gören
H2  AC to DC Yrd. Doç. Dr. Aytaç Gören ELK 2018  Contents W01 Basic Concepts in Electronics W02 AC to DC Conversion W03 Analysis of DC Circuits W04 Transistors and Applications (HBridge) W05 Op Amps
More informationLast time : energy storage elements capacitor.
Last time : energy storage elements capacitor. Charge on plates Energy stored in the form of electric field Passive sign convention Vlt Voltage drop across real capacitor can not change abruptly because
More informationLecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010. Dr.Prapun Suksompong 1 June 16, 2010
Sirindhorn International Institute of Technology Thammasat University School of Information, Computer and Communication Technology Lecture Notes: ECS 203 Basic Electrical Engineering Semester 1/2010 Dr.Prapun
More informationSlide 1 / 26. Inductance. 2011 by Bryan Pflueger
Slide 1 / 26 Inductance 2011 by Bryan Pflueger Slide 2 / 26 Mutual Inductance If two coils of wire are placed near each other and have a current passing through them, they will each induce an emf on one
More informationES250: 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;
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Print ] Eðlisfræði 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has
More informationBasic Laws Circuit Theorems Methods of Network Analysis NonLinear Devices and Simulation Models
EE Modul 1: Electric Circuits Theory Basic Laws Circuit Theorems Methods of Network Analysis NonLinear Devices and Simulation Models EE Modul 1: Electric Circuits Theory Current, Voltage, Impedance Ohm
More informationDiodes have an arrow showing the direction of the flow.
The Big Idea Modern circuitry depends on much more than just resistors and capacitors. The circuits in your computer, cell phone, Ipod depend on circuit elements called diodes, inductors, transistors,
More informationEE301 Lesson 14 Reading: 10.110.4, 10.1110.12, 11.111.4 and 11.1111.13
CAPACITORS AND INDUCTORS Learning Objectives EE301 Lesson 14 a. Define capacitance and state its symbol and unit of measurement. b. Predict the capacitance of a parallel plate capacitor. c. Analyze how
More informationCircuits with inductors and alternating currents. Chapter 20 #45, 46, 47, 49
Circuits with inductors and alternating currents Chapter 20 #45, 46, 47, 49 RL circuits Ch. 20 (last section) Symbol for inductor looks like a spring. An inductor is a circuit element that has a large
More informationThe Time Constant of an RC Circuit
The Time Constant of an RC Circuit 1 Objectives 1. To determine the time constant of an RC Circuit, and 2. To determine the capacitance of an unknown capacitor. 2 Introduction What the heck is a capacitor?
More informationInduced voltages and Inductance Faraday s Law
Induced voltages and Inductance Faraday s Law concept #1, 4, 5, 8, 13 Problem # 1, 3, 4, 5, 6, 9, 10, 13, 15, 24, 23, 25, 31, 32a, 34, 37, 41, 43, 51, 61 Last chapter we saw that a current produces a magnetic
More informationPhysics 2102 Lecture 19. Physics 2102
Physics 2102 Jonathan Dowling Physics 2102 Lecture 19 Ch 30: Inductors and RL Circuits Nikolai Tesla What are we going to learn? A road map Electric charge Electric force on other electric charges Electric
More informationFirst Year (Electrical & Electronics Engineering)
Z PRACTICAL WORK BOOK For The Course EE113 Basic Electrical Engineering For First Year (Electrical & Electronics Engineering) Name of Student: Class: Batch : Discipline: Class Roll No.: Examination Seat
More informationObjectives. Capacitors 262 CHAPTER 5 ENERGY
Objectives Describe a capacitor. Explain how a capacitor stores energy. Define capacitance. Calculate the electrical energy stored in a capacitor. Describe an inductor. Explain how an inductor stores energy.
More informationCircuit 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
More informationSERIESPARALLEL DC CIRCUITS
Name: Date: Course and Section: Instructor: EXPERIMENT 1 SERIESPARALLEL DC CIRCUITS OBJECTIVES 1. Test the theoretical analysis of seriesparallel networks through direct measurements. 2. Improve skills
More information= (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
More information1. Introduction and Chapter Objectives
Real Analog Circuits 1 Chapter 1: Circuit Analysis Fundamentals 1. Introduction and Chapter Objectives In this chapter, we introduce all fundamental concepts associated with circuit analysis. Electrical
More informationNodal 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
More informationCircuits. The light bulbs in the circuits below are identical. Which configuration produces more light? (a) circuit I (b) circuit II (c) both the same
Circuits The light bulbs in the circuits below are identical. Which configuration produces more light? (a) circuit I (b) circuit II (c) both the same Circuit II has ½ current of each branch of circuit
More informationEnergy in Electrical Systems. Overview
Energy in Electrical Systems Overview How can Potential Energy be stored in electrical systems? Battery Stored as chemical energy then transformed to electrical energy on usage Water behind a dam Water
More informationLecture 24. Inductance and Switching Power Supplies (how your solar charger voltage converter works)
Lecture 24 Inductance and Switching Power Supplies (how your solar charger voltage converter works) Copyright 2014 by Mark Horowitz 1 Roadmap: How Does This Work? 2 Processor Board 3 More Detailed Roadmap
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 Caution: The symbol E is used interchangeably for energy and EMF. 1) DATA: V b = 5.0 V, = 155 Ω, L = 8.400 10 2 H. In the diagram above, what is the voltage across the
More informationObjectives. Electric Current
Objectives Define electrical current as a rate. Describe what is measured by ammeters and voltmeters. Explain how to connect an ammeter and a voltmeter in an electrical circuit. Explain why electrons travel
More informationSeries and Parallel Circuits
Series and Parallel Circuits DirectCurrent Series Circuits A series circuit is a circuit in which the components are connected in a line, one after the other, like railroad cars on a single track. There
More informationBASIC ELECTRONICS AC CIRCUIT ANALYSIS. December 2011
AM 5202 BASIC ELECTRONICS AC CIRCUIT ANALYSIS December 2011 DISTRIBUTION RESTRICTION: Approved for Pubic Release. Distribution is unlimited. DEPARTMENT OF THE ARMY MILITARY AUXILIARY RADIO SYSTEM FORT
More informationSeries 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
More informationEdmund Li. Where is defined as the mutual inductance between and and has the SI units of Henries (H).
INDUCTANCE MUTUAL INDUCTANCE If we consider two neighbouring closed loops and with bounding surfaces respectively then a current through will create a magnetic field which will link with as the flux passes
More informationChapter 11. Inductors ISU EE. C.Y. Lee
Chapter 11 Inductors Objectives Describe the basic structure and characteristics of an inductor Discuss various types of inductors Analyze series inductors Analyze parallel inductors Analyze inductive
More informationUnit/Standard Number. High School Graduation Years 2010, 2011 and 2012
1 Secondary Task List 100 SAFETY 101 Demonstrate an understanding of State and School safety regulations. 102 Practice safety techniques for electronics work. 103 Demonstrate an understanding of proper
More information2. A conductor of length 2m moves at 4m/s at 30 to a uniform magnetic field of 0.1T. Which one of the following gives the e.m.f. generated?
Extra Questions  2 1. A straight length of wire moves through a uniform magnetic field. The e.m.f. produced across the ends of the wire will be maximum if it moves: a) along the lines of magnetic flux
More informationChapter 1. Fundamental Electrical Concepts
Chapter 1 Fundamental Electrical Concepts Charge, current, voltage, power circuits, nodes, branches Branch and node voltages, Kirchhoff Laws Basic circuit elements, combinations 01 fundamental 1 1.3 Electrical
More informationDepartment 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,
More informationAircraft Electrical System
Chapter 9 Aircraft Electrical System Introduction The satisfactory performance of any modern aircraft depends to a very great degree on the continuing reliability of electrical systems and subsystems.
More informationPeople s Physics Book
The Big Ideas: The name electric current is given to the phenomenon that occurs when an electric field moves down a wire at close to the speed of light. Voltage is the electrical energy density (energy
More information12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its selfinductance?
12. The current in an inductor is changing at the rate of 100 A/s, and the inductor emf is 40 V. What is its selfinductance? From Equation 325, L = E=(dI =dt) = 40 V=(100 A/s) = 0.4 H. 15. A cardboard
More informationThree phase circuits
Three phase circuits THREE PHASE CIRCUITS THREEPHASE ADVANTAGES 1. The horsepower rating of threephase motors and the kva rating of threephase transformers are 150% greater than singlephase motors
More informationExperiment #5, Series and Parallel Circuits, Kirchhoff s Laws
Physics 182 Summer 2013 Experiment #5 1 Experiment #5, Series and Parallel Circuits, Kirchhoff s Laws 1 Purpose Our purpose is to explore and validate Kirchhoff s laws as a way to better understanding
More informationExample: 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
More informationInductors & Inductance. Electronic Components
Electronic Components Induction In 1824, Oersted discovered that current passing though a coil created a magnetic field capable of shifting a compass needle. Seven years later, Faraday and Henry discovered
More informationMeasurement of Capacitance
Measurement of Capacitance PreLab Questions Page Name: Class: Roster Number: Instructor:. A capacitor is used to store. 2. What is the SI unit for capacitance? 3. A capacitor basically consists of two
More informationLine Reactors and AC Drives
Line Reactors and AC Drives Rockwell Automation Mequon Wisconsin Quite often, line and load reactors are installed on AC drives without a solid understanding of why or what the positive and negative consequences
More informationDiode Applications. by Kenneth A. Kuhn Sept. 1, 2008. This note illustrates some common applications of diodes.
by Kenneth A. Kuhn Sept. 1, 2008 This note illustrates some common applications of diodes. Power supply applications A common application for diodes is converting AC to DC. Although halfwave rectification
More informationInductors in AC Circuits
Inductors in AC Circuits Name Section Resistors, inductors, and capacitors all have the effect of modifying the size of the current in an AC circuit and the time at which the current reaches its maximum
More information2.1 Introduction. 2.2 Terms and definitions
.1 Introduction An important step in the procedure for solving any circuit problem consists first in selecting a number of independent branch currents as (known as loop currents or mesh currents) variables,
More informationApprentice Telecommunications Technician Test (CTT) Study Guide
Apprentice Telecommunications Technician Test (CTT) Study Guide 1 05/2014 Study Guide for Pacific Gas & Electric Company Apprentice Telecommunications Technician Qualifying Test (CTT) About the Test The
More informationSCHWEITZER ENGINEERING LABORATORIES, COMERCIAL LTDA.
Pocket book of Electrical Engineering Formulas Content 1. Elementary Algebra and Geometry 1. Fundamental Properties (real numbers) 1 2. Exponents 2 3. Fractional Exponents 2 4. Irrational Exponents 2 5.
More informationContent Map For Career & Technology
Content Strand: Applied Academics CTET11 analysis of electronic A. Fractions and decimals B. Powers of 10 and engineering notation C. Formula based problem solutions D. Powers and roots E. Linear equations
More informationLAB2 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
More informationJ.L. Kirtley Jr. Electric network theory deals with two primitive quantities, which we will refer to as: 1. Potential (or voltage), and
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.061 Introduction to Power Systems Class Notes Chapter 1: eiew of Network Theory J.L. Kirtley Jr. 1 Introduction
More informationDOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4
DOEHDBK1011/392 JUNE 1992 DOE FUNDAMENTALS HANDBOOK ELECTRICAL SCIENCE Volume 3 of 4 U.S. Department of Energy Washington, D.C. 20585 FSC6910 Distribution Statement A. Approved for public release;
More informationExercises on Voltage, Capacitance and Circuits. A d = (8.85 10 12 ) π(0.05)2 = 6.95 10 11 F
Exercises on Voltage, Capacitance and Circuits Exercise 1.1 Instead of buying a capacitor, you decide to make one. Your capacitor consists of two circular metal plates, each with a radius of 5 cm. The
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT
EDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 5  ELECTRICAL AND ELECTRONIC PRINCIPLES NQF LEVEL 3 OUTCOME 4  ALTERNATING CURRENT 4 Understand singlephase alternating current (ac) theory Single phase AC
More informationInductors. AC Theory. Module 3
Module 3 AC Theory What you ll learn in Module 3. Section 3.1 Electromagnetic Induction. Magnetic Fields around Conductors. The Solenoid. Section 3.2 Inductance & Back e.m.f. The Unit of Inductance. Factors
More informationVOLTAGE REGULATOR AND PARALLEL OPERATION
VOLTAGE REGULATOR AND PARALLEL OPERATION Generator sets are operated in parallel to improve fuel economy and reliability of the power supply. Economy is improved with multiple paralleled generators by
More informationELECTRICAL ENGINEERING Vol. I  Direct Current and Alternating Current Systems  N. Rajkumar DIRECT CURRENT AND ALTERNATING CURRENT SYSTEMS
DIRECT CURRENT AND ALTERNATING CURRENT SYSTEMS N. Rajkumar, Research Fellow, Energy Systems Group, City University Northampton Square, London EC1V 0HB, UK Keywords: Electrical energy, direct current, alternating
More informationSeries and Parallel Circuits
Direct Current (DC) Direct current (DC) is the unidirectional flow of electric charge. The term DC is used to refer to power systems that use refer to the constant (not changing with time), mean (average)
More informationChapter 7 DirectCurrent Circuits
Chapter 7 DirectCurrent Circuits 7. Introduction...77. Electromotive Force...73 7.3 Resistors in Series and in Parallel...75 7.4 Kirchhoff s Circuit Rules...77 7.5 VoltageCurrent Measurements...79
More informationBJT AC Analysis. by Kenneth A. Kuhn Oct. 20, 2001, rev Aug. 31, 2008
by Kenneth A. Kuhn Oct. 20, 2001, rev Aug. 31, 2008 Introduction This note will discuss AC analysis using the beta, re transistor model shown in Figure 1 for the three types of amplifiers: commonemitter,
More informationProblem Solving 8: RC and LR Circuits
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics Problem Solving 8: RC and LR Circuits Section Table and Group (e.g. L04 3C ) Names Hand in one copy per group at the end of the Friday Problem
More informationCHAPTER 28 ELECTRIC CIRCUITS
CHAPTER 8 ELECTRIC CIRCUITS 1. Sketch a circuit diagram for a circuit that includes a resistor R 1 connected to the positive terminal of a battery, a pair of parallel resistors R and R connected to the
More informationInductance. Motors. Generators
Inductance Motors Generators Selfinductance Selfinductance occurs when the changing flux through a circuit arises from the circuit itself. As the current increases, the magnetic flux through a loop due
More informationEE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits
EE 1202 Experiment #4 Capacitors, Inductors, and Transient Circuits 1. Introduction and Goal: Exploring transient behavior due to inductors and capacitors in DC circuits; gaining experience with lab instruments.
More informationOutline. Systems and Signals 214 / 244 & Energy Systems 244 / 344. Ideal Inductor. Ideal Inductor (cont... )
Outline Systems and Signals 214 / 244 & Energy Systems 244 / 344 Inductance, Leakage Inductance, Mutual Inductance & Transformers 1 Inductor revision Ideal Inductor NonIdeal Inductor Dr. P.J. Randewijk
More informationDirection of Induced Current
Direction of Induced Current Bar magnet moves through coil Current induced in coil A S N v Reverse pole Induced current changes sign B N S v v Coil moves past fixed bar magnet Current induced in coil as
More informationIntroduction to Electricity & Magnetism. Dr Lisa JardineWright Cavendish Laboratory
Introduction to Electricity & Magnetism Dr Lisa JardineWright Cavendish Laboratory Examples of uses of electricity Christmas lights Cars Electronic devices Human body Electricity? Electricity is the presence
More informationChapter 30 Inductance
Chapter 30 Inductance  Mutual Inductance  SelfInductance and Inductors  MagneticField Energy  The R Circuit  The C Circuit  The RC Series Circuit . Mutual Inductance  A changing current in
More informationCapacitors in Circuits
apacitors in ircuits apacitors store energy in the electric field E field created by the stored charge In circuit apacitor may be absorbing energy Thus causes circuit current to be reduced Effectively
More informationREPORT ON CANDIDATES WORK IN THE CARIBBEAN ADVANCED PROFICIENCY EXAMINATION MAY/JUNE 2008 ELECTRICAL AND ELECTRONIC TECHNOLOGY (TRINIDAD AND TOBAGO)
CARIBBEAN EXAMINATIONS COUNCIL REPORT ON CANDIDATES WORK IN THE CARIBBEAN ADVANCED PROFICIENCY EXAMINATION MAY/JUNE 2008 ELECTRICAL AND ELECTRONIC TECHNOLOGY (TRINIDAD AND TOBAGO) Copyright 2008 Caribbean
More informationMeshCurrent Method (Loop Analysis)
MeshCurrent Method (Loop Analysis) Nodal analysis was developed by applying KCL at each nonreference node. MeshCurrent method is developed by applying KVL around meshes in the circuit. A mesh is a loop
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 informationLecture  4 Diode Rectifier Circuits
Basic Electronics (Module 1 Semiconductor Diodes) Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Lecture  4 Diode Rectifier Circuits
More informationAP Physics Electricity and Magnetism #4 Electrical Circuits, Kirchoff s Rules
Name Period AP Physics Electricity and Magnetism #4 Electrical Circuits, Kirchoff s Rules Dr. Campbell 1. Four 240 Ω light bulbs are connected in series. What is the total resistance of the circuit? What
More informationDEGREE: Bachelor in Biomedical Engineering YEAR: 2 TERM: 2 WEEKLY PLANNING
SESSION WEEK COURSE: Electronic Technology in Biomedicine DEGREE: Bachelor in Biomedical Engineering YEAR: 2 TERM: 2 WEEKLY PLANNING DESCRIPTION GROUPS (mark X) SPECIAL ROOM FOR SESSION (Computer class
More informationChapter 12: Three Phase Circuits
Chapter 12: Three Phase Circuits 12.1 What Is a Three Phase Circuit? 12.2 Balance Three Phase Voltages 12.3 Balance Three Phase Y to Y Connection 12.4 Other Balance Three Phase Connections 12.5 Power in
More informationMutual Inductance and Transformers F3 3. r L = ω o
utual Inductance and Transformers F3 1 utual Inductance & Transformers If a current, i 1, flows in a coil or circuit then it produces a magnetic field. Some of the magnetic flux may link a second coil
More informationUsing the Impedance Method
Using the Impedance Method The impedance method allows us to completely eliminate the differential equation approach for the determination of the response of circuits. In fact the impedance method even
More informationHomework #11 20311721 Physics 2 for Students of Mechanical Engineering
Homework #11 20311721 Physics 2 for Students of Mechanical Engineering 2. A circular coil has a 10.3 cm radius and consists of 34 closely wound turns of wire. An externally produced magnetic field of
More informationAC Generators. Basic Generator
AC Generators Basic Generator A basic generator consists of a magnetic field, an armature, slip rings, brushes and a resistive load. The magnetic field is usually an electromagnet. An armature is any number
More informationCritical thinfilm processes such as deposition and etching take place in a vacuum
WHITEPAPER INTRODUCING POWER SUPPLIES AND PLASMA Critical thinfilm processes such as deposition and etching take place in a vacuum SYSTEMS chamber in the presence of a plasma. A plasma is an electrically
More informationULRASONIC GENERATOR POWER CIRCUITRY. Will it fit on PC board
ULRASONIC GENERATOR POWER CIRCUITRY Will it fit on PC board MAJOR COMPONENTS HIGH POWER FACTOR RECTIFIER RECTIFIES POWER LINE RAIL SUPPLY SETS VOLTAGE AMPLITUDE INVERTER INVERTS RAIL VOLTAGE FILTER FILTERS
More informationEpisode 126: Capacitance and the equation C =Q/V
Episode 126: Capacitance and the equation C =Q/V Having established that there is charge on each capacitor plate, the next stage is to establish the relationship between charge and potential difference
More informationRLC Resonant Circuits
C esonant Circuits Andrew McHutchon April 20, 203 Capacitors and Inductors There is a lot of inconsistency when it comes to dealing with reactances of complex components. The format followed in this document
More information= V peak 2 = 0.707V peak
BASIC ELECTRONICS  RECTIFICATION AND FILTERING PURPOSE Suppose that you wanted to build a simple DC electronic power supply, which operated off of an AC input (e.g., something you might plug into a standard
More informationARRL Morse Code Oscillator, How It Works By: Mark Spencer, WA8SME
The national association for AMATEUR RADIO ARRL Morse Code Oscillator, How It Works By: Mark Spencer, WA8SME This supplement is intended for use with the ARRL Morse Code Oscillator kit, sold separately.
More informationChapter 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
More informationImpedance Matching and Matching Networks. Valentin Todorow, December, 2009
Impedance Matching and Matching Networks Valentin Todorow, December, 2009 RF for Plasma Processing  Definition of RF What is RF? The IEEE Standard Dictionary of Electrical and Electronics Terms defines
More informationCreating a Usable Power Supply from a Solar Panel
Creating a Usable Power Supply from a Solar Panel An exploration in DC DC converters By Kathleen Ellis Advised by Dr. Derin Sherman Department of Physics, Cornell College November 21, 2012 Introduction
More informationCopyright 2011 Linear Technology. All rights reserved.
Copyright. All rights reserved. LTspice IV Getting Started Guide 2 Benefits of Using LTspice IV Stable SPICE circuit simulation with Unlimited number of nodes Schematic/symbol editor Waveform viewer Library
More informationSeries 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 endtoend. A parallel
More information45. The peak value of an alternating current in a 1500W device is 5.4 A. What is the rms voltage across?
PHYS Practice Problems hapters 8 hapter 8. 45. The peak value of an alternating current in a 5W device is 5.4 A. What is the rms voltage across? The power and current can be used to find the peak voltage,
More informationTable of Contents. The Basics of Electricity 2. Using a Digital Multimeter 4. Testing Voltage 8. Testing Current 10. Testing Resistance 12
Table of Contents The Basics of Electricity 2 Using a Digital Multimeter 4 IDEAL Digital Multimeters An Introduction The Basics of Digital Multimeters is designed to give you a fundamental knowledge of
More informationChapter 7. DC Circuits
Chapter 7 DC Circuits 7.1 Introduction... 73 Example 7.1.1: Junctions, branches and loops... 74 7.2 Electromotive Force... 75 7.3 Electrical Energy and Power... 79 7.4 Resistors in Series and in Parallel...
More informationLecture 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
More informationWhat is a multimeter?
What is a multimeter? A multimeter is a devise used to measure voltage, resistance and current in electronics & electrical equipment It is also used to test continuity between to 2 points to verify if
More informationBasic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati
Basic Electronics Prof. Dr. Chitralekha Mahanta Department of Electronics and Communication Engineering Indian Institute of Technology, Guwahati Module: 2 Bipolar Junction Transistors Lecture2 Transistor
More informationTECH TIP # 37 SOLVING SERIES/PARALLEL CIRCUITS THREE LAWS  SERIES CIRCUITS LAW # 1  THE SAME CURRENT FLOWS THROUGH ALL PARTS OF THE CIRCUIT
TECH TIP # 37 SOLVING SERIES/PARALLEL CIRCUITS Please study this Tech Tip along with assignment 4 in Basic Electricity. Parallel circuits differ from series circuits in that the current divides into a
More informationThe 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 shortcut methods. Sometimes
More informationSingle Transistor FM Transmitter Design
Single Transistor FM Transmitter Design In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency. FM is commonly used at VHF radio frequencies for
More information