Chapter 10 Objectives
|
|
- Carmella Marshall
- 5 years ago
- Views:
Transcription
1 Chapter 10 Engr8 Circuit Analysis Dr Curtis Nelson Chapter 10 Objectives Understand the following AC power concepts: Instantaneous power; Average power; Root Mean Squared (RMS) value; Reactive power; Coplex power; Power factor; Power factor correction. Understand how axiu real power is calculated and delivered to a load in an AC circuit. Engr8 - Chapter 10, Nilsson 10e 1
2 Instantaneous Power Instantaneous power is the power easured at any given instant in tie. In DC circuits, power is easured in watts as: v P vi i R R In AC circuits, voltage and current are tie-varying, so instantaneous power (also easured in watts) is tievarying. Power is still easured as: v P vi i R R Instantaneous AC Power p (t) v(t) i(t) In an AC circuit, voltage and current are expressed in general for as: v t) V cos( w t + q ) ( v i t) I cos( w t + q ) ( i Instantaneous power is then: p( t) VI cos( w t + qv)cos( wt + qi) Engr8 - Chapter 10, Nilsson 10e
3 Instantaneous Power - continued p( t) VI cos( w t + qv)cos( wt + qi) Using the trig identity cos( x )cos( y) 0.5cos( x - y) + 0.5cos( x + y) it can be shown that instantaneous power is: VI p t) ( v i v i {cos( q -q ) + cos(wt + q + q )} Note that the instantaneous power contains a constant ter as well as a coponent that varies with tie at twice the input frequency. Instantaneous Power Plot VI p t) ( v i v i {cos( q -q ) + cos(wt + q + q )} Engr8 - Chapter 10, Nilsson 10e 3
4 Instantaneous Power - continued VI p t) ( v i v i {cos( q -q ) + cos(wt + q + q )} The equation above can be further anipulated as follows: cos( a+ b) cosacos b - sina sinb cos( wt + q - q ) cos( q - q )cos( wt) -sin( q - q )sin( wt) v i v i v i pt ( ) V I cos( q ) cos( )cos( ) v - q + V I q v - q wt - V I sin( qv - q )sin( wt ) i i i Note that the instantaneous power still contains a constant ter as well as coponents that vary with tie at twice the input frequency. Instantaneous Power Plot pt ( ) V I cos( q ) cos( )cos( ) v - q + V I q v - q wt - V I sin( qv - q )sin( wt ) i i i Engr8 - Chapter 10, Nilsson 10e 4
5 Instantaneous vs. Average Power While instantaneous power is an interesting atheatical developent for AC circuits, it is not all that useful for deterining how uch power a circuit generates or absorbs since it varies with tie. Average Power is a better indicator of power in AC circuits. Average power is soeties called real power, because it describes the power in a circuit that is transfored fro electric to nonelectric energy, such as heat. Average Power The average power over an arbitrary interval fro t 1 to t is: where p(t) is the instantaneous power. When the power is periodic with period T, the average power can be calculated over any one period as: Engr8 - Chapter 10, Nilsson 10e 5
6 Average Power - continued pt ( ) V I cos( q ) cos( )cos( ) v - q + V I q v - q wt - V I sin( qv - q )sin( wt ) i i i To calculate average power, note that the last two ters in the equation above will integrate to zero since the average value of sin and cosine signals over one period is zero. Therefore, average power in AC circuits is: P AVG VI cos( q -q ) v i Exaple - Power Calculations Calculate the instantaneous and average power if: v(t) 80cos(10t + 0º)V i(t) 15cos(10t + 60º)A P inst (t) cos(0t + 80º)W P avg 459.6W Engr8 - Chapter 10, Nilsson 10e 6
7 Average Power for Circuit Eleents P AVG VI cos( q -q ) v i Since the voltage and current are in phase across a resistor, the average power absorbed by the resistor R is: P R, AVG 1 V R The average power absorbed by a purely reactive eleent is zero, since the current and voltage are 90 degrees out of phase: P C P, AVG L, AVG 0 Exaple - Average Power Calculate the average power absorbed by the resistor and inductor and find the average power supplied by the voltage source. P R 9.6W absorbed P L 0W P Source 9.6W delivered Engr8 - Chapter 10, Nilsson 10e 7
8 Effective or RMS Value Soeties using average AC power values can be confusing. For instance, the average DC power absorbed by a resistor is P V M I M while the average AC power is P V M I M /. By introducing a new quantity called effective value, the forulas for the average power absorbed by a resistor can be ade the sae for dc, sinusoidal, or any general periodic wavefor. The effective value of a periodic voltage is the DC voltage that delivers the sae average power to a resistor as the periodic AC voltage. Effective or RMS Value For any periodic function x(t), the effective or root ean squared (rs) value, is given by: X rs 1 T ò T 0 x dt Engr8 - Chapter 10, Nilsson 10e 8
9 Effective or RMS Value For exaple, the effective value of I I cos t is 1 T Irs I cos tdt T ò w 0 I T 1 Irs (1 cos t)dt T ò + w 0 Average power can then be written in two ways: P AVG P AVG V VI rs I rs cos( q -q ) v I cos( q -q ) v i i Effective Values of Coon Wavefors Engr8 - Chapter 10, Nilsson 10e 9
10 Textbook Proble Nilsson 10 th a) Find the rs value of the periodic voltage shown in the figure below. b) If the voltage is applied across a 40Ω resistor, find the average power dissipated by the resistor. V rs 8.8V RMS P 0W Coplex Power The average power in capacitors and inductors 0 because voltage and current have a 90º phase difference. However, there is still voltage across, and current through, inductors and capacitors so they are part of the overall power picture. We now investigate the part that inductors and capacitors play, leading us to define a new quantity called Coplex Power. Engr8 - Chapter 10, Nilsson 10e 10
11 Coplex Power - Triangle Coplex power contains both a real part (average power) and an iaginary part (reactive power) that together are represented in a power triangle. Coplex Power - Units Engr8 - Chapter 10, Nilsson 10e 11
12 Coplex Power The Equations P AVG V RMS I RMS cos(θ V - θ i ) P REACTIVE V RMS I RMS sin(θ V - θ i ) P APPARENT V RMS I RMS watts volt-aps-reactive volt-aps Coplex Power The Angle θ V - θ i is known as the Power Factor Angle. cos(θ V - θ i ) is known as the Power Factor (PF) For a purely resistive load, PF1; For a purely reactive load, PF0; For any practical circuit, 0 PF 1. Engr8 - Chapter 10, Nilsson 10e 1
13 Apparent Power & Power Factor Power factor is also defined as: average power P PF apparent power V I eff avg eff Coplex Power and Ipedance Triangles S Q IZI X q P q R Power triangle Ipedance triangle P pf cosq S R Z Engr8 - Chapter 10, Nilsson 10e 13
14 Exaple: Power Factor Calculate the power factor of the circuit below as seen by the source. What is the average power supplied by the source? pf (lagging) P AVG 118W Leading and Lagging Power Factor pf is lagging if the current lags the voltage (θ V - θ I is positive like in an inductive load); pf is leading if the current leads the voltage (θ V - θ I is negative like in a capacitive load). Engr8 - Chapter 10, Nilsson 10e 14
15 Exaple Proble Find the average power delivered to each of the two loads, the apparent power supplied by the source, and the power factor of the cobined loads. P avg 88 W P avg1 144 W P app S 70 VA PF 0.6 (lagging) Textbook Proble Nilsson 10 th For i g 50 + j0 A (rs), find the average and reactive power for the current source and state whether it is absorbing or delivering this power. P AVG W (delivering) P REAC 5.0 VAR (absorbing) Engr8 - Chapter 10, Nilsson 10e 15
16 Textbook Proble Nilsson 10 th Find the average power, the reactive power, and the apparent power absorbed by the load if v g 150cos50t V. P AVG 180 W P REAC 90 VAR P APP j90 VA More on Coplex Power S P + jq V rs I rs " V - " I V rs " V I rs -" I V rs I* rs Engr8 - Chapter 10, Nilsson 10e 16
17 Coplex Power - Suary Real (Average) power: Reactive power: Apparent power: Coplex power: P Re(S) Scos( q - q ) Watts Q I(S) Ssin( q - q ) VAR S + S VrsIrs P Q VA S P jq V I * + RMS RMS VA Q 0 for resistive loads (unity power factor); Q < 0 for capacitive loads (leading power factor); Q > 0 for inductive loads (lagging power factor). v v i i Exaple - Apparent Power and Power Factor A series connected RC load draws a current of when the applied voltage is i ( t) 4cos(100pt + 10 ) A v ( t) 10cos(100pt - 0 ) V Find the apparent power and the power factor of the load and deterine the eleent values that for the load. S 40 V pf (leading) C 1.µF R 6.0Ω Engr8 - Chapter 10, Nilsson 10e 17
18 Power Factor Correction The process of increasing the power factor without altering the voltage or current to the original load is known as power factor correction. Most loads are inductive. The power factor of the load can be iproved (to ake it closer to unity) by installing a capacitor in parallel with an inductive load. a) Original inductive load b) Inductive load with iproved power factor Power Factor Correction Capacitors Engr8 - Chapter 10, Nilsson 10e 18
19 Power Factor Correction Capacitors Power Factor Correction by Power Triangle The triangle below shows that the reactive power (Q 1 ) in a large inductive load can be reduced by an aount (Q C ) by adding a capacitor in parallel to the load. Q 1 Ptan θ 1 Q Ptan θ Q C Q 1 Q P(tan θ 1 tan θ ) Engr8 - Chapter 10, Nilsson 10e 19
20 Power Factor Correction by Power Triangle But Q C is also the aount of reactive power the capacitor ust provide: Q C V X rs C wcv rs The value of required parallel capacitance is then: Q C wv C rs P(tan q - tan q ) 1 wv rs Exaple - PF Correction #1 When connected to a 10 V RMS, 60Hz power line a load absorbs 4kW at a lagging power factor of 0.8. Find the value of capacitance necessary to raise the pf to 0.95 C 310.4µF Engr8 - Chapter 10, Nilsson 10e 0
21 Exaple - PF Correction # Find the value of parallel capacitance needed to correct a load of 140kVAR at 0.85 lagging pf to unity pf. Assue that the load is supplied by a 110V RMS, 60Hz line. C 30,691µF Textbook Proble Nilsson 10 th A group of sall appliances on a 60 Hz syste requires 0 kva at 0.85 pf lagging when operated at 15 V rs. The ipedance of the feeder supplying the appliances is j0.08 Ω. Find: a) The rs value of the voltage at the source end of the feeder. b) The average power loss in the feeder. V S V RMS P REAC 56 W Engr8 - Chapter 10, Nilsson 10e 1
22 Power Generation Hydro-Power Generation Solar Power Nuclear Power Generation Fossil Fuel Generation Wave Power Generation Gravity Light Project Maxiu Power Transfer An independent voltage source in series with an ipedance Z th delivers a axiu average power to that load ipedance Z L when it is the conjugate of Z th. Z L Z th * Engr8 - Chapter 10, Nilsson 10e
23 Maxiu Average Power Transfer In rectangular for, the Thevenin ipedance and load ipedances are: Z Z Th L R R L Th + jx + jx For axiu average power transfer, the load ipedance Z L ust be equal to the coplex conjugate of the Thevenin ipedance Z Th (i.e. the iaginary parts of the ipedance cancel each other out): Z R + jx R - jx Z L L L Z Z L Th * Th L Th Th * Th Maxiu Average Power Transfer When Z L Z * TH, the axiu power delivered to the load is: P ax V 4R TH, RMS Th If the load is purely resistive, then the value of R L that axiizes P L is the agnitude of the Thevenin ipedance. Note that the 4 factor in the denoinator above becoes 8 if the voltage is expressed as an average or peak value. Engr8 - Chapter 10, Nilsson 10e 3
24 Exaple: Maxiu Average Power Deterine the load ipedance Z L that axiizes the average power drawn fro the circuit below. Calculate the axiu average power. Z L * Z Th j W Pax. 3675W Chapter 10 Suary Understand the following AC power concepts: Instantaneous power; Average power; Root Mean Squared (RMS) value; Reactive power; Coplex power; Power factor; Power factor correction. Understand how axiu real power is calculated and delivered to a load in an AC circuit. Engr8 - Chapter 10, Nilsson 10e 4
Chapter 10 ACSS Power
Objectives: Power concepts: instantaneous power, average power, reactive power, coplex power, power factor Relationships aong power concepts the power triangle Balancing power in AC circuits Condition
More informationChapter 28: Alternating Current
hapter 8: Alternating urrent Phasors and Alternating urrents Alternating current (A current) urrent which varies sinusoidally in tie is called alternating current (A) as opposed to direct current (D).
More informationAC Power Analysis. Chapter Objectives:
AC Power Analysis Chapter Objectives: Know the difference between instantaneous power and average power Learn the AC version of maximum power transfer theorem Learn about the concepts of effective or value
More informationLecture 11 - AC Power
- AC Power 11/17/2015 Reading: Chapter 11 1 Outline Instantaneous power Complex power Average (real) power Reactive power Apparent power Maximum power transfer Power factor correction 2 Power in AC Circuits
More informationSinusoidal Response of RLC Circuits
Sinusoidal Response of RLC Circuits Series RL circuit Series RC circuit Series RLC circuit Parallel RL circuit Parallel RC circuit R-L Series Circuit R-L Series Circuit R-L Series Circuit Instantaneous
More information11. AC Circuit Power Analysis
. AC Circuit Power Analysis Often an integral part of circuit analysis is the determination of either power delivered or power absorbed (or both). In this chapter First, we begin by considering instantaneous
More informationBEF BEF Chapter 2. Outline BASIC PRINCIPLES 09/10/2013. Introduction. Phasor Representation. Complex Power Triangle.
BEF 5503 BEF 5503 Chapter BASC PRNCPLES Outline 1 3 4 5 6 7 8 9 ntroduction Phasor Representation Coplex Power Triangle Power Factor Coplex Power in AC Single Phase Circuits Coplex Power in Balanced Three-Phase
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 informationConsider a simple RC circuit. We might like to know how much power is being supplied by the source. We probably need to find the current.
AC power Consider a simple RC circuit We might like to know how much power is being supplied by the source We probably need to find the current R 10! R 10! is VS Vmcosωt Vm 10 V f 60 Hz V m 10 V C 150
More informationEXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection
OBJECT: To examine the power distribution on (R, L, C) series circuit. APPARATUS 1-signal function generator 2- Oscilloscope, A.V.O meter 3- Resisters & inductor &capacitor THEORY the following form for
More information12. Introduction and Chapter Objectives
Real Analog - Circuits 1 Chapter 1: Steady-State Sinusoidal Power 1. Introduction and Chapter Objectives In this chapter we will address the issue of power transmission via sinusoidal or AC) signals. This
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 0: Sinusoidal Steady-State Analysis Sinusoidal Sources If a circuit is driven by a sinusoidal source, after 5 tie constants, the circuit reaches a steady-state (reeber the RC lab with t τ). Consequently,
More informationBASIC PRINCIPLES. Power In Single-Phase AC Circuit
BASIC PRINCIPLES Power In Single-Phase AC Circuit Let instantaneous voltage be v(t)=v m cos(ωt+θ v ) Let instantaneous current be i(t)=i m cos(ωt+θ i ) The instantaneous p(t) delivered to the load is p(t)=v(t)i(t)=v
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 0: Sinusoidal Steady-State Analysis Sinusoidal Sources If a circuit is driven by a sinusoidal source, after 5 tie constants, the circuit reaches a steady-state (reeber the RC lab with t = τ). Consequently,
More informationPower Factor Improvement
Salman bin AbdulazizUniversity College of Engineering Electrical Engineering Department EE 2050Electrical Circuit Laboratory Power Factor Improvement Experiment # 4 Objectives: 1. To introduce the concept
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 6-7 pm, Room TBA First retrieve your EE2110 final and other course papers and notes! The test will be closed book
More informationChapter 9 Objectives
Chapter 9 Engr8 Circuit Analysis Dr Curtis Nelson Chapter 9 Objectives Understand the concept of a phasor; Be able to transform a circuit with a sinusoidal source into the frequency domain using phasor
More informationLecture 2 Introduction
EE 333 POWER SYSTEMS ENGNEERNG Lecture 2 ntroduction Dr. Lei Wu Departent of Electrical and Coputer Engineering Clarkson University Resilient Underground Microgrid in Potsda, NY Funded by NYSERDAR + National
More informationPH 222-2C Fall Electromagnetic Oscillations and Alternating Current. Lectures 18-19
H - Fall 0 Electroagnetic Oscillations and Alternating urrent ectures 8-9 hapter 3 (Halliday/esnick/Walker, Fundaentals of hysics 8 th edition) hapter 3 Electroagnetic Oscillations and Alternating urrent
More information04-Electric Power. ECEGR 452 Renewable Energy Systems
04-Electric Power ECEGR 452 Renewable Energy Systems Overview Review of Electric Circuits Phasor Representation Electrical Power Power Factor Dr. Louie 2 Introduction Majority of the electrical energy
More informationLecture 05 Power in AC circuit
CA2627 Building Science Lecture 05 Power in AC circuit Instructor: Jiayu Chen Ph.D. Announcement 1. Makeup Midterm 2. Midterm grade Grade 25 20 15 10 5 0 10 15 20 25 30 35 40 Grade Jiayu Chen, Ph.D. 2
More informationECE 421/521 Electric Energy Systems Power Systems Analysis I 2 Basic Principles. Instructor: Kai Sun Fall 2013
ECE 41/51 Electric Energy Systems Power Systems Analysis I Basic Principles Instructor: Kai Sun Fall 013 1 Outline Power in a 1-phase AC circuit Complex power Balanced 3-phase circuit Single Phase AC System
More informationELG3311: Assignment 3
LG33: ssignent 3 roble 6-: The Y-connected synchronous otor whose naeplate is shown in Figure 6- has a perunit synchronous reactance of 0.9 and a per-unit resistance of 0.0. (a What is the rated input
More informationREACTANCE. By: Enzo Paterno Date: 03/2013
REACTANCE REACTANCE By: Enzo Paterno Date: 03/2013 5/2007 Enzo Paterno 1 RESISTANCE - R i R (t R A resistor for all practical purposes is unaffected by the frequency of the applied sinusoidal voltage or
More informationPower and Energy Measurement
Power and Energy Measurement ENE 240 Electrical and Electronic Measurement Class 11, February 4, 2009 werapon.chi@kmutt.ac.th 1 Work, Energy and Power Work is an activity of force and movement in the direction
More information15-884/484 Electric Power Systems 1: DC and AC Circuits
15-884/484 Electric Power Systems 1: DC and AC Circuits J. Zico Kolter October 8, 2013 1 Hydro Estimated U.S. Energy Use in 2010: ~98.0 Quads Lawrence Livermore National Laboratory Solar 0.11 0.01 8.44
More informationEE313 Fall 2013 Exam #1 (100 pts) Thursday, September 26, 2013 Name. 1) [6 pts] Convert the following time-domain circuit to the RMS Phasor Domain.
Name If you have any questions ask them. Remember to include all units on your answers (V, A, etc). Clearly indicate your answers. All angles must be in the range 0 to +180 or 0 to 180 degrees. 1) [6 pts]
More informationLecture (5) Power Factor,threephase circuits, and Per Unit Calculations
Lecture (5) Power Factor,threephase circuits, and Per Unit Calculations 5-1 Repeating the Example on Power Factor Correction (Given last Class) P? Q? S? Light Motor From source 1000 volts @ 60 Htz 10kW
More informationPERIODIC STEADY STATE ANALYSIS, EFFECTIVE VALUE,
PERIODIC SEADY SAE ANALYSIS, EFFECIVE VALUE, DISORSION FACOR, POWER OF PERIODIC CURRENS t + Effective value of current (general definition) IRMS i () t dt Root Mean Square, in Czech boo denoted I he value
More informationRefresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas
Refresher course on Electrical fundamentals (Basics of A.C. Circuits) by B.M.Vyas A specifically designed programme for Da Afghanistan Breshna Sherkat (DABS) Afghanistan 1 Areas Covered Under this Module
More informationECE 420. Review of Three Phase Circuits. Copyright by Chanan Singh, Panida Jirutitijaroen, and Hangtian Lei, For educational use only-not for sale.
ECE 40 Review of Three Phase Circuits Outline Phasor Complex power Power factor Balanced 3Ф circuit Read Appendix A Phasors and in steady state are sinusoidal functions with constant frequency 5 0 15 10
More informationPower and Energy Measurement
Power and Energy Measurement EIE 240 Electrical and Electronic Measurement April 24, 2015 1 Work, Energy and Power Work is an activity of force and movement in the direction of force (Joules) Energy is
More informationmywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel
esson 6 Solution of urrent in Parallel and Seriesparallel ircuits n the last lesson, the following points were described:. How to compute the total impedance/admittance in series/parallel circuits?. How
More informationPre-Lab. Introduction
Pre-Lab Read through this entire lab. Perform all of your calculations (calculated values) prior to making the required circuit measurements. You may need to measure circuit component values to obtain
More informationSinusoidal Steady State Power Calculations
10 Sinusoidal Steady State Power Calculations Assessment Problems AP 10.1 [a] V = 100/ 45 V, Therefore I = 20/15 A P = 1 (100)(20)cos[ 45 (15)] = 500W, 2 A B Q = 1000sin 60 = 866.03 VAR, B A [b] V = 100/
More informationExercise Dr.-Ing. Abdalkarim Awad. Informatik 7 Rechnernetze und Kommunikationssysteme
Exercise1 1.10.015 Informatik 7 Rechnernetze und Kommunikationssysteme Review of Phasors Goal of phasor analysis is to simplify the analysis of constant frequency ac systems v(t) = max cos(wt + q v ) i(t)
More informationHomework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1. Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω.
Homework 2 SJTU233 Problem 1 Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω. Express Zab in polar form. Enter your answer using polar notation. Express argument in degrees.
More informationECE Spring 2017 Final Exam
ECE 20100 Spring 2017 Final Exam May 2, 2017 Section (circle below) Qi (12:30) 0001 Tan (10:30) 0004 Hosseini (7:30) 0005 Cui (1:30) 0006 Jung (11:30) 0007 Lin (9:30) 0008 Peleato-Inarrea (2:30) 0009 Name
More informationSinusoidal Steady-State Analysis
Chapter 4 Sinusoidal Steady-State Analysis In this unit, we consider circuits in which the sources are sinusoidal in nature. The review section of this unit covers most of section 9.1 9.9 of the text.
More informationECE 201 Fall 2009 Final Exam
ECE 01 Fall 009 Final Exam December 16, 009 Division 0101: Tan (11:30am) Division 001: Clark (7:30 am) Division 0301: Elliott (1:30 pm) Instructions 1. DO NOT START UNTIL TOLD TO DO SO.. Write your Name,
More informationPARALLEL A.C. CIRCUITS
C H A P T E R 4 earning Objectives Solving Parallel Circuits Vector or Phasor Method Admittance Method Application of Admittance Method Complex or Phasor Algebra Series-Parallel Circuits Series Equivalent
More information= 32.0\cis{38.7} = j Ω. Zab = Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1
Homework 2 SJTU233 Problem 1 Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω. Express Zab in polar form. Enter your answer using polar notation. Express argument in degrees.
More informationAlternating Current Circuits
Alternating Current Circuits AC Circuit An AC circuit consists of a combination of circuit elements and an AC generator or source. The output of an AC generator is sinusoidal and varies with time according
More informationWeek No. 6 Chapter Six: Power Factor Improvement
Week No. 6 Chapter Six: Power Factor Improvement The electrical energy is almost wholly generated, transmitted and distributed in the form of alternating current. Therefore, the question of power factor
More informationLO 1: Three Phase Circuits
Course: EEL 2043 Principles of Electric Machines Class Instructor: Dr. Haris M. Khalid Email: hkhalid@hct.ac.ae Webpage: www.harismkhalid.com LO 1: Three Phase Circuits Three Phase AC System Three phase
More information10.1 COMPLEX POWER IN CIRCUITS WITH AC SIGNALS
HAPER 10 Power in A ircuits HAPER OUINE 10.1 omplex Power in ircuits with A ignals 10. How to alculate omplex Power 10.3 omplex Power alculations in eries Parallel ircuits 10.4 Power Factor and pf orrection
More informationHandout 11: AC circuit. AC generator
Handout : AC circuit AC generator Figure compares the voltage across the directcurrent (DC) generator and that across the alternatingcurrent (AC) generator For DC generator, the voltage is constant For
More informationBASIC NETWORK ANALYSIS
SECTION 1 BASIC NETWORK ANALYSIS A. Wayne Galli, Ph.D. Project Engineer Newport News Shipbuilding Series-Parallel dc Network Analysis......................... 1.1 Branch-Current Analysis of a dc Network......................
More informationFigure 5.2 Instantaneous Power, Voltage & Current in a Resistor
ower in the Sinusoidal Steady-State ower is the rate at which work is done by an electrical component. It tells us how much heat will be produced by an electric furnace, or how much light will be generated
More informationCircuit Analysis-II. Circuit Analysis-II Lecture # 5 Monday 23 rd April, 18
Circuit Analysis-II Capacitors in AC Circuits Introduction ü The instantaneous capacitor current is equal to the capacitance times the instantaneous rate of change of the voltage across the capacitor.
More informationModule 4. Single-phase AC Circuits
Module 4 Single-phase AC Circuits Lesson 14 Solution of Current in R-L-C Series Circuits In the last lesson, two points were described: 1. How to represent a sinusoidal (ac) quantity, i.e. voltage/current
More informationEE5900 Spring Lecture 4 IC interconnect modeling methods Zhuo Feng
EE59 Spring Parallel LSI AD Algoriths Lecture I interconnect odeling ethods Zhuo Feng. Z. Feng MTU EE59 So far we ve considered only tie doain analyses We ll soon see that it is soeties preferable to odel
More informationModule 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Single-phase circuits ersion EE T, Kharagpur esson 6 Solution of urrent in Parallel and Seriesparallel ircuits ersion EE T, Kharagpur n the last lesson, the following points were described:. How
More informationThree Phase Circuits
Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/ OUTLINE Previously on ELCN102 Three Phase Circuits Balanced
More informationChapter 33. Alternating Current Circuits
Chapter 33 Alternating Current Circuits 1 Capacitor Resistor + Q = C V = I R R I + + Inductance d I Vab = L dt AC power source The AC power source provides an alternative voltage, Notation - Lower case
More informationWork, Energy and Power
1 Work, Energy and Power Work is an activity of force and movement in the direction of force (Joules) Energy is the capacity for doing work (Joules) Power is the rate of using energy (Watt) P = W / t,
More informationEE301 Three Phase Power
Learning Objectives a. Compute the real, reactive and apparent power in three phase systems b. Calculate currents and voltages in more challenging three phase circuit arrangements c. Apply the principles
More informationReview of DC Electric Circuit. DC Electric Circuits Examples (source:
Review of DC Electric Circuit DC Electric Circuits Examples (source: http://hyperphysics.phyastr.gsu.edu/hbase/electric/dcex.html) 1 Review - DC Electric Circuit Multisim Circuit Simulation DC Circuit
More informationChapter 6 Objectives
hapter 6 Engr8 ircuit Analysis Dr urtis Nelson hapter 6 Objectives Understand relationships between voltage, current, power, and energy in inductors and capacitors; Know that current must be continuous
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 informationUnit 21 Capacitance in AC Circuits
Unit 21 Capacitance in AC Circuits Objectives: Explain why current appears to flow through a capacitor in an AC circuit. Discuss capacitive reactance. Discuss the relationship of voltage and current in
More informationReview: Inductance. Oscillating Currents. Oscillations (cont d) LC Circuit Oscillations
Oscillating urrents h.30: Induced E Fields: Faraday s aw h.30: ircuits h.3: Oscillations and A ircuits eview: Inductance If the current through a coil of wire changes, there is an induced ef proportional
More informationExam 3 Solutions. 1. Which of the following statements is true about the LR circuit shown?
PHY49 Spring 5 Prof. Darin Acosta Prof. Paul Avery April 4, 5 PHY49, Spring 5 Exa Solutions. Which of the following stateents is true about the LR circuit shown? It is (): () Just after the switch is closed
More informationEE221 - Practice for the Midterm Exam
EE1 - Practice for the Midterm Exam 1. Consider this circuit and corresponding plot of the inductor current: Determine the values of L, R 1 and R : L = H, R 1 = Ω and R = Ω. Hint: Use the plot to determine
More informationBoise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
Objectives Boise State University Department of Electrical and Computer Engineering ECE 22L Circuit Analysis and Design Lab Experiment #4: Power Factor Correction The objectives of this laboratory experiment
More informationAnalysis of AC Power RMS and Phasors Power Factor. Power Factor. Eduardo Campero Littlewood
Power Factor Eduardo Campero Littlewood Universidad Autónoma Metropolitana Azcapotzalco Campus Energy Department Content 1 Analysis of AC Power 2 RMS and Phasors 3 Power Factor Recommended Bibliography
More informationMCE603: Interfacing and Control of Mechatronic Systems. Chapter 1: Impedance Analysis for Electromechanical Interfacing
MCE63: Interfacing and Control of Mechatronic Systems Chapter 1: Impedance Analysis for Electromechanical Interfacing Part B: Input and Output Impedance Cleveland State University Mechanical Engineering
More informationU V. r In Uniform Field the Potential Difference is V Ed
SPHI/W nit 7.8 Electric Potential Page of 5 Notes Physics Tool box Electric Potential Energy the electric potential energy stored in a syste k of two charges and is E r k Coulobs Constant is N C 9 9. E
More informationDriven RLC Circuits Challenge Problem Solutions
Driven LC Circuits Challenge Problem Solutions Problem : Using the same circuit as in problem 6, only this time leaving the function generator on and driving below resonance, which in the following pairs
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis
More informationELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT
Chapter 31: ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT 1 A charged capacitor and an inductor are connected in series At time t = 0 the current is zero, but the capacitor is charged If T is the
More informationSingle Phase Parallel AC Circuits
Single Phase Parallel AC Circuits 1 Single Phase Parallel A.C. Circuits (Much of this material has come from Electrical & Electronic Principles & Technology by John Bird) n parallel a.c. circuits similar
More informationECE 421/521 Electric Energy Systems Power Systems Analysis I 2 Basic Principles. Instructor: Kai Sun Fall 2014
ECE 41/51 Electric Energy Systems Power Systems Analysis I Basic Princiles Instructor: Kai Sun Fall 014 1 Outline Power in a 1-hase AC circuit Comlex ower Balanced 3-hase circuit Single Phase AC System
More informationNotes on Electric Circuits (Dr. Ramakant Srivastava)
Notes on Electric ircuits (Dr. Ramakant Srivastava) Passive Sign onvention (PS) Passive sign convention deals with the designation of the polarity of the voltage and the direction of the current arrow
More informationChapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW QUICK REFERENCE. Important Terms
Chapter 4 FORCES AND NEWTON S LAWS OF MOTION PREVIEW Dynaics is the study o the causes o otion, in particular, orces. A orce is a push or a pull. We arrange our knowledge o orces into three laws orulated
More informationChapter 1: Basics of Vibrations for Simple Mechanical Systems
Chapter 1: Basics of Vibrations for Siple Mechanical Systes Introduction: The fundaentals of Sound and Vibrations are part of the broader field of echanics, with strong connections to classical echanics,
More informationFeature Extraction Techniques
Feature Extraction Techniques Unsupervised Learning II Feature Extraction Unsupervised ethods can also be used to find features which can be useful for categorization. There are unsupervised ethods that
More informationExercise 2: Power Factor
Power in AC Circuits AC 2 Fundamentals Exercise 2: Power Factor EXERCISE OBJECTIVE When you have completed this exercise, you will be able to determine the power factor of ac circuits by using standard
More informationName (print): Lab (circle): W8 Th8 Th11 Th2 F8. θ (radians) θ (degrees) cos θ sin θ π/ /2 1/2 π/4 45 2/2 2/2 π/3 60 1/2 3/2 π/
Name (print): Lab (circle): W8 Th8 Th11 Th2 F8 Trigonometric Identities ( cos(θ) = cos(θ) sin(θ) = sin(θ) sin(θ) = cos θ π ) 2 Cosines and Sines of common angles Euler s Formula θ (radians) θ (degrees)
More informationTransformer. Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.).
. Transformers Transformer Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.). f the primary side is connected to an AC voltage source v (t), an AC flux (t) will be
More informationChapter 32A AC Circuits. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University
Chapter 32A AC Circuits A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University 2007 Objectives: After completing this module, you should be able to: Describe
More informationAC Circuits Homework Set
Problem 1. In an oscillating LC circuit in which C=4.0 μf, the maximum potential difference across the capacitor during the oscillations is 1.50 V and the maximum current through the inductor is 50.0 ma.
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 informationCircuit Analysis-III. Circuit Analysis-II Lecture # 3 Friday 06 th April, 18
Circuit Analysis-III Sinusoids Example #1 ü Find the amplitude, phase, period and frequency of the sinusoid: v (t ) =12cos(50t +10 ) Signal Conversion ü From sine to cosine and vice versa. ü sin (A ± B)
More informationPower Systems - Basic Concepts and Applications - Part I
PDHonline Course E104 (1 PDH) Power ystems Basic Concepts and Applications Part I Instructor: hihmin Hsu PhD PE 01 PDH Online PDH Center 57 Meadow Estates Drive Fairfax A 006658 Phone & Fax: 709880088
More informationECE2262 Electric Circuits. Chapter 6: Capacitance and Inductance
ECE2262 Electric Circuits Chapter 6: Capacitance and Inductance Capacitors Inductors Capacitor and Inductor Combinations Op-Amp Integrator and Op-Amp Differentiator 1 CAPACITANCE AND INDUCTANCE Introduces
More informationPeriodic Motion is everywhere
Lecture 19 Goals: Chapter 14 Interrelate the physics and atheatics of oscillations. Draw and interpret oscillatory graphs. Learn the concepts of phase and phase constant. Understand and use energy conservation
More informationMutual capacitor and its applications
Mutual capacitor and its applications Chun Li, Jason Li, Jieing Li CALSON Technologies, Toronto, Canada E-ail: calandli@yahoo.ca Published in The Journal of Engineering; Received on 27th October 2013;
More informationELECTRIC POWER CIRCUITS BASIC CONCEPTS AND ANALYSIS
Contents ELEC46 Power ystem Analysis Lecture ELECTRC POWER CRCUT BAC CONCEPT AND ANALY. Circuit analysis. Phasors. Power in single phase circuits 4. Three phase () circuits 5. Power in circuits 6. ingle
More informationECE Spring 2015 Final Exam
ECE 20100 Spring 2015 Final Exam May 7, 2015 Section (circle below) Jung (1:30) 0001 Qi (12:30) 0002 Peleato (9:30) 0004 Allen (10:30) 0005 Zhu (4:30) 0006 Name PUID Instructions 1. DO NOT START UNTIL
More informationChapter 2 General Properties of Radiation Detectors
Med Phys 4RA3, 4RB3/6R3 Radioisotopes and Radiation Methodology -1 Chapter General Properties of Radiation Detectors Ionizing radiation is ost coonly detected by the charge created when radiation interacts
More informationChapter 31: AC Circuits
hapter 31: A ircuits A urrents and Voltages In this chapter, we discuss the behior of circuits driven by a source of A. Recall that A means, literally, alternating current. An alternating current is a
More informationAn op amp consisting of a complex arrangement of resistors, transistors, capacitors, and diodes. Here, we ignore the details.
CHAPTER 5 Operational Amplifiers In this chapter, we learn how to use a new circuit element called op amp to build circuits that can perform various kinds of mathematical operations. Op amp is a building
More informationma x = -bv x + F rod.
Notes on Dynaical Systes Dynaics is the study of change. The priary ingredients of a dynaical syste are its state and its rule of change (also soeties called the dynaic). Dynaical systes can be continuous
More informationRLC Series Circuit. We can define effective resistances for capacitors and inductors: 1 = Capacitive reactance:
RLC Series Circuit In this exercise you will investigate the effects of changing inductance, capacitance, resistance, and frequency on an RLC series AC circuit. We can define effective resistances for
More informationECE 2100 Circuit Analysis
ECE 00 Crcut Analyss Lesson 3 Chapter : AC Power Analyss (nstant & Ae Power; Max Ae Power Transfer; Effecte or RMS alue, Power Factor, Coplex Power, Power Trangle, Power Factor Correcton Danel M. Ltynsk,
More informationCHAPTER 22 ELECTROMAGNETIC INDUCTION
CHAPTER 22 ELECTROMAGNETIC INDUCTION PROBLEMS 47. REASONING AND Using Equation 22.7, we find emf 2 M I or M ( emf 2 ) t ( 0.2 V) ( 0.4 s) t I (.6 A) ( 3.4 A) 9.3 0 3 H 49. SSM REASONING AND From the results
More informationPH 221-2A Fall Waves - I. Lectures Chapter 16 (Halliday/Resnick/Walker, Fundamentals of Physics 9 th edition)
PH 1-A Fall 014 Waves - I Lectures 4-5 Chapter 16 (Halliday/Resnick/Walker, Fundaentals of Physics 9 th edition) 1 Chapter 16 Waves I In this chapter we will start the discussion on wave phenoena. We will
More informationAC Electric Machines. Objectives. Introduction. 1. To understand what the meant by the term ac circuit. 2. To understand how to analyze ac circuits.
AC Electric Machines Objectives 1. To understand what the meant by the term ac circuit.. To understand how to analyze ac circuits. 3. To understand the basic construction and operation of an ac machine.
More informationCurrent, Resistance Electric current and current density
General Physics Current, Resistance We will now look at the situation where charges are in otion - electrodynaics. The ajor difference between the static and dynaic cases is that E = 0 inside conductors
More information