AC Power Analysis. Chapter Objectives:

Size: px
Start display at page:

Download "AC Power Analysis. Chapter Objectives:"

Transcription

1 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 Learn about the complex power, apparent power and power factor Understand the principle of conservation of AC power Learn about power factor correction

2 Apparent Power and Power Factor The Average Power depends on the value of voltage and current and the phase angle between them. 1 P VmI m v i V I v i 2 cos( ) cos( ) The Apparent Power is the product of the value of voltage and current. It is measured in Volt amperes (VA). 1 S V I V I 2 m m The Power Factor (pf) is the cosine of the phase difference between voltage and current. It is also the cosine of the angle of load impedance. The power factor may also be regarded as the ratio of the real power dissipated to the apparent power of the load. P pf cos( v i) S P Apparent Power Power Factor S pf

3 Apparent Power and Power Factor Not all the apparent power is consumed if the circuit is partly reactive. Purely resistive load (R) Purely reactive load (L or C) Resistive and reactive load (R and L/C) θ v θ i = 0, Pf = 1 θ v θ i = ±90 o, pf = 0 θ v θ i > 0 θ v θ i < 0 P/S = 1, all power are consumed P = 0, no real power consumption Lagging - inductive load Leading - capacitive load P/S < 1, Part of the apparent power is consumed

4

5 Power equipment are rated using their appparent power in KVA.

6 Apparent Power and Power Factor Both have same P Apparent Powers and pf s are different Generator of the second load is overloaded

7 Overloading of the generator of the second load is avoided by applying power factor correction. Apparent Power and Power Factor

8 Complex Power The COMPLEX Power S contains all the information pertaining to the power absorbed by a given load. 1 2 S VI V I I Z 2 V 2 Z V S V I I v V I ( ) v i V I cos( v i ) jv I sin( v i ) P jq Re{ S} j Im{ S} Real Power+ Reactive Power i

9 Complex Power The REAL Power is the only useful power delivered to the load. The REACTIVE Power represents the energy exchange between the source and reactive part of the load. It is being transferred back and forth between the load and the source The unit of Q is volt-ampere reactive (VAR) S P jq Re{ S} j Im{ S} =Real Power+Reactive Power S I Z ( R ) P jq 2 2 I jx P= V I cos( ) Re{ S} I 2 v i Q= V I sin( ) Im{} S 2 v i I R X

10 Resistive Circuit and Real Power v( t) V sin( t ) i( t) I sin( t) m 1 1 p( t) v( t) it ( ) VmI mcos( ) 1 cos(2 t) VmI msin( )sin(2 t) 2 2 V I cos( ) 1 cos(2 t) V I sin( )sin(2 t) V I V I pt ( ) is always Positive m cos(2 t) 0 RESISTIVE

11 Inductive Circuit and Reactive Power v( t) V sin( t ) i( t) I sin( t) m 1 1 pl( t) v( t) it ( ) VmI mcos( ) 1 cos( 2 t) VmImsin( )sin(2 t) 2 2 V I cos( ) 1 cos(2 t) V I sin( )sin(2 t) V pl I sin( 2 t) m 90 INDUCTIVE ( t) is equally both positive and negative, power is circulating

12 Inductive Circuit and Reactive Power If the average power is zero, and the energy supplied is returned within one cycle, why is a reactive power of any significance? At every instant of time along the power curve that the curve is above the axis (positive), energy must be supplied to the inductor, even though it will be returned during the negative portion of the cycle. This power requirement during the positive portion of the cycle requires that the generating plant provide this energy during that interval, even though this power is not dissipated but simply borrowed. The increased power demand during these intervals is a cost factor that must that must be passed on to the industrial consumer. Most larger users of electrical energy pay for the apparent power demand rather than the watts dissipated since the volt-amperes used are sensitive to the reactive power requirement. The closer the power factor of an industrial consumer is to 1, the more efficient is the plant s operation since it is limiting its use of borrowed power.

13 Capacitive Circuit and Reactive Power v( t) V sin( t ) i( t) I sin( t) m 1 1 pc ( t) v( t) it ( ) VmI mcos( ) 1 cos(2 t) VmI msin( )sin(2 t) 2 2 V I cos( ) 1 cos(2 t) V I sin( )sin(2 t) V I sin( 2 t) 90 CAPACITIVE p C m ( t) is equally both positive and negative, power is circulating

14 Complex Power The COMPLEX Power contains all the information pertaining to the power absorbed by a given load. 1 Complex Power= S P jq VI VI ( v i ) 2 Apparent Power= S S V I P Q Real Power= P Re{ S} Scos( ) Reactive Power=Q Im{ S} Ssin( ) P Power Factor= =cos( v i) S Real Power is the actual power dissipated by the load. v i v 2 2 Reactive Power is a measure of the energy exchange between source and reactive part of the load. i

15 Power Triangle The COMPLEX Power is represented by the POWER TRIANGLE similar to IMPEDANCE TRIANGLE. Power triangle has four items: P, Q, S and θ. a) Power Triangle b) Impedance Triangle Power Triangle Q 0 Resistive Loads (Unity Pf ) Q 0 Capacitive Loads (Leading Pf ) Q 0 Inductive Loads (Lagging Pf )

16 Power Triangle Finding the total COMPLEX Power of the three loads. P T Q T T Watt Var S 600 j

17 Power Triangle S P jq S S ( P P ) j( Q Q )

18 Real and Reactive Power Formulation

19 Real and Reactive Power Formulation

20 Real and Reactive Power Formulation

21 Real and Reactive Power Formulation v( t) V cos( t ) i( t) I cos( t ) m v m i ) p( t) V I cos( ) 1 cos 2( t ) V I sin( ) sin 2( t ) v i v v i = P 1 cos 2( t Q sin 2 ( t ) =Real Power R eactive Power v v v P is the REAL AVERAGE POWER Q is the maximum value of the circulating power flowing back and forward P V I cos Q V I rms rms rms rms sin

22 Real and Reactive Powers REAL POWER CIRCULATING POWER

23 Real and Reactive Powers V rms =100 V I rms =1 A Apparent power = V rms I rms =100 VA From p(t) curve, check that power flows from the supply into the load for the entire duration of the cycle! Also, the average power delivered to the load is 100 W. No Reactive power.

24 Real and Reactive Powers Power Flowing Back V rms =100 V I rms =1 A Apparent power = V rms I rms =100 VA From p(t) curve, power flows from the supply into the load for only a part of the cycle! For a portion of the cycle, power actually flows back to the source from the load! Also, the average power delivered to the load is 50 W! So, the useful power is less than in Case 1! There is reactive power in the circuit.

25 Practice Problem 11.13: The 60 resistor absorbs 240 Watt of average power. Calculate V and the complex power of each branch. What is the total complex power?

26 Practice Problem 11.13: The 60 resistor absorbs 240 Watt of average power. Calculate V and the complex power of each branch. What is the total complex power?

27 Practice Problem 11.14: Two loads are connected in parallel. Load 1 has 2 kw, pf=0.75 leading and Load 2 has 4 kw, pf=0.95 lagging. Calculate the pf of two loads and the complex power supplied by the source. LOAD 1 2 kw Pf=0.75 Leading LOAD 2 4 kw Pf=0.95 Lagging

28

29 Conservation of AC Power The complex, real and reactive power of the sources equal the respective sum of the complex, real and reactive power of the individual loads. a) Loads in Parallel b) Loads in Series For parallel connection: S V I V (I I ) V I V I S S * * * * * Same results can be obtained for a series connection.

30

31

32 Complex power is Conserved

12. Introduction and Chapter Objectives

12. 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 information

BASIC PRINCIPLES. Power In Single-Phase AC Circuit

BASIC 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 information

EXP. NO. 3 Power on (resistive inductive & capacitive) load Series connection

EXP. 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 information

Sinusoidal Steady State Analysis (AC Analysis) Part II

Sinusoidal Steady State Analysis (AC Analysis) Part II Sinusoidal Steady State Analysis (AC Analysis) Part II Amin Electronics and Electrical Communications Engineering Department (EECE) Cairo University elc.n102.eng@gmail.com http://scholar.cu.edu.eg/refky/

More information

Lecture 11 - AC Power

Lecture 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 information

Sinusoidal Response of RLC Circuits

Sinusoidal 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 information

Power Factor Improvement

Power 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 information

11. AC Circuit Power Analysis

11. 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 information

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.

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. 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 information

Refresher 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 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 information

Chapter 10 Objectives

Chapter 10 Objectives 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

More information

VTU E-LEARNING NOTES ON:

VTU E-LEARNING NOTES ON: VTU E-LEARNING NOTES ON: 10EE35 ELECTRICAL AND ELECTRONIC MEASUREMENTS AND INSTRUMENTATION BY DR. M.S. RAVIPRAKASHA PROFESSOR & HEAD DEPT. OF E&E ENGG. MALNAD COLLEGE OF ENGG. HASSAN 573 201. SUBJECT CODE

More information

ECE 421/521 Electric Energy Systems Power Systems Analysis I 2 Basic Principles. Instructor: Kai Sun Fall 2013

ECE 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 information

EE313 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.

EE313 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 information

ECE 420. Review of Three Phase Circuits. Copyright by Chanan Singh, Panida Jirutitijaroen, and Hangtian Lei, For educational use only-not for sale.

ECE 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 information

LO 1: Three Phase Circuits

LO 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 information

EE 3120 Electric Energy Systems Study Guide for Prerequisite Test Wednesday, Jan 18, pm, Room TBA

EE 3120 Electric Energy Systems Study Guide for Prerequisite Test Wednesday, Jan 18, 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 information

10.1 COMPLEX POWER IN CIRCUITS WITH AC SIGNALS

10.1 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 information

Lecture 05 Power in AC circuit

Lecture 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 information

Lecture (5) Power Factor,threephase circuits, and Per Unit Calculations

Lecture (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 information

04-Electric Power. ECEGR 452 Renewable Energy Systems

04-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 information

Power and Energy Measurement

Power 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 information

True Power vs. Apparent Power: Understanding the Difference Nicholas Piotrowski, Associated Power Technologies

True Power vs. Apparent Power: Understanding the Difference Nicholas Piotrowski, Associated Power Technologies True Power vs. Apparent Power: Understanding the Difference Nicholas Piotrowski, Associated Power Technologies Introduction AC power sources are essential pieces of equipment for providing flexible and

More information

Pre-Lab. Introduction

Pre-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 information

mywbut.com Lesson 16 Solution of Current in AC Parallel and Seriesparallel

mywbut.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 information

Week No. 6 Chapter Six: Power Factor Improvement

Week 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 information

Exercise 2: Power Factor

Exercise 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 information

Work, Energy and Power

Work, 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 information

Boise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab

Boise 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 information

EE301 Three Phase Power

EE301 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 information

Power and Energy Measurement

Power 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 information

Figure 5.2 Instantaneous Power, Voltage & Current in a Resistor

Figure 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 information

Toolbox: Electrical Systems Dynamics

Toolbox: Electrical Systems Dynamics Toolbox: Electrical Systems Dynamics Dr. John C. Wright MIT - PSFC 05 OCT 2010 Introduction Outline Outline AC and DC power transmission Basic electric circuits Electricity and the grid Image removed due

More information

15-884/484 Electric Power Systems 1: DC and AC Circuits

15-884/484 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 information

Analysis of AC Power RMS and Phasors Power Factor. Power Factor. Eduardo Campero Littlewood

Analysis 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 information

REACTANCE. By: Enzo Paterno Date: 03/2013

REACTANCE. 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 information

Circuit Analysis-II. Circuit Analysis-II Lecture # 5 Monday 23 rd April, 18

Circuit 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 information

Module 4. Single-phase AC circuits. Version 2 EE IIT, Kharagpur

Module 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 information

Three Phase Circuits

Three 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 information

Module 4. Single-phase AC Circuits

Module 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 information

Homework 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. 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 information

NZQA registered unit standard version 2 Page 1 of 6

NZQA registered unit standard version 2 Page 1 of 6 Page 1 of 6 Title Demonstrate and apply knowledge of capacitance, inductance, power factor, and power factor correction Level 3 Credits 7 Purpose This unit standard covers an introduction to alternating

More information

Brief Steady of Power Factor Improvement

Brief Steady of Power Factor Improvement International Journal of Electrical Engineering. ISSN 0974-2158 Volume 6, Number 5 (2013), pp. 531-539 International Research PublicationHouse http://www.irphouse.com Brief Steady of Power Factor Improvement

More information

EE221 - Practice for the Midterm Exam

EE221 - 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 information

ELECTRIC POWER CIRCUITS BASIC CONCEPTS AND ANALYSIS

ELECTRIC 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 information

Single Phase Parallel AC Circuits

Single 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 information

Work, Energy and Power

Work, 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 information

Electromagnetic Oscillations and Alternating Current. 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3.

Electromagnetic Oscillations and Alternating Current. 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3. Electromagnetic Oscillations and Alternating Current 1. Electromagnetic oscillations and LC circuit 2. Alternating Current 3. RLC circuit in AC 1 RL and RC circuits RL RC Charging Discharging I = emf R

More information

2 Signal Frequency and Impedances First Order Filter Circuits Resonant and Second Order Filter Circuits... 13

2 Signal Frequency and Impedances First Order Filter Circuits Resonant and Second Order Filter Circuits... 13 Lecture Notes: 3454 Physics and Electronics Lecture ( nd Half), Year: 7 Physics Department, Faculty of Science, Chulalongkorn University //7 Contents Power in Ac Circuits Signal Frequency and Impedances

More information

Three-phase AC Circuits. Measurement of Power in a Three-phase Circuit

Three-phase AC Circuits. Measurement of Power in a Three-phase Circuit Three-phase AC Circuits Lesson Measurement of Power in a Three-phase Circuit In the previous lesson, the phase and line currents for balanced delta-connected load fed from a three-phase supply, along with

More information

= 32.0\cis{38.7} = j Ω. Zab = Homework 2 SJTU233. Part A. Part B. Problem 2. Part A. Problem 1

= 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 information

ELECTROMAGNETIC OSCILLATIONS AND ALTERNATING CURRENT

ELECTROMAGNETIC 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 information

Chapter 10 ACSS Power

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 information

Alternating Current Circuits

Alternating 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 information

Physics 115. AC circuits Reactances Phase relationships Evaluation. General Physics II. Session 35. R. J. Wilkes

Physics 115. AC circuits Reactances Phase relationships Evaluation. General Physics II. Session 35. R. J. Wilkes Session 35 Physics 115 General Physics II AC circuits Reactances Phase relationships Evaluation R. J. Wilkes Email: phy115a@u.washington.edu 06/05/14 1 Lecture Schedule Today 2 Announcements Please pick

More information

PARALLEL A.C. CIRCUITS

PARALLEL 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

ECE Spring 2017 Final Exam

ECE 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 information

ECE 421/521 Electric Energy Systems Power Systems Analysis I 2 Basic Principles. Instructor: Kai Sun Fall 2014

ECE 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 information

Power System Engineering Prof. Debapriya Das Department of Electrical Engineering Indian Institute of Technology, Kharagpur

Power System Engineering Prof. Debapriya Das Department of Electrical Engineering Indian Institute of Technology, Kharagpur Power System Engineering Prof. Debapriya Das Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture 41 Application of capacitors in distribution system (Contd.) (Refer Slide

More information

Chapter 33. Alternating Current Circuits

Chapter 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 information

1 Phasors and Alternating Currents

1 Phasors and Alternating Currents Physics 4 Chapter : Alternating Current 0/5 Phasors and Alternating Currents alternating current: current that varies sinusoidally with time ac source: any device that supplies a sinusoidally varying potential

More information

Chapter 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 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 information

ECE 201 Fall 2009 Final Exam

ECE 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 information

Sinusoidal Steady State Power Calculations

Sinusoidal 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 information

Exercise Dr.-Ing. Abdalkarim Awad. Informatik 7 Rechnernetze und Kommunikationssysteme

Exercise 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 information

CHAPTER 22 ELECTROMAGNETIC INDUCTION

CHAPTER 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 information

ECE 476 Power System Analysis Fall 2014 Exam #1, Thursday, October 2, :30AM - 10:50AM

ECE 476 Power System Analysis Fall 2014 Exam #1, Thursday, October 2, :30AM - 10:50AM ECE 476 Power System Analysis Fall 4 Exam #, Thursday, October, 4. 9:3AM - :5AM Name: Problem (5 p) Two balanced 3-phase loads are connected in parallel. One is Y-connected and draws 75 kw (3-phase) at.8

More information

Handout 11: AC circuit. AC generator

Handout 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 information

Lecture 21. Resonance and power in AC circuits. Physics 212 Lecture 21, Slide 1

Lecture 21. Resonance and power in AC circuits. Physics 212 Lecture 21, Slide 1 Physics 1 ecture 1 esonance and power in A circuits Physics 1 ecture 1, Slide 1 I max X X = w I max X w e max I max X X = 1/w I max I max I max X e max = I max Z I max I max (X -X ) f X -X Physics 1 ecture

More information

Transformer. Transformer comprises two or more windings coupled by a common magnetic circuit (M.C.).

Transformer. 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 information

Chapter 15 Power And Harmonics in Nonsinusoidal Systems

Chapter 15 Power And Harmonics in Nonsinusoidal Systems Chapter 15 Power And Harmonics in Nonsinusoidal Systems 15.1. Average power in terms of Fourier series 15.2. RMS value of a waveform 15.3. Power factor THD Distortion and Displacement factors 15.4. Power

More information

Alternating Current. Chapter 31. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman

Alternating Current. Chapter 31. PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Chapter 31 Alternating Current PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 8_8_2008 Topics for Chapter 31

More information

BASIC NETWORK ANALYSIS

BASIC 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 information

AC Circuits Homework Set

AC 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 information

Charge The most basic quantity in an electric circuit is the electric charge. Charge is an electrical property of the atomic particles of which matter

Charge The most basic quantity in an electric circuit is the electric charge. Charge is an electrical property of the atomic particles of which matter Basic Concepts of DC Circuits Introduction An electric circuit is an interconnection of electrical elements. Systems of Units 1 Charge The most basic quantity in an electric circuit is the electric charge.

More information

Sinusoidal Steady-State Analysis

Sinusoidal 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 information

Unit-3. Question Bank

Unit-3. Question Bank Unit- Question Bank Q.1 A delta connected load draw a current of 15A at lagging P.F. of.85 from 400, -hase, 50Hz suly. Find & of each hase. Given P = = 400 0 I = 15A Ans. 4.98, 5.7mH So I P = 15 =8.66A

More information

Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian Institute of Technology, Kharagpur

Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian Institute of Technology, Kharagpur Power System Analysis Prof. A. K. Sinha Department of Electrical Engineering Indian Institute of Technology, Kharagpur Lecture - 9 Transmission Line Steady State Operation Welcome to lesson 9, in Power

More information

Note 11: Alternating Current (AC) Circuits

Note 11: Alternating Current (AC) Circuits Note 11: Alternating Current (AC) Circuits V R No phase difference between the voltage difference and the current and max For alternating voltage Vmax sin t, the resistor current is ir sin t. the instantaneous

More information

Announcements: Today: more AC circuits

Announcements: Today: more AC circuits Announcements: Today: more AC circuits I 0 I rms Current through a light bulb I 0 I rms I t = I 0 cos ωt I 0 Current through a LED I t = I 0 cos ωt Θ(cos ωt ) Theta function (is zero for a negative argument)

More information

ECE Spring 2015 Final Exam

ECE 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 information

CHAPTER ONE. 1.1 International System of Units and scientific notation : Basic Units: Quantity Basic unit Symbol as shown in table 1

CHAPTER ONE. 1.1 International System of Units and scientific notation : Basic Units: Quantity Basic unit Symbol as shown in table 1 CHAPTER ONE 1.1 International System of Units and scientific notation : 1.1.1 Basic Units: Quantity Basic unit Symbol as shown in table 1 Table 1 1.1.2 Some scientific notations : as shown in table 2 Table

More information

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS

SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS SINUSOIDAL STEADY STATE CIRCUIT ANALYSIS 1. Introduction A sinusoidal current has the following form: where I m is the amplitude value; ω=2 πf is the angular frequency; φ is the phase shift. i (t )=I m.sin

More information

Power Systems - Basic Concepts and Applications - Part I

Power Systems - Basic Concepts and Applications - Part I PDHonline Course E104A (1 PDH) Power Systems - Basic Concepts and Applications - Part I Instructor: Shih-Min Hsu, Ph.D., P.E. 01 PDH Online PDH Center 57 Meadow Estates Drive Fairfax, VA 030-6658 Phone

More information

ECE 2210 Final given: Spring 15 p1

ECE 2210 Final given: Spring 15 p1 ECE 2 Final given: Spring 15 Closed Book, Closed notes except preprinted yellow sheet, Calculators OK. Show all work to receive credit. Circle answers, show units, and round off reasonably 1. (15 pts)

More information

Series and Parallel ac Circuits

Series and Parallel ac Circuits Series and Parallel ac Circuits 15 Objectives Become familiar with the characteristics of series and parallel ac networks and be able to find current, voltage, and power levels for each element. Be able

More information

Review of Basic Electrical and Magnetic Circuit Concepts EE

Review of Basic Electrical and Magnetic Circuit Concepts EE Review of Basic Electrical and Magnetic Circuit Concepts EE 442-642 Sinusoidal Linear Circuits: Instantaneous voltage, current and power, rms values Average (real) power, reactive power, apparent power,

More information

Alternating Currents. The power is transmitted from a power house on high voltage ac because (a) Electric current travels faster at higher volts (b) It is more economical due to less power wastage (c)

More information

ECE 5260 Microwave Engineering University of Virginia. Some Background: Circuit and Field Quantities and their Relations

ECE 5260 Microwave Engineering University of Virginia. Some Background: Circuit and Field Quantities and their Relations ECE 5260 Microwave Engineering University of Virginia Lecture 2 Review of Fundamental Circuit Concepts and Introduction to Transmission Lines Although electromagnetic field theory and Maxwell s equations

More information

vba vbn vcb van vcn vac Figure 1. Three-phase line and phase voltages

vba vbn vcb van vcn vac Figure 1. Three-phase line and phase voltages . Chapter 5 Power Engineering Features Used Í, abs( ), real( ), imag( ), conj( ),

More information

AC 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. 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 information

Chapter 3 AUTOMATIC VOLTAGE CONTROL

Chapter 3 AUTOMATIC VOLTAGE CONTROL Chapter 3 AUTOMATIC VOLTAGE CONTROL . INTRODUCTION TO EXCITATION SYSTEM The basic function of an excitation system is to provide direct current to the field winding of the synchronous generator. The excitation

More information

Revised October 6, EEL , Henry Zmuda. 2. Three-Phase Circuits 1

Revised October 6, EEL , Henry Zmuda. 2. Three-Phase Circuits 1 Three Phase Circuitsit Revised October 6, 008. Three-Phase Circuits 1 Preliminary Comments and a quick review of phasors. We live in the time domain. We also assume a causal (nonpredictive) world. Real-world

More information

Learnabout Electronics - AC Theory

Learnabout Electronics - AC Theory Learnabout Electronics - AC Theory Facts & Formulae for AC Theory www.learnabout-electronics.org Contents AC Wave Values... 2 Capacitance... 2 Charge on a Capacitor... 2 Total Capacitance... 2 Inductance...

More information

SHREE DATTA SHETKARI SAHAKARI KARKHANA LTD. CHARITABLE TRUST SHREE DATTA POLYTECHNIC COLLEGE, DATTANAGAR CLASS TEST-01

SHREE DATTA SHETKARI SAHAKARI KARKHANA LTD. CHARITABLE TRUST SHREE DATTA POLYTECHNIC COLLEGE, DATTANAGAR CLASS TEST-01 SHREE DATTA SHETKARI SAHAKARI KARKHANA LTD. CHARITABLE TRUST SHREE DATTA POLYTECHNIC COLLEGE, DATTANAGAR CLASS TEST-01 Name of subject: Elect. & electronic Measurement Mark: 25 Institute Code: 1512 Subject

More information

Basics of Electric Circuits

Basics of Electric Circuits António Dente Célia de Jesus February 2014 1 Alternating Current Circuits 1.1 Using Phasors There are practical and economic reasons justifying that electrical generators produce emf with alternating and

More information

Power Systems - Basic Concepts and Applications - Part I

Power 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 information

Driven RLC Circuits Challenge Problem Solutions

Driven 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 information

10.1 Instantaneous Power 10.2 Average and Reactive Power 10.3 The RMS Value and Power Calculations 10.4 Complex Power

10.1 Instantaneous Power 10.2 Average and Reactive Power 10.3 The RMS Value and Power Calculations 10.4 Complex Power SINUSOIDAL STEADY-STATE STATE POWER CALCULATIONS C.T. Pan 1 10.1 Instantaneous Powe 10. Aveage and Reactive Powe 10.3 The RMS Value and Powe Calculations 10.4 Complex Powe C.T. Pan 10.5 Powe Calculations

More information

Module 4. Single-phase AC Circuits. Version 2 EE IIT, Kharagpur 1

Module 4. Single-phase AC Circuits. Version 2 EE IIT, Kharagpur 1 Module 4 Single-phase A ircuits ersion EE IIT, Kharagpur esson 4 Solution of urrent in -- Series ircuits ersion EE IIT, Kharagpur In the last lesson, two points were described:. How to represent a sinusoidal

More information