EE 221 AC Circuit Power Analysis. Instantaneous and average power RMS value Apparent power and power factor Complex power


 Florence Ophelia Baldwin
 2 years ago
 Views:
Transcription
1 EE 1 AC Circuit Power Analysis Instantaneous and average power RMS value Apparent power and power factor Complex power
2 Instantaneous Power Product of timedomain voltage and timedomain current p(t) = v(t) i(t) Determine maximum value Transients Steadystate steadystate As the transient dies out, the circuit returns to steadystate operation. Since the only source remaining in the circuit is dc, the inductor eventually acts as a short circuit absorbing zero power.
3 Power due to Sinusoidal Excitation v(t) = V m cos(ωt+θ) and i(t) = I m cos(ωt +ϕ) p(t) = V m I m cos(ωt+θ) cos(ωt +ϕ) = = ½ V m I m cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) trigonometric identity p(t) = ½ V m I m cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) instantaneous two parts average periodic constant independent of t the "average" wanted active or real periodic period is ½T average is zero unwanted
4 Power due to Sinusoidal Excitation p(t) = ½ V m I m cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) voltage V = 4 0 V, impedance Z = 60 Ω, ω = π/ 6 rad/s I = 60 A p(t) = + 4 cos(π / 360 ) W
5 Power due to Sinusoidal Excitation p(t) = ½ V m I m cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) Example 1: Average power delivered to resistor T P R =½V m I m cos(θ  ϕ) = ½ V m I m cos(0) 1.5 = ½ V m I m = ½ R I m = ½ V m / R = 1 W v(t), i(t), p(t) V = 45 V R = Ω time (s)
6 Power due to Sinusoidal Excitation p(t) = ½ V m I m cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) Example : Average power delivered to purely reactive elements T P X =½V m I m cos(θ  ϕ) = ½ V m I m cos(±90 ) = v(t), i(t), p(t) V = 45 V X = jω time (s)
7 Power due to Sinusoidal Excitation p(t) = ½ V m I m cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) Example 3: Voltage across impedance (V = o V and Z = o Ω) Determine active power absorbed. I = V / Z = 555 = 30 = j A 5 o V Z = j41.9 Ω I 30 o P = ½ 8.7 = ½ ( ) 8.7 = 57.4 W
8 Power due to Sinusoidal Excitation p(t) = ½ V m I m cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) Example 4: (Chapter 11, Problem 8.) In the circuit shown in Fig. 11.7, find the average power being (a) dissipated in the 3Ω resistor; (b) generated by the source. Z R 1 = 3+ = j3= 4+ j3ω 0.1 j0.3 + j5 5 9 Ignore 30 on Vs, IR = 5, IR = 6+ j8 10 (a) (b) P3 Ω = 3 = W 10 (+ j5)(4+ j3) Vs = 5 0 = V 6+ j8 1 Ps, gen = cos = 0.75 W
9 Maximum Power Transfer A simple loop circuit used to illustrate the derivation of the maximum power transfer theorem as it applies to circuits operating in the sinusoidal steady state. Z th = R th + j X th Z L = R L + j X L Z L = Z th * R L = R th and X L =  X th
10 Maximum Power Transfer Example: (Chapter 11, Problem 1.) For the circuit of Fig ; (a) what value of Z L will absorb a maximum average power? (b) What is the value of this maximum power? V Z th th 10j = 10 = V 10 + j5 j10(10 + j15) = = 8 j14ω 10 + j5 (a) (b) Z L = 8 + j14 Ω I L = PL,max = 8 = 180 W 16
11 Effective Values Measure for sinusoidal voltages and currents Power outlets: 60 Hz, "voltage of 115V" Not the mean of T (T/) Not the Amplitude ( 115V) Measure of effectiveness of a source in delivering power to a resistive load Effective value of periodic current is equal to the DC value that delivers the same average power to resistor i(t) R p(t) P R and compare to I DC R
12 Effective Values Mathematical expression P T T 1 R = i Rdt = T T 0 0 i dt = I DC R = I eff R I eff = 1 T T 0 i Rdt (Square) root of the mean of the square current rms value Defined for all periodic signals
13 Effective Values  Sinusoids i(t) = I m cos(ωt +ϕ) with a period of T = π/ω I eff = 1 T T Im cos ( ωt + ϕ) dt 0 = I m π ω ω / π cos(ωt + ϕ ) dt I = eff I m real quantity independent of phase angle equal to the amplitude example: 30 o A delivers the same as I DC = 1A
14 RMS value to compute average power In general P = ½ V m I m cos(θ  ϕ) = V eff I eff cos(θ  ϕ) For resistors P = V eff I eff = V eff / R = I eff R Note: We can use amplitude or rms value Use V and V rms to designate voltages
15 RMS value to compute average power Example: (Chapter 11, Problem 30.) The series combination of a 1kΩ resistor and a H inductor must not dissipate more than 50 mw of power at any instant. Assuming a sinusoidal current with ω =500 rad/s, what is the largest rms current that can be tolerated? The peak instantaneous power is 50 mw. The combination of elements yields Z = j1000 Ω = o Ω. o Vm 0 Vm 45 Arbitrarily designate V = V m 0, so that I = = A and V m = 1414 I m. Z 1414 We may write p(t) = ½ V m I m cos φ + ½ V m I m cos (ωt + φ) where φ = the angle of the current (45 o ). This function has a maximum value of ½ V m I m cos φ + ½ V m I m. Thus, 0.50 = ½ V m I m (1 + cos φ) = ½ (1414) I m (1.707) and I m = ma. In terms of rms current, the largest rms current permitted is 14.39m / = ma rms.
16 Apparent Power We had P = ½ V m I m cos(θ  ϕ) = V eff I eff cos(θ  ϕ) In case of direct current we would use voltage times current: S = V eff I eff This is not the average power Is the "apparent" power (S or AP) Measured in voltampere or VA (rather than W to avoid confusion) Magnitude of S is always greater or equal to magnitude of P: S P
17 Power Factor Defined as the ratio of average (real) power to apparent power PF = P / S = P / (V eff I eff ) In the sinusoidal case the power factor is PF = cos(θ  ϕ) θ  ϕ is the angle the voltage leads the current: PF angle note: Purely resistive load has PF = 1 Purely reactive load has PF = 0 PF = 0.5 means a phase angle of ±60 Resolve ambiguity PF leading or lagging for capacitive or inductive load
18 Apparent Power and Power Factor Example: (Chapter 11, Problem 30.) (a) Find the power factor at which the source in the circuit of Fig is operating. (b) Find the average power being supplied by the source. (c) What size capacitor should be placed in parallel with the source to cause its power factor to be unity? (d) Verify your answers with PSpice. (a) 10 Is = = A rms j j 16 PF = cos 6.5 = lag s (b) P = 10 s = 991.7W (c) j48 1 ZL = 4 + = 4 + (19 + j144) 3+ j j5.76 ZL = j5.76 Ω, YL = j5.76 j10π C =, C = 90.09µ F
19 Apparent Power and Power Factor Example: (see also chapter 10) (Chapter 11, Problem 30.) (d) Examine simulation output file (AC sweep at 60Hz). FREQ VM($N_0003,0) VP($N_0003,0) 6.000E E E+00 FREQ IM(V_PRINT1) IP(V_PRINT1) 6.000E E E+01 (a) and (b) are correct Next, add a µF capacitor in parallel with the source: FREQ IM(V_PRINT1) IP(V_PRINT1) 6.000E E E05 (c) is correct ( degrees is essentially zero, for unity PF).
20 Complex Power Simplifies power calculations We had p(t) = V eff I eff cos(θ  ϕ) + ½ V m I m cos(ωt + θ + ϕ) Where the average (real) power P = V eff I eff cos(θ  ϕ) Using complex nomenclature P = V eff I eff Re{e j(θ  ϕ) } = V eff Re{e j(θ) } I eff Re{e jϕ) } Hence P = Re{V eff I * eff} phasor voltage complex conjugate of phasor current Define S = V eff I * eff
21 Complex Power S = V eff I * eff can be written as S =V eff I eff e j(θ  ϕ) = P + jq magnitude equals apparent power S = S PF angle average (real) power reactive power Reactive power Q Imaginary part of complex power Dimensions are those of P, S, AP=S ( S ) Avoiding confusion by using voltamperereactive or VAr Q = V eff I eff sin(θ  ϕ) Physical interpretation: Time rate of energy flow back&forth between source and reactive loads Reactive components charge and discharge at ω ( current flows)
22 Complex Power (Example) p(t) = V eff I eff cos(θ  ϕ) + V eff I eff cos(ωt + θ + ϕ) S P Q voltage V = 4 0 o V, impedance Z = 60 o Ω, I = 60 o A, ω = π/ 6 rad/s p(t) = + 4 cos(π / 360 ) W voltage V =.83 0 o V rms, I = 60 o A rms S = P + jq = V I * = W + j 3.46VAr = 4 60 o VA
23 Power Triangle Commonly used graphical representation of S = P + jq = V I* = V (V/Z)* = VV* / Z* = V / Z* = I Z Useful relationships: P = S cos(θ), Q = S sin(θ), Θ = power angle = tan 1 (Q/P) Q = P tan(θ) Quadrant means 1st  power factor is lagging, inductive load 4th  power factor is leading, capacitive load Need only two quantities to find third Im S S Q Re P (4 60 o VA = W + j 3.46VAr)
24 Power and Phasors Another interpretation of active and reactive power components Current components In phase with voltage  I eff cos(θ  ϕ) 90 out of phase (quadrature component)  I eff sin(θ  ϕ) Multiplied by V results in P and Q Im θ  ϕ I eff V eff I eff cos(θ  ϕ) I eff sin θ  ϕ Re
25 Power and Phasors Example: (Chapter 11, Problem 4.) Both sources are operating at the same frequency. Find the complex power generated by each source and the complex power absorbed by each passive circuit element. Vx 100 Vx Vx j = 0 6+ j4 j Vx + j = + j0 6+ j4 6+ j4 V = V x I1 = = A 6+ j4 1 S 1. gen = = j 443VA.
26 Power and Phasors Example: (Chapter 11, Problem 4.) Both sources are operating at the same frequency. Find the complex power generated by each source and the complex power absorbed by each passive circuit element. S 1 S 6, abs = = j0 VA 1 = ( j4)9.806 = 0 + j19.3va j I = = , 5 1 S5abs = = j0 VA j4, abs S S, gen j10, abs 1 = ( j 100) = j 39.3VA = ( j 10) = 0 j 14.3VA = VA 10
27 Power Measurement Wattmeter(hours) measures active load Varmeter(hours) measures reactive load Average PF is used to adjust consumer's bill (industry has to pay for unwanted losses) Complex power delivered to individual loads equals their sum no matter how loads are connected S = V I* = V (I 1 + I )* = V (I* 1 + I* ) = VI* 1 + VI*
28 Power Factor Correction Large industrial consumers pay penalty when PF < 0.85 Caused by inductive loads (motors) Why: Causes increased Device ratings Transmission and distribution losses Example: $0./kVAr above 6% of average (real) power demand S = P + jq = P + j0.6p = P (1+j0.6) = P ( ) Targets cos(31.8 ) = 0.85 (pay penalty when PF < 0.85) Use compensation capacitors in parallel with load
29 Power Factor Correction Value of capacitance C = P ( tanθ tanθ ) corrects the PF angle from old to new at the specified frequency and voltage old ωv rms new Derived from Q = V rms /X c = V rms ωc (Q old Q new ) / V rms = ωc P(tan θ old tan θ new ) / V rms = ωc
30 Complex Power Example: Source of 115 Vrms supplies two loads. Loads are connected in parallel: 7kW / 3 kvar and 4kVA at 0.85 pf lagging. Find the pf of the equivalent load as seen from the input terminal. S 1 = j 3000 S = 4k [cos(θ) + j sin(θ)] = 4k [ j sin(cos 1 (0.85))] = j 107 S = S 1 + S = j 5107 = θ = tan 1 (Q / P) = tan 1 (5107 / 10400) = 6.15 cos(θ) = cos 6.15 = Z = V / S = 115 / = 1.14Ω Z = 1.14Ω 6.15 = j 0.5 Ω (remember: S = V / Z*)
7.1 POWER IN AC CIRCUITS
C H A P T E R 7 AC POWER he aim of this chapter is to introduce the student to simple AC power calculations and to the generation and distribution of electric power. The chapter builds on the material
More informationChapter 12. RL Circuits. Objectives
Chapter 12 RL Circuits Objectives Describe the relationship between current and voltage in an RL circuit Determine impedance and phase angle in a series RL circuit Analyze a series RL circuit Determine
More informationChapt ha e pt r e r 12 RL Circuits
Chapter 12 RL Circuits Sinusoidal Response of RL Circuits The inductor voltage leads the source voltage Inductance causes a phase shift between voltage and current that depends on the relative values of
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 informationChapter 12 Driven RLC Circuits
hapter Driven ircuits. A Sources... . A ircuits with a Source and One ircuit Element... 3.. Purely esistive oad... 3.. Purely Inductive oad... 6..3 Purely apacitive oad... 8.3 The Series ircuit...
More informationChapter 10. RC Circuits. Objectives
Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine
More informationEXPERIMENT 4: MEASUREMENT OF REACTANCE OFFERED BY CAPACITOR IN DIFFERENT FREQUENCY FOR RC CIRCUIT
Kathmandu University Department of Electrical and Electronics Engineering BASIC ELECTRICAL LAB (ENGG 103) EXPERIMENT 4: MEASUREMENT OF REACTANCE OFFERED BY CAPACITOR IN DIFFERENT FREQUENCY FOR RC CIRCUIT
More informationChapter 35 Alternating Current Circuits
hapter 35 Alternating urrent ircuits acircuits Phasor Diagrams Resistors, apacitors and nductors in acircuits R acircuits acircuit power. Resonance Transformers ac ircuits Alternating currents and
More informationFUNDAMENTALS OF ENGINEERING (FE) EXAMINATION
January 8, 008 1:55 Appc Sheet number 1 Page number 77 magenta black A P P E N D I X C FUNDAMENTALS OF ENGINEERING (FE) EXAMINATION C.1 INTRODUCTION The Fundamentals of Engineering (FE) examination 1 is
More informationAC Power. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department
by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU, Page 1 Voltage Waveform Consider the
More informationAlternatingCurrent Circuits
hapter 1 Alternatingurrent ircuits 1.1 A Sources... 11. Simple A circuits... 13 1..1 Purely esistive load... 13 1.. Purely Inductive oad... 15 1..3 Purely apacitive oad... 17 1.3 The Series ircuit...
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 informationε: Voltage output of Signal Generator (also called the Source voltage or Applied
Experiment #10: LR & RC Circuits Frequency Response EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage Sensor graph paper (optional) (3) Patch Cords Decade resistor, capacitor, and
More informationFrequency response: Resonance, Bandwidth, Q factor
Frequency response: esonance, Bandwidth, Q factor esonance. Let s continue the exploration of the frequency response of circuits by investigating the series circuit shown on Figure. C + V  Figure The
More informationIntroduction to Complex Numbers in Physics/Engineering
Introduction to Complex Numbers in Physics/Engineering ference: Mary L. Boas, Mathematical Methods in the Physical Sciences Chapter 2 & 14 George Arfken, Mathematical Methods for Physicists Chapter 6 The
More informationModule P5.4 AC circuits and electrical oscillations
F L E X I B L E L E A R N I N G A P P R O A C H T O P H Y S I C S Module P5.4 Opening items. Module introduction.2 Fast track questions.3 Ready to study? 2 AC circuits 2. Describing alternating currents
More informationUnderstanding Power Factor and How it Affects Your Electric Bill. Presented by Scott Peele PE
Understanding Power Factor and How it Affects Your Electric Bill Presented by Scott Peele PE Understanding Power Factor Definitions kva, kvar, kw, Apparent Power vs. True Power Calculations Measurements
More informationChapter 22: Alternating current. What will we learn in this chapter?
Chapter 22: Alternating current What will we learn in this chapter? Contents: Phasors and alternating currents Resistance and reactance Series R L C circuit Power in accircuits Series resonance Parallel
More informationCIRCUITS LABORATORY EXPERIMENT 3. AC Circuit Analysis
CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis 3.1 Introduction The steadystate behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the
More informationANALYTICAL METHODS FOR ENGINEERS
UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME  TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations
More informationNZQA registered unit standard 20431 version 2 Page 1 of 7. Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians
NZQA registered unit standard 0431 version Page 1 of 7 Title Demonstrate and apply fundamental knowledge of a.c. principles for electronics technicians Level 3 Credits 7 Purpose This unit standard covers
More informationApril 8. Physics 272. Spring Prof. Philip von Doetinchem
Physics 272 April 8 Spring 2014 http://www.phys.hawaii.edu/~philipvd/pvd_14_spring_272_uhm.html Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272  Spring 14  von Doetinchem  218 LC in parallel
More informationPower measurement in balanced 3 phase circuits and power factor improvement. 1 Power in Single Phase Circuits. Experiment no 1
Experiment no 1 Power measurement in balanced 3 phase circuits and power factor improvement 1 Power in Single Phase Circuits Let v = m cos(ωt) = cos(ωt) is the voltage applied to a RL circuit and i =
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 informationPhasors. Phasors. by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department. ^ V cos (wt + θ) ^ V sin (wt + θ)
V cos (wt θ) V sin (wt θ) by Prof. Dr. Osman SEVAİOĞLU Electrical and Electronics Engineering Department EE 209 Fundamentals of Electrical and Electronics Engineering, Prof. Dr. O. SEVAİOĞLU, Page 1 Vector
More informationDC and AC Impedance of Reactive Elements
8/30/2005 D and A Impedance of Reactive Elements.doc /7 D and A Impedance of Reactive Elements Now that we are considering timevarying signals, we need to consider circuits that include reactive elements
More informationBasic Electrical Theory
Basic Electrical Theory Power Principles and Phase Angle PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives At the end of this presentation the learner will be able to; Identify the characteristics
More information615xx, 616xx, 617xxx, 646x, 64xx, 65xx Series Programmable AC source
Chroma Systems Solutions, Inc. AC Power Definitions 615xx, 616xx, 617xxx, 646x, 64xx, 65xx Series Programmable AC source Keywords: Peak, RMS, Phase, Inrush Current, Power Factor, Crest Factor, Apparent
More informationReactance and Impedance
Reactance and Impedance Capacitance in AC Circuits Professor Andrew H. Andersen 1 Objectives Describe capacitive ac circuits Analyze inductive ac circuits Describe the relationship between current and
More information14: Power in AC Circuits
E1.1 Analysis of Circuits (20157265) AC Power: 14 1 / 11 Average Power E1.1 Analysis of Circuits (20157265) AC Power: 14 2 / 11 Average Power Intantaneous Power dissipated inr: p(t) = v2 (t) R E1.1 Analysis
More informationBasic AC Reactive Components IMPEDANCE
Basic AC Reactive Components Whenever inductive and capacitive components are used in an AC circuit, the calculation of their effects on the flow of current is important. EO 1.9 EO 1.10 EO 1.11 EO 1.12
More informationε rms ε substation HOMEWORK #11 Chapter 29
HOMEWOK # hapter 9 5 f the frequency in the circuit in Figure 98 is doubled, the capacitive reactance of the circuit will (a) double, (b) not change, (c) halve, (d) quadruple. Determine the oncept The
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 informationPart IV Modern Rectifiers and Power System Harmonics
Part IV Modern Rectifiers and Power System Harmonics Chapter 15 Chapter 16 Chapter 17 Chapter 18 Power and Harmonics in Nonsinusoidal Systems LineCommutated Rectifiers The Ideal Rectifier Low Harmonic
More informationProf. Anchordoqui Problems set # 11 Physics 169 May 5, 2015
rof. Anchordoqui roblems set # hysics 69 May 5, 5. A semicircular conductor of radius.5 m is rotated about the axis A at a constant rate of rev/min (Fig. ). A uniform magnetic field in all of the lower
More informationAlternating Current. Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin
Asist. Prof. Dr. Aytaç Gören Asist. Prof. Dr. Levent Çetin 30.10.2012 Contents Alternating Voltage Phase Phasor Representation of AC Behaviors of Basic Circuit Components under AC Resistance, Reactance
More informationChapter 10. RC Circuits ISU EE. C.Y. Lee
Chapter 10 RC Circuits Objectives Describe the relationship between current and voltage in an RC circuit Determine impedance and phase angle in a series RC circuit Analyze a series RC circuit Determine
More informationExperiment V: The AC Circuit, Impedance, and Applications to High and Low Pass Filters
Experiment : The AC Circuit, Impedance, and Applications to High and Low Pass Filters I. eferences Halliday, esnick and Krane, Physics, ol. 2, 4th Ed., Chapters 33 Purcell, Electricity and Magnetism, Chapter
More informationAPPLICATION NOTE  018
APPLICATION NOTE  018 Power Transformers Background Power Transformers are used within an AC power distribution systems to increase or decrease the operating voltage to achieve the optimum transmission
More informationALTERNATING CURRENTS
ALTERNATING CURRENTS VERY SHORT ANSWER QUESTIONS Q1. What is the SI unit of? Q2. What is the average value of alternating emf over one cycle? Q3. Does capacitor allow ac to pass through it? Q4. What
More informationA complex number W consists of real and imaginary parts a and b respectively, and the imaginary constant j which is the square root of negative one.
eactance and Impedance A Voltage and urrent In a D circuit, we learned that the relationship between voltage and current was V=I, also known as Ohm's law. We need to find a similar law for A circuits,
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 informationDirect versus Alternating Current Things We Can Measure
Phil Sherrod W4PHS Direct versus Alternating Current Things We Can Measure Direct Current (DC) Alternating Current (AC) Voltage Voltage (peak, RMS) Current Current (peak, effective) Power True power, Apparent
More informationBasic Electrical Theory
Basic Electrical Theory Impedance PJM State & Member Training Dept. PJM 2014 10/24/2013 Objectives Identify the components of Impedance in AC Circuits Calculate the total Impedance in AC Circuits Identify
More informationChapter 3 AUTOMATIC VOLTAGE CONTROL
Chapter 3 AUTOMATIC VOLTAGE CONTROL . INTRODUCTION TO EXCITATION SYSTEM The basic function of an excitation system is to provide necessary direct current to the field winding of the synchronous generator.
More informationIn this article, I provide an overview
QA Quality Assurance Reactive Power Primer In this article, I provide an overview of the three types of electrical power in ac circuits: real power, reactive power and apparent power. I also explain how
More informationLaboratory #2: AC Circuits, Impedance and Phasors Electrical and Computer Engineering EE University of Saskatchewan
Authors: Denard Lynch Date: Aug 30  Sep 28, 2012 Sep 23, 2013: revisionsdjl Description: This laboratory explores the behaviour of resistive, capacitive and inductive elements in alternating current
More informationLCR Series Circuits. AC Theory. Introduction to LCR Series Circuits. Module 9. What you'll learn in Module 9. Module 9 Introduction
Module 9 AC Theory LCR Series Circuits Introduction to LCR Series Circuits What you'll learn in Module 9. Module 9 Introduction Introduction to LCR Series Circuits. Section 9.1 LCR Series Circuits. Amazing
More informationChapter 5: Analysis of TimeDomain Circuits
Chapter 5: Analysis of TimeDomain Circuits This chapter begins the analysis of circuits containing elements with the ability to store energy: capacitors and inductors. We have already defined each of
More informationExtra Questions  1. 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A
Extra Questions  1 1. What current will flow in a 20Ω resistor when it is connected to a 50V supply? a) 0.4A b) 1.6A c) 2.5A 2. A current of 500mA flows in a resistance of 12Ω. What power is dissipated
More informationPower Factor Correction for Power Systems First Semester Report Spring Semester 2007
Power Factor Correction for Power Systems First Semester Report Spring Semester 2007 by Pamela Ackerman Prepared to partially fulfill the requirements for EE401 Department of Electrical and Computer Engineering
More informationL and C connected together. To be able: To analyse some basic circuits.
circuits: Sinusoidal Voltages and urrents Aims: To appreciate: Similarities between oscillation in circuit and mechanical pendulum. Role of energy loss mechanisms in damping. Why we study sinusoidal signals
More informationPHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA
PHASOR DIAGRAMS HANDSON RELAY SCHOOL WSU PULLMAN, WA. RON ALEXANDER  BPA What are phasors??? In normal practice, the phasor represents the rms maximum value of the positive half cycle of the sinusoid
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67  FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 3 TUTORIAL 1  SINGLE PHASE AC CIRCUITS
EDEXCE NATIONA CETIFICATE/DIPOMA UNIT 67  FUTHE EECTICA PINCIPES NQF EVE 3 OUTCOME 3 TUTOIA  SINGE PHASE AC CICUITS Unit content 3. Understand the behaviour of singlephase alternating current (AC) circuits
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 informationChapter 12. RL Circuits ISU EE. C.Y. Lee
Chapter 12 RL Circuits Objectives Describe the relationship between current and voltage in an RL circuit Determine impedance and phase angle in a series RL circuit Analyze a series RL circuit Determine
More informationThe Ideal Transformer. Description and Circuit Symbol
The Ideal Transformer Description and Circuit Symbol As with all the other circuit elements, there is a physical transformer commonly used in circuits whose behavior can be discussed in great detail. However,
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 informationCurrent and Temperature Ratings
Document 3611 Current and Temperature Ratings Introduction This application note describes: How to interpret Coilcraft inductor current and temperature ratings Our current ratings measurement method and
More informationRectifier circuits & DC power supplies
Rectifier circuits & DC power supplies Goal: Generate the DC voltages needed for most electronics starting with the AC power that comes through the power line? 120 V RMS f = 60 Hz T = 1667 ms) = )sin How
More information1 Introduction. 2 Complex Exponential Notation. J.L. Kirtley Jr.
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.06 Introduction to Power Systems Class Notes Chapter AC Power Flow in Linear Networks J.L. Kirtley Jr.
More informationLecture 22: Class C Power Amplifiers
Whites, EE 322 Lecture 22 Page 1 of 13 Lecture 22: lass Power Amplifiers We discovered in Lecture 18 (Section 9.2) that the maximum efficiency of lass A amplifiers is 25% with a resistive load and 50%
More informationPHASOR DIAGRAMS II Fault Analysis Ron Alexander Bonneville Power Administration
PHASOR DIAGRAMS II Fault Analysis Ron Alexander Bonneville Power Administration For any technician or engineer to understand the characteristics of a power system, the use of phasors and polarity are essential.
More informationCOMPLEX NUMBERS AND PHASORS
COMPLEX NUMBERS AND PHASORS 1 Professor Andrew E. Yagle, EECS 206 Instructor, Fall 2005 Dept. of EECS, The University of Michigan, Ann Arbor, MI 481092122 I. Abstract The purpose of this document is to
More informationVectors and Phasors. A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles. Owen Bishop
Vectors and phasors Vectors and Phasors A supplement for students taking BTEC National, Unit 5, Electrical and Electronic Principles Owen Bishop Copyrught 2007, Owen Bishop 1 page 1 Electronics Circuits
More informationHow to add sine functions of different amplitude and phase
Physics 5B Winter 2009 How to add sine functions of different amplitude and phase In these notes I will show you how to add two sinusoidal waves each of different amplitude and phase to get a third sinusoidal
More informationLecture 21. AC Circuits, Reactance.
Lecture 1. AC Circuits, Reactance. Outline: Power in AC circuits, Amplitude and RMS values. Phasors / Complex numbers. Resistors, Capacitors, and Inductors in the AC circuits. Reactance and Impedance.
More informationTrigonometry for AC circuits
Trigonometry for AC circuits This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationTrigonometry for AC circuits
Trigonometry for AC circuits This worksheet and all related files are licensed under the Creative Commons Attribution License, version 1.0. To view a copy of this license, visit http://creativecommons.org/licenses/by/1.0/,
More informationEðlisfræði 2, vor 2007
[ Assignment View ] [ Pri Eðlisfræði 2, vor 2007 31. Alternating Current Circuits Assignment is due at 2:00am on Wednesday, March 21, 2007 Credit for problems submitted late will decrease to 0% after the
More informationRC transients. EE 201 RC transient 1
RC transients Circuits having capacitors: At DC capacitor is an open circuit, like it s not there. Transient a circuit changes from one DC configuration to another DC configuration (a source value changes
More informationChapter 11. Inductors. Objectives
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 informationUnit2: Resistor/CapacitorFilters
Unit2: Resistor/CapacitorFilters Physics335 Student October 3, 27 Physics 335Section Professor J. Hobbs Partner: Physics335 Student2 Abstract Basic RCfilters were constructed and properties such as
More informationTransistor Tuned Amplifiers
5 Transistor Tuned Amplifiers 389 Transistor Tuned Amplifiers 5. Tuned Amplifiers 5. Distinction between Tuned Amplifiers and other Amplifiers 5.3 Analysis of Parallel Tuned Circuit 5.4 Characteristics
More informationApplication Guide. Power Factor Correction (PFC) Basics
Power Factor Correction (PFC) Basics Introduction Power Factor, in simple terms, is a number between zero and one that represents the ratio of the real power to apparent power. Real power (P), measured
More informationEinstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road, New Delhi , Ph. : ,
1 EMI & AC 1. Derive an expression for the impendance of a coil in AC ciruit. A current of 1.1 A flows through a coil when connected to a 110 V DC. When 110 V AC of 50 Hz is applied to the same coil, only
More informationThe electrical energy is almost exclusively
CHAPTER CHAPTER 6 Power Factor Improvement 6.1 Power Factor 6.2 Power Triangle 6.3 Disadvantages of Low Power Factor 6.4 Causes of Low Power Factor 6.5 Power Factor Improvement 6.6 Power Factor Improvement
More informationLABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER. Bridge Rectifier
LABORATORY 10 TIME AVERAGES, RMS VALUES AND THE BRIDGE RECTIFIER Fullwave Rectification: Bridge Rectifier For many electronic circuits, DC supply voltages are required but only AC voltages are available.
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 informationExperiment #11: LRC Circuit (Power Amplifier, Voltage Sensor)
Experiment #11: LRC Circuit (Power Amplifier, Voltage Sensor) Concept: circuits Time: 30 m SW Interface: 750 Windows file: RLC.SWS EQUIPMENT NEEDED Science Workshop Interface Power Amplifier (2) Voltage
More informationChapter 3. Simulation of NonIdeal Components in LTSpice
Chapter 3 Simulation of NonIdeal Components in LTSpice 27 CHAPTER 3. SIMULATION OF NONIDEAL COMPONENTS IN LTSPICE 3.1 PreLab The answers to the following questions are due at the beginning of the lab.
More informationECE207 Electrical Engineering Fall Lab 1 Nodal Analysis, Capacitor and Inductor Models
Lab 1 Nodal Analysis, Capacitor and Inductor Models Objectives: At the conclusion of this lab, students should be able to: use the NI mydaq to power a circuit using the power supply and function generator
More informationSeries & Parallel Impedance Parameters and Equivalent Circuits
Chroma ystems olutions, Inc. eries & arallel Impedance arameters and Equivalent Circuits Keywords: Impedance, capacitance, resistance Title: roduct Family: eries & arallel Impedance arameters and Equivalent
More informationThe current that flows is determined by the potential difference across the conductor and the resistance of the conductor (Ohm s law): V = IR P = VI
PHYS1000 DC electric circuits 1 Electric circuits Electric current Charge can move freely in a conductor if an electric field is present; the moving charge is an electric current (SI unit is the ampere
More informationKirchhoff s Laws in Dynamic Circuits
Kirchhoff s Laws in Dynamic Circuits Dynamic circuits are circuits that contain capacitors and inductors. Later we will learn to analyze some dynamic circuits by writing and soling differential equations.
More informationLab #4 Capacitors and Inductors. Capacitor and Inductor Transient Response
Capacitor and Inductor Transient Response Capacitor Theory Like resistors, capacitors are also basic circuit elements. Capacitors come in a seemingly endless variety of shapes and sizes, and they can all
More informationElectrical Resonance
Electrical Resonance (RLC series circuit) APPARATUS 1. RLC Circuit board 2. Signal generator 3. Oscilloscope Tektronix TDS1002 with two sets of leads (see Introduction to the Oscilloscope ) INTRODUCTION
More informationR f. V i. ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response
ET 438a Automatic Control Systems Technology Laboratory 4 Practical Differentiator Response Objective: Design a practical differentiator circuit using common OP AMP circuits. Test the frequency response
More informationAC RL and RC Circuits
AC RL and RC Circuits When a sinusoidal AC voltage is applied to an RL or RC circuit, the relationship between voltage and current is altered. The voltage and current still have the same frequency and
More informationChapter 15 10/14/2014
Chapter 15 Analyze series and parallel ac circuits to find Voltage Current Power Total impedance, admittance Apply known circuit theories Kirchhoff s current, voltage laws Voltage or current divider rule
More informationLecturer: James Grimbleby URL: http://www.personal.rdg.ac.uk/~stsgrimb/ email: j.b.grimbleby reading.ac.uk
AC Circuit Analysis Module: SEEA5 Systems and Circuits Lecturer: UL: http://www.personal.rdg.ac.uk/~stsgrimb/ email:.b.grimbleby reading.ac.uk Number of Lectures: ecommended text book: David Irwin and
More informationMotor Efficiency and Power Factor ME 416/516
Motor Efficiency and Power Factor Motivation More than half of all electric energy generated goes to power electric motors. Electric motor converts electric power into shaft power. In thermodynamics terms,
More informationInductive and Capacitive Reactance
Inductive and Capacitive Reactance Course No: E04005 Credit: 4 PDH A. Bhatia Continuing Education and Development, Inc. 9 Greyridge Farm Court Stony Point, NY 10980 P: (877) 3225800 F: (877) 3224774
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 informationPractice Problems  Chapter 33 Alternating Current Circuits
Multiple Choice Practice Problems  Chapter 33 Alternating Current Circuits 4. A highvoltage powerline operates at 500 000 Vrms and carries an rms current of 500 A. If the resistance of the cable is
More informationLC Resonant Circuits Dr. Roger King June Introduction
LC Resonant Circuits Dr. Roger King June 01 Introduction Secondorder systems are important in a wide range of applications including transformerless impedancematching networks, frequencyselective networks,
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 informationElectrical Fundamentals  Reactance and Impedance
PDHonline Course E239 (4 PDH) Electrical Fundamentals  Reactance and Impedance Instructor: A. Bhatia, B.E. 2012 PDH Online PDH Center 5272 Meadow Estates Drive Fairfax, VA 220306658 Phone & Fax: 7039880088
More informationFrequency response of a general purpose singlesided OpAmp amplifier
Frequency response of a general purpose singlesided OpAmp amplifier One configuration for a general purpose amplifier using an operational amplifier is the following. The circuit is characterized by:
More informationFREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY. We start with examples of a few filter circuits to illustrate the concept.
FREQUENCY RESPONSE AND PASSIVE FILTERS LABORATORY In this experiment we will analytically determine and measure the frequency response of networks containing resistors, AC source/sources, and energy storage
More information