10.1 COMPLEX POWER IN CIRCUITS WITH AC SIGNALS
|
|
- Clifford Skinner
- 5 years ago
- Views:
Transcription
1 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 10.1 OMPEX POWER IN IRUI WIH A IGNA What concept is illustrated in the plots in Figure 4.1? Explain the concept in the following equation and relate it to the plots: VI p p Pave VRM IRM Veff Ieff (10.1) Note: he RM and eff subscripts have identical meaning (RM will be used in this chapter, as it was in h. 4). What is true power? Real power? Figure 4.1 (reproduced) he previous power development is valid for what type of component in a circuit? Why? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 1
2 What is the phase relationship between the voltage and the current for inductors? For capacitors? Why for each? he graphical multiplication of v(t) and i(t) when they are ±90 out of phase is shown in Figure Which is leading, the voltage or the current leading? What is the average power in this case? Why? Is this result the same as the p(t) result for the resistive load? Why or why not? What is the significance of positive and negative power? First, explain the passive sign convention: What is positive power for inductors (Fig. 10.a)? Figure 10.1 What is positive power for capacitors (Fig. 10.a)? Figure 10. ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page
3 What is negative power for inductors (Fig. 10.b)? What is negative power for capacitors (Fig. 10.b)? hus, what is the net average power for ideal inductors and capacitors? How is energy storage in inductors and capacitors for A signals quantified? Need a power-like quantity that corresponds to energy storage for inductors and capacitors Need a method to express both electrical energy conversion and electrical energy storage with A signals Identify the following equations: E V E I (10.) 1 1 Note: calculus is needed to derive the stored energy expressions for A signals. Alternatively, an explanation: alculus average value of energy stored in a capacitor or an inductor expressed with RM values: E V E I (10.3) (ave) 1 1 RM (ave) RM Notation: he capital letter E shall be used to indicate D energy or average energy in the A case. Explain how the following equations were obtained: 1 V I E V V I X V I RM RM RM RM RM RM RM (10.4) V V V I E I I I 1 1 RM 1 RM RM RM RM RM RM X (10.5) What is striking between these two general results? What is the average energy stored in an inductor or a capacitor directly proportional to? What is the average energy stored in an inductor or a capacitor inversely proportional to? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 3
4 Does (V RM I RM )/() in this energy expression contain a power-like quantity? If so, what is it? If not, why not? What does the power-like quantity represent for inductors and capacitors? How can this power-like quantity be utilized for inductors and capacitors? Recall impedance: Z R jx What is the phase relationship between the voltage and the current for the real part of Z? Why? What is the phase relationship between the voltage and the current for the imaginary part of Z? Why? What is the phase relationship between the A voltage and current when the power is real? What happens to electrical energy for real power? What is the phase relationship between A voltage and current that represents stored energy? By analogy to impedance, what type of number is the power that represents energy storage? Based on the previous discussion, explain the following expression for complex power : P jq (10.6) where P = power in watts (W), Q = power in volt-amperes reactive (VARs), and = power in volt-amperes (VA). Note: do not confuse reactive power Q with electric charge Q know from context which one is appropriate Now relate V RM I RM to complex power: (in-phase part of V I ) 0 (90 out-of -phase part of V I ) 90 RM RM RM RM (in-phase part of V I ) j(90 out-of -phase part of V I ) (10.7) RM RM RM RM How does one separate the V RM I RM product into real and imaginary parts? tart with: V I ( V )( I ) V I ( )??? RM RM RM V RM I RM RM V I What is wrong with this equation? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 4
5 Has the total phase angle ( V + I ) ever appeared up to now? What is the phase shift between voltage and current that is physically significant for impedance? Hence, the phase angle should be the not the sum: VRM IRM ( V I) (10.8) How is the negative (opposite sign) of an angle obtained with complex numbers? Explain Figure I ( I ) I (10.9) RM RM I RM I Figure 10.3 hus, the complex conjugate is Explain each step that follows: V I ( V )( I ) V ( I ) (10.10) RM RM RM V RM I RM V RM I V I ( ) V I (10.11) RM RM V I RM RM What is? Refer to Figure 10.4: V I cos jv I sin P jq (10.1) RM RM RM RM P Re ( ) V I cos (10.13) RM RM Figure 10.4 where Re means Q Im ( ) V I sin RM RM (10.14) where Im means ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 5
6 V I cos jv I sin RM RM RM RM ( V I cos ) 0 ( V I sin ) 90 RM RM RM RM P jq (10.15) P jq (10.16) where: = in units of P = in units of = of complex power in rectangular form, Q = in units of = of complex power in rectangular form, = in units of = of complex power in polar form, and = in units of = of complex power in polar form. Note: he unit watt is reserved for power that represents energy conversion. he key complex power expression is (10.17) VI VI( V I) P jq Are the phasor voltage and current effective (RM) or peak values? Explain. Why is the VI product called apparent power for A signals? What is = V I? (10.18) What is Q = Q Q? (10.19) Why is the sign for Q positive? Why is the sign for Q negative? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 6
7 10. HOW O AUAE OMPEX POWER here are two ways to calculate the total complex power provided by a source to a circuit: a. or b. Determine the total phasor voltage and the total phasor current supplied by the source to the circuit (single source circuits only) hen use Equation (10.17): VI VI( V I) P jq Determine the real or reactive power of each component in the circuit Add all the real powers to obtain the total power P OA Add all the reactive powers to obtain the total reactive power Q OA (positive Q for inductors, negative Q for capacitors) hen form the total complex power: P jq (Multiple source circuits will be covered in the next section). Example (Explain each step.) Determine the total complex power provided by the source to the circuit shown in Figure : : V 100 V R = 10 X = 15 RM trategy: olution: Z R jx 10 j15 Figure 10.5 V 10 0 I A Z 10 j15 VI (10 0 )( ) (10 0 )( ) j VA (3.08 j4.6) VA 3.08 W j4.6 VAR ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 7
8 Why are both real power and reactive power present? Which complex power calculation method was demonstrated in this example? Explain each step as it relates to determining complex power using the second method: Note: All phasors are assumed to have RM magnitudes throughout this discussion. For a resistance, V I V I ( ) V I 0 0 P j0 P (10.0) R R R R R V I R R R R R VR PR VR IR IRR QR 0 (resistances only) (10.1) R Which of the numbers is complex in the previous equation? Explain: For a capacitor, V I V I ( ) V I jq jq (10.) V I V P Q V I I X (capacitors only) (10.3) 0 X For an inductance, V I V I ( ) V I jq jq (10.4) V I ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 8
9 V P Q V I I X (inductors only) (10.5) 0 X Explain how complex power is determined using the next equation: [ ] (10.6) VI P j Q Q where the summation sign is designated by the uppercase Greek letter sigma (). P is Q is Q is Example 10.. (Fill in the steps.) Determine the complex power in the circuit shown in Figure 10.5 repeated below. Given: Desired: trategy: Figure 10.5 olution: Answer: P jq 3.08 W j4.6 VAR (3.08 j4.6) VA VA ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 9
10 he complex power can be visualized using the power triangle. A plot in the complex number plane Defined by three quantities: - the origin - the real power on the real axis - the reactive power on the imaginary axis Example ketch and label the power triangle for the circuit in Figure Given: 3.08 W j4.6 VAR VA P = 3.08 W Q = 4.6 VAR = 5.55 VA = 56.3 Desired: power triangle trategy: Plot P and Q in approximate proportion ketch the triangle abel P, Q,, olution: Explain why the power triangle flips between the inductive and capacitive cases (Figure 10.7). Figure 10.7 ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 10
11 Determine the equivalent aspect of the following two equations: VI VI ( V I) (10.7) V V V V Z ( V I) Z I I I I (10.8) For example, check out the results in Examples and 10..: his fact is a useful check in complex power calculations. Form a summary statement for each relation that follows: 3.08 W j4.6 VAR VA Z R jx 10 j15 Z (10.9) VI VI( V I) P jq VR PR VR IR IRR QR 0 (10.30) R V P Q V I I X (10.31) 0 X V P Q V I I X (10.3) 0 X [ ] (10.33) VI P j Q Q ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 11
12 10.3 OMPEX POWER AUAION IN ERIE PARAE IRUI Example (Explain each step.) Determine the complex power provided by the source to the circuit shown in Figure 10.8 by (a) determining and summing the individual powers of the components, and (b) VI. Given: circuit in Figure 10.8 Desired: trategy: a. Z, I, V x using series parallel analysis Q = I X Q V X olution: a. Z x b. x P Vx R P j( Q Q ) V I ( Z R)( Z ) (13)( j13) Z Z 13 j13 R Z Z Z j x V I A Z x V IZ ( )( ) V x RM RM Figure 10.8 Q I X (.7343) (65) VAR Q Vx VAR X 13 Vx P W R 13 P j( Q Q ) j( ) W j7.06 VAR 44 W j7 VAR VI ( )( ) b. ( )( ) VA j W j7 VAR Is the circuit inductive or capacitive from an impedance viewpoint? Why? Is the circuit inductive or capacitive from a complex power viewpoint? Why? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 1
13 Multiple source circuits: onsider a circuit with more than one source. an the powers in each component due to each source be summed? Why or why not? an the voltages (or currents) for each component be summed? If so, under what condition? he complex power for each component is determined from that total phasor voltage (or current) for that component. he total complex power of the circuit is determined by summing the complex powers of the individual components. Example Determine the total complex power provided by the source to the circuit in Example he circuit schematic is repeated below (Figure 10.9). Figure 10.9 Given: Desired: trategy: he circuit from Figure 9.18 is repeated in Figure 10.9 with the current in each branch labeled. olution: (Perform all steps on separate paper.) ub-answers and answer to check as you proceed: For the source: I A, I A, I A b a c For the 150 source: I A, I A, I A c a b uperposition: I A, I A, I A a b c Answer: = ( ) + j( ) = j = 18.4 W j18.0 VAR ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 13
14 10.4 POWER FAOR AND PF ORREION What is the power factor angle? Definition of power factor (pf): How does the P/ ratio relate to in the power triangle (see Figure 10.7, repeated to the right)? Figure 10.7 onsider able 10.1 for the physical significance of pf. Explain the trend in pf versus power factor angle. ABE 10.1 power factor power factor angle When the power factor angle is ±90, what is the pf? Is the complex power real, reactive, or a mixture? Why? When the power factor angle is 0, what is the pf? Is the complex power real, reactive, or a mixture? Why? When the power factor is in the middle region between 1 and 0, is the complex power primarily real, reactive, or a mixture? Why? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 14
15 Given the power factor, can one tell whether the power factor angle is positive or negative? Why or why not? erminology applied to pf: leading or lagging. It is applied to the current relative to the voltage: If the power factor is leading, then the current leads the voltage. Is the circuit capacitive or inductive? Why? If the power factor is lagging, then the current lags the voltage. Is the circuit capacitive or inductive? Why? Major application of power factor: power factor correction Example: reat the circuit in Examples and 10.. as a block with complex power (Figure 10.1): Figure 10.1 Is the Q zero? Why or why not? Explain the following calculation: pf P leading j Is real, reactive, or both powers significantly present in the circuit? Explain. ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 15
16 What was added to the circuit in Fig. 10.1(b) as shown in Fig ? Figure Explain the mathematical statements that follow: P jq j( ) ( j0) VA 3.08 W What is the total complex power? What is the total real power? What is the total reactive power? pf P j j0 VI I A A V 10 0 Note: he original current in the circuit without pf correction (from Ex or 10..) is A. What are the primary effects of power factor correction with regards to each of the following aspects? (1) he power factor () he phase between the total circuit voltage and current (3) he circuit current What is the impact of (3) on wire sizes, power dissipation in wires, and costs? How should the component for pf correction be connected into the circuit (series or parallel)? Why? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 16
17 What type of component is added in parallel with the load in this example? Why? What is the value of the component to add in parallel in Figure 10.13? Identify what is known and what is unknown in the following equations: Q V X (10.35) X (10.36) Assume frequency is known. In this example, it is 60 Hz. Explain the following calculations: X V Q X mh 60 Example (Explain each step.) Determine (a) the reactance for power factor correction in the circuit shown in Figure 10.8 (repeated to the right). (b) Determine the component value if the frequency is 60 Hz. (c) Determine the pf both before and after pf correction. : W j7.08 VAR (from Example ) V V RM f = 60 Hz : a. X for pf correction Figure 10.8 b. value of or for pf correction c. pf before pf correction pf after pf correction : Qpf correction Im ( ) (inductive or capacitive, as appropriate) X V Q 1 X P pf ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 17
18 olution: (Explain each step.) Qpf correction Im ( ) 7.08 VAR (capacitive) X V Q X 60(145.39) F P pfbefore j pf after What is the difference and the significance of Figure with respect to Figure 10.8? Figure hus, what is power factor correction? What is the general approach to power factor correction? ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 18
19 Example (Explain or fill in each step, as appropriate.) Determine the reactance for power factor correction in the circuit shown in Figure Given: V V RM load 1: load : Figure Desired: : Determine for each load from pf: = cos 1 (pf). Determine for each load from V, I,, and leading/lagging status VI 1 Q Im ( ) (inductive or capacitive, as appropriate) olution: pf correction V X Q (Perform the calculations per the strategy. heck against the answers provided on the next page.) ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 19
20 45.00 (positive due to lagging pf) (negative due to leading pf) kva kva Q X (.97 j6.578) kva pf correction kvar (capacitive) earning Objectives Discussion: an you perform each learning objective for this chapter? (Examine each one.) As a result of successfully completing this chapter, you should be able to: 1. Describe why complex power is needed to express power in A circuits.. Describe complex power, apparent power, real power, reactive power, power factor angle, and power factor and the differences between them. 3. alculate complex power, apparent power, real power, reactive power, power factor angle, and power factor for components, groups of components, and entire circuits using two approaches: a. complex power equation in terms of phasor voltage and phasor current, and b. summing real or reactive powers of individual components. 4. Describe what power factor correction is and why it is important. 5. Determine the parallel reactance and component value required for power factor correction. ontemporary Electric ircuits, nd ed., Prentice-Hall, 008 lass Notes h. 10 Page 0
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 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 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 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 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 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 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 informationSeries Parallel Analysis of AC Circuits
HAE 9 eries arallel Analysis of A ircuits hapter Outline 9. A eries ircuits 9.2 A arallel ircuits 9.3 A eries arallel ircuits 9.4 Analysis of Multiple-ource A ircuits Using uperposition 9. A EIE IUI In
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 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 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 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 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 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 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 informationConsider Figure What is the horizontal axis grid increment?
Chapter Outline CHAPER 14 hree-phase Circuits and Power 14.1 What Is hree-phase? Why Is hree-phase Used? 14.2 hree-phase Circuits: Configurations, Conversions, Analysis 14.2.1 Delta Configuration Analysis
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 informationSeries 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 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 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 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 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 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 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 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 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 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 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 informationNote 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 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 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 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 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 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 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 informationModule 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 information1 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 informationChapter 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 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 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 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 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 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 informationf = 1 T 6 a.c. (Alternating Current) Circuits Most signals of interest in electronics are periodic : they repeat regularly as a function of time.
Analogue Electronics (Aero).66 66 Analogue Electronics (Aero) 6.66 6 a.c. (Alternating Current) Circuits Most signals of interest in electronics are periodic : they repeat regularly as a function of time.
More informationVTU 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 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 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 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 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 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 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 informationECE 241L Fundamentals of Electrical Engineering. Experiment 6 AC Circuits
ECE 241L Fundamentals of Electrical Engineering Experiment 6 AC Circuits A. Objectives: Objectives: I. Calculate amplitude and phase angles of a-c voltages and impedances II. Calculate the reactance and
More informationALTERNATING CURRENT
ATENATING UENT Important oints:. The alternating current (A) is generally expressed as ( ) I I sin ω t + φ Where i peak value of alternating current.. emf of an alternating current source is generally
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 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 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 informationChapter 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 informationSINUSOIDAL 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 informationSinusoidal Steady-State Analysis
Sinusoidal Steady-State Analysis Almost all electrical systems, whether signal or power, operate with alternating currents and voltages. We have seen that when any circuit is disturbed (switched on or
More information12 Chapter 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 informationElectrical Engineering Fundamentals for Non-Electrical Engineers
Electrical Engineering Fundamentals for Non-Electrical Engineers by Brad Meyer, PE Contents Introduction... 3 Definitions... 3 Power Sources... 4 Series vs. Parallel... 9 Current Behavior at a Node...
More informationRevised 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 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 informationLecture 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 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 informationBME/ISE 3511 Bioelectronics - Test Five Review Notes Fall 2015
BME/ISE 35 Bioelectronics - Test Five Review Notes Fall 205 Test Five Topics: RMS Resistive Power oss (I 2 R) A Reactance, Impedance, Power Factor R ircuit Analysis alculate Series R Impedance alculate
More informationECE 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 informationPHYS Fields and Waves
PHYS 2421 - Fields and Waves Idea: how to deal with alternating currents Edison wanted direct current, Tesla alternating current, who won? Mathematically: Instantaneous current: Instantaneous voltage:
More informationAnnouncements: 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 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 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 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 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 informationCourse Updates. Reminders: 1) Assignment #10 due Today. 2) Quiz # 5 Friday (Chap 29, 30) 3) Start AC Circuits
ourse Updates http://www.phys.hawaii.edu/~varner/phys272-spr10/physics272.html eminders: 1) Assignment #10 due Today 2) Quiz # 5 Friday (hap 29, 30) 3) Start A ircuits Alternating urrents (hap 31) In this
More informationTrue 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 informationBME/ISE 3511 Bioelectronics - Test Six Course Notes Fall 2016
BME/ISE 35 Bioelectronics - Test Six ourse Notes Fall 06 Alternating urrent apacitive & Inductive Reactance and omplex Impedance R & R ircuit Analyses (D Transients, Time onstants, Steady State) Electrical
More informationLearnabout 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 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 informationPhysics 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 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 informationSelf-Inductance. Φ i. Self-induction. = (if flux Φ 1 through 1 loop. Tm Vs A A. Lecture 11-1
Lecture - Self-Inductance As current i through coil increases, magnetic flux through itself increases. This in turn induces back emf in the coil itself When current i is decreasing, emf is induced again
More informationFIRST TERM EXAMINATION (07 SEPT 2015) Paper - PHYSICS Class XII (SET B) Time: 3hrs. MM: 70
FIRST TERM EXAMINATION (07 SEPT 205) Paper - PHYSICS Class XII (SET B) Time: 3hrs. MM: 70 Instructions:. All questions are compulsory. 2. Q.no. to 5 carry mark each. 3. Q.no. 6 to 0 carry 2 marks each.
More informationALTERNATING CURRENT. with X C = 0.34 A. SET UP: The specified value is the root-mean-square current; I. EXECUTE: (a) V = (0.34 A) = 0.12 A.
ATENATING UENT 3 3 IDENTIFY: i Icosωt and I I/ SET UP: The specified value is the root-mean-square current; I 34 A EXEUTE: (a) I 34 A (b) I I (34 A) 48 A (c) Since the current is positive half of the time
More informationPower 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 informationPhysics-272 Lecture 20. AC Power Resonant Circuits Phasors (2-dim vectors, amplitude and phase)
Physics-7 ecture 0 A Power esonant ircuits Phasors (-dim vectors, amplitude and phase) What is reactance? You can think of it as a frequency-dependent resistance. 1 ω For high ω, χ ~0 - apacitor looks
More informationElectrical Circuits Lab Series RC Circuit Phasor Diagram
Electrical Circuits Lab. 0903219 Series RC Circuit Phasor Diagram - Simple steps to draw phasor diagram of a series RC circuit without memorizing: * Start with the quantity (voltage or current) that is
More informationNZQA 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 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 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 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 information6.1 Introduction
6. Introduction A.C Circuits made up of resistors, inductors and capacitors are said to be resonant circuits when the current drawn from the supply is in phase with the impressed sinusoidal voltage. Then.
More informationECE 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 informationAlternating 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 informationAssessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526)
NCEA Level 3 Physics (91526) 2015 page 1 of 6 Assessment Schedule 2015 Physics: Demonstrate understanding of electrical systems (91526) Evidence Q Evidence Achievement Achievement with Merit Achievement
More informationReview 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 informationvba 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 informationC R. Consider from point of view of energy! Consider the RC and LC series circuits shown:
ircuits onsider the R and series circuits shown: ++++ ---- R ++++ ---- Suppose that the circuits are formed at t with the capacitor charged to value. There is a qualitative difference in the time development
More informationECEN 460 Exam 1 Fall 2018
ECEN 460 Exam 1 Fall 2018 Name: KEY UIN: Section: Score: Part 1 / 40 Part 2 / 0 Part / 0 Total / 100 This exam is 75 minutes, closed-book, closed-notes. A standard calculator and one 8.5 x11 note sheet
More informationI. Impedance of an R-L circuit.
I. Impedance of an R-L circuit. [For inductor in an AC Circuit, see Chapter 31, pg. 1024] Consider the R-L circuit shown in Figure: 1. A current i(t) = I cos(ωt) is driven across the circuit using an AC
More informationThe Basic Elements and Phasors
4 The Basic Elements and Phasors 4. INTRODUCTION The response of the basic R, L, and C elements to a sinusoidal voltage and current will be examined in this chapter, with special note of how frequency
More information