CHAPTER 5. Solutions for Exercises
|
|
- Julia Booth
- 6 years ago
- Views:
Transcription
1 HAPTE 5 Slutins fr Exercises E5. (a We are given v ( t 50 cs(00π t 30. The angular frequency is the cefficient f t s we have ω 00π radian/s. Then f ω / π 00 Hz T / f 0 ms m / 50 / 06. Furthermre, v(t attains a psitive peak when the argument f the csine functin is zer. Thus keeping in mind that ωt has units f radians, the psitive peak ccurs when π ω tmax 30 tmax ms 80 (b P avg / 5 W (c A plt f v(t is shwn in Figure 5.3 in the bk. E5. We use the trignmetric identity sin( z cs( z 90. Thus 00 sin(300π t cs(300πt 30 E5.3 ω πf 377 radian/s T / f 6.67 ms 55.6 m The perid crrespnds t 360 therefre 5 ms crrespnds t a phase angle f ( 5 / Thus the vltage is v ( t 55.6 cs(377t 08 E5.4 (a j cs( ω t + 0 sin( ωt 4.4 cs( ωt (b j j.6 + j cs( ω t sin( ωt cs( ωt (c j j 7.5 j sin( ω t cs( ωt cs( ωt 5.8
2 E5.5 The phasrs are and v lags v by 60 (r we culd say v leads v by 60 v leads v 3 by 5 (r we culd say v 3 lags v by 5 v leads v 3 by 75 (r we culd say v 3 lags v by 75 E5.6 (a E5.7 (a E5.8 (a Z jω j / 00 / j 50 Z (b The phasr diagram is shwn in Figure 5.0a in the bk. Z / jω j / 00 /( j Z (b The phasr diagram is shwn in Figure 5.0b in the bk. Z / 00 /(50 0 (b The phasr diagram is shwn in Figure 5.0c in the bk. E5.9 (a The transfrmed netwrk is: s Z j
3 i ( t 8.8 cs(500t j ω (b The phasr diagram is shwn in Figure 5.6b in the bk. (c i(t lags v s (t by 45. E5.0 The transfrmed netwrk is: Z /00 + /( j 50 + /( + j Z /( j A /( j /( A A Ω E5. The transfrmed netwrk is: We write K equatins fr each f the meshes: j ( 00 j 00 + j ( 0 Simplifying, we have 00 + j ( 00 + (00 j A and 0 ( t.44 cs(000t 45 A and i ( t cs(000t Slving we find A. Thus we have i. 3
4 E5. (a Fr a pwer factr f 00%, we have cs( θ, which implies that the current and vltage are in phase and θ 0. Thus, Q P tan( θ 0. Als P /[ cs( θ ] 5000 /[500 cs(0] 0 A. Thus we have 4.4 and m (b Fr a pwer factr f 0% lagging, we have cs( θ 0., which implies that the current lags the vltage by θ cs ( Thus, Q P tan( θ 4.49 ka. Als, we have P /[ cs( θ ] 50.0 A. Thus we have 70.7 A and m (c The current ratings wuld need t be five times higher fr the lad f part (b than fr that f part (a. Wiring csts wuld be lwer fr the lad f part (a. E5.3 The first lad is a 0 µ F capacitr fr which we have Z /( jω Ω θ 90 / Z A P cs( θ 0 Q sin( θ ka The secnd lad absrbs an apparent pwer f 0 kawith a pwer factr f 80% lagging frm which we have cs θ ( Ntice that we select a psitive angle fr θ because the lad has a lagging pwer factr. Thus we have P cs( θ 8.0 kw andq sin( θ 6 ka. Nw fr the surce we have: P P + P 8 kw Q Q + Q.3 s s ka P + Q ka / A s s s factr P s /( s s s pwer 00% 96.33% E5.4 First, we zer the surce and cmbine impedances in series and parallel t determine the Thévenin impedance. 4
5 Z t 50 j j j 50 /00 + / j j Then we analyze the circuit t determine the pen-circuit vltage. t c j00 n t t / Z E5.5 (a Fr a cmplex lad, maximum pwer is transferred fr * Z Z 00 j5 + jx. The Thévenin equivalent with the lad t attached is: The current is given by j j5 The lad pwer is P 00( / 6.5 W 5
6 (b Fr a purely resistive lad, maximum pwer is transferred fr Z Ω. The Thévenin equivalent with the t lad attached is: The current is given by j5 The lad pwer is P 03.(0.3456/ 6.57 W E5.6 The line-t-neutral vltage is 000 / N phase angle was specified in the prblem statement, s we will assume that the phase f an is zer. Then we have an bn cn The circuit fr the a phase is shwn belw. (We can cnsider a neutral cnnectin t exist in a balanced Y-Y cnnectin even if ne is nt physically present. The a-phase line current is an aa 00 + j Z The currents fr phases b and c are the same except fr phase bb c Y P cs( θ 3 cs( kw 6
7 Y Q sin( θ 3 sin( ka E5.7 The a-phase line-t-neutral vltage is an 000 / The phase impedance f the equivalent Y is Z / 3 50 / Ω. 0 Z Y Thus the line current is an aa A Z 6.67 Y Similarly, A and A. bb c Finally, the pwer is P 3( aa / y kw Answers fr Selected Prblems P5.* phase angle θ 60 t peak f 500 Hz T ms P W ms ω 000π rad/s 7.07 π 3 radians 7
8 4 P5.6* v ( t 8.8 cs(π 0 t 7 P5.9* P5.*.5 P5.5* P5.7* v s.58 ( t 4.4 cs( ωt 45 lags by 90 lags by 45 s leads s by 45 P5.* ( t 0 cs( 400πt + 30 v v ( t 5 cs(400πt + 50 ( t 0 cs( 400πt + 90 v 3 v ( t lagsv ( t by 0 v ( t lagsv3( t by 60 v ( t leadsv ( t by 60 3 P5.3* 5 cs( ω t cs( ωt sin( ωt 3.763cs( ωt P5.8* i Z 00π ( 0π 90 ( t ( 0π cs( 000πt 90 ( 0π sin( 000πt i ( t lagsv ( t by 90 8
9 P5.9* i Z Z Ω ( t cs( 000πt sin( 000πt i ( t leadsv ( t by 90 P5.3* ω 500 : Z ω 000 : Z 50 0 ω 000 : Z P5.34* lags s by 45 9
10 P5.37* leads s by P5.39* lags s by 6.56 P5.4* The peak value f i ( t is five times larger than the surce current! P5.45* P5.46*
11 P5.53* P5.59* This is a capacitive lad. P.5 kw Q.5 ka pwer factr 89.44% P 0 kw Q ka Apparent pwer 0.68 ka Pwer factr 93.57% leading P5.6* P kw s Q 3.84 ka s Apparent pwer 6 ka Pwer factr 84.6% lagging P5.64* (a (b µF The capacitr must be rated fr at least ka (c P5.67* (a The line current is smaller by a factr f 4 with the capacitr in place, reducing lsses in the line by a factr f 6. n (b (c P 50 W lad P 47. W lad
12 P5.70* lad lad.5 Ω 06. µ F P5.73* P5.74* A P 9.36 kw Z Ω P5.78* P aa AB AB lad P line kw 0.50 kw
ECE 2100 Circuit Analysis
ECE 00 Circuit Analysis Lessn 6 Chapter 4 Sec 4., 4.5, 4.7 Series LC Circuit C Lw Pass Filter Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 00 Circuit Analysis Lessn 5 Chapter 9 &
More informationECE 2100 Circuit Analysis
ECE 2100 Circuit Analysis Lessn 25 Chapter 9 & App B: Passive circuit elements in the phasr representatin Daniel M. Litynski, Ph.D. http://hmepages.wmich.edu/~dlitynsk/ ECE 2100 Circuit Analysis Lessn
More informationPart a: Writing the nodal equations and solving for v o gives the magnitude and phase response: tan ( 0.25 )
+ - Hmewrk 0 Slutin ) In the circuit belw: a. Find the magnitude and phase respnse. b. What kind f filter is it? c. At what frequency is the respnse 0.707 if the generatr has a ltage f? d. What is the
More informationRevision: August 19, E Main Suite D Pullman, WA (509) Voice and Fax
.7.4: Direct frequency dmain circuit analysis Revisin: August 9, 00 5 E Main Suite D Pullman, WA 9963 (509) 334 6306 ice and Fax Overview n chapter.7., we determined the steadystate respnse f electrical
More information2. Find i, v, and the power dissipated in the 6-Ω resistor in the following figure.
CSC Class exercise DC Circuit analysis. Fr the ladder netwrk in the fllwing figure, find I and R eq. Slutin Req 4 ( 6 ) 5Ω 0 0 I Re q 5 A. Find i, v, and the pwer dissipated in the 6-Ω resistr in the fllwing
More informationLab 11 LRC Circuits, Damped Forced Harmonic Motion
Physics 6 ab ab 11 ircuits, Damped Frced Harmnic Mtin What Yu Need T Knw: The Physics OK this is basically a recap f what yu ve dne s far with circuits and circuits. Nw we get t put everything tgether
More informationDr. Kasra Etemadi February 27, 2007
Dr. Kasra Eteadi February 7, 7 Chapter 4:Transients Chapter 5: Sinusidal Surces Chapter 6: nnsinusidal surces Furier Trasr Transer Functin Filters Lwpass Filters Highpass Filters andpass Filters Surce
More informationCalculus Placement Review. x x. =. Find each of the following. 9 = 4 ( )
Calculus Placement Review I. Finding dmain, intercepts, and asympttes f ratinal functins 9 Eample Cnsider the functin f ( ). Find each f the fllwing. (a) What is the dmain f f ( )? Write yur answer in
More informationSections 15.1 to 15.12, 16.1 and 16.2 of the textbook (Robbins-Miller) cover the materials required for this topic.
Tpic : AC Fundamentals, Sinusidal Wavefrm, and Phasrs Sectins 5. t 5., 6. and 6. f the textbk (Rbbins-Miller) cver the materials required fr this tpic.. Wavefrms in electrical systems are current r vltage
More informationChapter 10: Sinusoidal Steady-State Analysis
Chapter 10: Sinusoidal Steady-State Analysis 1 Objectives : sinusoidal functions Impedance use phasors to determine the forced response of a circuit subjected to sinusoidal excitation Apply techniques
More informationSupplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
More informationSupplementary Course Notes Adding and Subtracting AC Voltages and Currents
Supplementary Curse Ntes Adding and Subtracting AC Vltages and Currents As mentined previusly, when cmbining DC vltages r currents, we nly need t knw the plarity (vltage) and directin (current). In the
More informationModule B3. VLoad = = V S V LN
Mdule B Prblem The -hase lads are cnnected n arallel. One s a urely resste lad cnnected n wye. t cnsumes 00kW. The secnd s a urely nducte 00kR lad cnnected n wye. The thrd s a urely caacte 00kR lad cnnected
More informationFields and Waves I. Lecture 3
Fields and Waves I ecture 3 Input Impedance n Transmissin ines K. A. Cnnr Electrical, Cmputer, and Systems Engineering Department Rensselaer Plytechnic Institute, Try, NY These Slides Were Prepared by
More informationSeries and Parallel Resonances
Series and Parallel esnances Series esnance Cnsider the series circuit shwn in the frequency dmain. The input impedance is Z Vs jl jl I jc C H s esnance ccurs when the imaginary part f the transfer functin
More informationLHS Mathematics Department Honors Pre-Calculus Final Exam 2002 Answers
LHS Mathematics Department Hnrs Pre-alculus Final Eam nswers Part Shrt Prblems The table at the right gives the ppulatin f Massachusetts ver the past several decades Using an epnential mdel, predict the
More informationMICROWAVE COMMUNICATIONS AND RADAR
MICROWAVE COMMUNICATIONS AND RADAR Generic Architecture: Signal Amplificatin Guide Antenna Prcessing Micrwave r ptical Signal Prcessing Detectin Guide Antenna tuning, resnance waveguides transitins cupling
More informationCoupled Inductors and Transformers
Cupled nductrs and Transfrmers Self-nductance When current i flws thrugh the cil, a magnetic flux is prduced arund it. d d di di v= = = dt di dt dt nductance: = d di This inductance is cmmnly called self-inductance,
More informationLECTURES 4 AND 5 THREE-PHASE CONNECTIONS (1)
ECE 330 POWER CIRCUITS AND ELECTROMECHANICS LECTURES 4 AND 5 THREEPHASE CONNECTIONS (1) AcknwledgmentThese handuts and lecture ntes given in class are based n material frm Prf. Peter Sauer s ECE 330 lecture
More informationLEARNING : At the end of the lesson, students should be able to: OUTCOMES a) state trigonometric ratios of sin,cos, tan, cosec, sec and cot
Mathematics DM 05 Tpic : Trignmetric Functins LECTURE OF 5 TOPIC :.0 TRIGONOMETRIC FUNCTIONS SUBTOPIC :. Trignmetric Ratis and Identities LEARNING : At the end f the lessn, students shuld be able t: OUTCOMES
More informationIntroduction to Smith Charts
Intrductin t Smith Charts Dr. Russell P. Jedlicka Klipsch Schl f Electrical and Cmputer Engineering New Mexic State University as Cruces, NM 88003 September 2002 EE521 ecture 3 08/22/02 Smith Chart Summary
More informationIntroduction to Three-phase Circuits. Balanced 3-phase systems Unbalanced 3-phase systems
Intrductin t Three-hase Circuits Balanced 3-hase systems Unbalanced 3-hase systems 1 Intrductin t 3-hase systems Single-hase tw-wire system: Single surce cnnected t a lad using tw-wire system Single-hase
More informationSynchronous Motor V-Curves
Synchrnus Mtr V-Curves 1 Synchrnus Mtr V-Curves Intrductin Synchrnus mtrs are used in applicatins such as textile mills where cnstant speed peratin is critical. Mst small synchrnus mtrs cntain squirrel
More informationRelationships Between Frequency, Capacitance, Inductance and Reactance.
P Physics Relatinships between f,, and. Relatinships Between Frequency, apacitance, nductance and Reactance. Purpse: T experimentally verify the relatinships between f, and. The data cllected will lead
More informationChapter 30. Inductance
Chapter 30 nductance 30. Self-nductance Cnsider a lp f wire at rest. f we establish a current arund the lp, it will prduce a magnetic field. Sme f the magnetic field lines pass thrugh the lp. et! be the
More informationZVS Boost Converter. (a) (b) Fig 6.29 (a) Quasi-resonant boost converter with M-type switch. (b) Equivalent circuit.
EEL6246 Pwer Electrnics II Chapter 6 Lecture 6 Dr. Sam Abdel-Rahman ZVS Bst Cnverter The quasi-resnant bst cnverter by using the M-type switch as shwn in Fig. 6.29(a) with its simplified circuit shwn in
More informationCopyright Paul Tobin 63
DT, Kevin t. lectric Circuit Thery DT87/ Tw-Prt netwrk parameters ummary We have seen previusly that a tw-prt netwrk has a pair f input terminals and a pair f utput terminals figure. These circuits were
More informationEE 221 Practice Problems for the Final Exam
EE 1 Practce Prblems fr the Fnal Exam 1. The netwrk functn f a crcut s 1.5 H. ω 1+ j 500 Ths table recrds frequency respnse data fr ths crcut. Fll n the blanks n the table:. The netwrk functn f a crcut
More informationCorrections for the textbook answers: Sec 6.1 #8h)covert angle to a positive by adding period #9b) # rad/sec
U n i t 6 AdvF Date: Name: Trignmetric Functins Unit 6 Tentative TEST date Big idea/learning Gals In this unit yu will study trignmetric functins frm grade, hwever everything will be dne in radian measure.
More informationReview Problems 3. Four FIR Filter Types
Review Prblems 3 Fur FIR Filter Types Fur types f FIR linear phase digital filters have cefficients h(n fr 0 n M. They are defined as fllws: Type I: h(n = h(m-n and M even. Type II: h(n = h(m-n and M dd.
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationLecture 5: Equilibrium and Oscillations
Lecture 5: Equilibrium and Oscillatins Energy and Mtin Last time, we fund that fr a system with energy cnserved, v = ± E U m ( ) ( ) One result we see immediately is that there is n slutin fr velcity if
More informationLecture 7: Damped and Driven Oscillations
Lecture 7: Damped and Driven Oscillatins Last time, we fund fr underdamped scillatrs: βt x t = e A1 + A csω1t + i A1 A sinω1t A 1 and A are cmplex numbers, but ur answer must be real Implies that A 1 and
More informationLecture (5) Power Factor,threephase circuits, and Per Unit Calculations
Lecture (5) Power Factor,threephase circuits, and Per Unit Calculations 5-1 Repeating the Example on Power Factor Correction (Given last Class) P? Q? S? Light Motor From source 1000 volts @ 60 Htz 10kW
More informationCop yri ht 2006, Barr Mabillard.
Trignmetry II Cpyright Trignmetry II Standards 006, Test Barry ANSWERS Mabillard. 0 www.math0s.cm . If csα, where sinα > 0, and 5 cs α + β value f sin β, where tan β > 0, determine the exact 9 First determine
More informationFunction notation & composite functions Factoring Dividing polynomials Remainder theorem & factor property
Functin ntatin & cmpsite functins Factring Dividing plynmials Remainder therem & factr prperty Can d s by gruping r by: Always lk fr a cmmn factr first 2 numbers that ADD t give yu middle term and MULTIPLY
More informationChapter 3 Kinematics in Two Dimensions; Vectors
Chapter 3 Kinematics in Tw Dimensins; Vectrs Vectrs and Scalars Additin f Vectrs Graphical Methds (One and Tw- Dimensin) Multiplicatin f a Vectr b a Scalar Subtractin f Vectrs Graphical Methds Adding Vectrs
More informationAlgebra2/Trig: Trig Unit 2 Packet
Algebra2/Trig: Trig Unit 2 Packet In this unit, students will be able t: Learn and apply c-functin relatinships between trig functins Learn and apply the sum and difference identities Learn and apply the
More informationFourier Analysis, Low Pass Filters, Decibels
Lecture 8 Furier Analysis, Lw Pass Filters, Decibels ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Furth Edit, by Allan R. Hambley, 008 Pearsn Educat, Inc. Chapter 6 Frequency Respnse, Bde Plts,
More informationLecture 20a. Circuit Topologies and Techniques: Opamps
Lecture a Circuit Tplgies and Techniques: Opamps In this lecture yu will learn: Sme circuit tplgies and techniques Intrductin t peratinal amplifiers Differential mplifier IBIS1 I BIS M VI1 vi1 Vi vi I
More informationBASIC DIRECT-CURRENT MEASUREMENTS
Brwn University Physics 0040 Intrductin BASIC DIRECT-CURRENT MEASUREMENTS The measurements described here illustrate the peratin f resistrs and capacitrs in electric circuits, and the use f sme standard
More informationPhysics 2B Chapter 23 Notes - Faraday s Law & Inductors Spring 2018
Michael Faraday lived in the Lndn area frm 1791 t 1867. He was 29 years ld when Hand Oersted, in 1820, accidentally discvered that electric current creates magnetic field. Thrugh empirical bservatin and
More informationFlipping Physics Lecture Notes: Simple Harmonic Motion Introduction via a Horizontal Mass-Spring System
Flipping Physics Lecture Ntes: Simple Harmnic Mtin Intrductin via a Hrizntal Mass-Spring System A Hrizntal Mass-Spring System is where a mass is attached t a spring, riented hrizntally, and then placed
More informationGENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS. J.e. Sprott. Plasma Studies. University of Wisconsin
GENERAL FORMULAS FOR FLAT-TOPPED WAVEFORMS J.e. Sprtt PLP 924 September 1984 Plasma Studies University f Wiscnsin These PLP Reprts are infrmal and preliminary and as such may cntain errrs nt yet eliminated.
More informationPower Flow in Electromagnetic Waves. The time-dependent power flow density of an electromagnetic wave is given by the instantaneous Poynting vector
Pwer Flw in Electrmagnetic Waves Electrmagnetic Fields The time-dependent pwer flw density f an electrmagnetic wave is given by the instantaneus Pynting vectr P t E t H t ( ) = ( ) ( ) Fr time-varying
More informationMODULE 1. e x + c. [You can t separate a demominator, but you can divide a single denominator into each numerator term] a + b a(a + b)+1 = a + b
. REVIEW OF SOME BASIC ALGEBRA MODULE () Slving Equatins Yu shuld be able t slve fr x: a + b = c a d + e x + c and get x = e(ba +) b(c a) d(ba +) c Cmmn mistakes and strategies:. a b + c a b + a c, but
More informationChapter 5 Steady-State Sinusoidal Analysis
Chapter 5 Steady-State Sinusoidal Analysis Chapter 5 Steady-State Sinusoidal Analysis 1. Identify the frequency, angular frequency, peak value, rms value, and phase of a sinusoidal signal. 2. Solve steady-state
More information(2) Even if such a value of k was possible, the neutrons multiply
CHANGE OF REACTOR Nuclear Thery - Curse 227 POWER WTH REACTVTY CHANGE n this lessn, we will cnsider hw neutrn density, neutrn flux and reactr pwer change when the multiplicatin factr, k, r the reactivity,
More informationBicycle Generator Dump Load Control Circuit: An Op Amp Comparator with Hysteresis
Bicycle Generatr Dump Lad Cntrl Circuit: An Op Amp Cmparatr with Hysteresis Sustainable Technlgy Educatin Prject University f Waterl http://www.step.uwaterl.ca December 1, 2009 1 Summary This dcument describes
More informationHarmonic Motion (HM) Oscillation with Laminar Damping
Harnic Mtin (HM) Oscillatin with Lainar Daping If yu dn t knw the units f a quantity yu prbably dn t understand its physical significance. Siple HM r r Hke' s Law: F k x definitins: f T / T / Bf x A sin
More informationCHAPTER 45 COMPLEX NUMBERS
CHAPTER 45 COMPLEX NUMBERS EXERCISE 87 Page 50. Solve the quadratic equation: x + 5 0 Since x + 5 0 then x 5 x 5 ( )(5) 5 j 5 from which, x ± j5. Solve the quadratic equation: x x + 0 Since x x + 0 then
More informationSTUDENT NAME: STUDENT id #: WORK ONLY 5 QUESTIONS
GENERAL PHYSICS PH -A (MIROV) Exam 3 (03/31/15) STUDENT NAME: STUDENT i #: ------------------------------------------------------------------------------------------------------------------------------------------
More informationThree charges, all with a charge of 10 C are situated as shown (each grid line is separated by 1 meter).
Three charges, all with a charge f 0 are situated as shwn (each grid line is separated by meter). ) What is the net wrk needed t assemble this charge distributin? a) +0.5 J b) +0.8 J c) 0 J d) -0.8 J e)
More informationOscillator. Introduction of Oscillator Linear Oscillator. Stability. Wien Bridge Oscillator RC Phase-Shift Oscillator LC Oscillator
Oscillatr Intrductin f Oscillatr Linear Oscillatr Wien Bridge Oscillatr Phase-Shift Oscillatr L Oscillatr Stability Oscillatrs Oscillatin: an effect that repeatedly and regularly fluctuates abut the mean
More informationEKT103 ELECTRICAL ENGINEERING
EKT13 EECTRCA ENGNEERNG Chater 1 Three-Phase System 1 COURSE OUTCOME (CO) CO1: Ability to define and exlain the concet of single-hase and threehase system. 2 Revision A sinusoid is a signal that has the
More information1. Transformer A transformer is used to obtain the approximate output voltage of the power supply. The output of the transformer is still AC.
PHYSIS 536 Experiment 4: D Pwer Supply I. Intrductin The prcess f changing A t D is investigated in this experiment. An integrated circuit regulatr makes it easy t cnstruct a high-perfrmance vltage surce
More informationPhysics 102. Second Midterm Examination. Summer Term ( ) (Fundamental constants) (Coulomb constant)
ε µ0 N mp T kg Kuwait University hysics Department hysics 0 Secnd Midterm Examinatin Summer Term (00-0) July 7, 0 Time: 6:00 7:0 M Name Student N Instructrs: Drs. bdel-karim, frusheh, Farhan, Kkaj, a,
More informationPHYSICS 151 Notes for Online Lecture #23
PHYSICS 5 Ntes fr Online Lecture #3 Peridicity Peridic eans that sething repeats itself. r exaple, eery twenty-fur hurs, the Earth aes a cplete rtatin. Heartbeats are an exaple f peridic behair. If yu
More informationKinetics of Particles. Chapter 3
Kinetics f Particles Chapter 3 1 Kinetics f Particles It is the study f the relatins existing between the frces acting n bdy, the mass f the bdy, and the mtin f the bdy. It is the study f the relatin between
More informationLead/Lag Compensator Frequency Domain Properties and Design Methods
Lectures 6 and 7 Lead/Lag Cmpensatr Frequency Dmain Prperties and Design Methds Definitin Cnsider the cmpensatr (ie cntrller Fr, it is called a lag cmpensatr s K Fr s, it is called a lead cmpensatr Ntatin
More informationChapter 10: Sinusoids and Phasors
Chapter 10: Sinusoids and Phasors 1. Motivation 2. Sinusoid Features 3. Phasors 4. Phasor Relationships for Circuit Elements 5. Impedance and Admittance 6. Kirchhoff s Laws in the Frequency Domain 7. Impedance
More informationEE292: Fundamentals of ECE
EE292: Fundamentals of ECE Fall 2012 TTh 10:00-11:15 SEB 1242 Lecture 18 121025 http://www.ee.unlv.edu/~b1morris/ee292/ 2 Outline Review RMS Values Complex Numbers Phasors Complex Impedance Circuit Analysis
More informationQ1. In figure 1, Q = 60 µc, q = 20 µc, a = 3.0 m, and b = 4.0 m. Calculate the total electric force on q due to the other 2 charges.
Phys10 Secnd Majr-08 Zer Versin Crdinatr: Dr. I. M. Nasser Saturday, May 3, 009 Page: 1 Q1. In figure 1, Q = 60 µc, q = 0 µc, a = 3.0 m, and b = 4.0 m. Calculate the ttal electric frce n q due t the ther
More informationMATHEMATICS SYLLABUS SECONDARY 5th YEAR
Eurpean Schls Office f the Secretary-General Pedaggical Develpment Unit Ref. : 011-01-D-8-en- Orig. : EN MATHEMATICS SYLLABUS SECONDARY 5th YEAR 6 perid/week curse APPROVED BY THE JOINT TEACHING COMMITTEE
More informationPhys102 Final-061 Zero Version Coordinator: Nasser Wednesday, January 24, 2007 Page: 1
Crdinatr: Nasser Wednesday, January 4, 007 Page: 1 Q1. Tw transmitters, S 1 and S shwn in the figure, emit identical sund waves f wavelength λ. The transmitters are separated by a distance λ /. Cnsider
More informationMetering Principles & Configurations
Metering Principles & Cnfiguratins CT PT Startc Western Energy Cmpany DCS Presenters Western Energy Cmpany Mnte Wilke Electrical Superintendent Curt Brckel Electrical Supervisr Brady Clbert Electrical
More informationModule 4: General Formulation of Electric Circuit Theory
Mdule 4: General Frmulatin f Electric Circuit Thery 4. General Frmulatin f Electric Circuit Thery All electrmagnetic phenmena are described at a fundamental level by Maxwell's equatins and the assciated
More informationGeneral Amplifiers. Analog Electronics Circuits Nagamani A N. Lecturer, PESIT, Bangalore 85. Cascade connection - FET & BJT
Analg lectrnics Circuits Nagamani A N Lecturer, PST, Bangalre 85 mail nagamani@pes.edu General Amplifiers Cascade cnnectin - FT & BJT Numerical Cascde cnnectin arlingtn cnnectin Packaged arlingtn cnnectin
More informationANSWER KEY FOR MATH 10 SAMPLE EXAMINATION. Instructions: If asked to label the axes please use real world (contextual) labels
ANSWER KEY FOR MATH 10 SAMPLE EXAMINATION Instructins: If asked t label the axes please use real wrld (cntextual) labels Multiple Chice Answers: 0 questins x 1.5 = 30 Pints ttal Questin Answer Number 1
More informationMANIPAL INSTITUTE OF TECHNOLOGY
MANIPAL INSTITUTE OF TECHNOLOGY MANIPAL UNIVERSITY, MANIPAL SECOND SEMESTER B.Tech. END-SEMESTER EXAMINATION - MAY 013 SUBJECT: ENGINEERING PHYSICS (PHY101/10) Time: 3 Hrs. Max. Marks: 50 Nte: Answer any
More informationSinusoids and Phasors
CHAPTER 9 Sinusoids and Phasors We now begins the analysis of circuits in which the voltage or current sources are time-varying. In this chapter, we are particularly interested in sinusoidally time-varying
More informationECEN 4872/5827 Lecture Notes
ECEN 4872/5827 Lecture Ntes Lecture #5 Objectives fr lecture #5: 1. Analysis f precisin current reference 2. Appraches fr evaluating tlerances 3. Temperature Cefficients evaluatin technique 4. Fundamentals
More informationINDUCTANCE Self Inductance
DUCTCE 3. Sef nductance Cnsider the circuit shwn in the Figure. S R When the switch is csed the current, and s the magnetic fied, thrugh the circuit increases frm zer t a specific vaue. The increasing
More informationPre-Calculus Individual Test 2017 February Regional
The abbreviatin NOTA means Nne f the Abve answers and shuld be chsen if chices A, B, C and D are nt crrect. N calculatr is allwed n this test. Arcfunctins (such as y = Arcsin( ) ) have traditinal restricted
More information4) What is the magnitude of the net electric field at the center of the square?
Fur charges are n the fur crners f a square. Q = +5C, Q = -0C, Q 3 = +5C, Q 4 = -0C. The side length f each side f the square is 3 m. Q Q ) What is the directin f the frce n Q due t ONLY Q 4? (a) up (b)
More informationCLASS XI SET A PHYSICS
PHYSIS. If the acceleratin f wedge in the shwn arrangement is a twards left then at this instant acceleratin f the blck wuld be, (assume all surfaces t be frictinless) a () ( cs )a () a () cs a If the
More informationMath Final Exam Instructor: Ken Schultz April 28, 2006
Name Math 1650.300 Final Exam Instructr: Ken Schultz April 8, 006 Exam Guidelines D nt pen this exam until are instructed t begin. Fllw all instructins explicitly. Befre yu begin wrking, make sure yur
More informationHigher. Specimen NAB Assessment
hsn.uk.net Higher Mathematics UNIT Specimen NAB Assessment HSN50 This dcument was prduced speciall fr the HSN.uk.net website, and we require that an cpies r derivative wrks attribute the wrk t Higher Still
More informationCHAPTER 5. Exercises. the coefficient of t so we have ω = 200π
HPTER 5 Exerises E5. (a) We are given v ( ) 5 s(π 3 ). The angular frequeny is he effiien f s we have ω π radian/s. Then f ω / π Hz T / f ms m / 5 / 6. Furhermre, v() aains a psiive peak when he argumen
More informationAlternating 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 information18. (a) S(t) = sin(0.5080t- 2.07) (b) ~oo. (c)
Review Exercises fr Chapter P 5 1. (a) T =.985 x 10-p - 0.01p + 5.8p + 1.1 50 18. (a) S(t) = 5.7 + 5.7 sin(0.5080t-.07) ~ 0 110 150 (c) Fr T = 00 F, p,~ 8.9 lb/in.. (d) The mdel is based n data up t 100
More informationSolution to HW14 Fall-2002
Slutin t HW14 Fall-2002 CJ5 10.CQ.003. REASONING AND SOLUTION Figures 10.11 and 10.14 shw the velcity and the acceleratin, respectively, the shadw a ball that underges unirm circular mtin. The shadw underges
More informationChapter 6. Dielectrics and Capacitance
Chapter 6. Dielectrics and Capacitance Hayt; //009; 6- Dielectrics are insulating materials with n free charges. All charges are bund at mlecules by Culmb frce. An applied electric field displaces charges
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 informationLesson #14. Section BME 373 Electronics II J.Schesser
Feedback and Oscillatrs Lessn #4 Impedances Sectin 9.35 65 Types f ffeedback Type f ffeedback k(the utput tentity fed dback): Vltage Feedback s. Current Feedback β s. β Hw it is achieed (the means t fed
More informationMath 105: Review for Exam I - Solutions
1. Let f(x) = 3 + x + 5. Math 105: Review fr Exam I - Slutins (a) What is the natural dmain f f? [ 5, ), which means all reals greater than r equal t 5 (b) What is the range f f? [3, ), which means all
More informationPlan o o. I(t) Divide problem into sub-problems Modify schematic and coordinate system (if needed) Write general equations
STAPLE Physics 201 Name Final Exam May 14, 2013 This is a clsed bk examinatin but during the exam yu may refer t a 5 x7 nte card with wrds f wisdm yu have written n it. There is extra scratch paper available.
More informationRoot locus ( )( ) The given TFs are: 1. Using Matlab: >> rlocus(g) >> Gp1=tf(1,poly([0-1 -2])) Transfer function: s^3 + 3 s^2 + 2 s
The given TFs are: 1 1() s = s s + 1 s + G p, () s ( )( ) >> Gp1=tf(1,ply([0-1 -])) Transfer functin: 1 ----------------- s^ + s^ + s Rt lcus G 1 = p ( s + 0.8 + j)( s + 0.8 j) >> Gp=tf(1,ply([-0.8-*i
More information205MPa and a modulus of elasticity E 207 GPa. The critical load 75kN. Gravity is vertically downward and the weight of link 3 is W3
ME 5 - Machine Design I Fall Semester 06 Name f Student: Lab Sectin Number: Final Exam. Open bk clsed ntes. Friday, December 6th, 06 ur name lab sectin number must be included in the spaces prvided at
More informationFigure 1a. A planar mechanism.
ME 5 - Machine Design I Fall Semester 0 Name f Student Lab Sectin Number EXAM. OPEN BOOK AND CLOSED NOTES. Mnday, September rd, 0 Write n ne side nly f the paper prvided fr yur slutins. Where necessary,
More informationElectric Circuit Theory
Electric Circuit Theory Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Chapter 11 Sinusoidal Steady-State Analysis Nam Ki Min nkmin@korea.ac.kr 010-9419-2320 Contents and Objectives 3 Chapter Contents 11.1
More informationPreparation work for A2 Mathematics [2017]
Preparatin wrk fr A2 Mathematics [2017] The wrk studied in Y12 after the return frm study leave is frm the Cre 3 mdule f the A2 Mathematics curse. This wrk will nly be reviewed during Year 13, it will
More informationPreparation work for A2 Mathematics [2018]
Preparatin wrk fr A Mathematics [018] The wrk studied in Y1 will frm the fundatins n which will build upn in Year 13. It will nly be reviewed during Year 13, it will nt be retaught. This is t allw time
More information, which yields. where z1. and z2
The Gaussian r Nrmal PDF, Page 1 The Gaussian r Nrmal Prbability Density Functin Authr: Jhn M Cimbala, Penn State University Latest revisin: 11 September 13 The Gaussian r Nrmal Prbability Density Functin
More informationInterference is when two (or more) sets of waves meet and combine to produce a new pattern.
Interference Interference is when tw (r mre) sets f waves meet and cmbine t prduce a new pattern. This pattern can vary depending n the riginal wave directin, wavelength, amplitude, etc. The tw mst extreme
More informationPOWER AMPLIFIERS. 1. Explain what are classes A, B, AB and C amplifiers in terms of DC biasing using a MOSFET drain characteristic.
CTONIC 3 XCI OW AMII. xpla what are classes A, B, AB and C amplifiers terms f DC biasg usg a MOT dra characteristic.. efer t the graphs f page and the table at the tp f page 3 f the thery ntes t answer
More informationINSTRUCTIONAL PLAN Day 2
INSTRUCTIONAL PLAN Day 2 Subject: Trignmetry Tpic: Other Trignmetric Ratis, Relatinships between Trignmetric Ratis, and Inverses Target Learners: Cllege Students Objectives: At the end f the lessn, students
More informationPHYS 314 HOMEWORK #3
PHYS 34 HOMEWORK #3 Due : 8 Feb. 07. A unifrm chain f mass M, lenth L and density λ (measured in k/m) hans s that its bttm link is just tuchin a scale. The chain is drpped frm rest nt the scale. What des
More informationA Simple Set of Test Matrices for Eigenvalue Programs*
Simple Set f Test Matrices fr Eigenvalue Prgrams* By C. W. Gear** bstract. Sets f simple matrices f rder N are given, tgether with all f their eigenvalues and right eigenvectrs, and simple rules fr generating
More informationDispersion Ref Feynman Vol-I, Ch-31
Dispersin Ref Feynman Vl-I, Ch-31 n () = 1 + q N q /m 2 2 2 0 i ( b/m) We have learned that the index f refractin is nt just a simple number, but a quantity that varies with the frequency f the light.
More information