Module 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur


 Kristopher Parks
 2 years ago
 Views:
Transcription
1 Module 4 Singlephase A circuis ersion EE T, Kharagpur
2 esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur
3 n he las lesson, wo poins were described:. How o solve for he impedance, and curren in an ac circui, consising of single elemen, / /?. How o solve for he impedance, and curren in an ac circui, consising of wo elemens, and /, in series, and hen draw complee phasor diagram? n his lesson, he soluion of currens in simple circuis, consising of resisance, inducance and/or capaciance conneced in series, fed from single phase ac supply, is presened. Then, he circui wih all above componens in parallel is aken up. The process of drawing complee phasor diagram wih curren(s and volage drops in he differen componens is described. The compuaion of oal power and also power consumed in he differen componens, along wih power facor, is explained. One example of series circui are presened in deail, while he example of parallel circui will be aken up in he nex lesson. Keywords: Series and parallel circuis, impedance, admiance, power, power facor. Afer going hrough his lesson, he sudens will be able o answer he following quesions;. How o compue he oal reacance and impedance / admiance, of he series and parallel circuis, fed from single phase ac supply?. How o compue he differen currens and also volage drops in he componens, boh in magniude and phase, of he circui? 3. How o draw he complee phasor diagram, showing he currens and volage drops? 4. How o compue he oal power and also power consumed in he differen componens, along wih power facor? Soluion of urren in  Series ircui Series ( circui O D E A  Fig. 5. (a ircui diagram The volage balance equaion for he circui wih, and in series (Fig. 5.a, is di v i i d d sin ersion EE T, Kharagpur
4 The curren, i is of he form, i sin ( ± As described in he previous lesson (#4 on series ( circui, he curren in seady sae is sinusoidal in naure. The procedure given here, in brief, is followed o deermine he form of curren. f he expression for i sin ( is subsiued in he volage equaion, he equaion shown here is obained, wih he sides (HS & HS inerchanged. sin ( cos ( (/ cos ( sin or sin ( [ (/ ] cos ( sin The seps o be followed o find he magniude and phase angle of he curren, are same as described here (#4. So, he phase angle is an [ (/ ] / and he magniude of he curren is / where he impedance of he series circui is [ (/ ] Alernaively, he seps o find he rms value of he curren, using complex form of impedance, are given here. The impedance of he circui is ± ( where, ( (/, and an ( an (/ 0 0 ± ( ( 0 ( (/ Two cases are: (a nducive >, and (b apaciive <. (a nducive is posiive, under he condiion ( > ( /. The curren lags he volage by (aken as posiive, wih he volage phasor aken as reference. The power facor (lagging is less han (one, as The complee phasor diagram, wih he volage drops across he n his case, he circui is inducive, as oal reacance ( ( / ersion EE T, Kharagpur
5 componens and inpu volage (OA, and also curren (O, is shown in Fig. 5.b. The volage phasor is aken as reference, in all cases. may be observed ha O ( i D [ i ( ] DA [ i ( ] OA ( i using he Kirchoff s second law relaing o he volage in a closed loop. The phasor diagram can also be drawn wih he curren phasor as reference, as will be shown in he example given here. The expression for he average power is cos. The power is only consumed in he resisance,, bu no in inducance/capaciance (/, in all hree cases. E ( A ( O. D nducive ( > Fig 5. (b Phasor diagram is posiive, under he condiion ( > ( /. The curren lags he volage by (posiive. The power facor (lagging is less han (one, as The complee phasor diagram, wih he volage drops across he componens and inpu volage ( OA, and also curren ( O, is shown in Fig. 5.b. The volage phasor is aken as reference, in all cases. may be observed ha O ( i D [ i ( ] DA [ i ( ] OA ( i using he Kirchoff s second law relaing o he volage in a closed loop. The phasor diagram can also be drawn wih he curren phasor as reference, as will be shown in he example given here. The expression for he average power is cos. The power is only consumed in he resisance,, bu no in inducance/capaciance (/, in all hree cases. n his case, he circui is inducive, as oal reacance ( ( / ersion EE T, Kharagpur
6 (b apaciive E O. D ( ( A apaciive ( < Fig 5. (c Phasor diagram is negaive, under he condiion ( < ( /. The curren leads he volage by, which is negaive as per convenion described in he previous lesson. The volage phasor is aken as reference here. The complee phasor diagram, wih he volage drops across he componens and inpu volage, and also curren, is shown in Fig. 5.c. The power facor (leading is less The circui is now capaciive, as oal reacance ( ( / han (one, as 0 90, being negaive. The expression for he average power remains same as above. The hird case is resisive, as oal reacance ( / is zero (0, under he condiion ( /. The impedance is 0 0. The curren is now a uniy power facor ( 0, i.e. he curren and he volage are in phase. The complee phasor diagram, wih he volage drops across he componens and inpu (supply volage, and also curren, is shown in Fig. 5.d. This condiion can be ermed as resonance in he series circui, which is described in deail in lesson #7. The magniude of he impedance in he circui is minimum under his condiion, wih he magniude of he curren being maximum. One more poin o be noed here is ha he volage drops in he inducance, and also in he capaciance,, is much larger in magniude han he supply volage, which is same as he volage drop in he resisance,. The phasor diagram has been drawn approximaely o scale. ersion EE T, Kharagpur
7 E (.  ( O , (. OD D, A O esisive ( Fig. 5. (d Phasor diagram may be observed here ha wo cases of series ( &  circuis, as discussed in he previous lesson, are obained in he following way. The firs one (inducive is ha of (a, wih very large, i.e. / 0, which means ha is no here. The second one (capaciive is ha of (b, wih no being here ( or 0. Example 5. A resisance, is conneced in series wih an ironcored choke coil (r in series wih. The circui (Fig. 5.a draws a curren of 5 A a 40, 50 Hz. The volages across he resisance and he coil are 0 and 00 respecively. alculae, (a he resisance, reacance and impedance of he coil, (b he power absorbed by he coil, and (c he power facor (pf of he inpu curren. A r D Fig. 5. (a ircui diagram Soluion (O 5 A S (OA 40 f 50 Hz π f The volage drop across he resisance ( O 0 ersion EE T, Kharagpur
8 The resisance, / 0/ 5 4 Ω The volage drop across he coil ( A 00 The impedance of he coil, r / 00 / 5 40 Ω From he phasor diagram (Fig. 5.b, A E D A A 40, 50 Hz Fig. 5.(b: Phasor Diagram OA O A (0 (40 (00 cos cos AO OA O The power facor (pf of he inpu curren cos ( lag The phase angle of he oal impedance, cos ( npu volage, S ( OA 40 The oal impedance of he circui, 3,000 57,600 ( r / 40 / 5 48 Ω ( r ( Ω The oal resisance of he circui, r 4 r Ω The resisance of he coil, r Ω The reacance of he coil, π f Ω 39.9 The inducance of he coil, 0.7 H 7 0 π f π 50 The phase angle of he coil, cos ( r / cos (.67 / 40.0 cos ( r ( Ω The power facor (pf of he coil, cos ( lag The copper loss in he coil Example 5. r W S 3 7 mh ersion EE T, Kharagpur
9 An inducive coil, having resisance of 8 Ω and inducance of 80 mh, is conneced in series wih a capaciance of 00 μf across 50, 50 Hz supply (Fig. 5.3a. alculae, (a he curren, (b he power facor, and (c he volages drops in he coil and capaciance respecively. Soluion f 50 Hz  A 80 mh H 00 μf Ω 6 E D Fig. 5.3 (a ircui diagram π f π rad / s l F S ( OA 50 The impedance of he coil, ( Ω The oal impedance of he circui, ( ( ( Ω The curren drawn from he supply, A ( The curren is, A The power facor (pf cos cos ( lead D Ω Ω 9.6 A. ( A. E. ( Fig. 5.3 (b Phasor diagram ersion EE T, Kharagpur
10 Please noe ha he curren phasor is aken as reference in he phasor diagram (Fig. 5.3b and also here. The volage drop in he coil is, θ 0 ( ( The volage drop in he capaciance in, θ 0 ( Soluion of urren in Parallel ircui Parallel circui The circui wih all hree elemens,, & conneced in parallel (Fig. 5.4a, is fed o he ac supply. The curren from he supply can be compued by various mehods, of which wo are described here.  Firs mehod Fig. 5.4 (a ircui diagram. The curren in hree branches are firs compued and he oal curren drawn from he supply is he phasor sum of all hree branch currens, by using Kirchoff s firs law relaed o he currens a he node. The volage phasor ( is aken as reference. All currens, i.e. hree branch currens and oal curren, in seady sae, are sinusoidal in naure, as he inpu (supply volage is sinusoidal of he form, v sin Three branch currens are obained by he procedure given in brief. v, or i v / ( / sin sin, i where, ( / d i Similarly, v d So, i is, i ( / v d (/ (sin d [ /( ] cos sin ( 90 cos ersion EE T, Kharagpur
11 where, / ( wih, from which is obained as, d i v / ( i d d d d v i cos cos ( sin ( 90 sin ( where, / ( c wih / ( Toal (supply curren, i is cos cos sin i i i i sin ( cos ( sin The wo equaions given here are obained by expanding he rigonomeric form appearing in he las erm on HS, ino componens of cos and sin, and hen equaing he componens of cos and sin from he las erm and las bu one (previous. cos and ( sin From hese equaions, he magniude and phase angle of he oal (supply curren are, ( ( l an (/ (/ (/ an an an where, he magniude of he erm (admiance of he circui is, Please noe ha he admiance, which is reciprocal of impedance, is a complex quaniy. The angle of admiance or impedance, is same as he phase angle, of he curren, wih he inpu (supply volage aken as reference phasor, as given earlier. Alernaively, he seps required o find he rms values of hree branch currens and he oal (suuply curren, using complex form of impedance, are given here. Three branch currens are 90 ; 0 (/ 90 ersion EE T, Kharagpur
12 Of he hree branches, he firs one consiss of resisance only, he curren, is in phase wih he volage (. n he second branch, he curren, lags he volage by 90, as here is inducance only, while in he hird one having capaciance only, he curren, leads he volage 90. All hese cases have been presened in he previous lesson. The oal curren is ± ( c where,, and ( an an The wo cases are as described earlier in series circui. (a nducive O D A E nducive ( > Fig. 5.4 (b Phasor diagram n his case, he circui being inducive, he curren lags he volage by (posiive, as >, i.e. / >, or < /.This condiion is in conras o ha derived in he case of series circui earlier. The power facor is less han (one. The complee phasor diagram, wih he hree branch currens along wih oal curren, and also he volage, is shown in Fig. 5.4b. The volage phasor is aken as reference in all cases. may be observed here ha ( OD ( D ( ( O ersion EE T, Kharagpur
13 The Kirchoff s firs law relaed o he currens a he node is applied, as saed above. The expression for he average power is cos /. The power is only consumed in he resisance,, bu no in inducance/capaciance (/, in all hree cases. (b apaciive The circui is capaciive, as >, i.e. > /, or > /. The curren leads he volage by ( being negaive, wih he power facor less han (one. The complee phasor diagram, wih he hree branch currens along wih oal curren, and also he volage, is shown in Fig. 5.4c. The hird case is resisive, as, i.e. / or /. This is he same condiion, as obained in he case of series circui. may be noed ha wo currens, and, are equal in magniude as shown, bu opposie in sign (phase difference being 80, and he sum of hese currens is zero (0. The oal curren is in ( phase wih he volage ( 0, wih, he power facor being uniy. The complee phasor diagram, wih he hree branch currens along wih oal curren, and also he volage, is shown in Fig. 5.4d. This condiion can be ermed as resonance in he parallel circui, which is described in deail in lesson #7. The magniude of he impedance in he circui is maximum (i.e., he magniude of he admiance is minimum under his condiion, wih he magniude of he oal (supply curren being minimum. O D A E apaciive ( < Fig. 5.4 (c Phasor diagram ersion EE T, Kharagpur
14 The circui wih wo elemens, say &, can be solved, or derived wih being large ( 0 or / 0. O D, ( Second mehod  esisive ( (/( ( /( Fig. 5.4 (d Phasor Diagram efore going ino he deails of his mehod, he erm, Admiance mus be explained. n he case of wo resisance conneced in series, he equivalen resisance is he sum of wo resisances, he resisance being scalar (posiive. f wo impedances are conneced in series, he equivalen impedance is he sum of wo impedances, all impedances being complex. Please noe ha he wo erms, real and imaginary, of wo impedances and also he equivalen one, may be posiive or negaive. This was explained in lesson no.. f wo resisances are conneced in parallel, he inverse of he equivalen resisance is he sum of he inverse of he wo resisances. f wo impedances are conneced in parallel, he inverse of he equivalen impedance is he sum of he inverse of he wo impedances. The inverse or reciprocal of he impedance is ermed Admiance, which is complex. Mahemaically, his is expressed as As admiance ( is complex, is real and imaginary pars are called conducance (G and suscepance ( respecively. So, G. f impedance, wih being posiive, hen he admiance is where, 0 ( G E ( ersion EE T, Kharagpur
15 ; G Please noe he way in which he resul of he division of wo complex quaniies is obained. oh he numeraor and he denominaor are muliplied by he complex conugae of he denominaor, so as o make he denominaor a real quaniy. This has also been explained in lesson no.. The magniude and phase angle of and are / ( an ;, and G G an an ; To obain he curren in he circui (Fig. 5.4a, he seps are given here. The admiances of he hree branches are 90 ; The oal admiance, obained by he phasor sum of he hree branch admiances, is G ± 3 where, an ;, and G / ; / The oal impedance of he circui is G G G G ± The oal curren in he circui is obained as ± ± ± ( 0 0 where he magniude of curren is / The curren is he same as obained earlier, wih he value of subsiued in he above equaion. This is bes illusraed wih an example, which is described in he nex lesson. The soluion of he curren in he seriesparallel circuis will also be discussed here, along wih some examples. ersion EE T, Kharagpur
16 Problems 5. alculae he curren and power facor (lagging / leading for he following circuis (Fig. 5.5ad, fed from an ac supply of 00. Also draw he phasor diagram in all cases Ω 5 Ω 005 Ω  0 Ω (a (b 005 Ω 5 Ω (c  0 Ω Fig Ω  0 Ω (d Ω 5. A volage of 00 is applied o a pure resisor (, a pure capacior, and a lossy inducor coil, all of hem conneced in parallel. The oal curren is.4 A, while he componen currens are.5,.0 and. A respecively. Find he oal power facor and also he power facor of he coil. Draw he phasor diagram. 5.3 A Hz supply is conneced o a lamp having a raing of 00, 00 W, in series wih a pure inducance,, such ha he oal power consumed is he same, i.e. 00W. Find he value of. A capaciance, is now conneced across he supply. Find value of, o bring he supply power facor o uniy (.0. Draw he phasor diagram in he second case..(a Find he value of he load resisance ( o be conneced in series wih a real volage source ( S S in series, such ha maximum power is ransferred from he above source o he load resisance. (b Find he volage was 8Ω resisance in he circui shown in Fig. (b..(a Find he Theremin s equivalen circui (draw he ck. beween he erminals A, of he circui shown in Fig. (a. ersion EE T, Kharagpur
17 (b A circui shown in Fig. (b is supplied a 40, 50Hz. The wo volages and (magniude only is measured as 60 and 5 respecively. f he curren, is measured as A, find he values of, and. Also find he power facor of he circui (. Draw he complee phasor diagram. 3.(a Find he line curren, power facor, and acive (real power drawn from 3phase, 00, 50Hz, balanced supply in he circui shown in Fig. 3(a. (b n he circui shown in Fig. 3(b, he swich, S is pu in posiion a 0. Find i e (, > 0, if v c (06. Afer he circui reaches seady sae, he swich, S is brough o posiion, a T. Find i c (, > T. Swich he above waveform. 4.(a Find he average and rms values of he periodic waveform shown in Fig. 4(a. (b A coil of mh lowing a series resisance of Ω is conneced in parallel wih a capacior, and he combinaion is fed from 00 m (0., khz supply (source having an inernal resisance of 0Ω. f he circui draws power a uniy power facor (upf, deermine he value of he capacior, qualiy facor of he coil, and power drawn by he circui. Also draw he phasor diagram. ersion EE T, Kharagpur
18 is of Figures Fig. 5. (a ircui diagram ( in series (b Phasor diagram ircui is inducive ( l > (c Phasor diagram apaciive ( l < (d Phasor diagram esisive ( Fig. 5. (a ircui diagram (Ex. 5., Fig. 5.3 (a ircui diagram (Ex. 5., Fig. 5.4 (a ircui diagram ( in parallel (b Phasor diagram ircui is inducive ( l (b Phasor diagram (b Phasor diagram (c Phasor diagram apaciive ( l > (d Phasor diagram esisive ( l < l ersion EE T, Kharagpur
Circuit Types. () i( t) ( )
Circui Types DC Circuis Idenifying feaures: o Consan inpus: he volages of independen volage sources and currens of independen curren sources are all consan. o The circui does no conain any swiches. All
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationChapter 2: Principles of steadystate converter analysis
Chaper 2 Principles of SeadySae Converer Analysis 2.1. Inroducion 2.2. Inducor volsecond balance, capacior charge balance, and he small ripple approximaion 2.3. Boos converer example 2.4. Cuk converer
More informationEDEXCEL NATIONAL CERTIFICATE/DIPLOMA UNIT 67  FURTHER ELECTRICAL PRINCIPLES NQF LEVEL 3 OUTCOME 2 TUTORIAL 1  TRANSIENTS
EDEXEL NAIONAL ERIFIAE/DIPLOMA UNI 67  FURHER ELERIAL PRINIPLE NQF LEEL 3 OUOME 2 UORIAL 1  RANIEN Uni conen 2 Undersand he ransien behaviour of resisorcapacior (R) and resisorinducor (RL) D circuis
More information4kq 2. D) south A) F B) 2F C) 4F D) 8F E) 16F
efore you begin: Use black pencil. Wrie and bubble your SU ID Number a boom lef. Fill bubbles fully and erase cleanly if you wish o change! 20 Quesions, each quesion is 10 poins. Each quesion has a mos
More informationVoltage level shifting
rek Applicaion Noe Number 1 r. Maciej A. Noras Absrac A brief descripion of volage shifing circuis. 1 Inroducion In applicaions requiring a unipolar A volage signal, he signal may be delivered from a bipolar
More informationRC (ResistorCapacitor) Circuits. AP Physics C
(ResisorCapacior Circuis AP Physics C Circui Iniial Condiions An circui is one where you have a capacior and resisor in he same circui. Suppose we have he following circui: Iniially, he capacior is UNCHARGED
More informationInductance and Transient Circuits
Chaper H Inducance and Transien Circuis Blinn College  Physics 2426  Terry Honan As a consequence of Faraday's law a changing curren hrough one coil induces an EMF in anoher coil; his is known as muual
More informationRC Circuit and Time Constant
ircui and Time onsan 8M Objec: Apparaus: To invesigae he volages across he resisor and capacior in a resisorcapacior circui ( circui) as he capacior charges and discharges. We also wish o deermine he
More informationCapacitors and inductors
Capaciors and inducors We coninue wih our analysis of linear circuis by inroducing wo new passive and linear elemens: he capacior and he inducor. All he mehods developed so far for he analysis of linear
More information9. Capacitor and Resistor Circuits
ElecronicsLab9.nb 1 9. Capacior and Resisor Circuis Inroducion hus far we have consider resisors in various combinaions wih a power supply or baery which provide a consan volage source or direc curren
More information11. Properties of alternating currents of LCRelectric circuits
WS. Properies of alernaing currens of Lelecric circuis. Inroducion Socalled passive elecric componens, such as ohmic resisors (), capaciors () and inducors (L), are widely used in various areas of science
More informationENE 104 Electric Circuit Theory
Elecric Circui heory Lecure 0: AC Power Circui Analysis (ENE) Mon, 9 Mar 0 / (EE) Wed, 8 Mar 0 : Dejwoo KHAWPARSUH hp://websaff.ku.ac.h/~dejwoo.kha/ Objecives : Ch Page he insananeous power he average
More informationRC, RL and RLC circuits
Name Dae Time o Complee h m Parner Course/ Secion / Grade RC, RL and RLC circuis Inroducion In his experimen we will invesigae he behavior of circuis conaining combinaions of resisors, capaciors, and inducors.
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationLaboratory #3 Diode Basics and Applications (I)
Laboraory #3 iode asics and pplicaions (I) I. Objecives 1. Undersand he basic properies of diodes. 2. Undersand he basic properies and operaional principles of some dioderecifier circuis. II. omponens
More informationA Mathematical Description of MOSFET Behavior
10/19/004 A Mahemaical Descripion of MOSFET Behavior.doc 1/8 A Mahemaical Descripion of MOSFET Behavior Q: We ve learned an awful lo abou enhancemen MOSFETs, bu we sill have ye o esablished a mahemaical
More informationSteps for D.C Analysis of MOSFET Circuits
10/22/2004 Seps for DC Analysis of MOSFET Circuis.doc 1/7 Seps for D.C Analysis of MOSFET Circuis To analyze MOSFET circui wih D.C. sources, we mus follow hese five seps: 1. ASSUME an operaing mode 2.
More information2 Electric Circuits Concepts Durham
Chaper 3  Mehods Chaper 3  Mehods... 3. nroducion... 2 3.2 Elecrical laws... 2 3.2. Definiions... 2 3.2.2 Kirchhoff... 2 3.2.3 Faraday... 3 3.2.4 Conservaion... 3 3.2.5 Power... 3 3.2.6 Complee... 4
More informationDifferential Equations and Linear Superposition
Differenial Equaions and Linear Superposiion Basic Idea: Provide soluion in closed form Like Inegraion, no general soluions in closed form Order of equaion: highes derivaive in equaion e.g. dy d dy 2 y
More informationPulseWidth Modulation Inverters
SECTION 3.6 INVERTERS 189 PulseWidh Modulaion Inverers Pulsewidh modulaion is he process of modifying he widh of he pulses in a pulse rain in direc proporion o a small conrol signal; he greaer he conrol
More informationBasic Circuit Elements  Prof J R Lucas
Basic Circui Elemens  Prof J ucas An elecrical circui is an inerconnecion of elecrical circui elemens. These circui elemens can be caegorized ino wo ypes, namely acive elemens and passive elemens. Some
More informationPhysics 111 Fall 2007 Electric Currents and DC Circuits
Physics 111 Fall 007 Elecric Currens and DC Circuis 1 Wha is he average curren when all he sodium channels on a 100 µm pach of muscle membrane open ogeher for 1 ms? Assume a densiy of 0 sodium channels
More informationSection 5.1 The Unit Circle
Secion 5.1 The Uni Circle The Uni Circle EXAMPLE: Show ha he poin, ) is on he uni circle. Soluion: We need o show ha his poin saisfies he equaion of he uni circle, ha is, x +y 1. Since ) ) + 9 + 9 1 P
More information1. The graph shows the variation with time t of the velocity v of an object.
1. he graph shows he variaion wih ime of he velociy v of an objec. v Which one of he following graphs bes represens he variaion wih ime of he acceleraion a of he objec? A. a B. a C. a D. a 2. A ball, iniially
More informationModule 3. RL & RC Transients. Version 2 EE IIT, Kharagpur
Module 3  & C Transiens esson 0 Sudy of DC ransiens in  and C circuis Objecives Definiion of inducance and coninuiy condiion for inducors. To undersand he rise or fall of curren in a simple series
More informationµ r of the ferrite amounts to 1000...4000. It should be noted that the magnetic length of the + δ
Page 9 Design of Inducors and High Frequency Transformers Inducors sore energy, ransformers ransfer energy. This is he prime difference. The magneic cores are significanly differen for inducors and high
More informationHANDOUT 14. A.) Introduction: Many actions in life are reversible. * Examples: Simple One: a closed door can be opened and an open door can be closed.
Inverse Funcions Reference Angles Inverse Trig Problems Trig Indeniies HANDOUT 4 INVERSE FUNCTIONS KEY POINTS A.) Inroducion: Many acions in life are reversible. * Examples: Simple One: a closed door can
More informationFE Review Basic Circuits. William Hageman
FE eview Basic Circuis William Hageman 804 FE opics General FE 4. Elecriciy, Power, and Magneism 7 A. Elecrical fundamenals (e.g., charge, curren, volage, resisance, power, energy) B. Curren and volage
More informationSignal Processing and Linear Systems I
Sanford Universiy Summer 214215 Signal Processing and Linear Sysems I Lecure 5: Time Domain Analysis of Coninuous Time Sysems June 3, 215 EE12A:Signal Processing and Linear Sysems I; Summer 1415, Gibbons
More informationFourier series. Learning outcomes
Fourier series 23 Conens. Periodic funcions 2. Represening ic funcions by Fourier Series 3. Even and odd funcions 4. Convergence 5. Halfrange series 6. The complex form 7. Applicaion of Fourier series
More informationSwitching Regulator IC series Capacitor Calculation for Buck converter IC
Swiching Regulaor IC series Capacior Calculaion for Buck converer IC No.14027ECY02 This applicaion noe explains he calculaion of exernal capacior value for buck converer IC circui. Buck converer IIN IDD
More informationUsing RCtime to Measure Resistance
Basic Express Applicaion Noe Using RCime o Measure Resisance Inroducion One common use for I/O pins is o measure he analog value of a variable resisance. Alhough a builin ADC (Analog o Digial Converer)
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationState Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University
Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween
More informationBrown University PHYS 0060 INDUCTANCE
Brown Universiy PHYS 6 Physics Deparmen Sudy Guide Inducance Sudy Guide INTODUCTION INDUCTANCE Anyone who has ever grabbed an auomobile sparkplug wire a he wrong place, wih he engine running, has an appreciaion
More informationChabot College Physics Lab RC Circuits Scott Hildreth
Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard
More informationFullwave rectification, bulk capacitor calculations Chris Basso January 2009
ullwave recificaion, bulk capacior calculaions Chris Basso January 9 This shor paper shows how o calculae he bulk capacior value based on ripple specificaions and evaluae he rms curren ha crosses i. oal
More informationTransient Analysis of First Order RC and RL circuits
Transien Analysis of Firs Order and iruis The irui shown on Figure 1 wih he swih open is haraerized by a pariular operaing ondiion. Sine he swih is open, no urren flows in he irui (i=0) and v=0. The volage
More informationRelative velocity in one dimension
Connexions module: m13618 1 Relaive velociy in one dimension Sunil Kumar Singh This work is produced by The Connexions Projec and licensed under he Creaive Commons Aribuion License Absrac All quaniies
More informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More informationMaking Use of Gate Charge Information in MOSFET and IGBT Data Sheets
Making Use of ae Charge Informaion in MOSFET and IBT Daa Shees Ralph McArhur Senior Applicaions Engineer Advanced Power Technology 405 S.W. Columbia Sree Bend, Oregon 97702 Power MOSFETs and IBTs have
More informationFACULTY OF MATHEMATICAL STUDIES MATHEMATICS FOR PART I ENGINEERING. Lectures
FACULY OF MAHEMAICAL SUDIES MAHEMAICS FOR PAR I ENGINEERING Lecures MODULE 3 FOURIER SERIES Periodic signals Wholerange Fourier series 3 Even and odd uncions Periodic signals Fourier series are used in
More informationcooking trajectory boiling water B (t) microwave 0 2 4 6 8 101214161820 time t (mins)
Alligaor egg wih calculus We have a large alligaor egg jus ou of he fridge (1 ) which we need o hea o 9. Now here are wo accepable mehods for heaing alligaor eggs, one is o immerse hem in boiling waer
More information5.8 Resonance 231. The study of vibrating mechanical systems ends here with the theory of pure and practical resonance.
5.8 Resonance 231 5.8 Resonance The sudy of vibraing mechanical sysems ends here wih he heory of pure and pracical resonance. Pure Resonance The noion of pure resonance in he differenial equaion (1) ()
More informationPermutations and Combinations
Permuaions and Combinaions Combinaorics Copyrigh Sandards 006, Tes  ANSWERS Barry Mabillard. 0 www.mah0s.com 1. Deermine he middle erm in he expansion of ( a b) To ge he kvalue for he middle erm, divide
More informationFourier Series Solution of the Heat Equation
Fourier Series Soluion of he Hea Equaion Physical Applicaion; he Hea Equaion In he early nineeenh cenury Joseph Fourier, a French scienis and mahemaician who had accompanied Napoleon on his Egypian campaign,
More information6.003 Homework #4 Solutions
6.3 Homewk #4 Soluion Problem. Laplace Tranfm Deermine he Laplace ranfm (including he region of convergence) of each of he following ignal: a. x () = e 2(3) u( 3) X = e 3 2 ROC: Re() > 2 X () = x ()e d
More informationEconomics Honors Exam 2008 Solutions Question 5
Economics Honors Exam 2008 Soluions Quesion 5 (a) (2 poins) Oupu can be decomposed as Y = C + I + G. And we can solve for i by subsiuing in equaions given in he quesion, Y = C + I + G = c 0 + c Y D + I
More informationLLC Resonant Converter Reference Design using the dspic DSC
LLC Resonan Converer Reference Design using he dspic DSC 2010 Microchip Technology Incorporaed. All Righs Reserved. LLC Resonan Converer Webinar Slide 1 Hello, and welcome o his web seminar on Microchip
More informationConverter Topologies
High Sepup Raio DCDC Converer Topologies Par I Speaker: G. Spiazzi P. Teni,, L. Rosseo,, G. Spiazzi,, S. Buso,, P. Maavelli, L. Corradini Dep. of Informaion Engineering DEI Universiy of Padova Seminar
More informationComplex Fourier Series. Adding these identities, and then dividing by 2, or subtracting them, and then dividing by 2i, will show that
Mah 344 May 4, Complex Fourier Series Par I: Inroducion The Fourier series represenaion for a funcion f of period P, f) = a + a k coskω) + b k sinkω), ω = π/p, ) can be expressed more simply using complex
More informationLenz's Law. Definition from the book:
Lenz's Law Definiion from he book: The induced emf resuling from a changing magneic flux has a polariy ha leads o an induced curren whose direcion is such ha he induced magneic field opposes he original
More informationPHYS245 Lab: RC circuits
PHYS245 Lab: C circuis Purpose: Undersand he charging and discharging ransien processes of a capacior Display he charging and discharging process using an oscilloscope Undersand he physical meaning of
More informationCAPACITANCE AND INDUCTANCE
CHAPTER 6 CAPACITANCE AND INDUCTANCE THE LEARNING GOALS FOR THIS CHAPTER ARE: Know how o use circui models for inducors and capaciors o calculae volage, curren, and power Be able o calculae sored energy
More informationLecture10 BJT Switching Characteristics, Small Signal Model
1 Lecure1 BJT Swiching Characerisics, Small Signal Model BJT Swiching Characerisics: The circui in Fig.1(b) is a simple CE swich. The inpu volage waveform v s shown in he Fig.1(a) is used o conrol he
More informationINVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS
INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,
More informationSOLID MECHANICS TUTORIAL GEAR SYSTEMS. This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 3.
SOLI MEHNIS TUTORIL GER SYSTEMS This work covers elemens of he syllabus for he Edexcel module 21722P HN/ Mechanical Principles OUTOME 3. On compleion of his shor uorial you should be able o do he following.
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationAstable multivibrator using the 555 IC.(10)
Visi hp://elecronicsclub.cjb.ne for more resources THE 555 IC TIMER The 555 IC TIMER.(2) Monosable mulivibraor using he 555 IC imer...() Design Example 1 wih Mulisim 2001 ools and graphs..(8) Lile descripion
More informationsdomain Circuit Analysis
Domain ircui Analyi Operae direcly in he domain wih capacior, inducor and reior Key feaure lineariy i preered c decribed by ODE and heir Order equal number of plu number of Elemenbyelemen and ource ranformaion
More informationCHAPTER 21: Electromagnetic Induction and Faraday s Law
HAT : lecromagneic nducion and Faraday s aw Answers o Quesions. The advanage of using many urns (N = large number) in Faraday s experimens is ha he emf and induced curren are proporional o N, which makes
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationSignal Rectification
9/3/25 Signal Recificaion.doc / Signal Recificaion n imporan applicaion of juncion diodes is signal recificaion. here are wo ypes of signal recifiers, halfwae and fullwae. Le s firs consider he ideal
More informationMatrix Analysis of Networks
Marix Analysis of Neworks is edious o analyse large nework using normal equaions. is easier and more convenien o formulae large neworks in marix form. To have a nea form of soluion, i is necessary o know
More information2.6 Limits at Infinity, Horizontal Asymptotes Math 1271, TA: Amy DeCelles. 1. Overview. 2. Examples. Outline: 1. Definition of limits at infinity
.6 Limis a Infiniy, Horizonal Asympoes Mah 7, TA: Amy DeCelles. Overview Ouline:. Definiion of is a infiniy. Definiion of horizonal asympoe 3. Theorem abou raional powers of. Infinie is a infiniy This
More informationChapter 8 Copyright Henning Umland All Rights Reserved
Chaper 8 Copyrigh 19972004 Henning Umland All Righs Reserved Rise, Se, Twiligh General Visibiliy For he planning of observaions, i is useful o know he imes during which a cerain body is above he horizon
More informationYTM is positively related to default risk. YTM is positively related to liquidity risk. YTM is negatively related to special tax treatment.
. Two quesions for oday. A. Why do bonds wih he same ime o mauriy have differen YTM s? B. Why do bonds wih differen imes o mauriy have differen YTM s? 2. To answer he firs quesion les look a he risk srucure
More information23.3. Even and Odd Functions. Introduction. Prerequisites. Learning Outcomes
Even and Odd Funcions 23.3 Inroducion In his Secion we examine how o obain Fourier series of periodic funcions which are eiher even or odd. We show ha he Fourier series for such funcions is considerabl
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationAP Calculus AB 2013 Scoring Guidelines
AP Calculus AB 1 Scoring Guidelines The College Board The College Board is a missiondriven noforprofi organizaion ha connecs sudens o college success and opporuniy. Founded in 19, he College Board was
More informationLecture III: Finish Discounted Value Formulation
Lecure III: Finish Discouned Value Formulaion I. Inernal Rae of Reurn A. Formally defined: Inernal Rae of Reurn is ha ineres rae which reduces he ne presen value of an invesmen o zero.. Finding he inernal
More informationPart II Converter Dynamics and Control
Par II onverer Dynamics and onrol 7. A equivalen circui modeling 8. onverer ransfer funcions 9. onroller design 1. Inpu filer design 11. A and D equivalen circui modeling of he disconinuous conducion mode
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and
More informationChapter 4. Properties of the Least Squares Estimators. Assumptions of the Simple Linear Regression Model. SR3. var(e t ) = σ 2 = var(y t )
Chaper 4 Properies of he Leas Squares Esimaors Assumpions of he Simple Linear Regression Model SR1. SR. y = β 1 + β x + e E(e ) = 0 E[y ] = β 1 + β x SR3. var(e ) = σ = var(y ) SR4. cov(e i, e j ) = cov(y
More information23.3. Even and Odd Functions. Introduction. Prerequisites. Learning Outcomes
Even and Odd Funcions 3.3 Inroducion In his Secion we examine how o obain Fourier series of periodic funcions which are eiher even or odd. We show ha he Fourier series for such funcions is considerabl
More information8. TIMEVARYING ELECTRICAL ELEMENTS, CIRCUITS, & THE DYNAMICS
8. TIMEVARYING ELECTRICAL ELEMENTS, CIRCUITS, & THE DYNAMICS 8..1 Timevarying Resisors Le us firs consider he case of a resisor, a simple saic device. In addiion o he wo variables, volage and curren, which
More information2. Waves in Elastic Media, Mechanical Waves
2. Waves in Elasic Media, Mechanical Waves Wave moion appears in almos ever branch of phsics. We confine our aenion o waves in deformable or elasic media. These waves, for eample ordinar sound waves in
More informationChapter 2 Kinematics in One Dimension
Chaper Kinemaics in One Dimension Chaper DESCRIBING MOTION:KINEMATICS IN ONE DIMENSION PREVIEW Kinemaics is he sudy of how hings moe how far (disance and displacemen), how fas (speed and elociy), and how
More informationDiagnostic Examination
Diagnosic Examinaion TOPIC XV: ENGINEERING ECONOMICS TIME LIMIT: 45 MINUTES 1. Approximaely how many years will i ake o double an invesmen a a 6% effecive annual rae? (A) 10 yr (B) 12 yr (C) 15 yr (D)
More informationTLE 472x Family Stepper Motor Drivers. Current Control Method and Accuracy
Applicaion Noe, V 1.0, Augus 2001 ANPS063E TLE 472x Family Sepper Moor Drivers Curren Conrol Mehod and Accuracy by Frank Heinrichs Auomoive Power N e v e r s o p h i n k i n g.  1  TLE 472x sepper moor
More informationORDER INFORMATION TO pin 300 ~ 360mV AMC7150DLF 300 ~ 320mV AMC7150ADLF 320 ~ 340mV AMC7150BDLF 340 ~ 360mV AMC7150CDLF
www.addmek.com DESCRIPTI is a PWM power ED driver IC. The driving curren from few milliamps up o 1.5A. I allows high brighness power ED operaing a high efficiency from 4Vdc o 40Vdc. Up o 200KHz exernal
More informationDCDC Boost Converter with Constant Output Voltage for Grid Connected Photovoltaic Application System
DCDC Boos Converer wih Consan Oupu Volage for Grid Conneced Phoovolaic Applicaion Sysem PuiWeng Chan, Syafrudin Masri Universii Sains Malaysia Email: edmond_chan85@homail.com, syaf@eng.usm.my Absrac
More informationReturn Calculation of U.S. Treasury Constant Maturity Indices
Reurn Calculaion of US Treasur Consan Mauri Indices Morningsar Mehodolog Paper Sepeber 30 008 008 Morningsar Inc All righs reserved The inforaion in his docuen is he proper of Morningsar Inc Reproducion
More informationImagine a Source (S) of sound waves that emits waves having frequency f and therefore
heoreical Noes: he oppler Eec wih ound Imagine a ource () o sound waes ha emis waes haing requency and hereore period as measured in he res rame o he ource (). his means ha any eecor () ha is no moing
More informationINTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES
INTEREST RATE FUTURES AND THEIR OPTIONS: SOME PRICING APPROACHES OPENGAMMA QUANTITATIVE RESEARCH Absrac. Exchangeraded ineres rae fuures and heir opions are described. The fuure opions include hose paying
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationThyristor Based Speed Control Techniques of DC Motor: A Comparative Analysis
Inernaional Journal of Scienific and Research Publicaions, Volume 2, Issue 6, June 2012 1 Thyrisor Based Speed Conrol Techniques of DC Moor: A Comparaive Analysis Rohi Gupa, Ruchika Lamba, Subhransu Padhee
More informationI) EQUATION 1: SHUNTCONTROLLED
Swich Mode Power Supply (SMPS) Topologies (Par I) Auhor: Mohammad Kamil Microchip Technology Inc. EQUATION 1: SHUNTCONTROLLED REGULATOR POWER LOSS INTRODUCTION The indusry drive oward smaller, ligher
More informationPhysics 107 HOMEWORK ASSIGNMENT #2
Phsics 7 HOMEWORK ASSIGNMENT # Cunell & Johnson, 7 h ediion Chaper : Problem 5 Chaper : Problems 44, 54, 56 Chaper 3: Problem 38 *5 MulipleConcep Example 9 deals wih he conceps ha are imporan in his problem.
More informationAn empirical analysis about forecasting Tmall airconditioning sales using time series model Yan Xia
An empirical analysis abou forecasing Tmall aircondiioning sales using ime series model Yan Xia Deparmen of Mahemaics, Ocean Universiy of China, China Absrac Time series model is a hospo in he research
More information11/6/2013. Chapter 14: Dynamic ADAS. Introduction. Introduction. Keeping track of time. The model s elements
Inroducion Chaper 14: Dynamic DS dynamic model of aggregae and aggregae supply gives us more insigh ino how he economy works in he shor run. I is a simplified version of a DSGE model, used in cuingedge
More informationCHAPTER 3: ELECTRICAL MEASUREMENTS IN CONCRETE MATERIALS
26 CHAPTER 3: ELECTRICAL MEASUREMENTS IN CONCRETE MATERIALS This chaper provides a review of he hisory and applicaion of elecrical measuremens in concree. The definiion of elecrical conduciviy and he principles
More informationTechnical Description of S&P 500 BuyWrite Monthly Index Composition
Technical Descripion of S&P 500 BuyWrie Monhly Index Composiion The S&P 500 BuyWrie Monhly (BWM) index is a oal reurn index based on wriing he nearby ahemoney S&P 500 call opion agains he S&P 500 index
More informationDIFFERENTIAL EQUATIONS with TI89 ABDUL HASSEN and JAY SCHIFFMAN. A. Direction Fields and Graphs of Differential Equations
DIFFERENTIAL EQUATIONS wih TI89 ABDUL HASSEN and JAY SCHIFFMAN We will assume ha he reader is familiar wih he calculaor s keyboard and he basic operaions. In paricular we have assumed ha he reader knows
More informationThe Torsion of Thin, Open Sections
EM 424: Torsion of hin secions 26 The Torsion of Thin, Open Secions The resuls we obained for he orsion of a hin recangle can also be used be used, wih some qualificaions, for oher hin open secions such
More informationSwitched Mode Converters (1 Quadrant)
(1 Quadran) Philippe Barrade Laboraoire d Elecronique Indusrielle, LEI STI ISE Ecole Polyechnique Fédérale de Lausanne, EPFL Ch1015 Lausanne Tél: +41 21 693 2651 Fax: +41 21 693 2600 Philippe.barrade@epfl.ch
More informationPhysics 1402: Lecture 21 Today s Agenda
ecure 4 Physics 142: ecure 21 Tody s Agend Announcemens: nducion, R circuis Homework 6: due nex Mondy nducion / A curren Frdy's w ds N S B v B B S N B v 1 ecure 4 nducion Selfnducnce, R ircuis X X X X
More information4. International Parity Conditions
4. Inernaional ariy ondiions 4.1 urchasing ower ariy he urchasing ower ariy ( heory is one of he early heories of exchange rae deerminaion. his heory is based on he concep ha he demand for a counry's currency
More information