Circuit Variables. Unit: volt (V = J/C)
|
|
- Harvey Wiggins
- 5 years ago
- Views:
Transcription
1 Crcut Varables Scentfc nestgaton of statc electrcty was done n late 700 s and Coulomb s credted wth most of the dscoeres. He found that electrc charges hae two attrbutes: amount and polarty. There are two type of charges opposte charges attract and smlar polarty ones repel each other. Charge polarty s ndcated by poste and negate sgns because poste and negate charges cancel each other when brought together. As a results, the electrc charge can be descrbed by an algebrac number, q, wth unts of Coulomb (C). Because opposte charges attract each other, energy s expanded to separate them from each other. Ths energy s stored n the electrc feld between the two reseror of separated charges and s recoered when the charges are allowed to come together. The stored energy per unt charge s called the oltage or potental dfference between the two reseror of charges: = dw dq Unt: olt (V = J/C) Note that we need two reseror of charges. So oltage s between two ponts. We also use and sgns to ndcate the drecton for measurng. From defnton of oltage aboe, w s energy needed to moe a poste charge from reseror to reseror. One can defne a reference pont for measurng oltages (typcally shown as ground). The oltage between any pont and ths reference pont s call the potental of that pont. It s always assumed that s at the pont and the sgn s at the reference pont. Therefore, there s no need to ndcate and sgns for potental. Voltage between two ponts s the dfference between the potental of the two ponts (see fgure). Voltage between two charge reserors s analogous to heght dfference between two flud reseror and the same way, the potental of each pont s analogous to ts eleaton compared to some reference (e.g., sea leel). Potental Eleaton = V V = V V = V V h h h = h - - h 0 0 Sea Leel MAE40 Notes, Wnter 00
2 If we connect the charge reserors, electrc charges flow from one to other. The rate of the charge flow through a specfc area s called the electrc current: = dq dt Unt: Ampere (A = C/s) wth the current flowng n the drecton of the charge flow (t means that a poste current s assocated wth the flow of poste charge). In prncple, electrc charges generate an electrc feld and moton of the charged partcles (current) generates a magnetc feld. Ths electromagnetc feld nteracts wth all charges and affect them. The behaor of such a system s descrbed by Maxwell s equaton. Soluton of Maxwell s equatons, howeer, s dffcult and not needed expect for some cases (propagaton of electromagnetc wae and lght, antennas, etc.) In most releant engneerng cases the problem can be greatly smplfed by notng that electrc charges preferentally flow through a conductor (or a semconductor) as opposed to acuum, ar, or any nsulator. In ths case, the system can be descrbed as a crcut contanng crcut elements and connectng deal wres. Crcut theory s the scentfc dscplne that descrbes behaor of crcuts be and s bult upon the followng assumptons:. All of the electromagnetc phenomena occurs nsde each crcut element. They communcate wth the outsde world only through the oltage across and current that partcular element.. Crcut elements are connected to each other wth deal wres that do not mpede flow of charge. They can be stretched (makng them longer or shorter for example) wthout any effect on the crcut. 3. Net amount of charge cannot be accumulated n any crcut element or any locaton n the crcut. If a net charge of q enters a crcut element, the same amount of charge should leae the element. Ths means: (a) a crcut element should hae at least two termnals, (b) Because current traels through the system at a good fracton of speed of lght, we can safely assume that the total current enterng a crcut element s exactly equal to the current leang that element at any nstant tme. A note about current flow n a conductor. Consder a seres of beads on a wre. If another bead s added to the left end of wre, all of the bead moe one step to the rght and one bead wll fall off the rght end. Smlarly, when an electron enters one end of a wre, electrons n the system moe slghtly and another electron wll leae the other end of the wre. As such, whle electrons do not moe rapdly n a conductor, the current n the wre propagates at a good fracton of speed lght. Crcut Element Ideal Wre MAE40 Notes, Wnter 00
3 In the context of crcut defnton aboe, the mportant physcal quanttes are current and oltages (and electrc power). These are the crcut arables that form the bass for communcaton between crcut elements. The alue of oltage between two ponts,, s ncomplete unless the and sgns are assgned to the two ponts. Smlarly, the alue of current s ncomplete unless a reference current drecton s assgned. Howeer, as and are algebrac numbers, the assgned poston of and for oltage and drecton for the current s arbtrary the sgn of and flps accordng to ths choce. Internal of each crcut element mpose a relatonshp between the current flowng n the element and the oltage across that element. Ths relatonshp s called the element law or - characterstcs. Whle the choce of reference drectons for current through and oltage across an element s arbtrary, the element law or - characterstcs of an element depends on the reference drectons. To see ths pont, note that there exsts four possble choces for oltage and current drectons n a two-termnal crcut element: Passe Sgn Conenton Acte Sgn Conenton In two left cases, the current drecton s marked such that t flows from to sgns. Ths case s called the passe sgn conenton. In the two rght cases, current flows from to sgns. Ths case s referred to as acte sgn conenton. Obously, the - characterstc wll be dfferent n each case as the sgn of current or oltage s swtched. To resole ths confuson, we follow ths conenton:. - characterstcs of two-termnal element are wrtten assumng passe sgn conenton.. Use passe sgn conenton when markng current and oltages n a crcut as much as possble. So, n markng references for oltages and currents n the crcut, t s best to arbtrarly choose ether the oltage or current reference drecton and then use passe sgn conenton MAE40 Notes, Wnter 00 3
4 to mark the other arable. Note that t may not be possble or practcal to mark eery element usng passe sgn conenton. In ths case, A good rule s to mark eery element except oltage and current sources usng passe sgn conenton. Electrc power produced or absorbed n an element: Power: P = dw dt Unt: Watt (W=J/s). Snce = dw/dq and = dq/dt (both total derates), then: P = dw dt P = = dw dq dq dt Usng the defnton of the oltage, one fnds that f we use passe sgn conenton: P < 0 P > 0 Element s producng power Element s absorbng power Obously, f we use acte sgn conenton: P < 0 P > 0 Element s absorbng power Element s producng power Example: Fnd the power absorbed or suppled by elements A and B f =5Aand = 0 V. For element A, - P = = 5 0 = 3, 000 W = 3 kw A B Snce element A reference drectons follow passe sgn conenton and P>, element A s absorbng 3 kw of power. For element B, P = = 5 0 = 3, 000 W = 3 kw Snce element B reference drectons follow acte sgn conenton and P >,element B s supplyng 3 kw of power. MAE40 Notes, Wnter 00 4
5 Defntons KIRCHHOFF LAWS A crcut conssts of crcut elements attached to each other wth deal wres or connectors. Node: A node s a pont n the crcut that s connected to two or more crcut elements wth deal wres. Loop: A loop s a closed path n a crcut through at least two crcut elements whch return to startng node wthout passng through any node twce. Loop Node Node Note that a node should not be taken lterally as a geometrc pont on a specfc crcut dagram as the deal wres connectng the elements can be moed and stretched. For example, any pont on the deal wres connected to the four elements n the bottom of the fgure s a node (as hghlghted n the fgure). All these ponts represent the same node. Krchhoff Current Law (KCL): KCL follows from our assumpton that no net charge can be accumulated at any pont n the crcut (or n a node): Sum of currents enterng a node s equal to sum of currents leang a node. Alternately, as a current leang a node can be replaced wth a current enterng a node wth opposte sgn, KCL can be stated as: Krchhoff Current Law (KCL): or Algebrac sum of currents enterng a node s zero. Algebrac sum of currents leang a node s zero. I use the last erson of KCL n these notes as ths erson s also used n the node-oltage method. How to apply KCL. You should hae dentfed the nodes and mark currents and ther reference drectons on t.. Draw a closed path around the node and mark a startng a pont. 3. Go around the path n the clockwse drecton. Wheneer you pass a wre, wrte down the current wth a sgn f extng and a sgn f enterng. 4. Stop when you are back to the startng pont (and wrte = 0). MAE40 Notes, Wnter 00 5
6 Example: Wrte KCL for the marked node. 3 4 =0 3 4 Example: Fnd () (3) () = 0 = 4 A 3 Krchhoff Voltage Law (KVL): KVL follows from the defnton of the oltage between ponts. Voltage s defned as the amount energy to moe unt charge from one pont to another. Zero net energy should be expanded f a charge q s moed around a closed loop and s returned back to ts orgnal poston,.e., Σ W = qσ =0 Σ =0 Krchhoff Voltage Law (KVL): Algebrac sum of all oltages around any closed path n a crcut s zero. or Sum of oltage drops around a loop - Sum of oltage rses around a loop = 0. How to apply KVL. You should hae marked oltages and ther reference drectons on t.. Draw the loop and mark a startng a pont. 3. Go around the path n the clockwse drecton. Wheneer you go oer a crcut element, wrte down the oltage across element wth a sgn f enterng the termnal of an element and a sgn f enterng the termnal of an element. 4. Stop when you are back to the startng pont (and wrte = 0). MAE40 Notes, Wnter 00 6
7 Example: Wrte KVL for the marked loop. b _ b c a =0 a c KVLs and KCLs are constrants on crcut arables whch arse because of the crcut arrangement (attachment of connecton wres). In addton, nternal of each crcut element mpose a relatonshp between the current flowng n the element and the oltage across that element (element Laws or - characterstcs). Combnaton of these two set of constrants results n a unque set of alues for the crcut arables (currents and oltages). In a crcut wth E elements, there are E crcut arables ( and for each element). We need E equatons to fnd these crcut arables. If the crcut has N nodes, we can wrte N KCL equatons (KCL on the N th node s exactly the sum of KCL on the other N nodes). We can also wrte E N ndependent KVLs and E- characterstc equatons: No. of KCL equatons: N No. of KCV equatons: E N No. of - characterstcs: E Total E If the - characterstc s a lnear relatonshp between and, the element s a lnear element. If a crcut s made of lnear element, the resultng set of E equatons n E arables for a lnear algebrac set of equatons. In ths course, we only use lnear elements, thus, the term lnear crcut theory. MAE40 Notes, Wnter 00 7
8 Lnear Crcut Elements Resstor V = / R R - characterstc: = R Resstance R, Unt Ohm (Ω) Conductance G = /R, Unt Semens (S) P = = R P>0 : Resstor always absorbs power Independent Voltage Source (IVS) s - characterstc: = s for any s = s Independent Current Source (ICS) s s = s - characterstc: = s for any Some Obseratons:. - characterstcs (element laws) of lnear crcut element are lnes n - plane.. - characterstcs of IVS and ICS are ndependent of sgn conenton (e.g., equally correct for both passe and acte sgn conentons). 3. Resstors always absorb power. IVS and ICS can ether absorb or supply power. MAE40 Notes, Wnter 00 8
9 Short Crcut - characterstc: =0forany Note that a short crcut element s a specal case of a resstor (wth R =0)orandeal oltage source (wth s =0). Open Crcut - characterstc: =0forany Note that an open crcut element s a specal case of a resstor (wth R )orandeal current source (wth s =0). Swtch - characterstc: Swtch open: Open crcut = 0forany Swtch closed: Short crcut = 0forany MAE40 Notes, Wnter 00 9
10 Procedure Crcut Analyss usngkvl and KCL. Note how you can calculate problem unknown (e.g., power dsspaton n an element) from the crcut arables.. Go through the crcut n an orderly fashon (e.g., from left to rght, top to bottom). Take each element and a) Identfy nodes (termnals of each element should be connected to a node.) b) Assgn oltages and currents and ther reference drectons to each element. Use passe sgn conenton. c) Identfy crcut arables. Ths wll tell you how many equatons you hae to wrte. d) Wrte down - characterstcs equaton. 3. If you hae N nodes, wrte N KCLs. 4. Calculate no. of KVLs you need: N KV L =E (E) (N ) = E N (where E s no. of elements). Note that as some element laws (e.g., IVS, ICS) result n tral equatons for some crcut arables, t s better to count the crcut unknowns from step aboe and use N KV L = N unknowns N element laws N Nodes. 5. Choose N KV L loops and wrte KVLs. Choose loops that go through the smallest number of elements. 6. Sole the system of equatons and fnd crcut arables. 7. Check your soluton by applyng your soluton to some KVL and KCL (specally KVL on loops you hae not consdered). 8. Fnd problem unknown, f any, from the crcut arables. Note: It s not always possble or practcal to assgn passe sgn conenton to all elements. If so, note that - characterstcs of IVS and ICS are ndependent of sgn conenton. You do NOTneed to use passe sgn conenton for these elements. But be careful f you need to fnd power suppled or absorbed by IVS or ICS. Note: You can readly reduce the number of equatons to sole by half f you substtute - characterstcs equatons n KVLs and KCLs to get a set of E equatons n ether oltages or currents (or a combnaton of both). In fact, after you are fluent n usng the aboe procedure, you only need to mark ether the current or oltage for an element and use the element law to drectly wrte the other crcut arable on the crcut dagram. Then, wrte only KCLs and KVLs and sole. MAE40 Notes, Wnter 00 0
11 Example: Fnd. Followng the procedure, we frst mark the crcut arables ( unknowns: 0,,, 3, 4, 0,,, 3, 4, 5 ) and dentfy the nodes, and wrte the - characterstcs equatons: 0 = 5 0 = V 5 Ω 5Ω 70Ω 0 0Ω 8Ω = 5 3 = = 8 4 Note that we hae 6 elements so we hae crcut arables. Howeer, the IVS element law specfes the oltage across ts termnal, so we hae crcut arables whch hae to be found. The crcut has four nodes. Snce we need to wrte KCL only n N nodes, we choose not wrte KCL n the bottom node. the KCLs are: 0 5 = 0 3 = = 0 80 V 5 5 Ω Ω 5Ω 0 0Ω Ω We need to wrte N KV L = 5 3 = 3 KVLs. Choosng 3 loops wth smallest number elements, we get: 0 3 = 0 (80) = = 0 Aboe are eleen equatons n eleen unknowns that can be soled. The numbers of equatons to be soled can be haled by usng - characterstcs equatons to substtute n KVLs and KCLs. For example, f we substtute for oltages from - characterstcs equatons n KVLs, we get 6 equatons n 6 unknown currents: 0 5 = = 0 3 = = = = 0 MAE40 Notes, Wnter 00
12 Note: As can be seen, een relately small crcuts results n a large number equatons to be soled. Seeral technques for reducng the number of equaton to be soled are ntroduced next. MAE40 Notes, Wnter 00
matter consists, measured in coulombs (C) 1 C of charge requires electrons Law of conservation of charge: charge cannot be created or
Basc Concepts Oerew SI Prefxes Defntons: Current, Voltage, Power, & Energy Passe sgn conenton Crcut elements Ideal s Portland State Unersty ECE 221 Basc Concepts Ver. 1.24 1 Crcut Analyss: Introducton
More informationTitle Chapters HW Due date. Lab Due date 8 Sept Mon 2 Kirchoff s Laws NO LAB. 9 Sept Tue NO LAB 10 Sept Wed 3 Power
Schedule Date Day Class No. Ttle Chapters HW Due date Lab Due date 8 Sept Mon Krchoff s Laws..3 NO LAB Exam 9 Sept Tue NO LAB 10 Sept Wed 3 Power.4.5 11 Sept Thu NO LAB 1 Sept Fr Rectaton HW 1 13 Sept
More informationSelected Student Solutions for Chapter 2
/3/003 Assessment Prolems Selected Student Solutons for Chapter. Frst note that we know the current through all elements n the crcut except the 6 kw resstor (the current n the three elements to the left
More informationAnnouncements. Lecture #2
Announcements Lectures wll be n 4 LeConte begnnng Frday 8/29 Addtonal dscusson TA Denns Chang (Sectons 101, 105) Offce hours: Mo 2-3 PM; Th 5-6 PM Lab sectons begn Tuesday 9/2 Read Experment #1 onlne Download
More information6.01: Introduction to EECS I Lecture 7 March 15, 2011
6.0: Introducton to EECS I Lecture 7 March 5, 20 6.0: Introducton to EECS I Crcuts The Crcut Abstracton Crcuts represent systems as connectons of elements through whch currents (through arables) flow and
More informationEE 2006 Electric Circuit Analysis Spring January 23, 2015 Lecture 02
EE 2006 Electrc Crcut Analyss Sprng 2015 January 23, 2015 Lecture 02 1 Lab 1 Dgtal Multmeter Lab nstructons Aalable onlne Prnt out and read before Lab MWAH 391, 4:00 7:00 pm, next Monday or Wednesday (January
More informationI. INTRODUCTION. 1.1 Circuit Theory Fundamentals
I. INTRODUCTION 1.1 Crcut Theory Fundamentals Crcut theory s an approxmaton to Maxwell s electromagnetc equatons n order to smplfy analyss of complcated crcuts. A crcut s made of seeral elements (boxes
More informationSections begin this week. Cancelled Sections: Th Labs begin this week. Attend your only second lab slot this week.
Announcements Sectons begn ths week Cancelled Sectons: Th 122. Labs begn ths week. Attend your only second lab slot ths week. Cancelled labs: ThF 25. Please check your Lab secton. Homework #1 onlne Due
More information6.01: Introduction to EECS 1 Week 6 October 15, 2009
6.0: ntroducton to EECS Week 6 October 5, 2009 6.0: ntroducton to EECS Crcuts The Crcut Abstracton Crcuts represent systems as connectons of component through whch currents (through arables) flow and across
More informationEE 2006 Electric Circuit Analysis Fall September 04, 2014 Lecture 02
EE 2006 Electrc Crcut Analyss Fall 2014 September 04, 2014 Lecture 02 1 For Your Informaton Course Webpage http://www.d.umn.edu/~jngba/electrc_crcut_analyss_(ee_2006).html You can fnd on the webpage: Lecture:
More informationi I (I + i) 3/27/2006 Circuits ( F.Robilliard) 1
4V I 2V (I + ) 0 0 --- 3V 1 2 4Ω 6Ω 3Ω 3/27/2006 Crcuts ( F.obllard) 1 Introducton: Electrcal crcuts are ubqutous n the modern world, and t s dffcult to oerstate ther mportance. They range from smple drect
More informationI. INTRODUCTION. There are two other circuit elements that we will use and are special cases of the above elements. They are:
I. INTRODUCTION 1.1 Crcut Theory Fundamentals In ths course we study crcuts wth non-lnear elements or deces (dodes and transstors). We wll use crcut theory tools to analyze these crcuts. Snce some of tools
More informationMAE140 Linear Circuits (for non-electrical engs)
MAE4 Lnear Crcuts (for non-electrcal engs) Topcs coered Crcut analyss technques Krchoff s Laws KVL, KCL Nodal and Mesh Analyss Théenn and Norton Equalent Crcuts Resste crcuts, RLC crcuts Steady-state and
More informationIntroduction to circuit analysis. Classification of Materials
Introducton to crcut analyss OUTLINE Electrcal quanttes Charge Current Voltage Power The deal basc crcut element Sgn conventons Current versus voltage (I-V) graph Readng: 1.2, 1.3,1.6 Lecture 2, Slde 1
More informationMAE140 - Linear Circuits - Winter 16 Midterm, February 5
Instructons ME140 - Lnear Crcuts - Wnter 16 Mdterm, February 5 () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator
More informationIndependent Device Currents
Independent Dece Currents j Snce KCL = j k k Only one ndependent current can be defned for each termnal dece. Snce KCL = Only ndependent currents can be defned for a termnal dece. Snce KVL = Only ndependent
More informationEnergy Storage Elements: Capacitors and Inductors
CHAPTER 6 Energy Storage Elements: Capactors and Inductors To ths pont n our study of electronc crcuts, tme has not been mportant. The analyss and desgns we hae performed so far hae been statc, and all
More informationKIRCHHOFF CURRENT LAW
KRCHHOFF CURRENT LAW ONE OF THE FUNDAMENTAL CONSERATON PRNCPLES N ELECTRCAL ENGNEERNG CHARGE CANNOT BE CREATED NOR DESTROYED NODES, BRANCHES, LOOPS A NODE CONNECTS SEERAL COMPONENTS. BUT T DOES NOT HOLD
More informationLinearity. If kx is applied to the element, the output must be ky. kx ky. 2. additivity property. x 1 y 1, x 2 y 2
Lnearty An element s sad to be lnear f t satsfes homogenety (scalng) property and addte (superposton) property. 1. homogenety property Let x be the nput and y be the output of an element. x y If kx s appled
More informationECE 320 Energy Conversion and Power Electronics Dr. Tim Hogan. Chapter 1: Introduction and Three Phase Power
ECE 3 Energy Conerson and Power Electroncs Dr. Tm Hogan Chapter : ntroducton and Three Phase Power. eew of Basc Crcut Analyss Defntons: Node - Electrcal juncton between two or more deces. Loop - Closed
More informationChapter 6 Electrical Systems and Electromechanical Systems
ME 43 Systems Dynamcs & Control Chapter 6: Electrcal Systems and Electromechancal Systems Chapter 6 Electrcal Systems and Electromechancal Systems 6. INTODUCTION A. Bazoune The majorty of engneerng systems
More informationElectrical Circuits 2.1 INTRODUCTION CHAPTER
CHAPTE Electrcal Crcuts. INTODUCTION In ths chapter, we brefly revew the three types of basc passve electrcal elements: resstor, nductor and capactor. esstance Elements: Ohm s Law: The voltage drop across
More informationPhysics 4B. A positive value is obtained, so the current is counterclockwise around the circuit.
Physcs 4B Solutons to Chapter 7 HW Chapter 7: Questons:, 8, 0 Problems:,,, 45, 48,,, 7, 9 Queston 7- (a) no (b) yes (c) all te Queston 7-8 0 μc Queston 7-0, c;, a;, d; 4, b Problem 7- (a) Let be the current
More informationFundamental loop-current method using virtual voltage sources technique for special cases
Fundamental loop-current method usng vrtual voltage sources technque for specal cases George E. Chatzaraks, 1 Marna D. Tortorel 1 and Anastasos D. Tzolas 1 Electrcal and Electroncs Engneerng Departments,
More informationG = G 1 + G 2 + G 3 G 2 +G 3 G1 G2 G3. Network (a) Network (b) Network (c) Network (d)
Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence 6.002 í Electronc Crcuts Homework 2 Soluton Handout F98023 Exercse 21: Determne the conductance of each network
More informationMAE140 Linear Circuits (for non-electrical engs)
MAE4 Lnear Crcuts (for non-electrcal engs) Topcs coered Crcut analyss technques Krchoff s Laws KVL, KCL Nodal and Mesh Analyss Théenn and Norton Equalent Crcuts Resste crcuts, RLC crcuts Steady-state and
More informationMAE140 - Linear Circuits - Fall 13 Midterm, October 31
Instructons ME140 - Lnear Crcuts - Fall 13 Mdterm, October 31 () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator
More informationDC Circuits. Crossing the emf in this direction +ΔV
DC Crcuts Delverng a steady flow of electrc charge to a crcut requres an emf devce such as a battery, solar cell or electrc generator for example. mf stands for electromotve force, but an emf devce transforms
More informationVoltage and Current Laws
CHAPTER 3 Voltage and Current Laws KEY CONCEPTS INTRODUCTION In Chap. 2 we were ntroduced to ndependent voltage and current sources, dependent sources, and resstors. We dscovered that dependent sources
More informationPHY2049 Exam 2 solutions Fall 2016 Solution:
PHY2049 Exam 2 solutons Fall 2016 General strategy: Fnd two resstors, one par at a tme, that are connected ether n SERIES or n PARALLEL; replace these two resstors wth one of an equvalent resstance. Now
More informationChapter 6. Operational Amplifier. inputs can be defined as the average of the sum of the two signals.
6 Operatonal mpler Chapter 6 Operatonal mpler CC Symbol: nput nput Output EE () Non-nvertng termnal, () nvertng termnal nput mpedance : Few mega (ery hgh), Output mpedance : Less than (ery low) Derental
More informationChapter 10 Sinusoidal Steady-State Power Calculations
Chapter 0 Snusodal Steady-State Power Calculatons n Chapter 9, we calculated the steady state oltages and currents n electrc crcuts dren by snusodal sources. We used phasor ethod to fnd the steady state
More informationFE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)( ) 8/25/2010
FE REVEW OPERATONAL AMPLFERS (OP-AMPS)( ) 1 The Op-amp 2 An op-amp has two nputs and one output. Note the op-amp below. The termnal labeled l wth the (-) sgn s the nvertng nput and the nput labeled wth
More informationPhysics 4B. Question and 3 tie (clockwise), then 2 and 5 tie (zero), then 4 and 6 tie (counterclockwise) B i. ( T / s) = 1.74 V.
Physcs 4 Solutons to Chapter 3 HW Chapter 3: Questons:, 4, 1 Problems:, 15, 19, 7, 33, 41, 45, 54, 65 Queston 3-1 and 3 te (clockwse), then and 5 te (zero), then 4 and 6 te (counterclockwse) Queston 3-4
More informationMAE140 - Linear Circuits - Winter 16 Final, March 16, 2016
ME140 - Lnear rcuts - Wnter 16 Fnal, March 16, 2016 Instructons () The exam s open book. You may use your class notes and textbook. You may use a hand calculator wth no communcaton capabltes. () You have
More informationEE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING
EE215 FUNDAMENTALS OF ELECTRICAL ENGINEERING TaChang Chen Unersty of Washngton, Bothell Sprng 2010 EE215 1 WEEK 8 FIRST ORDER CIRCUIT RESPONSE May 21 st, 2010 EE215 2 1 QUESTIONS TO ANSWER Frst order crcuts
More informationFEEDBACK AMPLIFIERS. v i or v s v 0
FEEDBCK MPLIFIERS Feedback n mplers FEEDBCK IS THE PROCESS OF FEEDING FRCTION OF OUTPUT ENERGY (VOLTGE OR CURRENT) BCK TO THE INPUT CIRCUIT. THE CIRCUIT EMPLOYED FOR THIS PURPOSE IS CLLED FEEDBCK NETWORK.
More informationχ x B E (c) Figure 2.1.1: (a) a material particle in a body, (b) a place in space, (c) a configuration of the body
Secton.. Moton.. The Materal Body and Moton hyscal materals n the real world are modeled usng an abstract mathematcal entty called a body. Ths body conssts of an nfnte number of materal partcles. Shown
More informationINDUCTANCE. RC Cicuits vs LR Circuits
INDUTANE R cuts vs LR rcuts R rcut hargng (battery s connected): (1/ )q + (R)dq/ dt LR rcut = (R) + (L)d/ dt q = e -t/ R ) = / R(1 - e -(R/ L)t ) q ncreases from 0 to = dq/ dt decreases from / R to 0 Dschargng
More informationPHYSICS - CLUTCH CH 28: INDUCTION AND INDUCTANCE.
!! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A col of wre wth a VOLTAGE across each end wll have a current n t - Wre doesn t HAVE to have voltage source, voltage can be INDUCED V Common ways
More informationKirchhoff second rule
Krchhoff second rule Close a battery on a resstor: smplest crcut! = When the current flows n a resstor there s a voltage drop = How much current flows n the crcut? Ohm s law: Krchhoff s second law: Around
More information3.2 Terminal Characteristics of Junction Diodes (pp )
/9/008 secton3_termnal_characterstcs_of_juncton_odes.doc /6 3. Termnal Characterstcs of Juncton odes (pp.47-53) A Juncton ode I.E., A real dode! Smlar to an deal dode, ts crcut symbol s: HO: The Juncton
More informationWeek3, Chapter 4. Position and Displacement. Motion in Two Dimensions. Instantaneous Velocity. Average Velocity
Week3, Chapter 4 Moton n Two Dmensons Lecture Quz A partcle confned to moton along the x axs moves wth constant acceleraton from x =.0 m to x = 8.0 m durng a 1-s tme nterval. The velocty of the partcle
More informationCircuits II EE221. Instructor: Kevin D. Donohue. Instantaneous, Average, RMS, and Apparent Power, and, Maximum Power Transfer, and Power Factors
Crcuts II EE1 Unt 3 Instructor: Ken D. Donohue Instantaneous, Aerage, RMS, and Apparent Power, and, Maxmum Power pp ransfer, and Power Factors Power Defntons/Unts: Work s n unts of newton-meters or joules
More information8.022 (E&M) Lecture 8
8.0 (E&M) Lecture 8 Topcs: Electromotve force Crcuts and Krchhoff s rules 1 Average: 59, MS: 16 Quz 1: thoughts Last year average: 64 test slghtly harder than average Problem 1 had some subtletes math
More informationPhysics 114 Exam 2 Spring Name:
Physcs 114 Exam Sprng 013 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem Answer each of the followng questons. Ponts for each queston are ndcated n red wth the amount beng
More informationBoise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment
More informationCHAPTER 13. Exercises. E13.1 The emitter current is given by the Shockley equation:
HPT 3 xercses 3. The emtter current s gen by the Shockley equaton: S exp VT For operaton wth, we hae exp >> S >>, and we can wrte VT S exp VT Solng for, we hae 3. 0 6ln 78.4 mv 0 0.784 5 4.86 V VT ln 4
More informationTemperature. Chapter Heat Engine
Chapter 3 Temperature In prevous chapters of these notes we ntroduced the Prncple of Maxmum ntropy as a technque for estmatng probablty dstrbutons consstent wth constrants. In Chapter 9 we dscussed the
More informationCoupling Element and Coupled circuits. Coupled inductor Ideal transformer Controlled sources
Couplng Element and Coupled crcuts Coupled nductor Ideal transformer Controlled sources Couplng Element and Coupled crcuts Coupled elements hae more that one branch and branch oltages or branch currents
More informationGAUTENG DEPARTMENT OF EDUCATION SENIOR SECONDARY INTERVENTION PROGRAMME PHYSICAL SCIENCES GRADE 12 SESSION 1 (LEARNER NOTES)
PHYSICAL SCIENCES GRADE 1 SESSION 1 (LEARNER NOTES) TOPIC 1: MECHANICS PROJECTILE MOTION Learner Note: Always draw a dagram of the stuaton and enter all the numercal alues onto your dagram. Remember to
More informationDifference Equations
Dfference Equatons c Jan Vrbk 1 Bascs Suppose a sequence of numbers, say a 0,a 1,a,a 3,... s defned by a certan general relatonshp between, say, three consecutve values of the sequence, e.g. a + +3a +1
More informationBoise State University Department of Electrical and Computer Engineering ECE 212L Circuit Analysis and Design Lab
Bose State Unersty Department of Electrcal and omputer Engneerng EE 1L rcut Analyss and Desgn Lab Experment #8: The Integratng and Dfferentatng Op-Amp rcuts 1 Objectes The objectes of ths laboratory experment
More informationStructure and Drive Paul A. Jensen Copyright July 20, 2003
Structure and Drve Paul A. Jensen Copyrght July 20, 2003 A system s made up of several operatons wth flow passng between them. The structure of the system descrbes the flow paths from nputs to outputs.
More informationELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM
ELASTIC WAVE PROPAGATION IN A CONTINUOUS MEDIUM An elastc wave s a deformaton of the body that travels throughout the body n all drectons. We can examne the deformaton over a perod of tme by fxng our look
More informationCHAPTER 14 GENERAL PERTURBATION THEORY
CHAPTER 4 GENERAL PERTURBATION THEORY 4 Introducton A partcle n orbt around a pont mass or a sphercally symmetrc mass dstrbuton s movng n a gravtatonal potental of the form GM / r In ths potental t moves
More informationDEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA. 1. Matrices in Mathematica
demo8.nb 1 DEMO #8 - GAUSSIAN ELIMINATION USING MATHEMATICA Obectves: - defne matrces n Mathematca - format the output of matrces - appl lnear algebra to solve a real problem - Use Mathematca to perform
More informationVI. Transistor Amplifiers
VI. Transstor Amplfers 6. Introducton In ths secton we wll use the transstor small-sgnal model to analyze and desgn transstor amplfers. There are two ssues that we need to dscuss frst: ) What are the mportant
More informationInner Product. Euclidean Space. Orthonormal Basis. Orthogonal
Inner Product Defnton 1 () A Eucldean space s a fnte-dmensonal vector space over the reals R, wth an nner product,. Defnton 2 (Inner Product) An nner product, on a real vector space X s a symmetrc, blnear,
More informationKey component in Operational Amplifiers
Key component n Operatonal Amplfers Objectve of Lecture Descrbe how dependent voltage and current sources functon. Chapter.6 Electrcal Engneerng: Prncples and Applcatons Chapter.6 Fundamentals of Electrc
More informationAdvanced Circuits Topics - Part 1 by Dr. Colton (Fall 2017)
Advanced rcuts Topcs - Part by Dr. olton (Fall 07) Part : Some thngs you should already know from Physcs 0 and 45 These are all thngs that you should have learned n Physcs 0 and/or 45. Ths secton s organzed
More informationPHYSICS - CLUTCH 1E CH 28: INDUCTION AND INDUCTANCE.
!! www.clutchprep.com CONCEPT: ELECTROMAGNETIC INDUCTION A col of wre wth a VOLTAGE across each end wll have a current n t - Wre doesn t HAVE to have voltage source, voltage can be INDUCED V Common ways
More informationComplex Numbers, Signals, and Circuits
Complex Numbers, Sgnals, and Crcuts 3 August, 009 Complex Numbers: a Revew Suppose we have a complex number z = x jy. To convert to polar form, we need to know the magntude of z and the phase of z. z =
More informationElectricity and Magnetism Lecture 07 - Physics 121 Current, Resistance, DC Circuits: Y&F Chapter 25 Sect. 1-5 Kirchhoff s Laws: Y&F Chapter 26 Sect.
Electrcty and Magnetsm Lecture 07 - Physcs Current, esstance, DC Crcuts: Y&F Chapter 5 Sect. -5 Krchhoff s Laws: Y&F Chapter 6 Sect. Crcuts and Currents Electrc Current Current Densty J Drft Speed esstance,
More informationLaboratory 1c: Method of Least Squares
Lab 1c, Least Squares Laboratory 1c: Method of Least Squares Introducton Consder the graph of expermental data n Fgure 1. In ths experment x s the ndependent varable and y the dependent varable. Clearly
More informationFormulation of Circuit Equations
ECE 570 Sesson 2 IC 752E Computer Aded Engneerng for Integrated Crcuts Formulaton of Crcut Equatons Bascs of crcut modelng 1. Notaton 2. Crcut elements 3. Krchoff laws 4. ableau formulaton 5. Modfed nodal
More informationPHYS 705: Classical Mechanics. Calculus of Variations II
1 PHYS 705: Classcal Mechancs Calculus of Varatons II 2 Calculus of Varatons: Generalzaton (no constrant yet) Suppose now that F depends on several dependent varables : We need to fnd such that has a statonary
More informationPhysics 114 Exam 2 Fall 2014 Solutions. Name:
Physcs 114 Exam Fall 014 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse ndcated,
More information8 Derivation of Network Rate Equations from Single- Cell Conductance Equations
Physcs 178/278 - Davd Klenfeld - Wnter 2019 8 Dervaton of Network Rate Equatons from Sngle- Cell Conductance Equatons Our goal to derve the form of the abstract quanttes n rate equatons, such as synaptc
More informationName: PHYS 110 Dr. McGovern Spring 2018 Exam 1. Multiple Choice: Circle the answer that best evaluates the statement or completes the statement.
Name: PHYS 110 Dr. McGoern Sprng 018 Exam 1 Multple Choce: Crcle the answer that best ealuates the statement or completes the statement. #1 - I the acceleraton o an object s negate, the object must be
More informationModeling motion with VPython Every program that models the motion of physical objects has two main parts:
1 Modelng moton wth VPython Eery program that models the moton o physcal objects has two man parts: 1. Beore the loop: The rst part o the program tells the computer to: a. Create numercal alues or constants
More informationPhysics 2102 Spring 2007 Lecture 10 Current and Resistance
esstance Is Futle! Physcs 0 Sprng 007 Jonathan Dowlng Physcs 0 Sprng 007 Lecture 0 Current and esstance Georg Smon Ohm (789-854) What are we gong to learn? A road map lectrc charge lectrc force on other
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science Circuits and Electronics Spring 2001
Massachusetts Insttute of Technology Department of Electrcal Engneerng and Computer Scence Read Chapters 11 through 12. 6.002 Crcuts and Electroncs Sprng 2001 Homework #5 Handout S01031 Issued: 3/8/2001
More informationTUTORIAL PROBLEMS. E.1 KCL, KVL, Power and Energy. Q.1 Determine the current i in the following circuit. All units in VAΩ,,
196 E TUTORIAL PROBLEMS E.1 KCL, KVL, Power and Energy Q.1 Determne the current n the followng crcut. 3 5 3 8 9 6 5 Appendx E Tutoral Problems 197 Q. Determne the current and the oltage n the followng
More informationLecture #4 Capacitors and Inductors Energy Stored in C and L Equivalent Circuits Thevenin Norton
EES ntro. electroncs for S Sprng 003 Lecture : 0/03/03 A.R. Neureuther Verson Date 0/0/03 EES ntroducton to Electroncs for omputer Scence Andrew R. Neureuther Lecture # apactors and nductors Energy Stored
More informationE40M Device Models, Resistors, Voltage and Current Sources, Diodes, Solar Cells. M. Horowitz, J. Plummer, R. Howe 1
E40M Devce Models, Resstors, Voltage and Current Sources, Dodes, Solar Cells M. Horowtz, J. Plummer, R. Howe 1 Understandng the Solar Charger Lab Project #1 We need to understand how: 1. Current, voltage
More informationChapter 9 Complete Response of Circuits with Two Storage Elements
hapter 9 omplete Response of rcuts wth Two Storage Elements In hapter 8, we had rreducble storage element and a frst order crcut. In hapter 9, we wll hae rreducble storage elements and therefore, a second
More informationUnit 1. Current and Voltage U 1 VOLTAGE AND CURRENT. Circuit Basics KVL, KCL, Ohm's Law LED Outputs Buttons/Switch Inputs. Current / Voltage Analogy
..2 nt Crcut Bascs KVL, KCL, Ohm's Law LED Outputs Buttons/Swtch Inputs VOLTAGE AND CRRENT..4 Current and Voltage Current / Voltage Analogy Charge s measured n unts of Coulombs Current Amount of charge
More informationPHYS 705: Classical Mechanics. Newtonian Mechanics
1 PHYS 705: Classcal Mechancs Newtonan Mechancs Quck Revew of Newtonan Mechancs Basc Descrpton: -An dealzed pont partcle or a system of pont partcles n an nertal reference frame [Rgd bodes (ch. 5 later)]
More informationCopyright 2004 by Oxford University Press, Inc.
JT as an Amplfer &a Swtch, Large Sgnal Operaton, Graphcal Analyss, JT at D, asng JT, Small Sgnal Operaton Model, Hybrd P-Model, TModel. Lecture # 7 1 Drecton of urrent Flow & Operaton for Amplfer Applcaton
More informationPhysics 114 Exam 3 Spring Name:
Physcs 114 Exam 3 Sprng 015 Name: For gradng purposes (do not wrte here): Queston 1. 1... 3. 3. Problem 4. Answer each of the followng questons. Ponts for each queston are ndcated n red. Unless otherwse
More informationMAE140 - Linear Circuits - Fall 10 Midterm, October 28
M140 - Lnear rcuts - Fall 10 Mdterm, October 28 nstructons () Ths exam s open book. You may use whatever wrtten materals you choose, ncludng your class notes and textbook. You may use a hand calculator
More informationModule 1 : The equation of continuity. Lecture 1: Equation of Continuity
1 Module 1 : The equaton of contnuty Lecture 1: Equaton of Contnuty 2 Advanced Heat and Mass Transfer: Modules 1. THE EQUATION OF CONTINUITY : Lectures 1-6 () () () (v) (v) Overall Mass Balance Momentum
More information8 Derivation of Network Rate Equations from Single- Cell Conductance Equations
Physcs 178/278 - Davd Klenfeld - Wnter 2015 8 Dervaton of Network Rate Equatons from Sngle- Cell Conductance Equatons We consder a network of many neurons, each of whch obeys a set of conductancebased,
More informationElectrical Circuits II (ECE233b)
Electrcal Crcuts (ECE33b SteadyState Power Analyss Anests Dounas The Unersty of Western Ontaro Faculty of Engneerng Scence SteadyState Power Analyss (t AC crcut: The steady state oltage and current can
More informationR. W. Erickson. Department of Electrical, Computer, and Energy Engineering University of Colorado, Boulder
R. W. Erckson Department of Electrcal, Computer, and Energy Engneerng Unersty of Colorado, Boulder 3.5. Example: ncluson of semconductor conducton losses n the boost conerter model Boost conerter example
More informationCinChE Problem-Solving Strategy Chapter 4 Development of a Mathematical Model. formulation. procedure
nhe roblem-solvng Strategy hapter 4 Transformaton rocess onceptual Model formulaton procedure Mathematcal Model The mathematcal model s an abstracton that represents the engneerng phenomena occurrng n
More informationELG 2135 ELECTRONICS I SECOND CHAPTER: OPERATIONAL AMPLIFIERS
ELG 35 ELECTONICS I SECOND CHAPTE: OPEATIONAL AMPLIFIES Sesson Wnter 003 Dr. M. YAGOUB Second Chapter: Operatonal amplfers II - _ After reewng the basc aspects of amplfers, we wll ntroduce a crcut representng
More informationVote today! Physics 122, Fall November (c) University of Rochester 1. Today in Physics 122: applications of induction
Phscs 1, Fall 01 6 Noember 01 Toda n Phscs 1: applcatons of nducton Generators, motors and back EMF Transformers Edd currents Vote toda! Hdropower generators on the Nagara Rer below the Falls. The ste
More informationImportant Instructions to the Examiners:
Summer 0 Examnaton Subject & Code: asc Maths (70) Model Answer Page No: / Important Instructons to the Examners: ) The Answers should be examned by key words and not as word-to-word as gven n the model
More informationPhysics 1202: Lecture 11 Today s Agenda
Physcs 122: Lecture 11 Today s Agenda Announcements: Team problems start ths Thursday Team 1: Hend Ouda, Mke Glnsk, Stephane Auger Team 2: Analese Bruder, Krsten Dean, Alson Smth Offce hours: Monday 2:3-3:3
More informationRevision: December 13, E Main Suite D Pullman, WA (509) Voice and Fax
.9.1: AC power analyss Reson: Deceber 13, 010 15 E Man Sute D Pullan, WA 99163 (509 334 6306 Voce and Fax Oerew n chapter.9.0, we ntroduced soe basc quanttes relate to delery of power usng snusodal sgnals.
More informationDriving your LED s. LED Driver. The question then is: how do we use this square wave to turn on and turn off the LED?
0//00 rng your LE.doc / rng your LE s As we hae preously learned, n optcal communcaton crcuts, a dgtal sgnal wth a frequency n the tens or hundreds of khz s used to ampltude modulate (on and off) the emssons
More informationDiode. Current HmAL Voltage HVL Simplified equivalent circuit. V γ. Reverse bias. Forward bias. Designation: Symbol:
Dode Materal: Desgnaton: Symbol: Poste Current flow: ptype ntype Anode Cathode Smplfed equalent crcut Ideal dode Current HmAL 0 8 6 4 2 Smplfed model 0.5.5 2 V γ eal dode Voltage HVL V γ closed open V
More informationNumerical Transient Heat Conduction Experiment
Numercal ransent Heat Conducton Experment OBJECIVE 1. o demonstrate the basc prncples of conducton heat transfer.. o show how the thermal conductvty of a sold can be measured. 3. o demonstrate the use
More informationPhysics 5153 Classical Mechanics. Principle of Virtual Work-1
P. Guterrez 1 Introducton Physcs 5153 Classcal Mechancs Prncple of Vrtual Work The frst varatonal prncple we encounter n mechancs s the prncple of vrtual work. It establshes the equlbrum condton of a mechancal
More informationCircuit Theory I
16.1 Crcut Theory I Tngshu Hu Offce: Ball Hall 45 Phone: 4374, Fax: 37 Emal: tngshu@gmal.com Offce Hours: 9-1am, 11am-1pm, Monday, Wednesday http://faculty.uml.edu/thu/ http://faculty.uml.edu/thu/16.1/materal.htm
More informationFinite Element Modelling of truss/cable structures
Pet Schreurs Endhoven Unversty of echnology Department of Mechancal Engneerng Materals echnology November 3, 214 Fnte Element Modellng of truss/cable structures 1 Fnte Element Analyss of prestressed structures
More informationMathematical Preparations
1 Introducton Mathematcal Preparatons The theory of relatvty was developed to explan experments whch studed the propagaton of electromagnetc radaton n movng coordnate systems. Wthn expermental error the
More informationChapter 8. Potential Energy and Conservation of Energy
Chapter 8 Potental Energy and Conservaton of Energy In ths chapter we wll ntroduce the followng concepts: Potental Energy Conservatve and non-conservatve forces Mechancal Energy Conservaton of Mechancal
More information