Unit 1. Current and Voltage U 1 VOLTAGE AND CURRENT. Circuit Basics KVL, KCL, Ohm's Law LED Outputs Buttons/Switch Inputs. Current / Voltage Analogy
|
|
- Ashley Greer
- 5 years ago
- Views:
Transcription
1 ..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 flowng through a n a certan Measured n = Coulombs per second Current s usually denoted by the varable, I Voltage Electrc energy Analogous to mechancal potental energy (.e. ) Must measure ponts Measured n Volts (V) Common reference pont: Ground (GND) = 0V Often really connected to the ground Hgher Potental Conductve Materal (A Wre) Hgher Potental Lower Potental Lower Potental V 5V Charge = Water Voltage Source = Water Pressure v v 2 2 v GND
2 Meet The Components Most electronc crcuts are modeled wth the followng components Resstor Measures how well a materal conducts electrons Capactor & Inductor Measures materal's ablty to store charge and energy Transstor Basc amplfcaton or swtchng technology.5 Transstor Krchhoff's Laws Common sense rules that govern current and voltage Krchhoff's Current Law (KCL) Krchhoff's Voltage Law (KVL) Krchhoff's Current Law (KCL) The current flowng a locaton (a.k.a. node) must equal the current flowng of the locaton or put another way The sum of current at any locaton must An electronc component (e.g. resstor, transstor, etc.) 2 4 KCL says.6 Krchhoff's Current Law Remnder: KCL says Start by defnng a for each current It does not matter what drecton we choose When we solve for one of the currents we may get a current "Negatve" sgn smply means the drecton s of our orgnal ndcaton In the examples to the rght the top two examples the drectons chosen are fne but physcally n volaton of KCL but KCL helps us arrve at a consstent result snce solvng for one of the current values ndcates The of and 2 are the same They always flow n the drecton of each other (f one flows n the other flows out or vce versa) 2 KCL says mples 2 KCL says mples 2 KCL says 2 KCL says.7 Krchhoff's Laws Krchhoff's Voltage Law (KVL) The sum of voltages around a (.e. walkng around and returnng to the ) must equal 0 Defne "polarty" of voltage and then be consstent as you go around the loop obvously when you solve you may fnd a voltage to be negatve whch means you need to flp/reverse the polarty v KVL says: v v 2 v 4 2 v 4 KVL says: v 2 2 v 5.8 v 5
3 .9.0 A Bref Summary Nodes KCL and KVL are and no matter what knd of devces are used The yellow boxes could be ANY electronc devce: resstors, batteres, swtches, transstors, etc KVL and KCL wll stll apply In a few mnutes, we'll learn a law that only apples to resstors (or any devce that can be modeled as a resstor) Some KVL or KCL equatons may be Wrtng the equaton for loop {v,v2,v} and {v,v4,v5} may be suffcent and wrtng {v,v2,v4,v5} may not be necessary But as a novce, feel free to KVL says: v v 2 v =0 v v 2 v 4 v 5 =0 v v 4 v 5 =0 (Def.) An electrc node s the juncton of devces connected by wres voltage at any pont of the node How many nodes exst n the dagram to the rght? se KCL to solve for, 4, and 6 se KVL to solve for v, v8, v5 Practce KCL and KVL NODE D A 2V Hnt: Fnd a node or loop where there s only one unknown and that should cause a domno effect 9 A 9 9V 5V 2 8 v 8 NODE A A 4 v 4 v 5 4V NODE C 0.5A 8 5 NODE B V 5V. Resstance and Ohms Law Measure of how hard t s for current to flow through the substance Resstance = How much do you have to put to get a certan to flow Measured n Ohms (Ω) Ohm's Law I = or V = R => I Large Resstance R Small Resstance Schematc Symbol for a Resstor Ohm's Law ONLY apples to resstors (or devces that can be modeled as a resstor such as swtches and transstors).2
4 Seres & Parallel Resstance Seres resstors = one after the next wth no other dvergent path Parallel resstors = Spannng the same two ponts Seres and parallel resstors can be combned to an equvalent resstor wth value gven as shown Seres Connectons R R eff R=R= Parallel Connecton R eff R R eff = For only 2 resstors, ths smplfes to:. Solvng Voltage & Current Gven the crcut to the rght, let = 5V, R = 400 ohms, = 600 ohms Solve for the current through the crcut and voltages across each resstors (.e. V and V2) Snce everythng s n, KCL teaches us that the current through each component must be the, let's call t = Ths alone lets us compute V and V2 snce Ohm's law says V = and V2 = V = and V2 = Though unneeded, KVL teaches us that VV2=0 or that = V V2 v dd _ V R v v2 2.4 Voltage Supply Drawngs The voltage source () n the left dagram (.e. the crcle connected to the "Rest of Crcut") s shown n an alternate representaton n the rght dagram (.e. the trangle labeled "") In the left dagram we can easly see a KVL loop avalable There s stll a KVL loop avalable n the rght dagram _ V R Both are drawngs of the same crcut (.e. they are equvalent) Rest of Crcut Actual connecton wll be drawn lke ths.5 Shortcut: Voltage Dvders A shortcut applcaton of KVL, KCL, and Ohm's law when two resstors are n seres (must be n seres) When two resstors are n seres we can deduce an expresson for the voltage across one of them () = / ; (2) V = *R; () V2 = * Substtutng our expresson for nto (2) and () The voltage across one of the resstors s proportonal to the value of that resstor and the total seres resstance If you need 0 gallons of gas to drve 500 mles, how much gas you have you used up after drvng 200 mles? Gas =, Mleage = V tot R V V2 Voltage Dvder Eqn: If two resstors R and are n seres then voltage across R s: V = Memorze ths. We wll use t often!.6
5 .7.8 Solvng Voltage & Current Solvng Voltage & Current Reconsderng the crcut to the rght wth = 5V, R = 400 ohms, = 600 ohms Solve for the current through the crcut and voltages across each resstors (.e. V and V2) We can use the voltage dvder concept to mmedately arrve at the value of V2 2 _ V R Consder the crcut on the rght What s the relatonshp between V and V? Can you solve for the voltage V (n terms of Vs, R,, R)? Vs _ V R V R Can you solve for the voltage V2 (n terms of Vs, R,, R)?.9.20 A Problem Gven the followng parameters Vs=5V, R=4, = 2, R = 2 and R4 = 0 ohms. Can we use the voltage dvder concept to mmedately solve the voltage across or do we need to frst do some manpulaton? What about R4? Frst, fnd the total equvalent resstance (R eq ) seen by Vs and then solve for the voltage across each resstor LEDS AS OTPTS AND SWITCHES/BTTONS AS INPTS Frst collapse ths to a sngle equvalent resstance, R eq
6 Generatng Inputs & Measurng Outputs Where do nputs to a dgtal crcut orgnate? sually as from another dgtal crcut (.e. SB connectng to your laptop's man processng system) For our class rght now: A controlled by a human (can be on or off) How wll we know what voltage s comng out of a dgtal crcut? Could use a voltmeter or osclloscope (don't be afrad to use the equpment n our lab!) are commonly used to show the status of a dgtal output to a human A button or swtch (nput stmulus) Input Some dgtal processng/ control An LED Output Each key on your keyboard s essentally a dgtal nput generated by a push button (pressed or not pressed) The status ndcator on the Caps Lock button s smply an LED controlled by a dgtal output..2 (LghtEmttng) Dodes The smplest output we can control s an LED (Lghtemttng dode) whch s lke a tny lght bulb An LED glows ('on') when current through t (.e. when there s a voltage across t) LEDs are polarzed meanng they only work n one Longer leg orentaton ( leg must be at hgher voltage) LED Schematc Symbol Shorter leg ault/fles/magecache/product_full/p roducts/solarbotcsredled.gf 5V 0V Current flows = LED on 5V 0V BACKWARDS!! No Current flows = LED off.22 Longer leg connects to the sde wth the hgher voltage Shorter leg connects to the sde wth the lower voltage 0V 0V 5V 5V No voltage dfferental = No Current flows = LED off Man Pont: To be 'on', there must be a voltage dfference across the LED makng current flow. Need for Seres Resstor wth LEDs Problem: LEDs may allow too much current to flow whch may blow out the LED Soluton: se a seres resstor to lmt current Amount of current wll determne of LED R then and thus LED brghtness = V/R = (VsV LED ) / R sually R s a few hundred ohms ( ohms) No current lmtaton BAD Choose resstor to lmt current A dgtal (gate) output wll usually serve as our voltage source that can be ether '0' (0V) or '' (5V) Doesn't matter where resstor s placed as long as t s n seres Man Pont: LED's should always be connected wth a currentlmtng resstor Longer leg LED Schematc Symbol Breadboard vew.2 Shorter leg LED Connecton Approaches When lettng a dgtal output control an LED, the value (.e. '0' = low or '' = hgh voltage) that causes the LED to lght up depends on how the crcut s wred Ths box represents a dgtal output (e.g. your Arduno) that can generate a hgh () or low (0) voltage. What dgtal output value must be present for the LED to be on? Note: Gates can often (take n) more current than they can (push out), so opton 2 may be preferred but let's not worry about ths now let's use opton Opton 0 LED on LED off GND Model of dgtal output LED s on when gate outputs '' R Opton 2 LED off LED on LED s on when gate outputs '0' Man Pont: LED's can lght for ether a logc '' or '0' output t depends on how they are wred..24
7 Swtch and PushButton Inputs Swtches and pushbuttons can be n one of two confguratons: or Swtches can be opened or closed and then n that poston untl changed Pushbuttons are open by and requre you to push them to close the crcut (they then open when you release) Can be used as an nput to dgtal devce.25 Example pushbuttons Example swtch Swtches and Pushbuttons Important Note : We can model a button or swtch as a resstor of ether 0 ohms or nf. (very large) ohms When open a SW/PB looks lke an resstance (no current can flow) When closed a SW/PB looks lke a (R=0) and no voltage drops across t Queston: What voltage does an open or closed swtch (pushbutton) generate? Answer:. Important Note 2: SW or PBs don't produce dgtal 0's or 's, they control what voltage (PWR/GND) s connected to your devce SW SW SW SW = =.26 R=nf. (open crcut) R=0 (wre) V =?? V =?? Connectng a Swtch Swtches only the voltage gong nto a devce, they do not produce a voltage (0V or 5V) by themselves Opton : Attach one sde to GND and the other sde to the devce When the swtch=open, nothng s connected to the devce (a.k.a. ) A floatng nput may sometmes appears as zero, and other tmes as a one. We need the nputs to logc gates to be n ether the 0 or state not floatng Opton 2: When swtch closed => resstance connecton from power to ground = current flow BAD!!! (Ths s known as a "short crcut"). Vn = floatng = unknown Vn.27 Opton : Bad (floatng) Swtch Closed = 0V (Logc 0) to nput Swtch Open =??? (does not work) nlmted current flow when closed Opton 2: Bad (short crcut) Swtch Open = =5V (Logc ) to nput Swtch Closed = Short Crcut (does not work) Preferred Wrng of Swtches Soluton: Put GND on the far sde and a "pullup" resstor at the nput sde "Pullup resstor" used to hold the nput hgh unless somethng s forcng t to a zero SW open => Arduno nput looks lke nf. Resstance n seres wth Rp. Thus through Rp and thus no voltage drop across Rp Vn = SW closed => Drect wre from GND to nput nput = Also current flowng from to GND s lmted by Rp preventng a short crcut. sually Rp s large (0k ohms) to lmt current Analogy: Ths Photo by nknown Author s lcensed under CC BYSA Rp Vn Preferred: se a pullup resstor To calculate Vn: Vn = V RP Vn = RP = snce n wth resstance of Arduno nput Thus, Vn = Man Pont: Buttons & swtches should have GND connected to one sde & a pullup resstor on the other.28
8 Power & Ground Connectons Easy mstake when you're just learnng to wre up crcuts: Wre the nputs & outputs but forget to connect power and ground All crcuts and chps requre a connecton to a power source and ground Dgtal crcuts (aka "gates") Swtches Buttons Actual connecton Rest of Crcut GND wll be drawn lke ths.29 Summary KCL and KVL apply to ALL electronc devces Ohm's law apples ONLY to resstors and governs the relatonshp between the current through and the voltage across a resstor A resstor network can be collapsed to a sngle equvalent resstance by applyng seres and parallel transformatons If two or more resstors are n seres, the voltage across any of those resstors can be quckly found by applyng the voltage dvder equaton LEDs are used as dgtal outputs and must be wred n the correct drecton Swtches can be modeled as a small (0) resstance when closed or large (nf.) resstance when open.0
1.1. Unit 1. Circuit Basics KVL, KCL, Ohm's Law LED Outputs Buttons/Switch Inputs
1.1 nit 1 Circuit Basics KVL, KCL, Ohm's Law LED Outputs Buttons/Switch Inputs VOLTAGE AND CRRENT 1.2 1.3 Current and Voltage Charge is measured in units of Coulombs Current Amount of charge flowing through
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 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 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 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 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 informationmatter 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 informationUNIVERSITY OF UTAH ELECTRICAL & COMPUTER ENGINEERING DEPARTMENT. 10k. 3mH. 10k. Only one current in the branch:
UNIERSITY OF UTH ELECTRICL & COMPUTER ENGINEERING DEPRTMENT ECE 70 HOMEWORK #6 Soluton Summer 009. fter beng closed a long tme, the swtch opens at t = 0. Fnd (t) for t > 0. t = 0 0kΩ 0kΩ 3mH Step : (Redraw
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 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 informationELECTRONICS. EE 42/100 Lecture 4: Resistive Networks and Nodal Analysis. Rev B 1/25/2012 (9:49PM) Prof. Ali M. Niknejad
A. M. Nknejad Unversty of Calforna, Berkeley EE 100 / 42 Lecture 4 p. 1/14 EE 42/100 Lecture 4: Resstve Networks and Nodal Analyss ELECTRONICS Rev B 1/25/2012 (9:49PM) Prof. Al M. Nknejad Unversty of Calforna,
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 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 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 information( ) = ( ) + ( 0) ) ( )
EETOMAGNETI OMPATIBIITY HANDBOOK 1 hapter 9: Transent Behavor n the Tme Doman 9.1 Desgn a crcut usng reasonable values for the components that s capable of provdng a tme delay of 100 ms to a dgtal sgnal.
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 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 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 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 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 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 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 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 informationCircuit Variables. Unit: volt (V = J/C)
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
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 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 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 informationDepartment of Electrical and Computer Engineering FEEDBACK AMPLIFIERS
Department o Electrcal and Computer Engneerng UNIT I EII FEEDBCK MPLIFIES porton the output sgnal s ed back to the nput o the ampler s called Feedback mpler. Feedback Concept: block dagram o an ampler
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 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 informationEMF induced in a coil by moving a bar magnet. Induced EMF: Faraday s Law. Induction and Oscillations. Electromagnetic Induction.
Inducton and Oscllatons Ch. 3: Faraday s Law Ch. 3: AC Crcuts Induced EMF: Faraday s Law Tme-dependent B creates nduced E In partcular: A changng magnetc flux creates an emf n a crcut: Ammeter or voltmeter.
More informationFE REVIEW OPERATIONAL AMPLIFIERS (OP-AMPS)
FE EIEW OPEATIONAL AMPLIFIES (OPAMPS) 1 The Opamp An opamp has two nputs and one output. Note the opamp below. The termnal labeled wth the () sgn s the nvertng nput and the nput labeled wth the () sgn
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 informationUNIT I BASIC CIRCUIT CONCEPTS
UNIT I BASIC CIRCUIT CONCEPTS Crcut elements Krchhoff s Law V-I Relatonshp of R,L and C Independent and Dependent sources Smple Resstve crcuts Networks reducton Voltage dvson current source transformaton.
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 informationInductor = (coil of wire)
A student n 1120 emaled me to ask how much extra he should expect to pay on hs electrc bll when he strngs up a standard 1-strand box of ccle holday lghts outsde hs house. (total, cumulatve cost)? Try to
More information1 Matrix representations of canonical matrices
1 Matrx representatons of canoncal matrces 2-d rotaton around the orgn: ( ) cos θ sn θ R 0 = sn θ cos θ 3-d rotaton around the x-axs: R x = 1 0 0 0 cos θ sn θ 0 sn θ cos θ 3-d rotaton around the y-axs:
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 informationWeek 11: Differential Amplifiers
ELE 0A Electronc rcuts Week : Dfferental Amplfers Lecture - Large sgnal analyss Topcs to coer A analyss Half-crcut analyss eadng Assgnment: hap 5.-5.8 of Jaeger and Blalock or hap 7. - 7.3, of Sedra and
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 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 informationPhysics Electricity and Magnetism Lecture 12 - Inductance, RL Circuits. Y&F Chapter 30, Sect 1-4
Physcs - lectrcty and Magnetsm ecture - Inductance, Crcuts Y&F Chapter 30, Sect - 4 Inductors and Inductance Self-Inductance Crcuts Current Growth Crcuts Current Decay nergy Stored n a Magnetc Feld nergy
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 informationTHE SUMMATION NOTATION Ʃ
Sngle Subscrpt otaton THE SUMMATIO OTATIO Ʃ Most of the calculatons we perform n statstcs are repettve operatons on lsts of numbers. For example, we compute the sum of a set of numbers, or the sum of the
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 information12. The Hamilton-Jacobi Equation Michael Fowler
1. The Hamlton-Jacob Equaton Mchael Fowler Back to Confguraton Space We ve establshed that the acton, regarded as a functon of ts coordnate endponts and tme, satsfes ( ) ( ) S q, t / t+ H qpt,, = 0, and
More informationSurface Charge and Resistors
Surface Charge and Resstors Just after connecton: E may be the same everywhere nav naue thn thck na na thn thck ue ue After steady state s reached: thn thck na thn thck na thn thck ue thn ue thck E thn
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 informationMAGNETISM MAGNETIC DIPOLES
MAGNETISM We now turn to magnetsm. Ths has actually been used for longer than electrcty. People were usng compasses to sal around the Medterranean Sea several hundred years BC. However t was not understood
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 informationFrequency dependence of the permittivity
Frequency dependence of the permttvty February 7, 016 In materals, the delectrc constant and permeablty are actually frequency dependent. Ths does not affect our results for sngle frequency modes, but
More information(b) i(t) for t 0. (c) υ 1 (t) and υ 2 (t) for t 0. Solution: υ 2 (0 ) = I 0 R 1 = = 10 V. υ 1 (0 ) = 0. (Given).
Problem 5.37 Pror to t =, capactor C 1 n the crcut of Fg. P5.37 was uncharged. For I = 5 ma, R 1 = 2 kω, = 5 kω, C 1 = 3 µf, and C 2 = 6 µf, determne: (a) The equvalent crcut nvolvng the capactors for
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 informationPhysics 5153 Classical Mechanics. D Alembert s Principle and The Lagrangian-1
P. Guterrez Physcs 5153 Classcal Mechancs D Alembert s Prncple and The Lagrangan 1 Introducton The prncple of vrtual work provdes a method of solvng problems of statc equlbrum wthout havng to consder the
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 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 informationTransfer Characteristic
Eeld-Effect Transstors (FETs 3.3 The CMS Common-Source Amplfer Transfer Characterstc Electronc Crcuts, Dept. of Elec. Eng., The Chnese Unersty of Hong Kong, Prof. K.-L. Wu Lesson 8&9 Eeld-Effect Transstors
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 informationECSE Linearity Superposition Principle Superposition Example Dependent Sources. 10 kω. 30 V 5 ma. 6 kω. 2 kω
S-00 Lnearty Superposton Prncple Superposton xample Dependent Sources Lecture 4. sawyes@rp.edu www.rp.edu/~sawyes 0 kω 6 kω 8 V 0 V 5 ma 4 Nodes Voltage Sources Ref Unknown Node Voltage, kω If hae multple
More informationPhysics Courseware Electronics
Physcs ourseware Electroncs ommon emtter amplfer Problem 1.- In the followg ommon Emtter mplfer calculate: a) The Q pot, whch s the D base current (I ), the D collector current (I ) and the voltage collector
More informationHow Strong Are Weak Patents? Joseph Farrell and Carl Shapiro. Supplementary Material Licensing Probabilistic Patents to Cournot Oligopolists *
How Strong Are Weak Patents? Joseph Farrell and Carl Shapro Supplementary Materal Lcensng Probablstc Patents to Cournot Olgopolsts * September 007 We study here the specal case n whch downstream competton
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 informationEstimating Delays. Gate Delay Model. Gate Delay. Effort Delay. Computing Logical Effort. Logical Effort
Estmatng Delas Would be nce to have a back of the envelope method for szng gates for speed Logcal Effort ook b Sutherland, Sproull, Harrs Chapter s on our web page Gate Dela Model Frst, normalze a model
More informationTuring Machines (intro)
CHAPTER 3 The Church-Turng Thess Contents Turng Machnes defntons, examples, Turng-recognzable and Turng-decdable languages Varants of Turng Machne Multtape Turng machnes, non-determnstc Turng Machnes,
More information1 Derivation of Rate Equations from Single-Cell Conductance (Hodgkin-Huxley-like) Equations
Physcs 171/271 -Davd Klenfeld - Fall 2005 (revsed Wnter 2011) 1 Dervaton of Rate Equatons from Sngle-Cell Conductance (Hodgkn-Huxley-lke) Equatons We consder a network of many neurons, each of whch obeys
More informationDO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED.
EE 539 Homeworks Sprng 08 Updated: Tuesday, Aprl 7, 08 DO NOT DO HOMEWORK UNTIL IT IS ASSIGNED. THE ASSIGNMENTS MAY CHANGE UNTIL ANNOUNCED. For full credt, show all work. Some problems requre hand calculatons.
More informationLinear Feature Engineering 11
Lnear Feature Engneerng 11 2 Least-Squares 2.1 Smple least-squares Consder the followng dataset. We have a bunch of nputs x and correspondng outputs y. The partcular values n ths dataset are x y 0.23 0.19
More informationOver-Temperature protection for IGBT modules
Over-Temperature protecton for IGBT modules Ke Wang 1, Yongjun Lao 2, Gaosheng Song 1, Xanku Ma 1 1 Mtsubsh Electrc & Electroncs (Shangha) Co., Ltd., Chna Room2202, Tower 3, Kerry Plaza, No.1-1 Zhongxns
More informationC/CS/Phy191 Problem Set 3 Solutions Out: Oct 1, 2008., where ( 00. ), so the overall state of the system is ) ( ( ( ( 00 ± 11 ), Φ ± = 1
C/CS/Phy9 Problem Set 3 Solutons Out: Oct, 8 Suppose you have two qubts n some arbtrary entangled state ψ You apply the teleportaton protocol to each of the qubts separately What s the resultng state obtaned
More information4.1 The Ideal Diode. Reading Assignment: pp Before we get started with ideal diodes, let s first recall linear device behavior!
1/25/2012 secton3_1the_ideal_ode 1/2 4.1 The Ideal ode Readng Assgnment: pp.165-172 Before we get started wth deal dodes, let s frst recall lnear dece behaor! HO: LINEAR EVICE BEHAVIOR Now, the deal dode
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 informationComputer-Aided Circuit Simulation and Verification. CSE245 Fall 2004 Professor:Chung-Kuan Cheng
Computer-Aded Crcut Smulaton and Verfcaton CSE245 Fall 24 Professor:Chung-Kuan Cheng Admnstraton Lectures: 5:pm ~ 6:2pm TTH HSS 252 Offce Hours: 4:pm ~ 4:45pm TTH APM 4256 Textbook Electronc Crcut and
More information8.6 The Complex Number System
8.6 The Complex Number System Earler n the chapter, we mentoned that we cannot have a negatve under a square root, snce the square of any postve or negatve number s always postve. In ths secton we want
More informationErrors for Linear Systems
Errors for Lnear Systems When we solve a lnear system Ax b we often do not know A and b exactly, but have only approxmatons  and ˆb avalable. Then the best thng we can do s to solve ˆx ˆb exactly whch
More informationMath1110 (Spring 2009) Prelim 3 - Solutions
Math 1110 (Sprng 2009) Solutons to Prelm 3 (04/21/2009) 1 Queston 1. (16 ponts) Short answer. Math1110 (Sprng 2009) Prelm 3 - Solutons x a 1 (a) (4 ponts) Please evaluate lm, where a and b are postve numbers.
More informationGraphical Analysis of a BJT Amplifier
4/6/2011 A Graphcal Analyss of a BJT Amplfer lecture 1/18 Graphcal Analyss of a BJT Amplfer onsder agan ths smple BJT amplfer: ( t) = + ( t) O O o B + We note that for ths amplfer, the output oltage s
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 informationOpen Systems: Chemical Potential and Partial Molar Quantities Chemical Potential
Open Systems: Chemcal Potental and Partal Molar Quanttes Chemcal Potental For closed systems, we have derved the followng relatonshps: du = TdS pdv dh = TdS + Vdp da = SdT pdv dg = VdP SdT For open systems,
More informationDepartment of Statistics University of Toronto STA305H1S / 1004 HS Design and Analysis of Experiments Term Test - Winter Solution
Department of Statstcs Unversty of Toronto STA35HS / HS Desgn and Analyss of Experments Term Test - Wnter - Soluton February, Last Name: Frst Name: Student Number: Instructons: Tme: hours. Ads: a non-programmable
More informationELE B7 Power Systems Engineering. Power Flow- Introduction
ELE B7 Power Systems Engneerng Power Flow- Introducton Introducton to Load Flow Analyss The power flow s the backbone of the power system operaton, analyss and desgn. It s necessary for plannng, operaton,
More information3.6 Limiting and Clamping Circuits
3/10/2008 secton_3_6_lmtng_and_clampng_crcuts 1/1 3.6 Lmtng and Clampng Crcuts Readng Assgnment: pp. 184-187 (.e., neglect secton 3.6.2) Another applcaton of juncton dodes Q: What s a lmter? A: A 2-port
More information