PHY2049 Exam 2 solutions Fall 2016 Solution:
|
|
- Angel Cameron
- 5 years ago
- Views:
Transcription
1 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 you have a crcut s one resstor less. Repeat the procedure untl you have one equvalent resstance left ths s the answer.
2 General strategy: 1) Defne currents n each segment of elements connected n seres (drectons can be arbtrary). See how many unknown currents do you get (three n ths crcut). So, we need three equatons to fnd three unknown currents. Count number of loops (two n ths crcut), each of whch wll gve you a loop equaton for sum of potental dfferences. The remanng equaton (thrd equaton n ths problem) wll come from the juncton rule for currents. 2) For each loop, wrte down equatons for potentals: walk along each loop (n any drecton) and sum all dfferences of potentals as you jump over elements of a crcut; when you come back to the start pont, the sum must be zero. - left loop (walkng clockwse from the left-bottom corner): ε R 2 r 2ε R = 0 - rght loop (walkng clockwse from pont b): 2ε + 2 r 3 R ε = 0 3) For each juncton of wres, wrte down an equaton for currents: sum of ncomng currents = sum of outgong currents. Dscard equatons that are not ndependent. - Pont a: = In ths problem, we can stop: we already have three equatons for the three unknown. For curous mnds: Pont b gve the exact same equaton for currents as pont a,.e =. So, we have only one ndependent equaton for currents. 4) Solve the three equatons: ε R 2 r 2ε R = 0 2ε + 2 r 3 R ε = 0 = 2 + 3
3 Power dsspated by the resstor: P = 2 R In a dschargng RC crcut: (t) = q 0 τ e t/τ, where τ = RC Therefore: P(t) = (t) 2 R = q 0 P(t) P(0) = e 2t/τ 1 2 = e 2t/τ t = ln2 2 τ 2 τ 2 Re 2t/τ Power dsspated by the resstor r nsde the battery: P = 2 ε r, where s a current n the crcut, = R + r
4 Use the rght hand rule (do not forget that the charge s negatve!) Consder drecton of forces on each of the four wre segments makng the square loop. Left and rght wres carry the current parallel to the magnetc feld: force s zero. The top wre (use the rght hand rule): the force s out of page. The bottom wre: the force s nto the page. Hence, the loop wants to turn around the x-axs. In the gap wth the electrc feld, ons are accelerated and gan energy: K f K =U U f mv 2 2qV = qv v = 2 m In the space wth the magentc feld, ons follow a crcular path of radus r: m v2 r = qvb r = mv qb = m qb 2qV m ~ V B
5 Potental energy of a magnetc dpole n a magnetc feld: U =! µ! B = µbcosθ Torque of a magnetc dpole n a magnetc feld:! τ =! µ B! = µbsnθ! τ Therefore: U = tanθ (Keep n mnd that an angle between two vectors s between 0! and 180! ) Magnetc feld made by the wre wth current =12A: B = µ 0 2π r Consder forces on each sde of the loop wth current 2 = 2A!! The left segment of length b = 8cm, dstance a = 4cm away from the wre: F L = 2 b B(a) = 2 b µ 0 2π a.!! The rght segment of length b = 8cm, dstance 2a = 2 4cm away from the wre: F R = 2 b B(2a) = 2 b µ 0 2π 2a. These two forces are n opposte drectons, so the magntude of the net force along the x-axs s F L F R = µ 0 2 2π 2a b The forces on the top and bottom part of the loop are same n magntude (by symmetry) and opposte; so ther sum s zero.
6 Quadrant 2: The magnetc feld made by the wre wth current s out of the page B = µ 0 2π r = µ 0 ; 2π y wth current 2 nto the page B = µ 0 2 2π r = µ π x So the two felds would cancel each other, when ther magntudes are the same: µ 0 2π y = µ 0 2 2π x,.e. along a straght lne, gven by y = 2 x Quadrant 2: The magnetc feld made by the wre wth current s out of the page; wth current 2 out the page. So the two felds cannot cancel each other. Quadrant 3: Smlar to Quadrant 1 Quadrant 4: Smlar to Quadrant 2 The fgure represents an nfntely long wre wth current and a crcular loop, also wth current. The magnetc feld made by the current n the straght wre at the center of the crcle (.e. at a dstance d from the wre) s B = µ 0 and nto the page. 2π d The magnetc feld made by the current n the loop at the loop center s B = µ 0 (2π ) and out of the page. 4π d The magntude of the net feld s the dfference between the two,.e. µ 0 4π d (2π ) µ 0 2π d = µ 0 2π d π 1 ( )
7 Magnetc feld nsde a solenod of length l wth densty of wndngs n = N l (N s number of wndngs) and carryng current s B = µ 0 n = µ 0 N l. Hence, N = Bl. The nformaton on the radus of the solenod s rrelevant. µ 0 The nductance of the orgnal solenod s L = µ 0 n 2 N Al = µ 0 l The nductance of the new solenod: L new = µ 0 π (3N)2 r 2 = 9 2l 2 L 2 ( πr 2 )l = µ 0 π N 2 r 2. l The nduced EMF n an nductor s ε = L d dt, where d d at t =1 ms can be read off the graph: dt dt Therefore: ε = 900 V = 2A 8A 2ms = 3000 A s Potental on the rght s hgher than on the left, therefore V rght V left = 900 V
8 The magnetc feld produced by the central loop n places where loops 1 and 3 s out of the page. The magnetc feld s ncreasng. Therefore, the magnetc feld flux n loops 1 and 3 s out of the page and ncreasng,.e. dφ s also out of the page. dt Induced EMF n loops 1 and 2 s then ε = dφ,.e. clockwse, whch wll result n clockwse currents (n both loops). dt (Algn your rght hand thumb wth the drecton of dφ and curl your fngers to get the drecton of nduced EMF.) dt A col of area A wth N turns rotatng wth angular frequency ω = 2π f n magnetc fled B wll generate an nduced EMF ε(t) =ε max sn(ωt), where ε max =ANBω. If the col has resstance R, the current s then (t) = ε(t) =ε max R R sn(ωt) = max sn(ωt), where max = ANBω R. RMS value of current s rms = max 2. The energy stored n an LC crcut s conserved. Hence: q2 2C L = q 2 max 2C. (At the tme when the charge s maxmum, the current must be zero)
9 The decay tme constant n an RLC crcut s τ = 2L R. If both L and R are doubled, the decay tme does not change. (The nformaton on capactance C s rrelevant.) The ampltude of current n an RLC crcut drven by an external EMF s ε max max = X, where X = 1 R2 + ω d C ω L d 2 If a capastor C s connected to an external EMF of freqency f, RMS value of current n the crcut s rms = ε rms X C, where X C = 1 ω d C = 1 2π fc US rms =ε US rms 2π f US C UK rms =ε UK rms 2π f UK C Hence: US rms rms US f US ε UK rms f ε = rms = 0.6 UK UK
Physics 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 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 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 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 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 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 informationPHYS 1101 Practice problem set 12, Chapter 32: 21, 22, 24, 57, 61, 83 Chapter 33: 7, 12, 32, 38, 44, 49, 76
PHYS 1101 Practce problem set 1, Chapter 3: 1,, 4, 57, 61, 83 Chapter 33: 7, 1, 3, 38, 44, 49, 76 3.1. Vsualze: Please reer to Fgure Ex3.1. Solve: Because B s n the same drecton as the ntegraton path s
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 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 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 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 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 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 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 informationElectricity and Magnetism - Physics 121 Lecture 10 - Sources of Magnetic Fields (Currents) Y&F Chapter 28, Sec. 1-7
Electrcty and Magnetsm - Physcs 11 Lecture 10 - Sources of Magnetc Felds (Currents) Y&F Chapter 8, Sec. 1-7 Magnetc felds are due to currents The Bot-Savart Law Calculatng feld at the centers of current
More informationElectricity and Magnetism Review Faraday s Law
Electrcty and Magnetsm Revew Faraday s Law Lana Sherdan De Anza College Dec 3, 2015 Overvew Faraday s law Lenz s law magnetc feld from a movng charge Gauss s law Remnder: (30.18) Magnetc Flux feld S that
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 informationˆ (0.10 m) E ( N m /C ) 36 ˆj ( j C m)
7.. = = 3 = 4 = 5. The electrc feld s constant everywhere between the plates. Ths s ndcated by the electrc feld vectors, whch are all the same length and n the same drecton. 7.5. Model: The dstances to
More informationFields, Charges, and Field Lines
Felds, Charges, and Feld Lnes Electrc charges create electrc felds. (Gauss Law) Electrc feld lnes begn on + charges and end on - charges. Lke charges repel, oppostes attract. Start wth same dea for magnetc
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 informationCONDUCTORS AND INSULATORS
CONDUCTORS AND INSULATORS We defne a conductor as a materal n whch charges are free to move over macroscopc dstances.e., they can leave ther nucle and move around the materal. An nsulator s anythng else.
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 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 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 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 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 informationChapter 31. Induction and Magnetic Moment
Chapter 31 Inducton and Magnetc Moment CHAPTER 31 INDUCTION AND MAG- NETIC MOMENT In ths chapter we dscuss several applcatons of Faraday s law and the Lorentz force law. The frst s to the nductor whch
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 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 informationkq r 2 2kQ 2kQ (A) (B) (C) (D)
PHYS 1202W MULTIPL CHOIC QUSTIONS QUIZ #1 Answer the followng multple choce questons on the bubble sheet. Choose the best answer, 5 pts each. MC1 An uncharged metal sphere wll (A) be repelled by a charged
More informationWeek 9 Chapter 10 Section 1-5
Week 9 Chapter 10 Secton 1-5 Rotaton Rgd Object A rgd object s one that s nondeformable The relatve locatons of all partcles makng up the object reman constant All real objects are deformable to some extent,
More informationStudy Guide For Exam Two
Study Gude For Exam Two Physcs 2210 Albretsen Updated: 08/02/2018 All Other Prevous Study Gudes Modules 01-06 Module 07 Work Work done by a constant force F over a dstance s : Work done by varyng force
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 informationSection 8.1 Exercises
Secton 8.1 Non-rght Trangles: Law of Snes and Cosnes 519 Secton 8.1 Exercses Solve for the unknown sdes and angles of the trangles shown. 10 70 50 1.. 18 40 110 45 5 6 3. 10 4. 75 15 5 6 90 70 65 5. 6.
More informationElectricity and Magnetism Gauss s Law
Electrcty and Magnetsm Gauss s Law Ampère s Law Lana Sherdan De Anza College Mar 1, 2018 Last tme magnetc feld of a movng charge magnetc feld of a current the Bot-Savart law magnetc feld around a straght
More informationBoundaries, Near-field Optics
Boundares, Near-feld Optcs Fve boundary condtons at an nterface Fresnel Equatons : Transmsson and Reflecton Coeffcents Transmttance and Reflectance Brewster s condton a consequence of Impedance matchng
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 informationExam 2 Solutions. ε 3. ε 1. Problem 1
Exam 2 Solutions Problem 1 In the circuit shown, R1=100 Ω, R2=25 Ω, and the ideal batteries have EMFs of ε1 = 6.0 V, ε2 = 3.0 V, and ε3 = 1.5 V. What is the magnitude of the current flowing through resistor
More informationSolutions to Practice Problems
Phys A Solutons to Practce Probles hapter Inucton an Maxwell s uatons (a) At t s, the ef has a agntue of t ag t Wb s t Wb s Wb s t Wb s V t 5 (a) Table - gves the resstvty of copper Thus, L A 8 9 5 (b)
More informationDr. Fritz Wilhelm, Physics 230 E:\Excel files\230 lecture\ch26 capacitance.docx 1 of 13 Last saved: 12/27/2008; 8:40 PM. Homework: See website.
Dr. Frtz Wlhelm, Physcs 3 E:\Excel fles\3 lecture\ch6 capactance.docx of 3 Last saved: /7/8; 8:4 PM Homework: See webste. Table of ontents: h.6. Defnton of apactance, 6. alculatng apactance, 6.a Parallel
More informationJEE ADVANCE : 2015 P1 PHASE TEST 4 ( )
I I T / P M T A C A D E M Y IN D IA JEE ADVANCE : 5 P PHASE TEST (.8.7) ANSWER KEY PHYSICS CHEMISTRY MATHEMATICS Q.No. Answer Key Q.No. Answer Key Q.No. Answer Key. () () (). () () (). (9) () (). () ()
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 informationPES 1120 Spring 2014, Spendier Lecture 6/Page 1
PES 110 Sprng 014, Spender Lecture 6/Page 1 Lecture today: Chapter 1) Electrc feld due to charge dstrbutons -> charged rod -> charged rng We ntroduced the electrc feld, E. I defned t as an nvsble aura
More informationConservation of Angular Momentum = "Spin"
Page 1 of 6 Conservaton of Angular Momentum = "Spn" We can assgn a drecton to the angular velocty: drecton of = drecton of axs + rght hand rule (wth rght hand, curl fngers n drecton of rotaton, thumb ponts
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 informationB and H sensors for 3-D magnetic property testing
B and H sensors for 3-D magnetc property testng Zh We Ln, Jan Guo Zhu, You Guang Guo, Jn Jang Zhong, and Ha We Lu Faculty of Engneerng, Unversty of Technology, Sydney, PO Bo 123, Broadway, SW 2007, Australa
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 informationPhysics 2113 Lecture 14: WED 18 FEB
Physcs 2113 Jonathan Dowlng Physcs 2113 Lecture 14: WED 18 FEB Electrc Potental II Danger! Electrc Potental Energy, Unts : Electrc Potental Potental Energy = U = [J] = Joules Electrc Potental = V = U/q
More informationRotational Dynamics. Physics 1425 Lecture 19. Michael Fowler, UVa
Rotatonal Dynamcs Physcs 1425 Lecture 19 Mchael Fowler, UVa Rotatonal Dynamcs Newton s Frst Law: a rotatng body wll contnue to rotate at constant angular velocty as long as there s no torque actng on t.
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 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 11 Angular Momentum
Chapter 11 Angular Momentum Analyss Model: Nonsolated System (Angular Momentum) Angular Momentum of a Rotatng Rgd Object Analyss Model: Isolated System (Angular Momentum) Angular Momentum of a Partcle
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 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 informationSpring 2002 Lecture #13
44-50 Sprng 00 ecture # Dr. Jaehoon Yu. Rotatonal Energy. Computaton of oments of nerta. Parallel-as Theorem 4. Torque & Angular Acceleraton 5. Work, Power, & Energy of Rotatonal otons Remember the md-term
More informationVEKTORANALYS. GAUSS s THEOREM and STOKES s THEOREM. Kursvecka 3. Kapitel 6-7 Sidor 51-82
VEKTORANAY Kursvecka 3 GAU s THEOREM and TOKE s THEOREM Kaptel 6-7 dor 51-82 TARGET PROBEM EECTRIC FIED MAGNETIC FIED N + Magnetc monopoles do not est n nature. How can we epress ths nformaton for E and
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 information(b) This is about one-sixth the magnitude of the Earth s field. It will affect the compass reading.
Chapter 9 (a) The magntude of the magnetc feld due to the current n the wre, at a pont a dstance r from the wre, s gven by r Wth r = ft = 6 m, we have c4 T m AhbAg 6 33 T 33 T m b g (b) Ths s about one-sxth
More informationDesigning Information Devices and Systems II Spring 2018 J. Roychowdhury and M. Maharbiz Discussion 3A
EECS 16B Desgnng Informaton Devces and Systems II Sprng 018 J. Roychowdhury and M. Maharbz Dscusson 3A 1 Phasors We consder snusodal voltages and currents of a specfc form: where, Voltage vt) = V 0 cosωt
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 informationSection 8.3 Polar Form of Complex Numbers
80 Chapter 8 Secton 8 Polar Form of Complex Numbers From prevous classes, you may have encountered magnary numbers the square roots of negatve numbers and, more generally, complex numbers whch are the
More informationHO 40 Solutions ( ) ˆ. j, and B v. F m x 10-3 kg = i + ( 4.19 x 10 4 m/s)ˆ. (( )ˆ i + ( 4.19 x 10 4 m/s )ˆ j ) ( 1.40 T )ˆ k.
.) m.8 x -3 g, q. x -8 C, ( 3. x 5 m/)ˆ, and (.85 T)ˆ The magnetc force : F q (. x -8 C) ( 3. x 5 m/)ˆ (.85 T)ˆ F.98 x -3 N F ma ( ˆ ˆ ) (.98 x -3 N) ˆ o a HO 4 Soluton F m (.98 x -3 N)ˆ.8 x -3 g.65 m.98
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 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 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 informationVEKTORANALYS GAUSS THEOREM STOKES THEOREM. and. Kursvecka 3. Kapitel 6 7 Sidor 51 82
VEKTORANAY Kursvecka 3 GAU THEOREM and TOKE THEOREM Kaptel 6 7 dor 51 82 TARGET PROBEM Do magnetc monopoles est? EECTRIC FIED MAGNETIC FIED N +? 1 TARGET PROBEM et s consder some EECTRIC CHARGE 2 - + +
More informationSo far: simple (planar) geometries
Physcs 06 ecture 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap. to 3 Rotatonal quanttes as vectors Cross product Torque epressed as a vector Angular momentum defned Angular momentum as a vector
More informationCHAPTER 10 ROTATIONAL MOTION
CHAPTER 0 ROTATONAL MOTON 0. ANGULAR VELOCTY Consder argd body rotates about a fxed axs through pont O n x-y plane as shown. Any partcle at pont P n ths rgd body rotates n a crcle of radus r about O. The
More informationWaveguides and resonant cavities
Wavegudes and resonant cavtes February 8, 014 Essentally, a wavegude s a conductng tube of unform cross-secton and a cavty s a wavegude wth end caps. The dmensons of the gude or cavty are chosen to transmt,
More informationPhysics 111: Mechanics Lecture 11
Physcs 111: Mechancs Lecture 11 Bn Chen NJIT Physcs Department Textbook Chapter 10: Dynamcs of Rotatonal Moton q 10.1 Torque q 10. Torque and Angular Acceleraton for a Rgd Body q 10.3 Rgd-Body Rotaton
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 informationFrom Biot-Savart Law to Divergence of B (1)
From Bot-Savart Law to Dvergence of B (1) Let s prove that Bot-Savart gves us B (r ) = 0 for an arbtrary current densty. Frst take the dvergence of both sdes of Bot-Savart. The dervatve s wth respect to
More informationENGN 40 Dynamics and Vibrations Homework # 7 Due: Friday, April 15
NGN 40 ynamcs and Vbratons Homework # 7 ue: Frday, Aprl 15 1. Consder a concal hostng drum used n the mnng ndustry to host a mass up/down. A cable of dameter d has the mass connected at one end and s wound/unwound
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 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 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 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 informationPhysics Exam II Chapters 25-29
Physcs 114 1 Exam II Chaptes 5-9 Answe 8 of the followng 9 questons o poblems. Each one s weghted equally. Clealy mak on you blue book whch numbe you do not want gaded. If you ae not sue whch one you do
More informationThe Schrödinger Equation
Chapter 1 The Schrödnger Equaton 1.1 (a) F; () T; (c) T. 1. (a) Ephoton = hν = hc/ λ =(6.66 1 34 J s)(.998 1 8 m/s)/(164 1 9 m) = 1.867 1 19 J. () E = (5 1 6 J/s)( 1 8 s) =.1 J = n(1.867 1 19 J) and n
More informationMoments of Inertia. and reminds us of the analogous equation for linear momentum p= mv, which is of the form. The kinetic energy of the body is.
Moments of Inerta Suppose a body s movng on a crcular path wth constant speed Let s consder two quanttes: the body s angular momentum L about the center of the crcle, and ts knetc energy T How are these
More informationMEASUREMENT OF MOMENT OF INERTIA
1. measurement MESUREMENT OF MOMENT OF INERTI The am of ths measurement s to determne the moment of nerta of the rotor of an electrc motor. 1. General relatons Rotatng moton and moment of nerta Let us
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 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 informationPhys102 General Physics II
Electrc Potental/Energy Phys0 General Physcs II Electrc Potental Topcs Electrc potental energy and electrc potental Equpotental Surace Calculaton o potental rom eld Potental rom a pont charge Potental
More informationPhysics 207: Lecture 27. Announcements
Physcs 07: ecture 7 Announcements ake-up labs are ths week Fnal hwk assgned ths week, fnal quz next week Revew sesson on Thursday ay 9, :30 4:00pm, Here Today s Agenda Statcs recap Beam & Strngs» What
More informationNEWTON S LAWS. These laws only apply when viewed from an inertial coordinate system (unaccelerated system).
EWTO S LAWS Consder two partcles. 1 1. If 1 0 then 0 wth p 1 m1v. 1 1 2. 1.. 3. 11 These laws only apply when vewed from an nertal coordnate system (unaccelerated system). consder a collecton of partcles
More information13. One way of expressing the power dissipated by a resistor is P = ( V)
Current and esstance 9. One way of expressng the power dsspated by a resstor s ( ). Thus, f the potental dfference across the resstor s doubled, the power wll be ncreased by a factor of 4, to a value of
More informationThis model contains two bonds per unit cell (one along the x-direction and the other along y). So we can rewrite the Hamiltonian as:
1 Problem set #1 1.1. A one-band model on a square lattce Fg. 1 Consder a square lattce wth only nearest-neghbor hoppngs (as shown n the fgure above): H t, j a a j (1.1) where,j stands for nearest neghbors
More informationSpin-rotation coupling of the angularly accelerated rigid body
Spn-rotaton couplng of the angularly accelerated rgd body Loua Hassan Elzen Basher Khartoum, Sudan. Postal code:11123 E-mal: louaelzen@gmal.com November 1, 2017 All Rghts Reserved. Abstract Ths paper s
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 informationN S. 4/4/2006 Magnetic Fields ( F.Robilliard) 1
y F N +q + θ S v x z 4/4/6 Magnetc Felds ( F.obllard) 1 4/4/6 Magnetc Felds ( F.obllard) Introducton: It has been known, snce antquty, that when certan peces of rock are hung by a thread, from ther centre
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 informationb mg (b) This is about one-sixth the magnitude of the Earth s field. It will affect the compass reading.
Chapter 9 1 (a) The magntude of the magnetc feld due to the current n the wre, at a pont a dstance r from the wre, s gven by μ p r Wth r ft 61 m, we have c4p 1-7 TmA hb1ag p61 b mg 6 33 1 T 33 μ T (b)
More informationmeasurement and the charge the electric field will be calculated using E =. The direction of the field will be the . But, so
THE ELECTRIC FIELD 6 Conceptual Questons 6.. A tny, postve test charge wll be placed at the pont n space and the force wll be measured. From the force F measurement and the charge the electrc feld wll
More informationElectrochemistry Thermodynamics
CHEM 51 Analytcal Electrochemstry Chapter Oct 5, 016 Electrochemstry Thermodynamcs Bo Zhang Department of Chemstry Unversty of Washngton Seattle, WA 98195 Former SEAC presdent Andy Ewng sellng T-shrts
More informationUniversity of Bahrain College of Science Dept. of Physics PHYCS 102 FINAL EXAM
Unversty o Bahran College o Scence Dept. o Physcs PHYCS 10 FINAL XAM Date: 15/1/001 Tme:Two Hours Name:-------------------------------------------------ID#---------------------- Secton:----------------
More informationElectric Potential Energy & Potential. Electric Potential Energy. Potential Energy. Potential Energy. Example: Charge launcher
Electrc & Electrc Gravtatonal Increases as you move farther from Earth mgh Sprng Increases as you ncrease sprng extenson/comp resson Δ Increases or decreases as you move farther from the charge U ncreases
More informationLouisiana State University Physics 2102, Exam 3 April 2nd, 2009.
PRINT Your Name: Instructor: Louisiana State University Physics 2102, Exam 3 April 2nd, 2009. Please be sure to PRINT your name and class instructor above. The test consists of 4 questions (multiple choice),
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 informationTHE CURRENT BALANCE Physics 258/259
DSH 1988, 005 THE CURRENT BALANCE Physcs 58/59 The tme average force between two parallel conductors carryng an alternatng current s measured by balancng ths force aganst the gravtatonal force on a set
More information