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### lecture15

Course: PHYSICS 222, Spring 2011
School: Iowa Central Community...
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15 Review Lecture for Exam 1 (see lectures 1-14) No show slide - problems will be solved on the board

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15 Review Lecture for Exam 1 (see lectures 1-14) No show slide - problems will be solved on the board
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Iowa Central Community College - PHYSICS - 222
Lecture 14 will be presented by Professor Ruslan Prozorovlecture slides can be found athttp:/course.physastro.iastate.edu/phys222/Lectures%20(Prozorov)/Prozorov_14.pdf
Iowa Central Community College - PHYSICS - 222
ConcepTest 20.8a Magnetic Field of a Wire IMagnetic1) direction 1If the currents in these wires have2) direction 2the same magnitude, but opposite3) direction 3directions, what is the direction of4) direction 4the magnetic field at point P?5) th
Iowa Central Community College - PHYSICS - 222
8. Magnetic field of moving charge1) What is the problem with moving charge?2) For v=0 and a=0:(Coulombs law)3) ForqrE=k 2rr1k=4 0v=0 and a=0:()1 v2 c2 ( r r v c)E = kq( r r v c) 3Speed of light:4) ForB=0(c2 =v&lt;c and a=0: 0 qv rB=
Iowa Central Community College - PHYSICS - 222
vdAnNlA5. Magnetic forces on currentF = qv BlN nlAlv d = l v dF = Ftot = Nqvd B= nlAqvd B= nqAvd l B F = Il BnqAvd = I - angle between vd and BdF = Idl BF = IlB sin dF = IdlB sin Example: A straight wire carrying a current is placed i
Iowa Central Community College - PHYSICS - 222
III. Magnetism1. Electromagnetism in the laboratory and around us2. Electromagnetism is simple. (If you know what it is!)It is about:q - electric charges(magnetic charges do not exist)F - electromagnetic forcesE - electric fieldsB - magnetic field
Iowa Central Community College - PHYSICS - 222
Resistors in series and in parallel (review)IR1V1I = I1 = I 2I1R2IV2VII2V = V1 + V2I = I1 + I 2Req = R1 + R2ExampleR1 = 12VR1R2ER2 = 3012VI=== 0.26 AR1 + R1 + r 47V = V1 = V2111=+Req 15 30Req = 10rReq = 15 + 30R2111
Iowa Central Community College - PHYSICS - 222
12. RC circuitsi1) Charging capacitor = iR + vCdqq=R+dtCdqq+=dt RC R RCR(q = Q 1 e t / RCQ = CvC =C)(vC = 1 e t / RCV = i = I 0 e t / RCI0=R)qC2) Discharging capacitordqq+=dt RC Rq = q 0 e t / RC =0 RCvC = V0 e t
Iowa Central Community College - PHYSICS - 222
8. Power in electric circuitsIRVW QVP== IVttW = QVQ=ItV = IR2VP = IV = I R =R[ P] = 1W = 1V A = (1J / C ) (1C / s ) = 1J / s2Example: Two resistors, R1 = 5 , R2 = 10 , are connected in series.The battery has voltage of V = 12 V.a) F
Iowa Central Community College - PHYSICS - 222
6. Capacitance and capacitors6.1 Capacitors+Q+Q-Q+Q-QSymbol:6.2 CapacitanceDefinition:QC=VUnits:[C]= 1 F = 1 C / VV V V+ VC is independent from: Q and V (V is always proportional to Q)C depends on:the geometry of the systemthe dielectri
Iowa Central Community College - PHYSICS - 222
Two questions:(1) How to find the force, F on the electric charge, q excreted by the field E and/or B?F = qE + qv B(2) How fields E and/or B can be created?Maxwells equationsGausss law for electric fieldElectric charges create electric field: E E
Berkeley - EE - 221A
Berkeley - EE - 221A
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Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 1Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 9/4; Due 9/13Problem 1: Fields.(a) Dene addition and multiplication on cfw_0, 1 to form a eld. Show th
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 2Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 9/18; Due 9/27Problem 1: Useful properties of eigenvalues. Let A Rnm , B Rmn and let n m. Observe that
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 3Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 9/27; Due 10/4Problem 1: Dynamical systems, time invariance.Suppose that the output of a system is rep
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 4Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2006Issued 10/9; Due 10/18Dear 221A folks: Some problems like the ones below may be included on the midterm on Oct
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 5Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 10/23; Due 11/1Problem 1.Suppose A Cnn is such that det(A) = 0. Is det(eA ) = 0? Explain why or why no
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 6Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 11/6; Due 11/15Problem 1: Sti Dierential Equations.In the simulation of several engineering systems we
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 7Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 11/15; Due 11/27Problem 1. Show thatA0c0,b0where A Rnn , b Rn , cT Rn is completely controllable
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 8Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 11/27; Due 12/6Problem 1: State vs. Output Feedback.Consider the plant described by:XywhereA=07
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 9Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2007Issued 12/4; Due 12/15221A folks: Homework 9 is due at the nal exam. However, if youd like to hand in your hom
Berkeley - EE - 221A
1._ _ _ .-L.L-.-L-+-.) E GCS2-2-1Levl-vr'~ LA(G0A L~:0. nj Y1~cmU-fkhr 0 a&lt;vu e.,V-, mojmo~of fA'lJ il'\J.Lr i1-cr.O J -.~c: . :.'-'. . J.\ O~fa'-I1v- b-v- () fA.- tJLa yv~r Artd~/T1 w1J):-mo~Jzw- ()( Y1~ a nicfw_!;O'YZ
Berkeley - EE - 221A
EE221A Linear System TheoryFinal ExamProfessor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 201012/14/10, 3-6pmYour answers must be supported by analysis, proof, or counterexample.There are 9 questions: Pleas
Berkeley - EE - 221A
Berkeley - EE - 221A
EE221A Linear System TheoryMidterm TestProfessor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 200710/16/07, 9.30-11.00amYour answers must be supported by analysis, proof, or counterexample.There are 6 questio
Berkeley - EE - 221A
EE221A Linear System Theoryhttp:/inst.eecs.berkeley.edu/ee221a/Course OutlineProfessor C. TomlinDepartment of Electrical Engineering and Computer SciencesUniversity of California at BerkeleyFall 2011Lecture InformationLectures: TuTh 9.30-11, 521 C
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 1Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 9/1; Due 9/8Problem 1: Functions. Consider f : R3 R3 , dened1f (x) = Ax, A = 00as00110 , x R3
Berkeley - EE - 221A
EE221A Problem Set 1 Solutions - Fall 2011Note: these solutions are somewhat more terse than what we expect you to turn in, though the important thing isthat you communicate the main idea of the solution.Problem 1. Functions. It is a function; matrix m
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 2Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 9/8; Due 9/16All answers must be justied.Problem 1: Linearity. Are the following maps A linear?(a) A(
Berkeley - EE - 221A
EE221A Problem Set 2 Solutions - Fall 2011Problem 1. Linearity.a) Linear: A(u(t) + v (t) = u(t) + v (t) = A(u(t) + A(v (t)b) Linear:te (u(t ) + v (t )d =A(u(t) + v (t) =0te u(t )d +0te u(t )d0= A(u(t) + A(v (t)c) Linear:2s2A(a1 s + b1 s
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 3Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2010Issued 9/22; Due 9/30Problem 1. Let A : R3 R3 be a linear map. Consider two bases for R3 : E = cfw_e1 , e2 , e
Berkeley - EE - 221A
EE221A Problem Set 3 Solutions - Fall 2011Problem 1.a) A w.r.t. the standard basis is, by inspection,000 4 .022AE = 10b) Now consider the diagram from LN3, p.8. We are dealing with exactly this situation; we have one matrixrepresentation, and tw
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 4Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 9/30; Due 10/7Problem 1: Existence and uniqueness of solutions to dierential equations.Consider the fo
Berkeley - EE - 221A
EE221A Problem Set 4 Solutions - Fall 2011Problem 1. Existence and uniqueness of solutions to dierential equations.TTCall the rst system f (x, t) = x1 x2and the second one g (x) = x1 x2.a) Construct the Jacobians:D1 f (x, t) =1 et sin (x1 x2 )et
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 5Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 10/18; Due 10/27Problem 1: Dynamical systems, time invariance.Suppose that the output of a system is r
Berkeley - EE - 221A
EE221A Problem Set 5 Solutions - Fall 2011Problem 1. Dynamical systems, time invariance.i) To show that this is a dynamical system we have to identify all the ingredients:First we need a dierential equation of the form x = f (x, u, t): Let x(t) = y (t)
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 6Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 10/27; Due 11/4Problem 1: Linear systems. Using the denitions of linear and time-invariance discussed i
Berkeley - EE - 221A
EE221A Problem Set 6 Solutions - Fall 2011Problem 1. Linear systems.a) Call this dynamical system L = (U , , Y , s, r), where U = Rni , = Rn , Y = Rno . So clearly U , , Y are alllinear spaces over the same eld (R). We also have the response map(t, t0
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 7Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 11/3; Due 11/10Problem 1.A has characteristic polynomial (s 1 )5 (s 2 )3 , it has four linearly indepe
Berkeley - EE - 221A
EE221A Problem Set 7 Solutions - Fall 2011Problem 1.With the given information, we can determine the Jordan form J = T AT 1 of A to be,10J =1110111200120.012Thus,cos e10=cos eJe1 sin e1cos e1and cos eA = T 1 cos eJcos e01
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 8Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 11/10; Due 11/18Problem 1: BIBO Stability.fH , THiTHTCfC , TCVHVCiFigure 1: A simple heat ex
Berkeley - EE - 221A
EE221A Problem Set 8 Solutions - Fall 2011Problem 1. BIBO Stability.a) First write this LTI system in state space form,x = Ax + Bu=( +fC )VCVH=0.3 0.20.2 0.3y = Cx =10VC( +fH )VH01fCVCx+0.10x+0fHVH000.1u,uxwhere x := (TC
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 9Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 11/21; Due 12/1Problem 1: Lyapunov Equation.(a) Consider the linear map L : Rnn Rnn dened by L(P ) = A
Berkeley - EE - 221A
EE221A Linear System TheoryProblem Set 10Professor C. TomlinDepartment of Electrical Engineering and Computer Sciences, UC BerkeleyFall 2011Issued 12/2; Due 12/9Problem 1: Feedback control design by eigenvalue placement. Consider the dynamic system: