Electricity & Magnetism Exam Review, Study notes of Electromagnetism and Electromagnetic Fields Theory

Download Electricity & Magnetism Exam Review and more Study notes Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity! Your Comments Electricity & Magnetism Lecture 19, Slide 1 I am not feeling great about this midterm...some of this stuff is really confusing still and I don't know if I can shove everything into my brain in time, especially after spring break. Can you go over which topics will be on the exam Wednesday? This was a very confusing prelecture. Do you think you could go over thoroughly how the LC circuits work qualitatively? I may have missed something simple, but in question 1 during the prelecture why does the charge on the capacitor have to be 0 at t=0? I feel like that bit of knowledge will help me with the test wednesday I remember you mentioning several weeks ago that there was one equation you were going to add to the 2013 equation sheet... which formula was that? Thanks! Some Exam Stuff Exam Wed. night (March 27th) at 7:00  Covers material in Lectures 9 – 18  Bring your ID: Rooms determined by discussion section (see link)  Conflict exam at 5:15 Don’t forget: • Worked examples in homeworks (the optional questions) • Other old exams For most people, taking old exams is most beneficial Final Exam dates are now posted C I L Q LC Circuit Electricity & Magnetism Lecture 19, Slide 5   dt dI LVL    C Q VC  Circuit Equation: 0 dt dI L C Q dt dQ I  LC Q dt Qd  2 2 where Q dt Qd 2 2 2  LC 1  What is the potential difference across the inductor at t = 0? A) VL = 0 B) VL = Qmax/C C) VL = Qmax/2C Pendulum. At time t = 0 the capacitor is fully charged with Qmax and the current through the circuit is 0. L C The voltage across the capacitor is Qmax/C Kirchhoff's Voltage Rule implies that must also be equal to the voltage across the inductor since VL  VC CheckPoint 1a Electricity & Magnetism Lecture 19, Slide 6 CL k x m F = -kx a Same thing if we notice that and LC Circuits analogous to mass on spring Electricity & Magnetism Lecture 19, Slide 7 Q dt Qd 2 2 2  LC 1  m k x dt xd 2 2 2  C k 1  Lm  How much energy is stored in the capacitor when the current is a maximum ? A) U  Qmax 2/(2C) B) U  Qmax 2/(4C) C) U  0 Total Energy is constant! ULmax  ½ LImax 2 UCmax  Qmax 2/2C I  max when Q  0 CheckPoint 1c At time t = 0 the capacitor is fully charged with Qmax and the current through the circuit is 0. L C Electricity & Magnetism Lecture 19, Slide 10 The capacitor is charged such that the top plate has a charge Q0 and the bottom plate Q0. At time t  0, the switch is closed and the circuit oscillates with frequency   500 radians/s. What is the value of the capacitor C? A) C = 1 x 10-3 F B) C = 2 x 10-3 F C) C = 4 x 10-3 F L C L = 4 x 10-3 H  = 500 rad/s    CheckPoint 2a Electricity & Magnetism Lecture 19, Slide 11 LC 1  3 342 10 )104)(1025( 11      L C  Which plot best represents the energy in the inductor as a function of time starting just after the switch is closed? Current is changing  UL is not constant Initial current is zero L C closed at t = 0 Q0 Q0 CheckPoint 2b Energy proportional to I2  C cannot be negative Electricity & Magnetism Lecture 19, Slide 12 2 2 1 LIUL  Physics Truth #1: Even though the answer sometimes looks complicated… the physics under the hood is still very simple! Electricity & Magnetism Lecture 19, Slide 15 Q dt Qd 2 2 2  )cos()(   tQtQ o The elements of a circuit are very simple: This is all we need to know to solve for anything! Electricity & Magnetism Lecture 19, Slide 16 dt dI LVL  C Q VC  dt dQ I  IRVR  RCL VVVV  The switch in the circuit shown has been closed for a long time. At t  0, the switch is opened. What is QMAX, the maximum charge on the capacitor? Conceptual Analysis Once switch is opened, we have an LC circuit Current will oscillate with natural frequency 0 Strategic Analysis Determine initial current Determine oscillation frequency 0 Find maximum charge on capacitor Calculation C R L V Electricity & Magnetism Lecture 19, Slide 18 C R L V IL What is the direction of the current immediately after the switch is opened? A) clockwise B) counterclockwise Before switch is opened: Current moves down through L After switch is opened: Current continues to move down through L IL (t  0 ) > 0 VC (t  0 )  0 The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. Calculation Current through inductor immediately after switch is opened is the same as the current through inductor immediately before switch is opened Electricity & Magnetism Lecture 19, Slide 21 A) B) C) D) C R L V Calculation VL  0Before switch is opened: VL  0 IL IL IL The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. C R L V What is the magnitude of the current right after the switch is opened? Current through inductor immediately after switch is opened is the same as the current through inductor immediately before switch is opened IL (t  0 ) > 0 VC (t  0 )  0 V  ILR Electricity & Magnetism Lecture 19, Slide 22 L C VIo  C L R V Io 2  R V Io  R V Io 2  A) B) C) D) What is Qmax, the maximum charge on the capacitor during the oscillations? IL (t  0 )  V/R VC (t  0 )  0 Hint: Energy is conserved Calculation The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. C R L V IL Electricity & Magnetism Lecture 19, Slide 23 LC R V Q max CVQ 2 1 max  CVQ max LCR V Q max C Q LI 2 max2 2 1 2 1  LC R V LCIQ  maxmax C When Q is max (and I is 0) L Qmax C Q U 2 max 2 1  CL Imax When I is max (and Q is 0) 2 2 1 LIU 