Electricity & Magnetism Lecture 18

Transcription

1 Electricity & Magnetism ecture 18 Today s Concepts: A) Induc4on B) R Circuits Electricity & Magne/sm ecture 18, Slide 1

2 Extended deadline for next few FlipItPhysics homework:! 80% extended by one week. Some upcoming FlipIt checkpoints include ques4ons on ab Materials Class schedule now includes Tipler chapter references

3 Tipler Concordance Physics 141 Spring 2017 Date Unit # Topics FlipItPhysics Unit Due Date Wed, Jan 4 19 Electrostatics 01/11/ ,21-2 Fri, Jan 6 19 Coulomb's aw Coulomb's aw 21-3 Mon, Jan 9 19 Electric Fields Electric Fields Wed, Jan Electric Field ines and Flux Electric Flux and Field ines 01/18/ ,21-5 Fri, Jan Gauss' aw Gauss' aw 22-1,22-2 Mon, Jan Gauss' aw Calculations Wed, Jan Electric Potential Energy 01/23/ , Fri, Jan Electric Potential Electric Potential 23-1,23-2,23-3 Mon, Jan Current and Resistance Electric Current 01/29/ ,23-6 Wed, Jan Series and Parallel Circuits 24-1,24-2,24-3 Fri, Jan Error Propagation, Digital Meters Kirchhoff's Rules 02/01/ ,25-2,25-3 Mon, Jan Kirchhoff's aws Conductors and Capacitors 25-4,25-4 Wed, Feb 1 24 Capacitance Capacitors 24-3 Fri, Feb 3 Midterm Mon, Feb 6 24 RC Circuits RC Circuits 26-1,26-2 Wed, Feb 8 25 Magnetic Forces and Fields Electric Magnetism 02/20/2017 Fri, Feb Current Forces and Torques on Currents 26-3, (26-4) Mon, Feb 13 Break 27-1,27-2 Wed, Feb 15 Break 27-4 Fri, Feb 17 Break 28-1,28-2,28-3,28-4 Mon, Feb 20 26s1 Magnetism from Electricity Ampere's aw, Biot-Savart aw 03/10/2017 Wed, Feb 22 26s2 Faraday's AC Circuits aw and the Motional EMF ,28-8 Fri, Feb 24 27s1 Oscilloscope Verification of Faraday's aw Faraday's aw 03/10/ ,29-2 Mon, Feb 27 26s3 and Maxwell's Equations Induction and R Circuits Wed, Mar 1 27s2 AC Circuits RC Circuits 29-3,29-4 Fri, Mar 3 Practice AC Circuits Mon, Mar 6 Practice AC Circuits: Resonance and Power Wed, Mar 8 practical exam 30-1,30-2 Fri, Mar 10 practical exam 30-3,30-4 Mon, Mar Electromagnetic Energy Transport Waves and Displacement Current and E-M Wa 03/20/ , Wed, Mar Polarization Properties of Electromagnetic Waves Fri, Mar Polarization Polarization 31-1,31-2,31-3,31-5 Mon, Mar Reflection Refraction, and Prisms Images and Reflection and Refraction 03/22/ ,32-2 Wed, Mar enses enses, Mirrors 04/03/ Fri, Mar 24 Midterm 2 enses and Mirrors Mon, Mar Combination Optical Instruments Wed, Mar Interference 04/03/ ,33-2 Fri, Mar Interference & Diffraction Mon, Apr 3 32 Electric & Gravitational Forces Intro to Quantum Mechanics 04/07/2017 Tipler 6 th Wed, Apr 5 32 More Quantum 36-1,36-2 Fri, Apr 7 32 Review Mon, Apr 10 Final Exam 8:30=11:30

4 Stuff you said.. Will there be more lab ac4vi4es involving oscilloscopes? Unlike lab ac4vi4es involving magnets, the oscilloscopes are foreign, new, and curiously interes4ng to play/learn with due to the above? What are the exact differences between the Capacitor and Inductor. In which situa4on would I use the Capacitor instead of the Inductor or vice versa? Capacitors are yin Inductors are yang

5 Comments what's the difference between integral b dot da and integral b dot ds. When do we use each one! B DA is for Gauss law! B ds is for Ampere s law How is energy stored in a magne4c field, similar to capacitors storing energy as an electric field?! It just is. Both electric fields and magne4c fields store energy like a spring stores energy when compressed

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7 Today s Experiment oop area A E = B dt = A db dt If there are more turns N in the loop, E = B dt = NA db dt Electricity & Magne/sm ecture 18, Slide 2

8 From the Prelecture: Self Inductance Wrap a wire into a coil to make an inductor ε = di dt Electricity & Magne/sm ecture 18, Slide 2

9 What this really means: emf induced across tries to keep I constant. ε = di dt current I Inductors prevent discon4nuous current changes! It s like iner4a! Electricity & Magne/sm ecture 18, Slide 3

10 CheckPoint 2 Two solenoids are made with the same cross sec/onal area and total number of turns. Inductor B is twice as long as inductor A (1/2) 2 2 Compare the inductance of the two solenoids A) A = 4 B B) A = 2 B C) A = B D) A = (1/2) B E) A = (1/4) B Electricity & Magne/sm ecture 18, Slide 4

11 How to think about R circuits Episode 1: I = 0 When no current is flowing ini4ally: I = V/R V R R V BATT At t = 0: I = 0 V = V BATT V R = 0 ( is like a giant resistor) V BATT At t >> /R: V = 0 V R = V BATT I = V BATT /R ( is like a short circuit) Electricity & Magne/sm ecture 18, Slide 5

12 CheckPoint 4 In the circuit, the switch has been open for a long /me, and the current is zero everywhere. At /me t = 0 the switch is closed. What is the current I through the ver/cal resistor immediately arer the switch is closed? I = 0 (+ is in the direc/on of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = V/2R E) I = V/R Electricity & Magne/sm ecture 18, Slide 6

13 R Circuit (ong Time) What is the current I through the ver/cal resistor arer the switch has been closed for a long /me? (+ is in the direc/on of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = V/2R E) I = V/R Electricity & Magne/sm ecture 18, Slide 7

14 How to Think about R Circuits Episode 2: V BATT When steady current is flowing initially: V I = 0 R R R I = V/R At t = 0: I = V BATT /R V R = IR V = V R At t >> /R: I = 0 V = 0 V R = 0 Electricity & Magne/sm ecture 18, Slide 8

15 ARer a long /me, the switch is opened, abruptly disconnec/ng the baxery from the circuit. What is the current I through the ver/cal resistor immediately arer the switch is opened? (+ is in the direc/on of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = V/2R E) I = V/R CheckPoint 6 Electricity & Magne/sm ecture 18, Slide 9

16 Why is there Exponential Behavior? I + V V = di dt + R V = IR where Electricity & Magne/sm ecture 18, Slide 10

17 I R V V BATT ecture: Prelecture: Did we mess up? No: The resistance is simply twice as big in one case. Electricity & Magne/sm ecture 18, Slide 11

18 CheckPoint 8 ARer long /me at 0, moved to 1 ARer long /me at 0, moved to 2 A]er switch moved, which case has larger 4me constant? A) Case 1 B) Case 2 C) The same Electricity & Magne/sm ecture 18, Slide 12

19 CheckPoint 10 ARer long /me at 0, moved to 1 ARer long /me at 0, moved to 2 Immediately a]er switch moved, in which case is the voltage across the inductor larger? A) Case 1 B) Case 2 C) The same I0 is V/R in both cases A) V(0) = I0*2R B) V(0) = I0*3R Electricity & Magne/sm ecture 18, Slide 13

20 CheckPoint 12 ARer long /me at 0, moved to 1 ARer long /me at 0, moved to 2 V A]er switch moved for finite 4me, in which case is the current through the inductor larger? A) Case 1 B) Case 2 C) The same A) τ1 = /2R B) τ2 = /3R τ2 τ1 Electricity & Magne/sm ecture 18, Slide 14

21 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 R 3 What is di /dt, the 4me rate of change of the current through the inductor immediately a]er switch is closed Conceptual Analysis Once switch is closed, currents will flow through this 2-loop circuit. KVR and KCR can be used to determine currents as a func4on of 4me. Strategic Analysis Determine currents immediately a]er switch is closed. Determine voltage across inductor immediately a]er switch is closed. Determine di /dt immediately a]er switch is closed. Electricity & Magne/sm ecture 18, Slide 15

22 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 I = 0 R 3 What is I, the current in the inductor, immediately arer the switch is closed? A) I = V/R 1 up B) I = V/R 1 down C) I = 0 Electricity & Magne/sm ecture 18, Slide 16

23 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 R 3 I (t = 0 +) = 0 What is the magnitude of I 2, the current in R 2, immediately a]er the switch is closed? A) B) C) D) Electricity & Magne/sm ecture 18, Slide 17

24 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 I 2 R 3 I (t = 0 +) = 0 I 2 (t = 0 +) = V/(R 1 + R 2 + R 3 ) What is the magnitude of V, the voltage across the inductor, immediately a]er the switch is closed? A) B) C) D) E) Electricity & Magne/sm ecture 18, Slide 18

25 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. What is di /dt, the 4me rate of change of the current through the inductor immediately a]er switch is closed V R 1 R 2 R 3 V (t = 0 +) = V(R 2 + R 3 )/(R 1 + R 2 + R 3 ) A) B) C) D) Electricity & Magne/sm ecture 18, Slide 19

26 Follow Up The switch in the circuit shown has been closed for a long 4me. What is I 2, the current through R 2? V R 1 R 2 R 3 (Posi4ve values indicate current flows to the right) A) B) C) D) Electricity & Magne/sm ecture 18, Slide 20

27 Follow Up 2 The switch in the circuit shown has been closed for a long 4me at which point, the switch is opened. What is I 2, the current through R 2 immediately a]er V R 1 R 2 I 2 R 3 switch is opened? (Posi4ve values indicate current flows to the right) A) B) C) D) E) Electricity & Magne/sm ecture 18, Slide 21