Lect18 - Physics 212 Lecture 18 50 40 30 20 10 0 Confused...

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Unformatted text preview: Physics 212 Lecture 18 50 40 30 20 10 0 Confused Avg = 2.9 Confident Physics 212 Lecture 18, Slide 1 Physics Announcements and your comments • Exam 2 March 31, Wednesday after Spring Break. Covers: Lectures 9-17, Hwks 5-8 and first 2 Qs of Hwk 9 Class on Tue after Spring Break will be review for Exam 2 Your comments: • Any chance of NCAA tournament games streaming on the side projectors? • Help! I thought we were done with circuits but it looks like I'm not that lucky. Please illuminate this tricky concept! • Everything was extraordinarily confusing. • My friends are currently dismantling a microwave to try and make a microwave gun. Questions? Comments? Concerns? I think it's pretty cool stuff, personally. • Why am I up at 12:40 am doing this? On a more serious note, in the prelecture, the example given for the discharging inductor circuit had 2R for the resistance. Will this work for any multiple of R, or is the resulting jump in V general in all cases? Physics 212 Lecture 18, Slide 2 Physics One more • For the past couple of weeks, my friends and I decided to pass some of the down time in lecture by observing people who are sleeping across the room. I just wanted to say that the guy who sits in the right section and falls asleep every lecture, you always look like you're going to fall out of your chair and it has given us much amusement and entertainment, so thank you for falling asleep in class for our enjoyment. :) Maybe someday if i meet you I will buy you one of those neck pillow things... • Due to a family emergency I need to cancel my office hrs at 3PM today. Physics 212 Lecture 18, Slide 3 Physics From the prelecture: Self Inductance Wrap a wire into a coil to make an “inductor”… ε = -L dI dt Physics 212 Lecture 18, Slide 4 Physics What this really means: emf induced across L tries to keep I constant εL = -L dI dt L current I Inductors prevent discontinuous current changes ! It’s like inertia! Physics 212 Lecture 18, Slide 5 Physics Preflight 2 Two solenoids are made with the same cross sectional area and total number of turns. Inductor B is twice as long as inductor A L = μ 0 n 2π r 2 z (1/2)2 2 Compare the inductance of the two solenoids A) LA = 4 LB B) LA = 2 LB C) LA = LB D) LA = (1/2) LB E) LA = (1/4) LB 50 40 30 20 10 0 Physics 212 Lecture 18, Slide 6 Physics WHAT ARE INDUCTORS AND CAPACITORS GOOD FOR? Inside your i-clicker Physics 212 Lecture 18, Slide 7 Physics How to think about RL circuits Episode 1: Episode When no current is flowing initially: I=0 L R VL I=V/R L R I τ = L/R VBATT VBATT τ = L/R At t = 0: At t >> L/R: At VL = 0 VR = VBATT I = VBATT/R I=0 VL = VBATT VR = 0 (L is like a giant resistor) (L is like a short circuit) Physics 212 Lecture 18, Slide 8 Physics Preflight 4 In the circuit above, the switch has been open for a long time, and the current is zero everywhere. At time t=0 the switch is closed. What is the current I through the vertical resistor immediately after the switch is closed? (+ is in the direction of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = -V/2R E) I = -V/R Before: IL = 0 After: IL = 0 I = + V/2R 40 30 20 10 0 BB I I IL=0 Physics 212 Lecture 18, Slide 9 Physics RL Circuit (Long Time) What is the current I through the vertical resistor after the switch has been closed for a long time? (+ is in the direction of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = -V/2R E) I = -V/R BB - + + - After a long time in any static circuit: VL = 0 KVR: VL + IR = 0 Physics 212 Lecture 18, Slide 10 Physics VBATT How to think about RL circuits Episode 2: Episode When steady current is flowing initially: VL I=0 R L I=V/R R L R τ = L/R τ = L/R I = VBATT/R VR = IR VL = VR At t = 0: At t >> L/R: At I=0 VL = 0 VR = 0 Physics 212 Lecture 18, Slide 11 Physics Preflight 6 After a long time, the switch is opened, abruptly disconnecting the battery from the circuit. What is the current I through the vertical resistor immediately after the switch is opened? (+ is in the direction of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = -V/2R E) I = -V/R Current through inductor cannot change DISCONTINUOUSLY circuit when switch opened BB 35 30 L IL=V/R R 25 20 15 10 5 0 Physics 212 Lecture 18, Slide 12 Physics Why is there exponential behavior ? − I L R + VL τ = L/R V=L dI dt V = IR − τ = L/R + dI L + IR = 0 dt I (t ) = I 0e −tR / L = I 0e −t / τ L where τ = R Physics 212 Lecture 18, Slide 13 Physics I L R VL VBATT τ = L/R Lecture: Prelecture: Did we mess up?? No: The resistance is simply twice as big in one case. Physics 212 Lecture 18, Slide 14 Physics Preflight 8 After long time at 0, moved to 1 After long time at 0, moved to 2 BB After switch moved, which case has larger time constant? A) Case 1 B) Case 2 C) The same 50 40 30 20 10 0 L τ1 = 2R L τ2 = 3R Physics 212 Lecture 18, Slide 15 Physics Preflight 10 After long time at 0, moved to 1 After long time at 0, moved to 2 BB Immediately after switch moved, in which case is the voltage across the inductor larger? A) Case 1 After switch moved: B) Case 2 V VL1 = 2 R C) The same R Before switch moved: I = 40 30 20 10 0 V R VL 2 = V 3R R Physics 212 Lecture 18, Slide 16 Physics Preflight 12 After long time at 0, moved to 1 After long time at 0, moved to 2 BB After switch moved for finite time, in which case is the current through the inductor larger? A) Case 1 After awhile B) Case 2 I1 = Ie −t / τ C) The same 1 50 40 30 20 10 0 Immediately after: I1 = I 2 I 2 = Ie −t / τ 2 τ1 > τ 2 Physics 212 Lecture 18, Slide 17 Physics The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. Calculation R1 V L R2 R3 What is dIL/dt, the time rate of change of the current through the inductor immediately after 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 function of time. • Strategic Analysis – – – Determine currents immediately after switch is closed. Determine voltage across inductor immediately after switch is closed. Determine dIL/dt immediately after switch is closed. Physics 212 Lecture 18, Slide 18 Physics The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. Calculation R1 V L R2 BB IL = 0 R3 What is IL, the current in the inductor, immediately after the switch is closed? (A) IL =V/R1 up (B) IL =V/R1 down (C) IL = 0 INDUCTORS: Current cannot change discontinuously ! Current through inductor immediately AFTER switch is closed IS THE SAME AS the current through inductor immediately BEFORE switch is closed Immediately before switch is closed: IL = 0 since no battery in loop Immediately Physics 212 Lecture 18, Slide 19 Physics The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. Calculation R1 V L R2 BB R3 IL(t=0+) = 0 What is the magnitude of I2, the current in R2, immediately after the switch is closed? V V V (A) I 2 = (B) I 2 = (C) I 2 = (D) I 2 = VR2 R3 R2 + R3 R1 + R2 + R3 R1 R2 + R3 We know IL = 0 immediately after switch is closed R1 I Immediately after switch is closed, V circuit looks like: I= R2 R3 V R1 + R2 + R3 Physics 212 Lecture 18, Slide 20 Physics The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. Calculation R1 V L R2 I2 BB R3 IL(t=0+) = 0 I2(t=0+) = V/(R1+R2+R3) What is the magnitude of VL, the voltage across the inductor, immediately after the switch is closed? (A) VL = V R2 + R3 R1 (B) VL = V (C) VL = 0 23 2 3 (D) VL = V (E) VL = V R1 ( R2 + R3 ) R1 + R2 + R3 RR R +R Kirchhoff’s Voltage Law, VL-I2 R2 -I2 R3 =0 =0 VL = I2 (R2+R3) VL = V ( R2 + R3 ) R1 + R2 + R3 Physics 212 Lecture 18, Slide 21 Physics The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. Calculation R1 V L R2 BB What is dIL/dt, the time rate of change of the current through the inductor immediately after switch is closed R3 VL(t=0+) = V(R2+R3)/(R1+R2+R3) dI V R2 + R3 dI (A) L = (B) L = 0 dt L R1 dt dI V R2 + R3 (C) L = dt L R1 + R2 + R3 dI L V = (D) dt L The time rate of change of current through the inductor (dIL /dt) = VL /L dI L V R2 + R3 = dt L R1 + R2 + R3 Physics 212 Lecture 18, Slide 22 Physics The switch in the circuit shown has been closed for a long time. Follow Up R1 V L R2 BB What is I2, the current through R2 ? (Positive values indicate current flows to the right) R3 (A) I 2 = + V R2 + R3 (B) I 2 = + V ( R2 R3 ) R1 + R2 + R3 (C) I 2 = 0 (D) I 2 = − V R2 + R3 After a long time, dI/dt = 0 Therefore, the voltage across L = 0 Therefore the voltage across R2 + R3 = 0 Therefore the current through R2 + R3 must be zero !! Physics 212 Lecture 18, Slide 23 Physics The switch in the circuit shown has been closed for a long time at which point, the switch is opened. Follow Up 2 R1 V IL L R3 R2 I2 BB What is I2, the current through R2 immediately after switch is opened ? (Positive values indicate current flows to the right) (A) I 2 = + V R1 + R2 + R3 (B) I 2 = + R V (C) I 2 = 0 1 (D) I 2 = − R V (E) I 2 = − 1 V R1 + R2 + R3 Current through inductor immediately AFTER switch is opened IS THE SAME AS the current through inductor immediately BEFORE switch is opened Immediately BEFORE switch is opened: IL = V/R1 Immediately AFTER switch is opened: IL flows in right loop Therefore, IL = -V/R1 Physics 212 Lecture 18, Slide 24 Physics ...
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This note was uploaded on 02/21/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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