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 = 2.7 Confident Physics 212 Lecture 18, Slide 1 Music Who is the Artist? A) B) C) D) E) Stephane Grappelli Dave Brubeck Itzhak Perlman & Oscar Peterson Hot Club of Cowtown Hot Cowtown Regina Carter Theme of the week Jazz by violin players from other genres… Pretty cool !! Physics 212 Lecture 18, Slide 2 Physics 212 Lecture 18 50 40 30 20 10 0 Confused Avg = 2.7 Confident Physics 212 Lecture 18, Slide 3 From the prelecture: Self Inductance Wrap a wire into a coil to make an “inductor”… Wrap ε = -L dI dt Physics 212 Lecture 18, Slide 4 What this really means: emf induced across L tries to keep I constant induced tries εL = -L dI dt L current I Inductors prevent discontinuous current changes ! It’s like inertia! Physics 212 Lecture 18, Slide 5 Preflight 2 Two solenoids are made with the same cross sectional area and Two total number of turns. Inductor B is twice as long as inductor A twice L = µ0 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 WHAT ARE INDUCTORS AND CAPACITORS GOOD FOR? Inside your i-clicker Physics 212 Lecture 18, Slide 7 How to think about RL circuits Episode 1: How Episode When no current is flowing initially: VL I=0 L τ = L/R I=V/R R L R I VBATT At t = 0: I=0 VL = VBATT VR = 0 (L is like a giant resistor) τ = L/R VBATT At t >> L/R: At VL = 0 VR = VBATT I = VBATT/R (L is like a short circuit) Physics 212 Lecture 18, Slide 8 Preflight 4 In the circuit above, the switch In has been open for a long time, and the current is zero everywhere. BB I At time t=0 the switch is closed. At What is the current I through the What vertical resistor immediately after the switch is closed? the (+ is in the direction of the arrow) A) I = V/R A) B) I = V/2R C) I = 0 D) I = -V/2R D) E) I = -V/R I IL=0 40 Before: IL = 0 30 After: IL = 0 20 10 I = + V/2R 0 Physics 212 Lecture 18, Slide 9 RL Circuit (Long Time) What is the current I through the vertical resistor after the What switch has been closed for a long time? switch BB (+ is in the direction of the arrow) (+ A) I = V/R A) B) I = V/2R C) I = 0 D) I = -V/2R D) E) I = -V/R + + After a long time in any static circuit: VL = 0 - - KVR: VL + IR = 0 Physics 212 Lecture 18, Slide 10 10 VBATT How to think about RL circuits Episode 2: How Episode When steady current is flowing initially: VL τ = L/R I=0 R L R L R I=V/R At t = 0: I = VBATT/R VR = IR IR VL = VR τ = L/R At t >> L/R: At I=0 VL = 0 VR = 0 Physics 212 Lecture 18, Slide 11 11 Preflight 6 After a long time, the switch is After opened, abruptly disconnecting the battery from the circuit. the What is the current I through the What vertical resistor immediately after the switch is opened? the (+ is in the direction of the arrow) (+ A) I = V/R A) B) I = V/2R C) I = 0 D) I = -V/2R D) E) I = -V/R Current through inductor Current cannot change DISCONTINUOUSLY DISCONTINUOUSLY circuit when circuit switch opened switch BB 50 L 40 IL=V/R R 30 20 10 0 Physics 212 Lecture 18, Slide 12 12 Why is there exponential behavior ? V=L dI dt L + + I − VL R τ = L/R 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 13 I L VL R 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 14 Preflight 8 After long time at 0, moved to 1 After long time at 0, moved to 2 BB After switch moved, which case After has larger time constant? has A) Case 1 B) Case 2 C) The same L τ1 = 2R L τ2 = 3R 60 50 40 30 20 10 0 Physics 212 Lecture 18, Slide 15 15 Preflight 10 After long time at 0, moved to 1 After long time at 0, moved to 2 BB Immediately after switch moved, Immediately in which case is the voltage across the inductor larger? across A) Case 1 After switch moved: B) Case 2 V VL1 = 2 R C) The same R V Before switch moved: I = R VL 2 = V 3R R 60 50 40 30 20 10 0 Physics 212 Lecture 18, Slide 16 16 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, After in which case is the current through the inductor larger? through A) Case 1 After awhile B) Case 2 I1 = Ie−t / τ C) The same 1 Immediately after: I1 = I 2 I 2 = Ie −t / τ τ1 > τ 2 2 50 40 30 20 10 0 Physics 212 Lecture 18, Slide 17 17 Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 V What is dIL/dt, the time rate of change of the current through the inductor immediately after switch is closed R2 L R3 • 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 18 Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 V R2 BB L 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 (B) (C) IL = 0 (C) INDUCTORS: Current cannot change discontinuously ! INDUCTORS: Current Current through inductor immediately AFTER switch is closed Current AFTER switch IS THE SAME AS IS the current through inductor immediately BEFORE switch is closed the BEFORE switch Immediately before switch is closed: IL = 0 since no battery in loop Immediately since Physics 212 Lecture 18, Slide 19 19 Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 V R2 BB L 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 Immediately circuit looks like: circuit I= R2 V R1 + R2 + R3 R3 Physics 212 Lecture 18, Slide 20 20 Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 V R2 I2 BB L R3 I2(t=0+) = V/(R1+R2+R3) IL(t=0+) = 0 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 RR R +R 23 2 3 (D) VL = V (E) VL = V R1 ( R2 + R3 ) R1 + R2 + R3 Kirchhoff’s Voltage Law, VL-I2 R2 -I2 R3 =0 VL = I2 (R2+R3) VL = V ( R2 + R3 ) R1 + R2 + R3 Physics 212 Lecture 18, Slide 21 21 Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 R2 BB V What is dIL/dt, the time rate of change of the current through the inductor immediately after switch is closed dI V R2 + R3 dI (A) L = (B) L = 0 dt L R1 dt L R3 VL(t=0+) = V(R2+R3)/(R1+R2+R3) 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 22 Follow Up The switch in the circuit shown has been closed for a long time. What is I2, the current through R2 ? (Positive values indicate current flows to the right) (A) I 2 = + V R2 + R3 (B) I 2 = + (B) V ( R2 R3 ) R1 + R2 + R3 R1 R2 BB V L (C) I 2 = 0 R3 (D) I 2 = − V R2 + R3 After a long time, dI/dt = 0 After dI/dt 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 23 Follow Up 2 The switch in the circuit shown has been closed for a long time at which point, the switch is opened. R1 V What is I2, the current through R2 immediately after switch is opened ? (Positive values indicate current flows to the right) (A) I2 = + V R1 + R2 + R3 V (B) I 2 = + R 1 (C) I 2 = 0 R2 I2 IL BB L R3 V (D) I 2 = − R (E) I 2 = − 1 V R1 + R2 + R3 Current through inductor immediately AFTER switch is opened Current AFTER switch IS THE SAME AS IS the current through inductor immediately BEFORE switch is opened the BEFORE switch Immediately BEFORE switch is opened: IL = V/R1 BEFORE switch Immediately AFTER switch is opened: IL flows in right loop switch Therefore, IL = -V/R1 Physics 212 Lecture 18, Slide 24 24 ...
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