Physics 212 Lecture 18 Slide 1 Music Who

Physics 212 Lecture 18, Slide 1

Music Who is the Artist? A) B) C) D) E) Arturo Sandoval Tiempo Libre Chucho Valdes & Afro-Cuban Messengers Freddie Omar con su banda Los Hombres Calientes Legendary Cuban piano player Hadn’t been in the U. S. in many years Stop at Krannert in Fa 10

Your Comments “glad this all makes sense before spring break. . . haha just kidding, im completely lost here. ” “so if no current goes across the inductor to start, how does it have an emf? Also, how does an emf have a direction? Flux is a dot product with the B field and area, and a change in a scalar (flux) over a change in another scalar (time) should give a scalar back right? am I missing something here or just over-thinking it? ” “The final checkpoint was confusing. Please go over how to determine current direction at different times of the switch being open or closed as well. ” “I get most of this stuff, but I’m confused on the last checkpoint. Please go over it!” Difficult checkpoints today! “Bringing back the circuits with switches makes me nervous. ” “If you make this appear extremely intuitive in class, We’ll work on the qualitative I will love you forever. ” picture of inductors in circuits “Explaining the intuition behind the solenoids and inductors would help a bunch for this lecture!” “I'm going to need some in. DUCTance tape to keep all this info from falling out of my brain. ” 05 Physics 212 Lecture 18, Slide 3

Some Exam Stuff • Exam THURSDAY (Mar. 29) at 7: 00 – Covers material in Lectures 9 – 18 (through today’s lecture) – Bring your ID: Rooms determined by discussion section (see link) – Conflict exam at 5: 15 – sign up in your gradebook before Fri. night (Mar. 16, 10: 00 p. m. ) – If you have conflicts with both of these, contact Prof. Park Physics 212 Lecture 18, Slide 4

From the prelecture: Self Inductance Wrap a wire into a coil to make an “inductor”… e = -L d. I dt Physics 212 Lecture 18, Slide 6

What this really means: emf induced across L tries to keep I constant e. L = -L d. I dt L current I Inductors prevent discontinuous current changes ! It’s like inertia! Physics 212 Lecture 18, Slide 7

Checkpoint 1 Two solenoids are made with the same cross sectional area and total number of turns. Inductor B is twice as long as inductor A 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 “n halved and z doubled. Using the equation, L in case B is half of the L in case A. ” “Both have same radius and both have 8 loops. ” “B is twice as long so is twice as large ” Physics 212 Lecture 18, Slide 8

Checkpoint 1 Two solenoids are made with the same cross sectional 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) LA = 4 LB B) LA = 2 LB C) LA = LB D) LA = (1/2) LB E) LA = (1/4) LB Physics 212 Lecture 18, Slide 9

WHAT ARE INDUCTORS AND CAPACITORS GOOD FOR? ” Can you have capacitors and inductors in the same circuit? “why inductors are important as opposed to capacitors. why use one instead of the other? ” Inside your i-clicker Physics 212 Lecture 18, Slide 10

How to think about RL circuits Episode 1: When no current is flowing initially: VL I=0 L I=V/R R L t = L/R R I VBATT At t = 0: I=0 VL = VBATT VR = 0 (L is like a giant resistor) VBATT t = L/R At t >> L/R: VL = 0 VR = VBATT I = VBATT/R (L is like a short circuit) Physics 212 Lecture 18, Slide 11

Checkpoint 2 a In the circuit, 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/2 R C) I = 0 D) I = -V/2 R E) I = -V/R “V_L == V, so applying KVL to the right loop, I == V/R. ” “At t=0, no current flows through the inductor. The two resistors are in series. Hence, the overall resistance = 2 R. Therefore, I = V/ 2 R. ” “the current runs through the solenoid, not the resistor. ” Physics 212 Lecture 18, Slide 12

Checkpoint 2 a In the circuit, the switch has been open for a long time, and the current is zero everywhere. I At time t=0 the switch is closed. What is the current I through the vertical resistor immediately after the switch is closed? I IL=0 (+ is in the direction of the arrow) A) I = V/R B) I = V/2 R C) I = 0 D) I = -V/2 R E) I = -V/R Before: IL = 0 After: IL = 0 I = + V/2 R Physics 212 Lecture 18, Slide 13

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/2 R C) I = 0 D) I = -V/2 R E) I = -V/R After a long time in any static circuit: VL = 0 - + + - KVR: VL + IR = 0 Physics 212 Lecture 18, Slide 14

VBATT How to think about RL circuits Episode 2: When steady current is flowing initially: VL I=0 R L R I=V/R At t = 0: I = VBATT/R VR = IR VL = V R t = L/R At t >> L/R: I=0 VL = 0 VR = 0 Physics 212 Lecture 18, Slide 15

Checkpoint 2 b 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/2 R C) I = 0 D) I = -V/2 R E) I = -V/R “After the battery is disconnected, there will be a current of V/R because the inductor will have the initial voltage of the battery. ” “It dissapates from the inductor through the resistor” “After long time V across solenoid is zero. Zero voltage zero current” Physics 212 Lecture 18, Slide 16

Checkpoint 2 b 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/2 R C) I = 0 D) I = -V/2 R E) I = -V/R Current through inductor cannot change DISCONTINUOUSLY circuit when switch opened L IL=V/R R Physics 212 Lecture 18, Slide 17

Why is there exponential behavior ? I - V=L d. I dt L + VL + R t = L/R V = IR t = L/R where Physics 212 Lecture 18, Slide 18

I L VL R VBATT t = L/R Lecture: Prelecture: Did we mess up? ? No: The resistance is simply twice as big in one case. Physics 212 Lecture 18, Slide 19

Checkpoint 3 a After long time at 0, moved to 1 After switch moved, which case has larger time constant? A) Case 1 B) Case 2 C) The same After long time at 0, moved to 2 “Time constant is L/R, so the lower the resistance, the larger the time constant. ” “more resistors to run into in case 2” “The time it takes to get to switch one should be the same to get to switch #2” Physics 212 Lecture 18, Slide 20

Checkpoint 3 a After long time at 0, moved to 1 After long time at 0, moved to 2 After switch moved, which case has larger time constant? A) Case 1 B) Case 2 C) The same Physics 212 Lecture 18, Slide 21

Checkpoint 3 b After long time at 0, moved to 1 Immediately after switch moved, in which case is the voltage across the inductor larger? A) Case 1 B) Case 2 C) The same After long time at 0, moved to 2 “It has less resistance to decrease the initial voltage from the battery. ” “More resistance v=IR. R larger so V is larger. ” “full battery voltage appears across the inductors” Physics 212 Lecture 18, Slide 22

Checkpoint 3 b After long time at 0, moved to 1 After long time at 0, moved to 2 Immediately after switch moved, in which case is the voltage across the inductor larger? A) Case 1 After switch moved: B) Case 2 C) The same Before switch moved: Physics 212 Lecture 18, Slide 23

Checkpoint 3 c After long time at 0, moved to 1 After long time at 0, moved to 2 After switch moved for finite time, “Greater time constant means that the current in which case is the current will decay more slowly in case 1. ” through the inductor larger? A) Case 1 “The resistance allows the curent to last for B) Case 2 longer. ” C) The same “The currents are 0. ” Physics 212 Lecture 18, Slide 24

Checkpoint 3 c After long time at 0, moved to 1 After long time at 0, moved to 2 After switch moved for finite time, in which case is the current through the inductor larger? A) Case 1 After awhile B) Case 2 C) The same Immediately after: Physics 212 Lecture 18, Slide 25

Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. What is d. IL/dt, the time rate of change of the current through the inductor immediately after switch is closed R 1 V R 2 L R 3 • 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 d. IL/dt immediately after switch is closed. Physics 212 Lecture 18, Slide 26

Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R 1 V R 2 L IL = 0 R 3 What is IL, the current in the inductor, immediately after the switch is closed? (A) IL =V/R 1 up (B) IL =V/R 1 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 Physics 212 Lecture 18, Slide 27

Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R 1 V R 2 L R 3 IL(t=0+) = 0 What is the magnitude of I 2, the current in R 2, immediately after the switch is closed? (A) (B) (C) (D) We know IL = 0 immediately after switch is closed R 1 Immediately after switch is closed, V circuit looks like: I R 2 R 3 Physics 212 Lecture 18, Slide 28

Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R 1 V IL(t=0+) = 0 R 2 L I 2 R 3 I 2(t=0+) = V/(R 1+R 2+R 3) What is the magnitude of VL, the voltage across the inductor, immediately after the switch is closed? (A) (B) (C) (D) (E) Kirchhoff’s Voltage Law, VL-I 2 R 2 -I 2 R 3 =0 VL = I 2 (R 2+R 3) Physics 212 Lecture 18, Slide 29

Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. What is d. IL/dt, the time rate of change of the current through the inductor immediately after switch is closed (A) (B) (C) R 1 V R 2 L R 3 VL(t=0+) = V(R 2+R 3)/(R 1+R 2+R 3) (D) The time rate of change of current through the inductor (d. I L /dt) = VL /L Physics 212 Lecture 18, Slide 30

Follow Up The switch in the circuit shown has been closed for a long time. What is I 2, the current through R 2 ? (Positive values indicate current flows to the right) (A) (B) R 1 V R 2 L (C) R 3 (D) After a long time, d. I/dt = 0 Therefore, the voltage across L = 0 Therefore the voltage across R 2 + R 3 = 0 Therefore the current through R 2 + R 3 must be zero !! Physics 212 Lecture 18, Slide 31

Follow Up 2 The switch in the circuit shown has been closed for a long time at which point, the switch is opened. R 1 (A) (B) (C) I 2 IL V What is I 2, the current through R 2 immediately after switch is opened ? (Positive values indicate current flows to the right) R 2 L (D) R 3 (E) 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/R 1 Immediately AFTER switch is opened: IL flows in right loop Therefore, IL = -V/R 1 Physics 212 Lecture 18, Slide 32