Lect18 - Physics 212 Ph Lecture 18 Physics 212 Lecture 18,...

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Unformatted text preview: Physics 212 Ph Lecture 18 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 AfroFreddie Omar con su banda Los Hombres Calientes Hombres Calientes Theme of the week: Great Piano Players from Classic to Current He also did a spectacular show at Krannert last fall Legendary Cuban piano player Hasn’t been in the U.S. in seven years A real treat !! Your Your Comments “OMG NO MORE MAGNETIC FIELDS. IM SOOOOOO HAPPY HAPPY” “How can a neutral spiral of metal oppose the slowing down of charge flow. I still don't have a warm and fuzzy fuzzy grasp of Faraday's law!!!!” Inductor stores energy in its magnetic field! “I don't really get why the voltage doubles when the switch is opened. I'd like some clarifications. Thanks! Thanks!” “Checkpoint 2, what happens when the switch turns on right away to the current” Difficult checkpoints today! “Can we go over the entire last checkpoint” “How do you find the voltage across the inductor when there is no power source?” “Hooray for circuits” “I HATE CIRCUITS....right when things started to become exciting with magnetism, we have to go back to circuits...I'm really disliking the physics department at this moment” “I'm going to need some inDUCTance tape to keep all this info from falling out of my brain.” 05 Physics 212 Lecture 18, Slide 3 Some Some Exam Stuff • Exam Next Wednesday ( Oct. 26) 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 TONIGHT (Oct. 20, 10:00 p.m.) – If you have conflicts with both of these, contact Prof. Park Physics 212 Lecture 18, Slide 4 News News Flash • Final exams: – Wed. Dec 14 7:00 – 10:00 p.m. – Thu. Dec. 15 1:30 – 4:30 p.m. Dec 15 4:30 Physics 212 Lecture 18, Slide 5 From From the prelecture: Self Inductance Wrap a wire into a coil to make an “inductor”… = -L dI dt Physics 212 Lecture 18, Slide 6 What What this really means: emf induced across L tries to keep I constant L = -L dI dt L current I Inductors prevent discontinuous current changes ! It’s like inertia! Physics 212 Lecture 18, Slide 7 Checkpoint 1 Two Two solenoids are made with the same cross sectional area and total 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 “z increases by two but n decreases by 2. so .5^2*2=.5 for Lb Lb” “number of turns and length cancel out” “same amount of turns, only difference is z, which is 2” Physics 212 Lecture 18, Slide 8 Checkpoint 1 Two Two solenoids are made with the same cross sectional area and total total number of turns. Inductor B is twice as long as inductor A LB 0 n 2r 2 z (1/2)2 2 LB 1 L A 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 i- Physics 212 Lecture 18, Slide 10 How How to think about RL circuits Episode 1: Episode When no current is flowing initially: VL I=0 L I=V/R I=V/R R L = L/R R I VBATT At t = 0: I=0 VL = VBATT VR = 0 (L is like a giant resistor) VBATT = 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 2a In the circuit, the switch has In been open for a long time, and the current is zero everywhere. At At time t=0 the switch is closed. What is the current I through the vertical resistor immediately after the the switch is closed? (+ (+ is in the direction of the arrow) A) A) I = V/R B) I = V/2R C) I = 0 D) I = -V/2R E) I = -V/R “At t=0 the inductor will have a voltage drop of V so the parallel resistor must have the same voltage drop and V=IR.” “Since there is no current in the inductor, the current through through the vertical resistor will just be V/Req or V/2R” “No current will go through the resistor at the start because it will all go through the inductor.” Physics 212 Lecture 18, Slide 12 Checkpoint 2a In the circuit, the switch has In 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 the switch is closed? I IL=0 (+ (+ 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: Before: IL = 0 After: IL = 0 I = + V/2R Physics 212 Lecture 18, Slide 13 RL Circuit (Long Time) Wh What is the current I through the vertical resistor after the switch switch has been closed for a long time? time? (+ (+ is in the direction of the arrow) A) A) I = V/R B) I = V/2R C) I = 0 D) I = -V/2R E) I = -V/R V/ V/ + + After a long time in any static circuit: VL = 0 - - KVR: VL + IR = 0 Physics 212 Lecture 18, Slide 14 VBATT How How to think about RL circuits Episode 2: Episode When steady current is flowing initially: VL I=0 R L R L R I=V/R At t = 0: I = VBATT/R VR = IR VL = VR = L/R = L/R At t >> L/R: I=0 VL = 0 VR = 0 Physics 212 Lecture 18, Slide 15 Checkpoint 2b After a long time, the switch is After the opened, opened, abruptly disconnecting the battery from the circuit. What is the current I through the vertical vertical resistor immediately after the switch is opened? 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 “The voltage is the voltage of the battery, so the current equals that voltage divided by the resistance. ” “Immediately after the switch is opened, the current will still be the same as right before the switch was opened (after having been closed for a long time, so V/2R.” “Doesn't change. No current when switch is opened.” Physics 212 Lecture 18, Slide 16 Checkpoint 2b After a long time, the switch is After the opened, opened, abruptly disconnecting the battery from the circuit. What is the current I through the vertical vertical resistor immediately after the switch is opened? 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 circuit when switch opened L IL=V/R R Current through inductor cannot change DISCONTINUOUSLY Physics Physics 212 Lecture 18, Slide 17 Why is there exponential behavior ? I V=L dI dt L + VL + R = L/R V = IR = L/R dI L IR 0 dt I (t ) I 0e tR / L I 0e t / L where R Physics 212 Lecture 18, Slide 18 I L VL R VBATT = 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 3a 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 “The time constant depends on L/R, and since R total total is smaller in case 1, the time constant is greater. ” “The resistance is greater in case 2 and the constant is directly proportional to R.” “Each closed loop has the same equivelant resistance.” Physics 212 Lecture 18, Slide 20 Checkpoint 3a 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 L 1 2R L 2 3R Physics 212 Lecture 18, Slide 21 Checkpoint 3b 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 B) Case 2 C) The same “The resistance in case 1 is smaller, so the current is bigger ” “resistors added in series in case two will contribute to the greater voltage” “The max voltage is twice the voltage of the battery, which is the same in both cases” Physics 212 Lecture 18, Slide 22 Checkpoint 3b 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 across the inductor larger? A) Case 1 After switch moved: B) Case 2 V VL1 2 R C) The same Before switch moved: I V R VL 2 R V 3R R Physics 212 Lecture 18, Slide 23 Checkpoint 3c After long time at 0, moved to 1 After long time at 0, moved to 2 After switch moved for finite time, “Case one has a bigger time constant ” in which case is the current through the inductor larger? “Case 2 has a smaller time constant so the decay of A) Case 1 current will be smaller, lasting longer. ” B) Case 2 C) The same “The current depends on the characteristics of th the inductor, therefore the current running through will be same. ” Physics Physics 212 Lecture 18, Slide 24 Checkpoint 3c 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 through the inductor larger? A) Case 1 After awhile B) Case 2 I1 Ie t / C) The same 1 Immediately after: I1 I 2 I 2 Ie t / 1 2 2 Physics 212 Lecture 18, Slide 26 Calculation Calculation The switch in the circuit shown has been been open for a long time. At t = 0, At the switch is closed. What is dIL/dt, the time rate of change of the current through the th inductor immediately after switch is closed R1 V 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 Physics 212 Lecture 18, Slide 27 Calculation Calculation The switch in the circuit shown has been been open for a long time. At t = 0, At the switch is closed. R1 V R2 L IL = 0 R3 Wh What is IL, the current in the inductor, immediately after the switch th th is closed? (A) IL =V/R1 up (B) IL =V/R1 down (C) I L = 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 BEFORE Immediately Immediately before switch is closed: IL = 0 since no battery in loop Physics Physics 212 Lecture 18, Slide 28 Calculation Calculation The switch in the circuit shown has been been open for a long time. At t = 0, At the switch is closed. R1 V R2 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 (D) R2 R3 R1 R2 R3 R1 R2 R3 We know IL = 0 immediately after switch is closed R1 Immediately after switch is closed, V circuit looks like: I I R2 V R1 R2 R3 R3 Physics 212 Lecture 18, Slide 29 Calculation Calculation The switch in the circuit shown has been been open for a long time. At t = 0, At the switch is closed. R1 V R2 L IL(t=0+) = 0 I2 R3 I2(t=0+) = V/(R1+R2+R3) Wh 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 (D) VL V R2 R3 R2 R3 (E) VL V R1 ( R2 R3 ) R1 R2 R3 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 30 Calculation Calculation The switch in the circuit shown has been been open for a long time. At t = 0, At the switch is closed. What is dIL/dt, the time rate of change of the current through the th inductor immediately after switch is closed dI V R2 R3 dI (A) L (B) L 0 dt L R1 dt R1 R2 V 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 31 Follow Follow Up The switch in the circuit shown has been 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 V ( R2 R3 ) R1 R2 R3 R1 V R2 L (C) I 2 0 R3 (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 32 Follow Follow Up 2 The switch in the circuit shown has been been closed for a long time at which point, the switch is opened. 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 V R1 R1 V (C) I 2 0 R2 I2 IL L (D) I 2 R3 V R1 (E) I 2 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 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 33 ...
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