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Physics 212 Lecture 18

Physics 212 Lecture 18. d I. dt. Wrap a wire into a coil to make an “inductor”…. e = -L. From the prelecture: Self Inductance. d I. dt. e L = - L. What this really means :. emf induced across L tries to keep I constant. L. current I.

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Physics 212 Lecture 18

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  1. Physics 212 Lecture 18

  2. dI dt Wrap a wire into a coil to make an “inductor”… e = -L From the prelecture: Self Inductance

  3. dI dt eL= -L What this really means: emf induced across L tries to keep I constant L current I Inductors prevent discontinuous current changes ! It’s like inertia!

  4. I(t) dI dt e = -L e + - - V1 + V2 I(t) Suppose dI/dt > 0. Induced EMF tries to counteract this change (Lenz’s Law). Voltage across inductor V1 – V2 = VL = + L dI/dt > 0

  5. Checkpoint 1 2 (1/2)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 Compare the inductance of the two solenoids A) LA = 4 LBB) LA = 2 LBC) LA = LBD) LA = (1/2) LBE) LA = (1/4) LB

  6. WHAT ARE INDUCTORS AND CAPACITORS GOOD FOR? Inside your i-clicker

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

  8. Checkpoint 2a I IL=0 I After: IL = 0 I = + V/2R 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/RB) I = V/2RC) I = 0 D) I = -V/2RE) I = -V/R Before: IL = 0

  9. RL Circuit (Long Time) - + + - KVR:VL + IR = 0 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/RB) I = V/2RC) I = 0 D) I = -V/2RE) I = -V/R After a long time in any static circuit: VL = 0

  10. Checkpoint 2b circuit when switch opened L R IL=V/R 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/RB) I = V/2RC) I = 0 D) I = -V/2RE) I = -V/R Current through inductor cannot change DISCONTINUOUSLY

  11. 3 2 VL t = L/R dI 1 4 V1 – V2 = L dt t = L/R where Why is there exponential behavior ? I L R V3-V4 = IR

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

  13. 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? • Case 1 • Case 2 • The same

  14. Checkpoint 3b Before switch moved: 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? • Case 1 • Case 2 • The same After switch moved:

  15. Checkpoint 3c Immediately after: 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? • Case 1 • Case 2 • The same After awhile

  16. Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. What is dIL/dt, the time rate of change of the current through the inductor immediately after switch is closed R1 R2 V 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.

  17. Calculation IL = 0 What is IL, the current in the inductor, immediately after the switch is closed? • IL =V/R1 up(B) IL =V/R1 down (C) IL = 0 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 The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 R2 V L R3 INDUCTORS: Current cannot change discontinuously !

  18. Calculation R1 R2 I Immediately after switch is closed, circuit looks like: V R3 The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 R2 V L R3 IL(t=0+) = 0 What is the magnitude of I2, the current in R2, immediately after the switch is closed? • (B) (C) (D) We know IL = 0 immediately after switch is closed

  19. Calculation What is the magnitude of VL, the voltage across the inductor, immediately after the switch is closed? • (B) (C) (D) (E) I2 The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 R2 V L R3 I2(t=0+) = V/(R1+R2+R3) IL(t=0+) = 0 Kirchhoff’s Voltage Law, VL-I2 R2 -I2 R3 =0 VL = I2 (R2+R3)

  20. Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. What is dIL/dt, the time rate of change of the current through the inductor immediately after switch is closed R1 R2 V L R3 VL(t=0+) = V(R2+R3)/(R1+R2+R3) • (B) (C) (D) The time rate of change of current through the inductor (dIL /dt) = VL /L

  21. 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) R1 R2 V L R3 • (B) (C) (D) 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 !!

  22. Follow Up 2 I2 • (B) (C) (D) (E) The switch in the circuit shown has 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) R1 R2 IL V L R3 Current through inductor immediately AFTER switch is opened IS THE SAME AS the current through inductor immediately BEFORE switch is opened Immediately BEFOREswitch is opened: IL = V/R1 ImmediatelyAFTERswitch is opened: IL flows in right loop Therefore, IL = -V/R1

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