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Physics 212 Lecture 17 Original:Mats Selen Modified:W.Geist

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**From the prelecture: Self Inductance**

Wrap a wire into a coil to make an “inductor”… dI dt e = -L

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**What this really means:**

emf induced across L tries to keep I constant dI dt eL = -L L current I Inductors prevent abrupt current changes ! Its like inertia!

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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

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Inside your i-clicker

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**At t >> L/R: At t = 0: How to think about RL circuits Episode 1:**

When no current is flowing initially: At t >> L/R: VL = 0 VR = VBATT I = VBATT/R (L is like a short circuit) R I=V/R L VBATT VL I t = L/R I=0 L R VBATT At t = 0: I = 0 VL = VBATT VR = 0 (L is like a huge resistance)

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**Circuit in Preflight (IL = 0 before switch is closed)**

CD What is IR right after closing switch? A) I = V/R B) I = V/2R C) I = 0 D) I = -V/2R E) I = -V/R IR L IL=0 R V R Current through L is 0 right after switch closed Remember – current through inductor cant change abruptly

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**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

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**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/R B) I = V/2R C) I = 0 D) I = -V/2R E) I = -V/R KVR: VL + IR = 0 + - After a long time in any static circuit: VL = 0

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**At t >> L/R: At t = 0: How to think about RL circuits Episode 2:**

When steady current is flowing initially: VL t = L/R At t >> L/R: I = 0 VL = 0 VR = 0 R I=0 L I=V/R L R VBATT I = VBATT/R VR = IR VL = VR (L is like a battery) At t = 0:

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**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 CD IL=V/R L R V R +’ve Current through inductor cant change abruptly. IL is the same just before and just after switch opens = V/R.

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**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

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**Why is there exponential behavior ?**

VL t = L/R dI dt V = L V = IR + - I L R I at t=0 where

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**I L R t = L/R Lecture: Prelecture: Did we mess up??**

VL VBATT t = L/R Lecture: Prelecture: No: The resistance is simply twice as big in one case.

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**Calculation Conceptual Analysis Strategic Analysis**

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 C 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. The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

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Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 R2 V Immediately before switch is closed: IL = 0 since no battery in loop IL = 0 L R3 What is the direction of IL, the current in the inductor, immediately after the switch is closed? IL flows up (B) IL flows down (C) IL = 0 INDUCTORS: Current cannot change discontinuously ! The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. Current through inductor immediately AFTER switch is closed IS THE SAME AS the current through inductor immediately BEFORE switch is closed

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**Immediately after switch is closed, circuit looks like:**

Calculation 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) The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. We know IL = 0 immediately after switch is closed Immediately after switch is closed, circuit looks like: R1 V R2 R3 I

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Calculation The switch in the circuit shown has been open for a long time. At t = 0, the switch is closed. R1 R2 I2 V L 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? (B) (C) (D) (E) The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class. The voltage across the inductor, VL, is also equal to the voltage across R2 + R3 The voltage across R2 + R3 = I2(R2 + R3) Therefore:

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**Calculation Hint: (B) (C) (D)**

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) Hint: (B) (C) (D) The time rate of change of current through the inductor (dIL /dt) = VL /L

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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 !! The purpose of this Check is to jog the students minds back to when they studied work and potential energy in their intro mechanics class.

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IR L IL R V = 0 (current all going through the “short circuit” inductor) R A long time later the current in the circuit is no-longer changing. VL = 0 Inductor looks like a short circuit

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