Electricity & Magnetism Lecture 18

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Roger Johnston
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1 Electricity & Magnetism ecture 18 Today s Concepts: A) Induc4on B) R Circuits Electricity & Magne4sm ecture 18, Slide 1

2 Stuff you said.. Will there be more lab ac4vi4es involving oscilloscopes? Unlike lab ac4vi4es involving magnets, the oscilloscopes are foreign, new, and curiously interes4ng to play/learn with due to the above? What are the exact differences between the Capacitor and Inductor. In which situa4on would I use the Capacitor instead of the Inductor or vice versa? Capacitors are yin Inductors are yang

4 From the Prelecture: Self Inductance Wrap a wire into a coil to make an inductor ε = di dt Electricity & Magne4sm ecture 18, Slide 2

5 What this really means: emf induced across tries to keep I constant. ε = di dt current I Inductors prevent discon4nuous current changes! It s like iner4a! Electricity & Magne4sm ecture 18, Slide 3

CheckPoint 2 Two solenoids are made with the same

A = 4 B B) A = 2 B C) A = B D) A = (1/2) B E) A =

6 CheckPoint 2 Two solenoids are made with the same cross sec4onal 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) A = 4 B B) A = 2 B C) A = B D) A = (1/2) B E) A = (1/4) B Electricity & Magne4sm ecture 18, Slide 4

7 How to think about R circuits Episode 1: I = 0 When no current is flowing ini4ally: I = V/R V R R V BATT At t = 0: I = 0 V = V BATT V R = 0 ( is like a giant resistor) V BATT At t >> /R: V = 0 V R = V BATT I = V BATT /R ( is like a short circuit) Electricity & Magne4sm ecture 18, Slide 5

$What is the current I through the ver4cal resistor immediately a\er the switch is closed?$

8 CheckPoint 4 In the circuit, the switch has been open for a long 4me, and the current is zero everywhere. At 4me t = 0 the switch is closed. What is the current I through the ver4cal resistor immediately a\er the switch is closed? I = 0 (+ is in the direc4on of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = V/2R E) I = V/R Electricity & Magne4sm ecture 18, Slide 6

9 R Circuit (ong Time) What is the current I through the ver4cal resistor a\er the switch has been closed for a long 4me? (+ is in the direc4on of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = V/2R E) I = V/R Electricity & Magne4sm ecture 18, Slide 7

10 How to Think about R Circuits Episode 2: V BATT When steady current is flowing initially: V I = 0 R R R I = V/R At t = 0: I = V BATT /R V R = IR V = V R At t >> /R: I = 0 V = 0 V R = 0 Electricity & Magne4sm ecture 18, Slide 8

$A\er a long 4me, the switch is opened, abruptly disconnec4ng the baaery from the$ $What is the current I through the ver4cal resistor immediately a\er the switch is$

11 A\er a long 4me, the switch is opened, abruptly disconnec4ng the baaery from the circuit. What is the current I through the ver4cal resistor immediately a\er the switch is opened? (+ is in the direc4on of the arrow) A) I = V/R B) I = V/2R C) I = 0 D) I = V/2R E) I = V/R CheckPoint 6 Electricity & Magne4sm ecture 18, Slide 9

12 Why is there Exponential Behavior? I + V V = di dt + R V = IR where Electricity & Magne4sm ecture 18, Slide 10

13 I R V V BATT ecture: Prelecture: Did we mess up? No: The resistance is simply twice as big in one case. Electricity & Magne4sm ecture 18, Slide 11

14 CheckPoint 8 A\er long 4me at 0, moved to 1 A\er long 4me at 0, moved to 2 A\er switch moved, which case has larger 4me constant? A) Case 1 B) Case 2 C) The same Electricity & Magne4sm ecture 18, Slide 12

15 CheckPoint 10 A\er long 4me at 0, moved to 1 A\er long 4me at 0, moved to 2 Immediately a\er switch moved, in which case is the voltage across the inductor larger? A) Case 1 B) Case 2 C) The same I0 is V/R in both cases A) V(0) = I0*2R B) V(0) = I0*3R Electricity & Magne4sm ecture 18, Slide 13

16 CheckPoint 12 A\er long 4me at 0, moved to 1 A\er long 4me at 0, moved to 2 V A\er switch moved for finite 4me, in which case is the current through the inductor larger? A) Case 1 B) Case 2 C) The same A) τ1 = /2R B) τ2 = /3R τ2 τ1 Electricity & Magne4sm ecture 18, Slide 14

17 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 R 3 What is di /dt, the 4me rate of change of the current through the inductor immediately a\er switch is closed 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 func4on of 4me. Strategic Analysis Determine currents immediately a\er switch is closed. Determine voltage across inductor immediately a\er switch is closed. Determine di /dt immediately a\er switch is closed. Electricity & Magne4sm ecture 18, Slide 15

18 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 I = 0 R 3 What is I, the current in the inductor, immediately a\er the switch is closed? A) I = V/R 1 up B) I = V/R 1 down C) I = 0 Electricity & Magne4sm ecture 18, Slide 16

19 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 R 3 I (t = 0 +) = 0 What is the magnitude of I 2, the current in R 2, immediately a\er the switch is closed? A) B) C) D) Electricity & Magne4sm ecture 18, Slide 17

20 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. V R 1 R 2 I 2 R 3 I (t = 0 +) = 0 I 2 (t = 0 +) = V/(R 1 + R 2 + R 3 ) What is the magnitude of V, the voltage across the inductor, immediately a\er the switch is closed? A) B) C) D) E) Electricity & Magne4sm ecture 18, Slide 18

21 Calculation The switch in the circuit shown has been open for a long 4me. At t = 0, the switch is closed. What is di /dt, the 4me rate of change of the current through the inductor immediately a\er switch is closed V R 1 R 2 R 3 V (t = 0 +) = V(R 2 + R 3 )/(R 1 + R 2 + R 3 ) A) B) C) D) Electricity & Magne4sm ecture 18, Slide 19

22 Follow Up The switch in the circuit shown has been closed for a long 4me. What is I 2, the current through R 2? V R 1 R 2 R 3 (Posi4ve values indicate current flows to the right) A) B) C) D) Electricity & Magne4sm ecture 18, Slide 20

23 Follow Up 2 The switch in the circuit shown has been closed for a long 4me at which point, the switch is opened. What is I 2, the current through R 2 immediately a\er V R 1 R 2 I 2 R 3 switch is opened? (Posi4ve values indicate current flows to the right) A) B) C) D) E) Electricity & Magne4sm ecture 18, Slide 21

Electricity & Magnetism Lecture 18

Electricity & Magnetism Lecture 18 Electricity & Magnetism ecture 18 Today s Concepts: A) Induc4on B) R Circuits Electricity & Magne/sm ecture 18, Slide 1 Extended deadline for next few FlipItPhysics homework:! 80% extended by one week.