Physics 2112 Unit 18

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1 Physics 2112 Unit 18 Today s Concepts: A) Induction B) Circuits Electricity & Magnetism ecture 18, Slide 1

2 Where we are.. Just finished introducing magnetism Will now apply magnetism to AC circuits Unit 17, Slide 2

3 What you thought Doing physics during vacation is the best This one was rough, could we do a lot of examples in class? Which direction does the current flow after an inductor becomes the only thing powering a circuit. will need to study the concepts behind the graphs; how current and voltage behaves before and after switches are changed. Dr. Carter, I may have found a loophole. What if there is a loop within a loop? Can we call it loopception? Something is amiss here.. Comparing the circuits confused me. However, I'm happy to be done with the magnetism unit. The whole idea of inductance is still a bit confusing. Current in a loop creates magnetic flux which creates an oppositely directed emf in the same loop which would create an oppositely directed current? Electricity & Magnetism ecture 18, Slide 3

4 emember Example 17.6 (solenoid)?? 1. Changing current in outer set of loops 2. Caused changing magnetic field in inner loops 3. Induced changing current in inner loops. What if you only had the outer set of loops? Would changing current in that induce anything? Unit 17, Slide 4

5 Self Inductance Define: I B Depends only on the geometry of the coils Voltage drop in a coil d d( I) B dt dt di dt caused by changes in the current in that same coil Electricity & Magnetism ecture 18, Slide 5

6 Example 18.1 (Inductance of Solenoid) What is the inductance of a long coil of wire (a solenoid)? Electricity & Magnetism ecture 18, Slide 6

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 n 2 r 2 z B 0 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 & Magnetism ecture 18, Slide 7

8 What we thought Two solenoids are made with the same cross sectional area and total number of turns. Inductor B is twice as long as inductor A 2 2 B 0 n r z 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 B) The length z doubles, but the turns per unit length halves and when it's squared it will be one fourth. the end result is that B becomes half of A. C) the only difference between the two is their length, z, and by increasing the length the number of turns per unit length, n, is cut in half so they cancel out D) everything else is the same except the length which is linearly proportional to the inductance of the solenoid. Electricity & Magnetism ecture 18, Slide 8

9 Wrong eason?? Two solenoids are made with the same cross sectional area and total number of turns. Inductor B is twice as long as inductor A 2 2 B 0 n r z 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 B) z is twice the amount in b B) If everything else is the same except length, then 2B = A. C) current per unit length is still constant Electricity & Magnetism ecture 18, Slide 9

10 What the minus sign means B 0 n r z n *volume 2 0 di A Increasing current DV < 0 V A > V B B dt Acts like a resistor I AB DV AB Electricity & Magnetism ecture 18, Slide 10

11 What the minus sign means.. A B di dt decreasing current DV > 0 V A < V B Acts like a battery I AB DV AB However you try to change the current through an inductor, the inductor resists that change. Electricity & Magnetism ecture 18, Slide 11

12 What this really means: emf induced across tries to keep I constant. di dt current I Inductors prevent discontinuous current changes! It s like inertia! Units of inductance are Henrys (H) [Tm 2 /A] Electricity & Magnetism ecture 18, Slide 12

13 Time Constant I 0 I V (1 e t / ) V BATT Electricity & Magnetism ecture 18, Slide 13

14 Example 18.2 (Current in Solenoid) S 12V= V BATT =120W A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120W resistor and a 12V battery. What is the current through the resistor 0.01sec after the switch is closed? What is the current through the resistor 2.0 sec after the switch is closed? I V (1 e t / ) Would the current have been at 0.01sec if the inductor had an internal resistance of 20W? Electricity & Magnetism ecture 18, Slide 14

15 How to think about circuits: When no current is flowing initially: I 0 I = V/ V I V BATT At t = 0: I 0 V V BATT V 0 ( is like a giant resistor) V BATT At t >> /: V 0 V V BATT I V BATT / ( is like a short circuit) Electricity & Magnetism ecture 18, Slide 15

16 CheckPoint 2A 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 I after the switch is closed? (+ is in the direction of the arrow) A) I V/ B) I V/2 C) I 0 D) I V/2 E) I V/ Electricity & Magnetism ecture 18, Slide 16

17 What is the current I through the vertical resistor immediately after the switch is closed? What we thought.. (+ is in the direction of the arrow) I A) I V/ B) I V/2 C) I 0 D) I V/2 E) I V/ I A) The resistance is parallel with the inductor, so it's normal function shouldn't be affected. B) The inductor resists a change in current. So at t=0, there should be no current going through the inductor and all the current should be going through the 2 resistors. I would then be equal to I=V/2 C) Since there is no resistance through, no current will travel through the vertical resistor. Electricity & Magnetism ecture 18, Slide 17

18 Confusion about question. What is the current I through the vertical resistor immediately after the switch is closed? (+ is in the direction of the arrow) I A) I V/ B) I V/2 C) I 0 D) I V/2 E) I V/ C) there is no current at t=0 I I mean a little dt of time after t=0 Electricity & Magnetism ecture 18, Slide 18

19 Circuit (ong 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/ B) I V/2 C) I 0 D) I V/2 E) I V/ After a long time in any static circuit: V 0 Electricity & Magnetism ecture 18, Slide 19

20 CheckPoint 2B 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/ B) I V/2 C) I 0 D) I V/2 E) I V/ Electricity & Magnetism ecture 18, Slide 20

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/ B) I V/2 C) I 0 D) I V/2 E) I V/ What we thought.

21 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/ B) I V/2 C) I 0 D) I V/2 E) I V/ What we thought.. A) The voltage across the solenoid is initially V, so the resistor must have an equal voltage drop V and current will be V/ C) After a long time, the current through will be zero. After a long time in a static circuit, the current will go to zero because the Vl goes to zero. E) I think it will go the opposite way because that was the direction that the current was flowing into the inductor right before the switch was opened.. Electricity & Magnetism ecture 18, Slide 21

22 How to Think about Circuits Episode 2: V BATT When steady current is flowing initially: I = 0 V I V/ At t 0: I V BATT / V I V V At t >> /: I 0 V 0 V 0 Electricity & Magnetism ecture 18, Slide 22

23 Why is there Exponential Behavior? V di dt + I + V I V di dt + I 0 I( t) I 0 e t/ I 0 e t / where Electricity & Magnetism ecture 18, Slide 23

24 Quick comment I V V BATT ecture: Prelecture: Did we mess up? No: The resistance is simply twice as big in one case. Electricity & Magnetism ecture 18, Slide 24

25 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 Electricity & Magnetism ecture 18, Slide 25

26 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 Electricity & Magnetism ecture 18, Slide 26

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

27 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 Before switch moved: V I After switch moved: V V 1 2 V V 2 3 Electricity & Magnetism ecture 18, Slide 27

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 the

28 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 the inductor larger? A) Case 1 B) Case 2 C) The same Immediately after: I1 I2 After awhile I I 1 2 Ie Ie t / 1 t / 1 > 2 2 Electricity & Magnetism ecture 18, Slide 28

29 Energy Stored Estored Power 1 I 2 For inductor 2 d( energy) dt VI E stored 1 2 Q C 2 ecall for capacitor Energy stored in the magnetic field Energy stored in the electric field Unit 18, Slide 29

30 Example 18.3 (Energy in Solenoid) S 12V= V BATT =100W A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120W resistor and a 12V battery. What is the energy stored in the inductor 0.01sec after the switch is closed? What is the energy stored in the inductor 2.0 sec after the switch is closed? Estored 1 I 2 2 Electricity & Magnetism ecture 18, Slide 30

31 Question 120V The switch has been in the open position for a long time in the circuit drawn above. What is the total current out of the battery, I tot, immediately after the switch is closed? (The inductor is ideal.) A. 0A B. 4A C. 6A D. 12A E. -4A

32 Question 120V The switch has been in the open position for a long time in the circuit drawn above. What is the current across the resistor, I 1, immediately after the switch is closed? (The inductor is ideal.) A. 0A B. 4A C. 6A D. 12A E. -4A

33 Question 120 V The switch has been in the open position for a long time in the circuit drawn above. What is the current across the inductor, I 2, immediately after the switch is closed? (The inductor is ideal.) A. 0A B. 4A C. 6A D. 12A E. -4A

34 Question 120 V The switch has been in the open position for a long time in the circuit drawn above. What is the voltage drop across the inductor immediately after the switch is closed? (The inductor is ideal.) A. 0V B. 80V C. 90V D. 120V E. 240V

35 Question 120V The switch has been in the closed position for a long time in the circuit drawn above. What is the current across the inductor, I 2? (The inductor is ideal.) A. 0A B. 4A C. 6A D. 12A E. -4A

36 Question 120 V The switch has been in the closed position for a long time in the circuit drawn above. What is the voltage difference across the inductor immediately after the switch is opened? (The inductor is ideal.) A. 0V B. 80V C. 90V D. 120V E. 240V

37 Question 120V The switch has been in the closed position for a long time in the circuit drawn above. What is the current across the inductor, I 2 immediately after the switch is open? (The inductor is ideal.) A. 0A B. 4A C. 6A D. 12A E. -4A

38 Question 120 V The switch has been in the closed position for a long time in the circuit drawn above. What is the rate change for the current through the inductor immediately after the switch is opened? (The inductor is ideal.) A. 6A/sec B. 80A/sec C. 90A/sec D. 120A/sec E. 240A/sec

39 Question 120 V The switch has been in the open position for a long time in the circuit drawn above. Which point has a higher electrical potential immediately after the switch is closed? (The inductor is ideal.) A B A. V A > V B B. V A = V B C. V A < V B

40 Question 120 V The switch has been in the closed position for a long time in the circuit drawn above. Which point has a higher electrical potential? (The inductor is ideal.) A B A. V A > V B B. V A = V B C. V A < V B

41 Question 120 V The switch has been in the closed position for a long time in the circuit drawn above. Which point has a higher electrical potential immediately after the switch is opened? (The inductor is ideal.) A B A. V A > V B B. V A = V B C. V A < V B

Electricity & Magnetism Lecture 18

Electricity & Magnetism Lecture 18 Electricity & Magnetism ecture 18 Today s Concepts: A) Induc4on B) R Circuits Electricity & Magne4sm ecture 18, Slide 1 Stuff you said.. Will there be more lab ac4vi4es involving oscilloscopes? Unlike