1. Physics 2112 Unit 18 Today’s Concepts: A) Induction B) RL Circuits Electricity & Magnetism Lecture 18, Slide 1

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

3. Remember Example 17.6 (solenoid)?? Unit 17, Slide 3 1.Changing current in outer loop 2.Caused changing magnetic field in inner loop 3.Induced changing current in inner loop. What if you only had one loop? Would changing current in that induce anything?

4. Self Inductance Electricity & Magnetism Lecture 18, Slide 4 Define: Depends only on the geometry of the coils Voltage drop in a coil …caused by changes in the current in that same coil

5. L What is the inductance of a solenoid? Example 18.1 (Inductance of Solenoid) Electricity & Magnetism Lecture 18, Slide 5

6. 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) L A  4 L B B) L A  2 L B C) L A  L B D) L A  (1/2) L B E) L A  (1/4) L B Checkpoint 1 Electricity & Magnetism Lecture 18, Slide 6

7. Increasing current What the minus sign means….. Electricity & Magnetism Lecture 18, Slide 7  V < 0 V A > V B AA Acts like a resistor I AB  V AB

8. decreasing current What the minus sign means….. Electricity & Magnetism Lecture 18, Slide 8  V > 0 V A < V B AB Acts like a battery I AB  V AB However you try to change the current through an inductor, the inductor resists that change.

9. current I L dI dt  L  L emf induced across L tries to keep I constant. Inductors prevent discontinuous current changes! It’s like inertia! What this really means: Electricity & Magnetism Lecture 18, Slide 9 Units of inductance are Henrys (H) [Tm 2 /A]

10. R L V BATT I  0 Time Constant Electricity & Magnetism Lecture 18, Slide 10

11. R=100  L 12V= V BATT S Example 18.2 (Current in Solenoid) Electricity & Magnetism Lecture 18, Slide 11 A solenoid has 6500 loops in a length of 10cm and a radius of 6cm. It is attached to a 120  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? Would the current have been at 0.01sec if the inductor had an internal resistance of 20  ?

12. R L At t = 0: I  0 V L  V BATT V R  0 ( L is like a giant resistor) V BATT I  0 At t  L/R: V L  0 V R  V BATT I  V BATT /R ( L is like a short circuit) R I = V/R L V BATT When no current is flowing initially: How to think about RL circuits: Electricity & Magnetism Lecture 18, Slide 12 VLVL I

13. 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 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. II CheckPoint 2A Electricity & Magnetism Lecture 18, Slide 13

14. 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 After a long time, the switch is opened, abruptly disconnecting the battery from the circuit. CheckPoint 2B Electricity & Magnetism Lecture 18, Slide 14

15. R L V BATT I  V/RI  V/R At t  L/R: I  0 V L  0 V R  0 R I = 0 L R I  V BATT /R V R  IR V L  V R At t  0: When steady current is flowing initially: How to Think about RL Circuits Episode 2: VLVL Electricity & Magnetism Lecture 18, Slide 15

16. R I V  IR dI dt V  L L     Why is there Exponential Behavior? VLVL Electricity & Magnetism Lecture 18, Slide 16 where

17. Inside your i-clicker ” 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?” What are Inductors and Capacitors Good For? Electricity & Magnetism Lecture 18, Slide 17

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

19. 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 CheckPoint 3A Electricity & Magnetism Lecture 18, Slide 19

20. A) Case 1 B) Case 2 C) The same CheckPoint 3B Electricity & Magnetism Lecture 18, Slide 20 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?

21. A) Case 1 B) Case 2 C) The same CheckPoint 3C Electricity & Magnetism Lecture 18, Slide 21 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?

22.  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 dI L /dt immediately after switch is closed. R1R1 L V R2R2 R3R3 Example 18.3 (3R and L circuit) The switch in the circuit shown has been open for a long time. At t  0, the switch is closed. Electricity & Magnetism Lecture 18, Slide 22 What is dI L /dt, the time rate of change of the current through the inductor immediately after switch is closed?