Exam 2 this Sunday 6:10-7: min, on Busch (same number of questions as Exam 1, extra time if you need)

Transcription

1 Exam 2 this Sunday 6:10-7: min, on Busch (same number of questions as Exam 1, extra time if you need) Come down and play with the RC circuit demo: Flip switches and see how long it takes for the bulb to dim Congrats on 3/3 to: Baksi, Balance, Alison Bansil, Buznitsky, Caponigro, El-Hawwat, Faytelson, Feng, Gordon, Johnson, Kershaw, Kraut, Lai, Laya, May, Meer, Nonna, Oduro, Ozair, Popat, Ravichandran, Rivera, Rondel, Scallo, Scot, Simmons, Stephen, Thuel, Tournoux, Turkhud, Vij, Zimmerman 4/9/14 Phys 272 1

2 Magnetic field inside a solenoid (n turns/length) with changing i! B C Uniform B field out of the page B = µ 0 ni 4/12/17 Phys 272 2

3 clicker C wire of resistance R made into a loop C n ^ points out of page B(t) out of page and increasing with time Which direction does the induced current flow? (A) Clockwise (B) Counterclockwise (C) The current is zero The induced current produces a magnetic flux that OPPOSES THE CHANGE 4/12/17 Phys 272 3

4 B(t) out of page increasing with time wire of resistance R made into a loop C n ^ points out of page Φ(t) = B(t) A LENZ S LAW direction of induced current: current flowing in loop creates an additional magnetic flux that OPPOSES dφ/dt If Φ is increasing, additional flux is negative If Φ is decreasing, additional flux is positive 4/12/17 Phys 272 4

5 i Magnetic field at the center due to clockwise i is into the page Magnetic flux due to current in loop is negative 4/12/17 Phys 272 5

6 i Magnetic field at the center due to counterclockwise i is out of the page Magnetic flux due to current in loop is positive 4/12/17 Phys 272 6

7 B(t) out of page increasing with time wire of resistance R made into a loop C n ^ points out of page Φ(t) = B(t) A LENZ S LAW direction of induced current: current flowing in loop creates an additional magnetic flux that OPPOSES dφ/dt If Φ is increasing, additional flux is negative so induced current is clockwise (If Φ is decreasing, additional flux is positive so induced current is counterclockwise) 4/12/17 Phys 272 7

8 clicker C wire of resistance R made into a loop C n ^ points out of page B(t) out of page and increasing with time Which direction does the induced current flow? (A) Clockwise (B) Counterclockwise (C) The current is zero The induced current produces a magnetic flux that OPPOSES THE CHANGE 4/12/17 Phys 272 8

9 clicker C wire of resistance R made into a loop C n ^ points out of page B(t) out of page and increasing with time Which direction does the induced current flow? (A) Clockwise (B) Counterclockwise (C) The current is zero The induced current produces a magnetic flux that OPPOSES THE CHANGE 4/12/17 Phys 272 9

10 OTHER WAYS TO CHANGE THE MAGNETIC FLUX THROUGH A LOOP Move the loop into or out of a region with B field Rotate the loop in a uniform field: angle between B and n changes, so Φ changes Electric generator Change the size of the loop in a uniform field Examples: pull the loop closed a moving metal rod on U-shaped wire 4/12/17 Phys

11 Chapter 30 Inductors and simple time-varying circuits Part 2 Phys

12 Introduction to time-varying circuits Circuit with variable resistor R(t) Circuit with variable emf E(t) Current depends on time i(t) The rules we learned for time-independent circuits are still true: Take a snapshot at time t The voltage change through each circuit element is computed the same way as before Loop rule and junction rule hold at each time t 4/9/14 Phys

13 clicker In the circuit shown, E is 20 V at t=0 and is decreased at a rate of 5.0 V per second. What is the current through the 5.0 Ω resistor at t = 2.0 sec? (a) 4.0 A (b) 3.0 A (c) 2.0 A (d) 1.0 A (e) 0.0 A 4/9/14 Phys

14 Introduction to time-varying circuits Circuit with variable resistor R(t) Circuit with variable emf E(t) Current depends on time i(t) The rules we learned for time-independent circuits are still true: Take a snapshot at time t The voltage change through each circuit element is computed the same way as before Loop rule and junction rule hold at each time t For this simple circuit, E(t) = i(t) R(t) 4/9/14 Phys

15 RC circuits i(t) Switch closed to a position at t=0 Initial q = 0 +q(t) -q(t) 4/9/14 Phys

16 RC circuits i(t) +q(t) -q(t) the time it takes for the current to decrease by a factor of e time constant RC ln 2 = the time it takes for the current to decrease by a factor of 2 4/9/14 Phys

17 Discharge the capacitor the time it takes for the current to decrease by a factor of e time constant RC ln 2 = the time it takes for the current to decrease by a factor of 2 4/9/14 Phys

18 Discharge the capacitor the time it takes for the current to decrease by a factor of e time constant RC ln 2 = the time it takes for the current to decrease by a factor of 2 What happened to the energy stored in the capacitor? i 2 R in the resistor dissipated as heat 4/9/14 Phys

19 Clicker (to be answered with the demo) If I put a second identical capacitor in parallel with the original what will happen to the time it takes for the current to drop by a factor of 2? (a) Doubles (b) Stays the same (c) Decreases by a factor of two (d) None of the above 4/9/14 Phys

20 A new circuit element: the inductor 4/9/14 Phys

21 Loop with resistance R=0 and current i Current i in loop produces a magnetic flux through coil Φ = L i L is called the self-inductance of the coil Units: 1 T m 2 / A = 1 H (1 henry) If the current changes, the magnetic flux will change Φ(t) = L i(t) Effect is to create electric fields in the loop These fields induce current that opposes the change in current Like inserting a battery with E = dφ(t)/dt 4/9/14 Phys

22 A new circuit element: the inductor The rule: as you go through the inductor in the direction of the current arrow, the voltage difference is -L di(t)/dt i Note that if i does not vary with time, there is NO voltage difference 4/9/14 Phys

23 30.9: RL Circuits: i Switch closed to a position at t=0 Phys