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Physics 212 Lecture 11: RC Circuits Change in Schedule

This update informs of the rescheduled Exam 2 on July 12 for the RC Circuit topic covering charging, discharging scenarios, Kirchoff's Voltage Rule, and capacitor behavior in circuits.

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Physics 212 Lecture 11: RC Circuits Change in Schedule

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  1. Physics 212 Lecture 11 RC Circuits Change in schedule Exam 2 will be on Thursday, July 12 from 8 – 9:30 AM.

  2. RC Circuit Charging a C b Vbattery R C a Vbattery R b • Capacitor uncharged, switch is moved to position “a” • Kirchoff’s Voltage Rule • Initially (q = q0 = 0) • Long Term (Ic =0) I In general: 11

  3. A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. After the switch S1 has been closed for a long time Immediately after the switch S1 is closed: VR = 0 I = 0 V2 = V V = Q/C Q = 0 V1 = 0 Checkpoint 1a & Checkpoint 1b • V1 = V V2 = V B) V1 = 0 V2 = V Close S1, V1 = voltage across C immediately after V2 = voltage across C a long time after C) V1 = 0 V2 = 0 D) V1 = V V2 = 0 13

  4. R R I=0 I C V C V VC = Q/C = 0 VC = V For t  At t = 0 Close S1 at t=0 (leave S2 open) R C V 2R S1 S2 15

  5. RC Circuit (Discharging) a C - + I b Vbattery R V a C b Vbattery R • Capacitor has q0 = CV, switch is moved to position “b” • Kirchoff’s Voltage Rule • Initially (q=q0) • Long Term (Ic =0) In general: -I 19

  6. A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. Checkpoint 1c IR + - After being closed a long time, switch 1 is opened and switch 2 is closed. What is the current through the right resistor immediately after switch 2 is closed? A. IR = 0 B. IR = V/3R C. IR = V/2R D. IR = V/R A B C D 22

  7. A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. I V C V 2R Checkpoint 1c IR + - After being closed a long time, switch 1 is opened and switch 2 is closed. What is the current through the right resistor immediately after switch 2 is closed? A. IR = 0 B. IR = V/3R C. IR = V/2R D. IR = V/R A B C D 22

  8. A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. Checkpoint 1d Now suppose both switches are closed. What is the voltage across the capacitor after a very long time? A. VC = 0 B. VC = V C. VC = 2V/3 A B C 26

  9. A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. Checkpoint 1d Now suppose both switches are closed. What is the voltage across the capacitor after a very long time? A. VC = 0 B. VC = V C. VC = 2V/3 A B C • After both switches have been closed for a long time • The current through the capacitor is zero • The current through R = current through 2R • Vcapacitor = V2R • V2R = 2/3 V 26

  10. I No current flows through the capacitor after a long time. This will always be the case if the sources of EMF don’t change with time. R C V VC 2R VC = (2/3)V Close both S1 and S2 andwait a long time… R C V 2R S1 S2 I = V/(3R) V2R = I(2R) = (2/3)V = VC 27

  11. DEMO – ACT 1 Both bulbs light V(bulb 1) = V(bulb 2) = V V(bulb 2) = 0 Bulb 2 S R R V Bulb 1 C • What will happen after I close the switch? • Both bulbs come on and stay on. • Both bulbs come on but then bulb 2 fades out. • Both bulbs come on but then bulb 1 fades out. • Both bulbs come on and then both fade out. No initial charge on capacitor No final current through capacitor 30

  12. DEMO – ACT 2 Capacitor discharges through both resistors Bulb 2 R S R V Bulb 1 C • Suppose the switch has been closed a long time. • Now what will happen after open the switch? • Both bulbs come on and stay on. • Both bulbs come on but then bulb 2 fades out. • Both bulbs come on but then bulb 1 fades out. • Both bulbs come on and then both fade out. Capacitor has charge (=CV) 32

  13. Calculation S R1 R2 R3 C V In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time ? • Circuit behavior described by Kirchhoff’s Rules: • KVR:SVdrops = 0 • KCR:SIin = Siout • S closed and C charges to some voltage with some time constant • Determine currents and voltages in circuit a long time after S closed 35

  14. Calculation S In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time ? R1 R2 R3 C V Immediately after S is closed: what is I2, the current through C what is VC, the voltage across C? (A) Only I2 = 0(B) Only VC = 0(C) Both I2 and VC = 0 (D) Neither I2 nor VC = 0 • Why? • We are told that C is initially uncharged (V = Q/C) • I2 cannot be zero because charge must flow in order to charge C 37

  15. Calculation (A) (B) (C) (D) (E) S R1 R2 R3 V VC = 0 I1 S In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time ? R1 R2 R3 C V • Immediately after S is closed, what is I1, the current through R1 ? • Why? • Draw circuit just after S closed (knowing VC = 0) • R1is in series with the parallel combination of R2and R3 39

  16. Calculation I R1 R3 VC IC = 0 V S In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time ? R1 R2 R3 C V After S has been closed “for a long time”, what is IC, the current through C ? (A) (B) (C) • Why? • After a long time in a static circuit, the current through any capacitor approaches 0 ! • This means we redraw circuit with open circuit in middle leg 41

  17. Calculation After S has been closed “for a long time”, what is VC, the voltage across C ? (A) (B) (C) (D) (E) I I R1 R3 VC V S In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time ? R1 R2 R3 C V • Why?? • VC = V3 = IR3 = (V/(R1+R3))R3 43

  18. Challenge R2 We get: C R3 In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. S R1 R2 R3 C V What is tc, the charging time constant? • Strategy • Write down KVR and KCR for the circuit when S is closed • 2 loop equations and 1 node equation • Use I2 = dQ2/dt to obtain one equation that looks like simple charging RC circuit ( (Q/”C”) + “R”(dQ/dt) – “V” = 0 ) • Make correspondence: “R” = ?, and “C” = ?, then t = “R” ”C” C

  19. How do exponentials work? “Fraction of initial charge that remains” “How many time constants worth of time that have elapsed” 45

  20. RC = 2 RC = 1 Time constant: t = RC The bigger t is, the longer it takes to getthe same change… 47

  21. The two circuits shown below contain identical capacitors that hold the same charge at t = 0. Circuit 2 has twice as much resistance as circuit 1. RC = 2 RC = 1 Checkpoint 2a • Which circuit has the largest time constant? • Circuit 1 • Circuit 2 • Same t = RequivC 49

  22. The two circuits shown below contain identical capacitors that hold the same charge at t = 0. Circuit 2 has twice as much resistance as circuit 1. Checkpoint 2b Which of the following statements best describes the charge remaining on each of the the two capacitors for any time after t = 0? A. Q1 < Q2 B. Q1 > Q2 C. Q1 = Q2 D. Q1 < Q2 at first, then Q1 > Q2 after long time E. Q1 > Q2 at first, then Q1 < Q2 after long time 50

  23. The two circuits shown below contain identical capacitors that hold the same charge at t = 0. Circuit 2 has twice as much resistance as circuit 1. Checkpoint 2b Which of the following statements best describes the charge remaining on each of the the two capacitors for any time after t = 0? A. Q1 < Q2 B. Q1 > Q2 C. Q1 = Q2 D. Q1 < Q2 at first, then Q1 > Q2 after long time E. Q1 > Q2 at first, then Q1 < Q2 after long time 50

  24. The two circuits shown below contain identical capacitors that hold the same charge at t = 0. Circuit 2 has twice as much resistance as circuit 1. RC = 2 RC = 1 Look at plot !!! Checkpoint 2b Checkpoint 2b Which of the following statements best describes the charge remaining on each of the the two capacitors for any time after t = 0? A. Q1 < Q2 B. Q1 > Q2 C. Q1 = Q2 D. Q1 < Q2 at first, then Q1 > Q2 after long time E. Q1 > Q2 at first, then Q1 < Q2 after long time Q = Q0e-t/RC

  25. “Dynamic” random access memory Charge capacitor – store a logical “1” Discharge capacitor – store a logical “0” Capacitor discharges through resistance between plates. Only holds Q for < 1 msec. Charge Q must be “refreshed” constantly, So memory is called dynamic.

  26. 1. Capacitor is an open circuit for dc (direct current). VC = Q/C and IC = dQ/dt. If ICis flowing then Q is changing, so VC is changing. But in a dc circuit, nothing changes with time, so we must have IC = 0. IC C R V R IC = 0 +Q VC = V C V -Q For t  Situation once things stop changing.

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