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

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1 Physics 212 Lecture 11 ircuits hange in schedule Exam 2 will be on Thursday, July 12 from 8 9:30 AM. Physics 212 Lecture 11, Slide 1

2 ircuit harging apacitor uncharged, switch is moved to position a Kirchoff s oltage ule a q - battery + +I = 0 Initially (q = q 0 = 0) 0 I 0 battery 0 battery b I I = 0 battery Long Term (I c =0) 11 q battery q battery 0 0 In general: q dq battery 0 dt q t q e t / ( ) (1 ) I() t I e 0 t / Physics 212 Lecture 11, Slide 2

3 A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. heckpoint 1a & heckpoint 1b lose S1, 1 = voltage across immediately after 2 = voltage across a long time after Immediately after the switch S 1 is closed: A) 1 = 2 = B) 1 = 0 2 = ) 1 = 0 2 = 0 D) 1 = 2 = 0 After the switch S 1 has been closed for a long time Q = 0 = Q/ 1 = 0 I = 0 = 0 2 = 13 Physics 212 Lecture 11, Slide 3

4 2 lose S 1 at t=0 (leave S 2 open) S1 S2 I I=0 = Q/ = 0 = 15 At t = 0 For t Physics 212 Lecture 11, Slide 4

5 ircuit (Discharging) apacitor has q 0 =, switch is moved to position b Kirchoff s oltage ule a q I 0 Initially (q=q 0 ) q0 I 0 0 q0 I0 Long Term (I c =0) 19 q 0 0 q 0 I() t battery In general: q dq 0 dt q() t dq dt q e 0 t / q0 e t / b -I + - Physics 212 Lecture 11, Slide 5 I

6 A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. heckpoint 1c I + - After being closed a long time, switch 1 is opened and switch 2 is closed. What is the A current through the right resistor immediately after switch 2 is closed? B A. I = 0 B. I = /3. I = /2 D. I = / D 22 Physics 212 Lecture 11, Slide 6

7 A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. heckpoint 1c I + - After being closed a long time, switch 1 is opened and switch 2 is closed. What is the A current through the right resistor immediately after switch 2 is closed? B A. I = 0 B. I = /3. I = /2 D. I = / D I 2 22 Physics 212 Lecture 11, Slide 7

8 A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. heckpoint 1d Now suppose both switches are closed. What is the voltage across the capacitor after a A very long time? B A. = 0 B. =. = 2/3 26 Physics 212 Lecture 11, Slide 8

9 A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. heckpoint 1d Now suppose both switches are closed. What is the voltage across the capacitor after a A very long time? B A. = 0 B. =. = 2/3 After both switches have been closed for a long time The current through the capacitor is zero The current through = current through 2 26 capacitor = 2 2 = 2/3 Physics 212 Lecture 11, Slide 9

10 2 lose both S1 and S2 and wait a long time S1 S2 I 2 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. I = /(3) 2 = I(2) = (2/3) = = (2/3) 27 Physics 212 Lecture 11, Slide 10

11 DEMO AT 1 S Bulb 2 Bulb 1 No initial charge on capacitor What will happen after I close the switch? A) Both bulbs come on and stay on. B) Both bulbs come on but then bulb 2 fades out. ) Both bulbs come on but then bulb 1 fades out. D) Both bulbs come on and then both fade out. (bulb 1) = (bulb 2) = Both bulbs light 30 No final current through capacitor (bulb 2) = 0 Physics 212 Lecture 11, Slide 11

12 DEMO AT 2 Bulb 2 S Bulb 1 Suppose the switch has been closed a long time. Now what will happen after open the switch? A) Both bulbs come on and stay on. B) Both bulbs come on but then bulb 2 fades out. ) Both bulbs come on but then bulb 1 fades out. D) Both bulbs come on and then both fade out. apacitor has charge (=) apacitor discharges through both resistors 32 Physics 212 Lecture 11, Slide 12

13 alculation S In this circuit, assume,, and i are known. initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time? ircuit behavior described by Kirchhoff s ules: K: S drops = 0 K: SI in = Si out S closed and charges to some voltage with some time constant Determine currents and voltages in circuit a long time after S closed 35 Physics 212 Lecture 11, Slide 13

14 alculation 1 S 2 3 In this circuit, assume,, and i are known. initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time? Immediately after S is closed: what is I 2, the current through what is, the voltage across? (A) Only I 2 = 0 (B) Only = 0 () Both I 2 and = 0 (D) Neither I 2 nor = 0 Why? We are told that is initially uncharged ( = Q/) I 2 cannot be zero because charge must flow in order to charge 37 Physics 212 Lecture 11, Slide 14

15 I 1 S 1 2 alculation In this circuit, assume,, and i are known. initially uncharged and then switch S is closed. 3 What is the voltage across the capacitor after a long time? Immediately after S is closed, what is I 1, the current through 1? (A) (B) () (D) (E) Why? Draw circuit just after S closed (knowing = 0) 1 is in series with the parallel combination of 2 and 3 S 1 2 = Physics 212 Lecture 11, Slide 15

16 S 1 2 alculation 3 In this circuit, assume,, and i are known. initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time? After S has been closed for a long time, what is I, the current through? 0 1 (A) (B) () 2 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 I 1 I = 0 3 Physics 212 Lecture 11, Slide 16

17 S 1 2 alculation 3 In this circuit, assume,, and i are known. initially uncharged and then switch S is closed. What is the voltage across the capacitor after a long time? After S has been closed for a long time, what is, the voltage across? (A) (B) () (D) (E) I I Why?? = 3 = I 3 = (/( )) Physics 212 Lecture 11, Slide 17

18 S 1 2 hallenge In this circuit, assume,, and i are known. initially uncharged and then switch S is closed. 3 What is t c, the charging time constant? Strategy Write down K and K for the circuit when S is closed 2 loop equations and 1 node equation Use I 2 = dq 2 /dt to obtain one equation that looks like simple charging circuit ( (Q/ ) + (dq/dt) = 0 ) Make correspondence: =?, and =?, then t = We get: t c Physics 212 Lecture 11, Slide 18

19 How do exponentials work? Qt Q Q t Q e t 0.6 Fraction of initial charge that remains How many time constants worth of time that have elapsed t Physics 212 Lecture 11, Slide 19

20 Qt Q Q t Q e t = 2 Time constant: t = 0.1 The bigger t is, the longer it takes to get the same change 0 = t 47 Physics 212 Lecture 11, Slide 20

21 The two circuits shown below contain identical capacitors that hold the same charge at t = 0. ircuit 2 has twice as much resistance as circuit 1. heckpoint 2a Which circuit has the largest time constant? A) ircuit 1 B) ircuit 2 ) Same t = equiv = 2 = Physics 212 Lecture 11, Slide 21

22 The two circuits shown below contain identical capacitors that hold the same charge at t = 0. ircuit 2 has twice as much resistance as circuit 1. heckpoint 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. Q 1 < Q 2 B. Q 1 > Q 2. Q 1 = Q 2 D. Q 1 < Q 2 at first, then Q 1 > Q 2 after long time E. Q 1 > Q 2 at first, then Q 1 < Q 2 after long time 50 Physics 212 Lecture 11, Slide 22

23 The two circuits shown below contain identical capacitors that hold the same charge at t = 0. ircuit 2 has twice as much resistance as circuit 1. heckpoint 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. Q 1 < Q 2 B. Q 1 > Q 2. Q 1 = Q 2 D. Q 1 < Q 2 at first, then Q 1 > Q 2 after long time E. Q 1 > Q 2 at first, then Q 1 < Q 2 after long time 50 Physics 212 Lecture 11, Slide 23

24 The two circuits shown below contain identical capacitors that hold the same charge at t = 0. ircuit 2 has twice as much resistance as circuit 1. heckpoint heckpoint 2b 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. Q 1 < Q 2 B. Q 1 > Q 2. Q 1 = Q 2 1 D. Q 1 < Q 2 at first, then Q 1 > Q 2 after long time E. Q 1 > Q 2 at first, then Q 1 < Q 2 after long time Q = Q 0 e -t/ Look at plot!!! = 2 = 1 Physics 212 Lecture 11, Slide

25 Dynamic random access memory harge capacitor store a logical 1 Discharge capacitor store a logical 0 apacitor discharges through resistance between plates. Only holds Q for < 1 msec. harge Q must be refreshed constantly, So memory is called dynamic. Physics 212 Lecture 8, Slide 25

26 1. apacitor is an open circuit for dc (direct current). = Q/ and I = dq/dt. If I is flowing then Q is changing, so is changing. But in a dc circuit, nothing changes with time, so we must have I = 0. I +Q -Q I = 0 = For t Situation once things stop changing. Physics 212 Lecture 11, Slide 26

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