Lect11 - Physics 212 Lecture 11 Today's Concept: RC...

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Unformatted text preview: Physics 212 Lecture 11 Today's Concept: RC Circuits (Circuits with resistors & capacitors & batteries) 40 30 20 10 0 Confused Avg = 3.0 Confident Physics 212 Lecture 11, Slide 1 Physics Announcement • Need new “rules of engagement” in class. • Last time it was way too noisy—so much so that I was totally distracted and so were many of you judging from the complaints I got. • If you wish to talk when we are not doing clicker questions, please step out in the hall to do so. • When I am talking, for me and for the courtesy of those around you, please remain quiet. • Q17 in preflight (about “exam prep tool”) was a mistake. Physics 212 Lecture 11, Slide 2 Physics Key Concepts: 1) Understanding the behavior of capacitors in circuits with resistors 2) Understanding the RC time constant Today’s Plan: 1) Examples with switches closing and opening - What changes? - What is constant? 2) Example problem 3) Exponentials Physics 212 Lecture 11, Slide 3 Physics 07 • Capacitor uncharged, Switch is moved to position “a” a a • Kirchoff’s Voltage Rule C C RC Circuit (Charging) −Vbattery + q + IR = 0 C b b R R • Short Term (q = q0 = 0) −Vbattery + 0 + I 0 R = 0 Vbattery I0 = R • Long Term (Ic =0) q∞ −Vbattery + + 0 ⋅ R = 0 C q∞ = CVbattery Intermediate q dq −Vbattery + + R = 0 C dt q(t ) = q∞ (1 − e −t / RC ) I (t ) = I 0e −t / RC Physics 212 Lecture 11, Slide 4 Physics 11 Preflight 2 70 60 • Immediately after the switch S1 is closed • The charge on the capacitor is zero • The voltage across the capacitor is zero • Vcapacitor = Q/C = 0 50 40 30 20 10 0 13 Physics 212 Lecture 11, Slide 5 Physics Preflight 4 70 60 time • The current through the capacitor is zero • The voltage across the capacitor is the battery voltage • Vcapacitor = V 15 • After the switch S1 has been closed for a long 50 40 30 20 10 0 Physics 212 Lecture 11, Slide 6 Physics R V C 2R Close S1 at t=0 (leave S2 open) S1 S2 R At t = 0 R At t = big I V C VC = Q/C =0 V I=0 C VC = V 15 Physics 212 Lecture 11, Slide 7 Physics RC Circuit (Discharging) • Capacitor has q0 = CV, Switch is moved to position “b” aa • Kirchoff’s Voltage Rule C C q + + IR = 0 C • Short Term (q=q0) b b R R Vbattery + IR = 0 −Vbattery I0 = R • Long Term (Ic =0) Intermediate V q∞ + 0⋅ R = 0 C q∞ = 0 19 q dq + + R=0 C dt q(t ) = q0e −t / RC I (t ) = I 0e −t / RC Physics 212 Lecture 11, Slide 8 Physics Preflight 6 BB A B C D 50 I V C 2R 40 V 30 20 10 0 22 Physics 212 Lecture 11, Slide 9 Physics R V C 2R Open S1 at t=big and close S2 S1 S2 I V C 2R I = V/2R V 23 Physics 212 Lecture 11, Slide 10 Physics Preflight 8 BB A B C time • The current through the capacitor is zero • The current through R = current through 2R • Vcapacitor = V2R • V2R = 2/3 V 26 • After both switches have been closed for a long 40 30 20 10 0 Physics 212 Lecture 11, Slide 11 Physics R V C 2R Close both S1 and S2 and wait a long time… S1 I R V C S2 No current flows through the capacitor after a long time. This will always be This VC 2R the case in any static the circuit!! circuit!! VC = 2V/3 27 Physics 212 Lecture 11, Slide 12 Physics DEMO – ACT 1 Bulb 2 S V Bulb 1 R R C BB What will happen after I close the switch? A) B) C) D) 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. V(bulb 1) = V(bulb 2) = V V(bulb 2) = 0 Both bulbs light Physics 212 Lecture 11, Slide 13 Physics No initial charge on capacitor 30 No final current through capacitor through DEMO – ACT 2 Bulb 2 S V Bulb 1 R R C BB Suppose the switch has been closed a long time. Now what will happen after I open the switch? A) B) C) D) 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 discharges through both resistors Physics 212 Lecture 11, Slide 14 Physics Capacitor has charge (=CV) 32 Calculation S R1 V R2 C R3 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 ? • Conceptual Analysis: – – – Circuit behavior described by Kirchhoff’s Rules: • KVR: ΣVdrops = 0 • KCR: ΣIin = ΣIout S closed and C charges to some voltage with some time constant Determine currents and voltages in circuit a long time after S closed • Strategic Analysis 35 Physics 212 Lecture 11, Slide 15 Physics Calculation R1 V S R2 C R3 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 ? Immediately after S is closed: what is I2, the current through C what is VC, the voltage across C? (A) Only I2 = 0 BB (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 Physics 212 Lecture 11, Slide 16 Physics I1 R1 V Calculation S R2 C R3 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 ? • Immediately after S is closed, what is I1, the current through R1 ? V R1 V R1 + R3 V R1 + R2 + R3 V ⎛1 1⎞ R1 + ⎜ + ⎟ ⎝ R2 R3 ⎠ −1 V R1 + R2 + R3 R1 R2 + R2 R3 + R1 R3 BB (A) (B) (C) (D) S R2 VC = 0 (E) • Why?? – Draw circuit just after S closed (knowing VC = 0) R1 is in series with the parallel combination of R2 and R3 R1 V R3 – 39 Physics 212 Lecture 11, Slide 17 Physics Calculation R1 V S R2 C R3 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 ? After S has been closed “for a long time”, what is IC, the current through C ? V R1 (A) V R2 (B) 0 (C) I BB • 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 R1 V IC = 0 VC R3 41 Physics 212 Lecture 11, Slide 18 Physics Calculation R1 V S R2 C R3 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 ? After S has been closed “for a long time”, what is VC, the voltage across C ? V R3 R1 + R3 R2 V R1 + R2 V V R2 RR R1 + 2 3 R2 + R3 BB 0 (A) (B) (C) (D) (E) I R3 I • Why?? VC = V3 = IR3 = (V/(R1+R3))R3 R1 V VC 43 Physics 212 Lecture 11, Slide 19 Physics Challenge R1 V S R2 C R3 In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. What is τc, 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 τ = “R”∏ ”C” I got: τ c = ⎜ R2 + ⎝ ⎛ R1 R3 ⎞ ⎟C ( R1 + R3 ) ⎠ Physics 212 Lecture 11, Slide 20 Physics How do exponentials work? 1 Q ( t ) = Q0e − t RC Q (t ) Q0 0.9 0.8 0.7 0.6 “Fraction of initial 0.5 charge that remains” 0.4 0.3 0.2 0.1 0 0 1 2 3 4 5 6 7 8 9 10 “How many time constants worth of time that have elapsed” 45 t RC Physics 212 Lecture 11, Slide 21 Physics Q (t ) Q0 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 Q ( t ) = Q0e − t RC RC = 2 0.2 0.1 Time constant: τ = RC RC RC = 1 0 0 1 2 3 4 5 6 7 8 9 10 The bigger τ is, the longer it takes to drain the charge… 47 t Physics 212 Lecture 11, Slide 22 Physics Preflight 10 Which circuit has the largest time constant? A) Circuit 1 B) C) Circuit 2 Same 80 60 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 τ = Requiv/C 49 40 20 0 0.2 0.1 0 0 RC = 2 RC = 1 1 2 3 4 5 6 7 8 9 10 Physics 212 Lecture 11, Slide 23 Physics Preflight 12 BB 40 30 20 10 0 50 Physics 212 Lecture 11, Slide 24 Physics Preflight 12 1 0.9 0.8 0.7 0.6 0.5 Q= Q0e-t/RC 0.4 0.3 0.2 0.1 0 0 Look at plot !!! RC = 2 RC = 1 1 Physics 212 Lecture 711, Slide 25 Physics 4 5 6 2 3 8 9 10 ...
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This note was uploaded on 02/21/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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