# 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) Physics 212 Lecture 11, Slide 1 Physics Music Who is the Artist? BB A) B) C) D) E) Albert Collins Buddy Guy Coco Montoya John Mayall Tommy Castro One of my favorite blues guitar players He does a great live show He Started out as drummer for Albert Collins Started Also played in Bluesbreakers with John Mayall Physics 212 Lecture 11, Slide 2 Physics Your Comments “im extremely confused on the whole short term vs long term change in capacitors” We will try to make this clear today “difference between equations for charging and discharging. difference How much are we expected to know about all these equations.” How All equations are just applications of Kirchhoff’s Rules to circuits You need to know the solution to one differential equation (exponential) “The time constant and exponential decay” We will work on this towards the end of the lecture 40 “have no problems with your material; however, I feel have the rising noise level during lecture to be irritating” the Me Too ! Me Please hold it down except during clicker questions Please 30 20 10 “It doesnt matter what I say here, nobody listens to it..” No Comment 05 0 Confused Confident Physics 212 Lecture 11, Slide 3 Physics Key Concepts: 1) Understanding the behavior of capacitors Understanding in circuits with resistors in 2) Understanding the RC time constant Today’s Plan: 1) Examples with switches Examples closing and opening closing - What changes? - What is constant? 2) Example problem 3) Exponentials 07 Physics 212 Lecture 11, Slide 4 Physics RC Circuit (Charging) • Capacitor uncharged, Switch is moved to position “a” a a • Kirchoff’s Voltage Rule C C −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) 11 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 5 Physics Preflight 2 & Preflight 4 BB A) V1 = V B) V1 = 0 C) V1 = 0 D) V1 = V Close S1, Close V1 = voltage across C immediately after V2 = voltage across C a long time after Immediately after the Immediately switch S1 is closed: switch Q=0 13 V = Q/C V1 = 0 V2 = V V2 = V V2 = 0 V2 = 0 After the switch S1 has has been closed for a long time been I=0 VR = 0 V2 = V Physics 212 Lecture 11, Slide 6 Physics Close S1 at t=0 (leave S2 open) R C V S1 2R S2 R R I=0 I V C V C VC = Q/C Q/C =0 15 VC = V At t = 0 At t = big 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) I b b R R Vbattery + IR = 0 −Vbattery I0 = R • Long Term (Ic =0) q∞ + 0⋅ R = 0 C q∞ = 0 19 Intermediate q dq + + R=0 C dt q(t ) = q0e −t / RC V -I I (t ) = I 0e −t / RC Physics 212 Lecture 11, Slide 8 Physics IR Preflight 6 BB + - A B C D 50 40 I V C V 2R 30 20 10 0 22 Physics 212 Lecture 11, Slide 9 Physics Open S1 at t=big and close S2 R C V S1 2R S2 V I V C 2R I = V/2R 23 Physics 212 Lecture 11, Slide 10 Physics Preflight 8 BB A B C 40 • After both switches have been closed for a long After time time • The current through the capacitor is zero • The current through R = current through 2R • Vcapacitor = V2R • V2R = 2/3 V 26 30 20 10 0 Physics 212 Lecture 11, Slide 11 Physics Close both S1 and S2 and wait a long time… R C V S1 2R S2 I No current flows No through the capacitor after a long time. This R C V IR +VC = V I = V/(3R) 27 VC 2R will always be the case in any static circuit!! in VC = V – R(V/(3R)) VC = (2/3)V Physics 212 Lecture 11, Slide 12 Physics DEMO – ACT 1 DEMO Bulb 2 BB S V Bulb 1 R R C 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. No initial charge No on capacitor on 30 No final current No through capacitor through V(bulb 1) = V(bulb 2) = V V(bulb 2) = 0 Both bulbs light Physics 212 Lecture 11, Slide 13 Physics DEMO – ACT 2 DEMO Bulb 2 BB R S V Bulb 1 R C Suppose the switch has been closed a long time. Now what will happen after 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 has charge (=CV) 32 Capacitor discharges through both resistors Physics 212 Lecture 11, Slide 14 Physics Calculation S R1 R2 C V 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 ? long • 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 • Strategic Analysis – 35 Determine currents and voltages in circuit a long time after S closed Physics 212 Lecture 11, Slide 15 Physics Calculation S R1 R2 C V 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 ? long Immediately after S is closed: what is I2, the current through C what is VC, the voltage across C? (A) Only I2 = 0 (A) BB (B) Only VC = 0 (C) Both I2 and VC = 0 (D) Neither I2 nor VC = 0 (B) (C) • Why?? – – 37 We are told that C is initially uncharged (V = Q/C) I2 cannot be zero because charge must flow in order to charge C Physics 212 Lecture 11, Slide 16 Physics Calculation I1 S R1 R2 C V In this circuit, assume V, C, and Ri are known. C initially uncharged and then switch S is closed. R3 What is the voltage across the capacitor after a long time ? long • Immediately after S is closed, what is I1, the current through R1 ? V R1 V R1 + R3 V R1 + R2 + R3 (A) (A) (B) V RR R1 + 2 3 R2 + R3 (D) (D) (C) • Why?? – – 39 BB R1 + R2 + R3 V R1 R2 + R2 R3 + R1 R3 (E) S Draw circuit just after S closed (knowing VC = 0) R1 is in series with the parallel combination of R2 and R3 R1 V R2 R3 VC = 0 Physics 212 Lecture 11, Slide 17 Physics Calculation S R1 R2 C V 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 ? long After S has been closed “for a long time”, what is IC, the current through C ? V R1 V R2 0 (A) (B) (C) BB I • Why?? – – 41 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 IC = 0 VC R3 V Physics 212 Lecture 11, Slide 18 Physics Calculation S R1 R2 C V 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 ? long After S has been closed “for a long time”, what is VC, the voltage across C ? R3 V R1 + R3 (A) (A) R2 V R1 + R2 (B) V (C) • Why?? – V VC = V3 = IR3 = (V/(R1+R3))R3 R2 RR R1 + 2 3 R2 + R3 (D) (D) I BB 0 (E) I R1 VC R3 V 43 Physics 212 Lecture 11, Slide 19 Physics Challenge 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 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: RR R2 + 1 3 C τc = R1 + R3 Physics 212 Lecture 11, Slide 20 Physics How do exponentials work? Q ( t ) = Q0e 1 Q (t ) Q0 − t RC 0.9 0.8 0.7 0.6 “Fraction of initial 0.5 Fraction charge that remains” 0.4 charge 0.3 0.2 0.1 0 0 1 2 3 “How many time constants worth How of time that have elapsed” of 45 4 5 6 7 8 9 10 t RC Physics 212 Lecture 11, Slide 21 Physics Q (t ) 0.9 Q0 0.8 1 Q ( t ) = Q0e − t RC 0.7 0.6 0.5 0.4 0.3 RC = 2 0.2 0.1 Time constant: τ = RC RC RC = 1 0 0 The bigger τ is, The the longer it takes to get the same change… 47 1 2 3 4 5 6 7 8 9 10 t Physics 212 Lecture 11, Slide 22 Physics Preflight 10 Which circuit has the largest time constant? 1 0.9 A) Circuit 1 0.8 0.7 B) Circuit 2 0.6 C) Same 80 60 0.5 0.4 0.3 τ = Requiv/C RC = 2 40 0.2 20 0.1 RC = 1 0 0 49 0 1 2 3 4 5 6 7 8 9 10 Physics 212 Lecture 11, Slide 23 Physics Preflight 12 BB 35 30 25 20 15 10 5 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 RC = 2 0.2 Look at plot !!! 0.1 RC = 1 0 0 1 Physics 212 Lecture 711, Slide 25 Physics 4 5 6 2 3 8 9 10 ...
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