{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online