Your omments THIS IS SOOOO HAD. I get the concept and mathematical expression. But I do not get links among everything. ery confusing prelecture especially what happens when switches are closed/opened and what happens during long periods of time. My brain just fell on the ground. Please help me pick it back up. It's been a while since I have been this lost after watching a prelecture. I cannot visualize these concepts as well. I understood what was used in the questions, but are the differential equations that they used going to be on exams? They were derived very quickly and if they're very important I would like to go over them a little more. This lecture was not too bad. My only concern is for the challenging circuits I am sure will appear on the homework. I would like to do more problems like the those in class if that's possible. It is difficult relating all these relationships together. Also I'm having trouble determining when something is being charged and when it is being discharged. Electricity & Magnetism Lecture 11, Slide 1
Physics 212 Lecture 11 Today s oncept: ircuits Electricity & Magnetism Lecture 11, Slide 3
The 212 Differential Equations We describe the world (electrical circuits, problems in heat transfer, control systems, financial markets, etc.) using differential equations You only need to know the solutions of two basic differential equations dq 1 t / q 0 q qconste dt 2 dq 2 0 sin dt 2 const q q q t Physics 212 Lecture 11, Slide 5
apacitors in ircuits Solve by applying Kirchhoff s ules to circuit. Need to understand some key phrases. IMMEDIATELY After === harge on capacitor is same as immediately before After a LONG TIME === urrent through capacitor = 0 After xx seconds === Exponentially more difficult! Electricity & Magnetism Lecture 11, Slide 6
Kirchoff s oltage ule q battery I 0 Short Term (q q 0 0) battery I0 Long Term (I c 0) ircuit (harging) apacitor uncharged, Switch is moved to position a battery 0 I0 0 q battery 0 0 q battery I + - a battery Intermediate b q dq battery 0 dt t / q( t) q 1 e I( t) dq dt I 0 e t / + - Electricity & Magnetism Lecture 11, Slide 7 + -
heckpoint 1 A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. lose S1, 1 voltage across immediately after 2 voltage across a long time after Immediately after the switch S 1 is closed: Q is same as immediately before 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 I 0 Electricity & Magnetism Lecture 11, Slide 9
lose S 1 at t = 0 (leave S 2 open) 2 S1 S2 I I 0 Q initial / 0 At t 0 At t big Electricity & Magnetism Lecture 11, Slide 10
heckpoint 1 A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. lose S1, 1 voltage across immediately after 2 voltage across a long time after Immediately after the switch S 1 is closed: Q is same as immediately before 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 I 0 Electricity & Magnetism Lecture 11, Slide 11
ircuit (Discharging) apacitor has q 0 battery, Switch is moved to position b Kirchoff s oltage ule q I 0 Short Term (q q 0 ) I 0 battery I 0 battery Long Term (I c 0) q 0 0 q 0 a battery battery Intermediate q dq dt q( t) q e I( t) I 0 0 e 0 t / t / b I I Electricity & Magnetism Lecture 11, Slide 12
heckpoint 1c A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. I 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. I = 0 B. I = /3. I = /2 D. I = / I 2 Electricity & Magnetism Lecture 11, Slide 13
heckpoint 1 d A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. Now suppose both switches are closed. What is the voltage across the capacitor after a very long time? A. = 0 B. =. = 2/3 A) The capacitor would discharge completely as t approaches infinity B) The capacitor will become fully charged after a long time. ) urrent through capacitor is zero Electricity & Magnetism Lecture 11, Slide 15
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 in any static circuit!! Outer Loop I 2I - 0 I /(3) ight Loop + - 2I 0 =2I (2/3) Electricity & Magnetism Lecture 11, Slide 16
heckpoint 1 d A circuit is wired up as shown below. The capacitor is initially uncharged and switches S1 and S2 are initially open. Now suppose both switches are closed. What is the voltage across the capacitor after a very long time? A. = 0 B. =. = 2/3 a) The capacitor would discharge completely as t approaches infinity b) The capacitor will become fully charged after a long time. c) urrent through capacitor is zero Electricity & Magnetism Lecture 11, Slide 17
DEMO licker Question 1 Bulb 2 S Bulb 1 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. No initial charge on capacitor No final current through capacitor (bulb 1) (bulb 2) (bulb 2) 0 Both bulbs light Electricity & Magnetism Lecture 11, Slide 18
DEMO licker Question 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 Electricity & Magnetism Lecture 11, Slide 19
alculation S 1 2 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? onceptual Analysis: ircuit behavior described by Kirchhoff s ules: K: S drops 0 K: S I in S I out S closed and charges to some voltage with some time constant Strategic Analysis Determine currents and voltages in circuit a long time after S closed Electricity & Magnetism Lecture 11, Slide 20
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 Electricity & Magnetism Lecture 11, Slide 21
alculation I 1 S 1 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 1, the current through 1? 1 2 3 1 1 3 1 1 2 1 2 2 3 2 3 A B D E 3 1 3 2 3 Why? Draw circuit just after S closed (knowing 0) 1 is in series with the parallel combination of 2 and 3 S 1 2 0 3 Electricity & Magnetism Lecture 11, Slide 22
alculation S 1 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? After S has been closed for a long time, what is I 2, the current through 2? Why? 2 1 0 A B After a long time in a static circuit, the current through any capacitor approaches 0! This means we edraw circuit with open circuit in middle leg I 1 I 0 3 Electricity & Magnetism Lecture 11, Slide 23
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? After S has been closed for a long time, what is, the voltage across? 3 2 1 3 1 2 2 3 1 0 2 3 A B D E Why? 1 3 I 3 (/( 1 3 )) 3 3 I 2 I Electricity & Magnetism Lecture 11, Slide 24
heckpoint 2 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. Which circuit has the largest time constant? A) ircuit 1 B) ircuit 2 ) Same 1 0.9 0.8 0.7 0.6 0.5 0.4 equiv 0.3 0.2 0.1 0 = 1 = 2 0 1 2 3 4 5 6 7 8 9 10 Electricity & Magnetism Lecture 11, Slide 28
heckpoint 2 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. 1 0.9 0.8 0.7 0.6 0.5 Q Q 0 e -t/ Look at plot! 0.4 0.3 = 2 0.2 0.1 = 1 0 0 1 2 3 4 5 6 7 8 9 10 Electricity & Magnetism Lecture 11, Slide 30