Your Comments. This was a very confusing prelecture. Do you think you could go over thoroughly how the LC circuits work qualitatively?

Transcription

1 Your omments I am not feeling great about this mierm...some of this stuff is really confusing still and I don't know if I can shove everything into my brain in time, especially after spring break. an you go over which topics will be on the exam Wednesday? This was a very confusing prelecture. Do you think you could go over thoroughly how the circuits work qualitatively? I may have missed something simple, but in question 1 during the prelecture why does the charge on the capacitor have to be 0 at t=0? I feel like that bit of knowledge will help me with the test wednesday I remember you mentioning several weeks ago that there was one equation you were going to add to the 013 equation sheet... which formula was that? Thanks! Electricity & Magnetism ecture 19, Slide 1

2 Some Exam Stuff Exam Wed. night (March 7th) at 7:00 overs material in ectures 9 18 Bring your ID: ooms determined by discussion section (see link) onflict exam at 5:15 Don t forget: Worked examples in homeworks (the optional questions) Other old exams For most people, taking old exams is most beneficial Final Exam dates are now posted

3 The Big Ideas 9-18 Kirchoff s ules Sum of voltages around a loop is zero Sum of currents into a node is zero Kirchoff s rules with capacitors and inductors In and circuits: charge and current involve exponential functions with time constant: charging and discharging E.g. apacitors and inductors store energy Magnetic fields Q dq Q I Generated by electric currents (no magnetic charges) Magnetic forces only on charges in motion Easiest to calculate with Ampere s aw hanging magnetic fields can generate electric fields! FAADAY S AW F mag qvxb B d 0 I d d E d EMF B da mag enclosed Physics 1 ecture 19, Slide 3

4 Physics 1 ecture 19 Today s oncepts: A) Oscillation Frequency B) Energy ) Damping Electricity & Magnetism ecture 19, Slide 4

5 ircuit I di Q Q Q di ircuit Equation: 0 I dq d Q Q d Q Q where 1 Electricity & Magnetism ecture 19, Slide 5

6 heckpoint 1a At time t = 0 the capacitor is fully charged with Q max and the current through the circuit is 0. What is the potential difference across the inductor at t = 0? A) = 0 B) = Q max / ) = Q max / since The voltage across the capacitor is Q max / Kirchhoff's oltage ule implies that must also be equal to the voltage across the inductor Pendulum. Electricity & Magnetism ecture 19, Slide 6

7 ircuits analogous to mass on spring d Q Q 1 d x x k m k a m F = -kx x Same thing if we notice that k 1 and m Electricity & Magnetism ecture 19, Slide 7

8 Time Dependence I Electricity & Magnetism ecture 19, Slide 8

9 heckpoint 1b At time t = 0 the capacitor is fully charged with Q max and the current through the circuit is 0. What is the potential difference across the inductor at when the current is maximum? A) = 0 B) = Q max / ) = Q max / di/ is zero when current is maximum Electricity & Magnetism ecture 19, Slide 9

10 heckpoint 1c At time t = 0 the capacitor is fully charged with Q max and the current through the circuit is 0. How much energy is stored in the capacitor when the current is a maximum? A) U Q max /() B) U Q max /(4) ) U 0 Total Energy is constant! U max ½ I max U max Q max / I max when Q 0 Electricity & Magnetism ecture 19, Slide 10

11 heckpoint a The capacitor is charged such that the top plate has a charge Q 0 and the bottom plate Q 0. At time t 0, the switch is closed and the circuit oscillates with frequency 500 radians/s. = 4 x 10-3 H = 500 rad/s What is the value of the capacitor? A) = 1 x 10-3 F B) = x 10-3 F ) = 4 x 10-3 F (510 )(410 ) Electricity & Magnetism ecture 19, Slide 11

12 heckpoint b closed at t = 0 Q 0 Q 0 Which plot best represents the energy in the inductor as a function of time starting just after the switch is closed? U 1 I Energy proportional to I cannot be negative urrent is changing U is not constant Initial current is zero Electricity & Magnetism ecture 19, Slide 1

13 heckpoint c When the energy stored in the capacitor reaches its maximum again for the first time after t 0, how much charge is stored on the top plate of the capacitor? closed at t = 0 Q 0 Q 0 A) Q 0 B) Q 0 / ) 0 D) Q 0 / E) Q 0 Q is maximum when current goes to zero dq I urrent goes to zero twice during one cycle Electricity & Magnetism ecture 19, Slide 13

14 Add : Damping Just like circuit but energy but the oscillations get smaller because of oncept makes sense but answer looks kind of complicated Electricity & Magnetism ecture 19, Slide 14

15 Physics Truth #1: Even though the answer sometimes looks complicated Q( t) Q cos( t ) o the physics under the hood is still very simple! d Q Q Electricity & Magnetism ecture 19, Slide 15

16 The elements of a circuit are very simple: di Q dq I I This is all we need to know to solve for anything! Electricity & Magnetism ecture 19, Slide 16

17 The switch in the circuit shown has been closed for a long time. At t 0, the switch is opened. What is Q MAX, the maximum charge on the capacitor? alculation onceptual Analysis Once switch is opened, we have an circuit urrent will oscillate with natural frequency 0 Strategic Analysis Determine initial current Determine oscillation frequency 0 Find maximum charge on capacitor Electricity & Magnetism ecture 19, Slide 18

18 alculation The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. I What is I, the current in the inductor, immediately after the switch is opened? Take positive direction as shown. A) I < 0 B) I 0 ) I > 0 urrent through inductor immediately after switch is opened is the same as the current through inductor immediately before switch is opened before switch is opened: all current goes through inductor in direction shown Electricity & Magnetism ecture 19, Slide 19

19 alculation The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. I 0 I (t 0 ) > 0 The energy stored in the capacitor immediately after the switch is opened is zero. A) TUE B) FASE before switch is opened: di / ~ 0 0 BUT: since they are in parallel 0 after switch is opened: cannot change abruptly 0 U ½ 0! IMPOTANT: NOTE DIFFEENT ONSTAINTS AFTE SWITH OPENED UENT through INDUTO cannot change abruptly OTAGE across APAITO cannot change abruptly Electricity & Magnetism ecture 19, Slide 0

20 alculation The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. I I (t 0 ) > 0 (t 0 ) 0 What is the direction of the current immediately after the switch is opened? A) clockwise B) counterclockwise urrent through inductor immediately after switch is opened is the same as the current through inductor immediately before switch is opened Before switch is opened: urrent moves down through After switch is opened: urrent continues to move down through Electricity & Magnetism ecture 19, Slide 1

21 alculation The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. I (t 0 ) > 0 (t 0 ) 0 What is the magnitude of the current right after the switch is opened? A) I o B) I o ) I D) o I o urrent through inductor immediately after switch is opened is the same as the current through inductor immediately before switch is opened Before switch is opened: I I 0 0 I I Electricity & Magnetism ecture 19, Slide

22 alculation The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. Hint: Energy is conserved I (t 0 ) / (t 0 ) 0 I What is Q max, the maximum charge on the capacitor during the oscillations? A) Q B) Q max ) D) 1 max Q Q max max I max Q max 1 I 1 Q max When I is max (and Q is 0) 1 U I When Q is max (and I is 0) 1 Qmax U Q max I max Electricity & Magnetism ecture 19, Slide 3

23 Follow-Up The switch in the circuit shown has been closed for a long time. At t = 0, the switch is opened. I Is it possible for the maximum voltage on the capacitor to be greater than? A) YES B) NO I max / Q max Q max max max can be greater than IF: > We can rewrite this condition in terms of the resonant frequency: 1 O > 0 > 0 We will see these forms again when we study A circuits! Electricity & Magnetism ecture 19, Slide 4