electricity & magnetism lecture 19 lecture 19 - lcr circuits.… · ! smartphysics will con5nue...

Today’sConcepts:

A)Oscilla5onFrequency

B)Energy

C)Damping

Electricity & MagnetismLecture 19

Electricity&Magne/smLecture19,Slide1

“Whydocapacitorsstartoffwithachargeofzerowhentheswitchisopened?shouldn'ttheystartoffwithcharge?“

Italldependsonhowthecircuitwasstarted.Youhavetodeterminetheini5alcondi5onsfromtheproblemstatement

WhatistheuseofLCandRLCcircuits?

“There are a lot of formulas in this section”“Please explain the meaning of cos(ωt + x)”

Differen/alEqua/onsDoDetermineMuchBehaviourinPhysics.Wewillshowcorrespondingequa/onsin

mechanicstoday

“Allofthisstuff,IwishwecouldgoslowerbutIknowwecant.”

TOOTRUE:Hanginthere,we’lldoourbesttoworkontheissues….

Your Comments


Weshouldinvitetheprelecturenarratorovertoourclassforapizzaparty.Imean,he'sprobablynotbusy,justavoiceactorlivinginhisMom'sbasement.

Prof. Gary Glading

Prac5calTestisonMonday,March7orWednesdayMarch9.! Wewillhaveaprac5sesessionsonFriday! CoversDCCircuitsandtheOscilloscope(LCorRCCircuit)! 50min! smartPhysicswillcon5nueMonandWedcoveringthesetopicstheore5cally! Prac5seexamishere:! Youmayalsoprac5seoncircuitsofyourown(eg.LCRcircuitsandresonance)

Some Practical Test Stuff


http://www.sfu.ca/phys/141/1121/PTestSample.pdf

http://www.sfu.ca/phys/141/1121/PTestSample.pdf

C

I

L Q

LC Circuit


+

− +

−

CircuitEqua/on:

where

“tank”

CL

k

x

m

F = -kx a

Samethingifweno/cethatand


CLI

+ +

−−

Time Dependence


Wikipedia Animation“LCCircuit”

https://en.wikipedia.org/wiki/LC_circuit

https://en.wikipedia.org/wiki/LC_circuit

https://upload.wikimedia.org/wikipedia/commons/c/cb/Tuned_circuit_animation_500ms_labels.gif



Whatisthepoten/aldifferenceacrosstheinductoratt = 0?A)VL = 0 B)VL = Qmax/C C)VL = Qmax/2C

Pendulum.

At/met = 0 thecapacitorisfullychargedwithQmaxandthecurrentthroughthecircuitis0. L C

ThevoltageacrossthecapacitorisQmax/CKirchhoff'sVoltageRuleimpliesthatmustalsobeequaltothevoltageacrosstheinductor

sinceVL = VC

CheckPoint 2


dI/dtiszerowhencurrentismaximum

CheckPoint 4


Whatisthepoten/aldifferenceacrosstheinductorwhenthecurrentismaximum?A)VL = 0 B)VL = Qmax/C C)VL = Qmax/2C


Howmuchenergyisstoredinthecapacitorwhenthecurrentisamaximum?A)U = Qmax

2/(2C) B)U = Qmax

2/(4C) C)U = 0 TotalEnergyisconstant!ULmax = ½ LImax

2

UCmax = Qmax2/2C

I = max when Q = 0

CheckPoint 6



Thecapacitorischargedsuchthatthetopplatehasacharge+Q0 andthebo]omplate−Q0. At/met = 0, theswitchisclosedandthecircuitoscillateswithfrequencyω = 500 radians/s.

WhatisthevalueofthecapacitorC?

A)C = 1 x 10-3 F B) C = 2 x 10-3 F C) C = 4 x 10-3 F

L C

L = 4 x 10-3 Hω = 500 rad/s+ +

−−

CheckPoint 8


Whichplotbestrepresentstheenergyintheinductorasafunc5onof5mestar5ngjusta`ertheswitchisclosed?

Currentischanging⇒ULisnotconstant

Ini/alcurrentiszero

L C

closedatt = 0+Q0

−Q0

CheckPoint 10

Energypropor/onaltoI2⇒Ccannotbenega/ve


Whentheenergystoredinthecapacitorreachesitsmaximumagainforthefirst/meaaert = 0,howmuchchargeisstoredonthetopplateofthecapacitor?

A) +Q0B)+Q0 /2C) 0D)−Q0/2E)−Q0

CheckPoint 12

L C

closedatt = 0+Q0

−Q0

CurrentgoestozerotwiceduringonecycleElectricity&Magne/smLecture19,Slide12

Qismaximumwhencurrentgoestozero

…butanswerlookskindofcomplicatedConceptmakessense…

JustlikeLCcircuitbuttheoscilla/onsgetsmallerbecauseofR

Add R: Damping


Physics Truth #1:

Eventhoughtheanswersome5meslookscomplicated…

thephysicsunderthehoodiss5llverysimple!


Theelementsofacircuitareverysimple:

Thisisallweneedtoknowtosolveforanything!


Startwithsomeini5alV, I, Q, VL Nowtakea5ny5mestepdt (1 ms)

Repeat…

A Different Approach


Theswitchinthecircuitshownhasbeenclosedforalong/me.Att = 0,theswitchisopened.

WhatisQMAX,themaximumchargeonthecapacitor?

ConceptualAnalysisOnceswitchisopened,wehaveanLCcircuitCurrentwilloscillatewithnaturalfrequencyω0

StrategicAnalysisDetermineini5alcurrentDetermineoscilla5onfrequencyω0

Findmaximumchargeoncapacitor

Calculation

C

R

LV


WhatisIL,thecurrentintheinductor,immediatelyaaertheswitchisopened?Takeposi/vedirec/onasshown.

A)IL < 0 B) IL = 0 C) IL > 0

beforeswitchisopened:allcurrentgoesthroughinductorindirec5onshown


Calculation

C

R

LV

IL

Currentthroughinductorimmediatelya`erswitchisopenedisthesameas

thecurrentthroughinductorimmediatelybeforeswitchisopened


Theenergystoredinthecapacitorimmediatelyaaertheswitchisopenediszero.

A)TRUEB)FALSE

VC = 0

BUT:VL = VC sincetheyareinparallel

dIL/dt ∼ 0 ⇒ VL = 0beforeswitchisopened:

VCcannotchangeabruptly

a`erswitchisopened:

IMPORTANT:NOTEDIFFERENTCONSTRAINTSAFTERSWITCHOPENEDCURRENTthroughINDUCTORcannotchangeabruptlyVOLTAGEacrossCAPACITORcannotchangeabruptly

Calculation

C

R

LV

ILTheswitchinthecircuitshownhasbeenclosedforalong/me.Att = 0,theswitchisopened.

IL (t = 0 +) > 0

VC = 0

VC = 0

UC = ½ CVC2 = 0 !


C

R

LV

IL

Whatisthedirec/onofthecurrentimmediatelyaaertheswitchisopened?

A)clockwiseB)counterclockwise

Beforeswitchisopened:CurrentmovesdownthroughL

A`erswitchisopened:Currentcon5nuestomovedownthroughL

IL (t = 0 +) > 0 VC (t = 0 +) = 0


Calculation




A)B)C)D)

C

R

LV

Calculation

VL = 0Beforeswitchisopened: VL = 0

IL

IL IL

Theswitchinthecircuitshownhasbeenclosedforalong/me.Att = 0,theswitchisopened. C

R

LV

Whatisthemagnitudeofthecurrentrightaaertheswitchisopened?



IL (t = 0 +) > 0 VC (t = 0 +) = 0

V = ILRElectricity&Magne/smLecture19,Slide21

A)B)C)D)

WhatisQmax,themaximumchargeonthecapacitorduringtheoscilla5ons?

IL (t = 0 +) = V/R VC (t = 0 +) = 0Hint:Energyisconserved

CalculationTheswitchinthecircuitshownhasbeenclosedforalong/me.Att = 0,theswitchisopened.

C

R

LV

IL


C

WhenQismax(andIis0)

LQmax

CL

Imax

WhenIismax(andQis0)

Follow-Up

IsitpossibleforthemaximumvoltageonthecapacitortobegreaterthanV ?

A)YESB)NO

Wecanrewritethiscondi5onintermsoftheresonantfrequency:

WewillseetheseformsagainwhenwestudyACcircuits!

C

R

LV

IL


Imax = V/R


VmaxcanbegreaterthanVIF:

OR

FlipItPhysics Problem

Atwhat5me,doesthecurrentthroughtheinductor I3reachavaluethatis63%ofitsmaximumvalue?

ApplyKirchhoff'srulesto(1)outerloop,(2)innerloopand(3)thejunc5on.

FlipItPhysics Problem

EliminateI1andI2and.Findtheequa5onforI3

electricity & magnetism lecture 19 lecture 19 - lcr circuits.… · ! smartphysics will con5nue...

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