PHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101...

3/20/2012 PHY 114 A Spring 2012 -- Lecture 14 1

PHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101

Plan for Lecture 14 (Chapter 32):

Inductance

1.Inductors as a circuit element

2.RL, LC, and RLC circuits

3.Energy stored in an inductor


Remember to send in your chapter reading questions…


Web assign question -- hint

1000 turns/m

dtdN B

cΦ

−=E


Web assign question -- hint

A ( ) ( )tRBRBB ωπθπ cos

2cos

2

22

==⋅=Φ ABθ = ωt


Electric generator:

θ = ωt

( )( )

( )tNBAdt

tBAdN

ωω

ω

sin

cos

=

−=E


( )( )

( )

( ) ( )tItR

NBAR

I

RtNBA

dttBAdN

ωωω

ωω

ω

sinsin

:bygiven is coil in thecurrent , is coilgenerator in the resistance theIf

sin

cos

max≡==

=

−=

E

E

Electric generator:

I t


JB

sB

0

0

:form alDifferenti

:form Integral

:law sAmpere'

µ

µ

=×∇

=⋅∫ inId

Summary:

( )

0

0

:form alDifferenti

:form Integral

:law sGauss'

ερ

ε

=⋅∇

=⋅∫

E

ArE inQd ( )0

0

=⋅∇

=⋅∫B

ArB d

( ) ( )

t

dAr dtddE

∂∂

−=×∇

⋅−=⋅ ∫∫BE

Bsr

:law sFaraday'


Faraday’s law for EMF induced in a current loop:

dtd BΦ

−=E: of Examples

dtd BΦ

dtdIN

dtdB

I

NIB

0

0

: with timechanging is If

:solenoid inside Field

µ

µ

=

=


“Mutual” inductance

=Nc

turns/m1000=

sNA

dtdIANN

dtdN s

cB

cc

0µ−=

Φ−=E


“Self” inductance

dtdIAN

dtdIANN

dtdN ss

sB

ss

200 µµ

−=−=Φ

−=E

L inductance

Amp/s 1Volt 1 Henry 1

:inductance of Units

=


Inductors in a circuit Example: LR circuit

dtdIL−=E

0

:closedswitch With

=−−dtdILRIEMFE


Example: LR circuit

0

:closedswitch With

=−−dtdILRIEMFE

( )

( )

−=

−=

−−

=−

−=−=

−− 01)(

ln

:equation aldifferenti Solve

0

ttLR

EMF

EMF

EMF

EMFEMF

eR

tI

ttLRI

R

dtLR

IR

dI

IRL

RILR

LdtdI

E

E

E

EE


Example: LR circuit

t

I

( )

( )( )

Volts/Amp/s)Volts/(Amp

/ 1

1)(

:closedswitch With

/0

0

=

=−=

−=

−−

−−

τ

ττ RLeR

eR

tI

ttEMF

ttLR

EMF

E

E


The LR circuit reminds us of:

A. Why physics class is so beautiful. B. Why physics class is so terrible. C. RC circuit. D. Money in the bank.


Energy storage in inductor:

dtdIL−=E

2

2

2

21

21

21

LIU

LIddU

dtLIdtddtI

dtdILdt

dtdQVVdQdU

=⇒

=⇒

====


Example: LR circuit continued

( ) ( )11

1)(

0

:placed wireandopen switch With

ttLR

EMFttLR

eR

eItI

dtLR

IdI

dtdILRI

−−−−==

−=

=−−

E

I

t


LC circuit This circuit has the following time dependence after the switch is closed: A. Charge decays with time B. Charge increases with time C. Charge remains constant

with time D. Charge increases and

decreases with time


LC circuit

01

0

0

:closedswitch With

2

2

2

2

=+

=−−

=−−

QLCdt

Qddt

QdLCQ

dtdIL

CQ

( )

LC

tQtQQtQ

1 where

cos)(:)0( assumingSolution

max

max

≡

===

ω

ω

s

LC1

VoltsCoulombs

Amp/sVolts

1

FaradHenry11

:unitsCheck

=⋅

=

⋅=≡ω


LC circuit For L=1 H, C=1 F; ω=1 rad/s

Q/Qmax

t

ω=2πf


The LC circuit is mathematically analogous to: A. Nothing seen previously seen in class B. An elastic bouncing ball C. A swinging pendulum D. A mass attached to a spring E. All above, except A

The LC circuit is useful:

A. Because of its mathematical analogies B. Physicists like simple formulae like cos(ωt) C. It could be useful in science experiments D. It could be useful for toys E. It could be useful for everyday appliances


LRC circuit:

01

0

2

2

=−++

=−−−

E

E

QCdt

dQRdt

QdL

RIdtdIL

CQ

( )2

2/

21'

)'cos(1)(:0)0( assumingSolution

−=

−=

==−

LR

LC

teCtQtQ

LRt

ω

ωE

Q/CE

t

PHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101...

Documents

Transcript of PHY 114 A General Physics II 11 AM-12:15 PM TR Olin 101...