Lecture 19-Lecture 19-11Potential Difference Across Inductor

0dt

dILIR

V I r

V

+

-

I

internal resistance

• Analogous to a battery

• An ideal inductor has r=0

• All dissipative effects are to be included in the internal resistance (i.e., those of the iron core if any)

0dt

dILIR

Lecture 19-Lecture 19-22 Ways to Change Magnetic Flux

• Changing the magnitude of the field within a conducting loop (or coil).

• Changing the area of the loop (or coil) that lies within the magnetic field.

• Changing the relative orientation of the field and the loop.

motor generator

cosB BA

http://www.wvic.com/how-gen-works.htm

Lecture 19-Lecture 19-33 Alternating Current (AC)

= Electric current that changes direction periodically

ac generator is a device which creates an ac emf/current.

ac motor =

ac generator run in reverse

A sinusoidally oscillating EMF is induced in a loop of wire that rotates in a uniform magnetic field.

cos cosB NBA NBA t

sinBdNBA t

dt

2

2 fT

where

http://www.wvic.com/how-gen-works.htm http://www.pbs.org/wgbh/amex/edison/sfeature/acdc.html

Lecture 19-Lecture 19-44 Resistive Load

Start by considering simple circuits with one element (R, C, or L) in addition to the driving emf. Pick a resistor R first.

vR(t) and I(t) in phase

Kirchhoff’s Loop Rule:

0 , sinpeakt I t R t t

sinR peak

peak peak

v t I t R t

V

sinpeakVI t t

R

Ipeak

+ --

I(t)

Lecture 19-Lecture 19-55

City lights viewed in a motion blurred exposure. The AC blinking causes the lines to be dotted rather than continuous (quote from Wikipedia)

Lecture 19-Lecture 19-66 Power Dissipated by Resistive Load

VR and I in phase

22

2 2

sin

sin

peak

peak

P I R I t R

I R t

Power:

Lecture 19-Lecture 19-77Average Power

2

2 2sinpeak

P I R

I R t

2 2 2sinav peakP I R I R t

2

sin 0

1sin

2t

t

but

21

2 peaa kvP I R

Lecture 19-Lecture 19-88 Root-Mean-Square Values

2 21

2 pea ak sv rmI R I RP

2 0.71

02

7rms pea peakkI I I I

Similarly,

2 1 1

2 2pear k p ss k rmm eaI R I R av rms rmsP I

2 2 2 21sin

2peak peakI I t I

1.412peak rms rmsI I I

Lecture 19-Lecture 19-99Non-scored Test Quiz

Which of the following statement is true?

rmspeak II 2 rmspeak VV 2

rmspeak II2

1

rmspeak II 2

rmspeak II2

1

rmspeak VV 2

rmspeak VV2

1

rmspeak VV2

1

A.

B.

C.

D.

Lecture 19-Lecture 19-1010Capacitive Load

I(t) leads v(t) by 90 (1/4 cycle)

Loop Rule:

( )( ) 0

sinpeak

q tt

Ct

( ) ( )( )

cospeak

dq t d tI t C

dt dtC t

( )( ) sinpeak

q tv t t

C

Power: ,

,

( ) ( ) ( ) cos sin

sin 22

peak C peak

C peak peak

p t I t v t I t V t

V It

0avP

+ --

Lecture 19-Lecture 19-1111Inductive Load

vL(t) leads I(t) by 90 (1/4 cycle)

Kirchhoff’s Loop Rule:

( )( ) 0

( ) sinpeak

dI tt L

dtt t

( )( ) sinL peak

dI tv t L t

dt

Power: ,

,

( ) ( ) ( ) cos sin

sin 22

L peak L peak

L peak peak

p t I t v t I t V t

V It

0avP

( ) cospeakI t tL

+ --

Lecture 19-Lecture 19-1212

--

Capacitive vs Inductive Load

I(t) leads v(t) by 90

1CX

C

capacitive reactance

+

--+

vL(t) leads I(t) by 90

LX Linductive reactance

,L peak p akL eV IX

,C peak p akC eV IX 0avP vL

Lecture 19-Lecture 19-1313(Ideal) LC Circuit

0cos( )peakQ Q t

• From Kirchhoff’s Loop Rule

0Q dI

LC dt

• From Energy Conservation22

21.

2 2 2peakQQ

E LI constC C

0dE

dt 0

Q dQ dILI

C dt dt 0

Q dIL

C dt

same

0

1

LC

Natural Frequency

harmonic oscillator with angular frequency

2

2

10

d QQ

dt LC

dQI

dt

)sin( 00 tQdt

dQI peak

Lecture 19-Lecture 19-1414LC Oscillations

221

, ,2 2E B

Q dQU U LI I

C dt

No Resistance = No dissipation

Lecture 19-Lecture 19-1515

Physics 241 –Quiz 16b – March 20, 2008

In most of Europe, the peak voltage of household outlets is 311 V. What is the rms voltage?

a) 110 V

b) 141 V

c) 156 V

d) 220 V

e) 311 V

Lecture 19-Lecture 19-1616

Physics 241 –Quiz 16c – March 20, 2008

In Japan, the rms voltage of household outlets is 100V. What is the peak voltage?

a) 200 V

b) 141 V

c) 100 V

d) 50 V

e) 71 V