Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

AC

circuits

•Id

ealiz

ed A

C c

ircuit

–am

plit

ude,

phase

–po

wer

•Im

pedance

–re

sis

tance

–re

acta

nce

•S

ingle

com

ponents

–re

sis

tors

–capacitors

–in

ducto

rs

•R

LC

circuit

–re

son

ance

•F

ilters

•T

ransfo

rmers

–po

wer

tran

sm

issio

n

–R

ectifie

rs, A

C-D

C c

onve

rsio

n

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Altern

ating v

oltage

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Idealiz

ed A

C c

ircuit

Eq

uiv

cir

cuit

pHtL

=iHtL v

HtL=

i 0 v

0 s

inHw

tL sinHw

t+fL

=i 0 v

0Asi

n2Hw

tL cosHf

L+si

nHw

tL cosHw

tL sinHfL

pêêê=

1 Dt Ÿ 0D

tpHtL

„t=

1 2 i

0 v

0 c

osHf

L

Z =

im

ped

ance

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Impedance

Zim

ped

ance

Rre

sist

ance

Cre

acta

nce

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Avera

ge P

ow

er

pêêê=

1 2 i

0 v

0 c

osHf

L=

1 2 i

02 z c

osHf

L=

1 2 i

02 R

=i R

MS

2 R

i RM

S=A Ÿ 0

Dt i2 „

tE1ê2=@1 2

i02D1

ê2=

1 è!!!! 2 i

0

Co

mp

are

:

P =

I2R

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Impedance o

f re

sis

tors

toy

v=

iR

i=

v 0 R s

inHw

tL

z=

R,f=

0

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Impedance o

f in

ducto

rsto

y

v=

L„

i

„t i=-

v 0 wL c

osHw

tL=v 0 w

L s

inIw

t-p 2M

z=w

L,f=-

p 2

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Impedance o

f capacitors

toy

v=

Q C=

1 C Ÿi

„t

i=

v0 w

Ccos Hw

tL=v

0 w

Csi

nIw

t+

p 2M

z=

1 wC

,f=

p 2

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

The r

esonant R

LC

circuit

toy I

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

LR

C:

impedance a

nd p

hase

f=

Arc

Tan C

L-C

C

R

z=@R

2+HC

L-C

CL2D1

ê2

=AR

2+Iw

L-

1 wCM2E1

ê2

=RA1

+IL R

wM2 Hw

2-w

02L2 E1

ê2

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

LR

C:

curr

ent

i 0=

v 0 z=

v 0 R

1

B1+L2

R2 w

2 Iw

2-w

02M2F1ê2

i 0=

v 0 R*

wR

Cw`

w0

1w=w

0

R wL

wp

w0

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

LR

C:

pow

er

P=

1 2 i

02 R

=1 2 v

02 z2 R

z>

RA1

+4 IL R

M2 dw

2E1ê2

flDw=

2 dw=

R L

toy 2

Qª

w0

Dw=

è!!!!!

!!!!LêC R

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

RC

filt

ers

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

LC

& R

L f

ilters

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Tra

nsfo

rmers

DV

1=-

N1 „F „t

DV

2=-

N2 „F „t=

N2

N1 D

V1

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Pow

er

transm

issio

n

Phys

208,

Fall

2006

No

v.

15-1

7,

2006

AC

Cir

cuit

s

Rectifiers

and A

C/D

C c

onvers

ion

Eff

ect o

f filte

r is

to

sm

oo

th r

ectifie

d w

ave

form

.