Ch33 AC Circuits

8/12/2019 Ch33 AC Circuits

1/15

Alternating Current (AC)Circuits

AC Voltages and Phasors

Resistors, Inductors and Capacitors in AC

Circuits RLC Circuits

Power and Resonance


2/15

AC Sources and Phasors

Consider a sinusoidal voltage source: )sin()( max tVtV

This source can be represented graphically as a vector called a phasor:

t

time

T

Vmax

-Vmax

VmaxV(t)

b

c

b

c

d

e

d

a,e

a

Great web page:http://www.phys.unsw.edu.au/%7Ejw/AC.html


3/15

Resistors in AC Circuits

R

R

vtV

vv

sin

0

max

tItR

V

R

vi RR sinsin max

max

R

VI maxmax

Since both have the

same arguments inthe sine term, iRand

vRare in line, they

are in phase.

tRIvR sinmax


4/15

tIiR sinmax

tRIRitR

22

max

2sin)(

tRIRit R 22

max

2sin)(

maxmax

22

max

707.02

21

II

I

RIRI

rms

rmsav

maxmax 707.02

VV

Vrms

Root Mean Square (RMS) Currentand Voltage


5/15

Announcements

Cell phones on silent

Check mid-term grades.


6/15

Inductors in AC Circuits

dt

diLtV

vv L

sin

0

max

tdtL

Vdi sinmax

tL

VdiiL

cosmax

2sinmax

t

L

ViL

LX

V

L

VI maxmaxmax

LXL

tXIv LL sinmax

InductiveReactance

For a sinusoidal voltage,the current in the inductor

always lagsthe voltage

across it by 90.


7/15


Filter for woofer

Low frequencies

pass through

High frequencies

get blocked.VR

FrequencyWoofer


8/15

Capacitors in AC Circuits

tVvv C sinmax

tVCq sinmax

2sin

cos

max

max

tVCi

tVCdt

dq

i

C

C

CX

VVCI maxmaxmax

CXC

1

Capacitive

Reactance

tXIv CC sinmax

For a sinusoidal voltage,the current in the

capacitor always leads

the voltage across it by

90.


9/15


Filter for tweeter

High frequencies

pass through

Low frequencies

get blocked.VR

FrequencyTweeters


10/15

RLC Series Circuit

tVv sinmax

tIi sinmax

tVtRIv RR sinsinmax

tVtXIv LLL

cos2

sinmax

tVtXIv CCC

cos2

sinmax

CLR vvvv


11/15

Using Phasors in a RLC Circuit

22maxmax

2

maxmax

2

maxmax

22

max

CL

CL

CLR

XXRIV

XIXIRIV

VVVV

22max

max

CL XXR

VI

22 CL XXRZ Impedance

ZIV maxmax

R

XX CL1tan


12/15

R = 425 W

L = 1.25 H

C = 3.5 mF

= 377 s-1

Vmax= 150 V

W

758

5.3377

111 FsC

XCm

W 47125.1377 1 HsLXL

WWWW 513758471425 2222 CL XXRZ

AV

Z

VI 292.0

513

150maxmax

W

W

WW

34

425

758471tantan 11

R

XX CL

VARIVR 124425292.0max W

VAXIV LL 138471292.0max W

VAXIV CC 221758292.0max W

tVvC 377cos221

tVvL 377cos138

tVvR 377sin124

Example 33.5


13/15

Power in an AC Circuit

tVtIvi sinsin maxmax

sincossincossin

sinsincoscossin

maxmax

2

maxmax

maxmax

ttVItVI

tttVI

cos2

1maxmax VIav

cosrmsrmsav VI

RIVvR maxmax cos

22

max

max

maxmax RIIV

RIVI rmsrmsav

RIrmsav2

For a purely resistive load, =0

rmsrmsav VI

No power loss occurs in

an ideal capacitor orinductor.


14/15

Resonance in Series RLC Circuits

Z

VI rmsrms

22

CL

rmsrms

XXR

VI

A circuit is in resonance when its current is maximum.

Irms

=maxwhenXL-X

C=0

CL

XX CL

0

0

1

LC

10 Resonance Frequency

Tuner for radio!


15/15

www.barlowwadley.it

Inductor

Variable

Capacitors

LC

10

Ch33 AC Circuits

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