22 Alternating Current

What is the phase?

Examples: RC & RL circuits

Phasors & Alternating-Current (AC)

Root-mean-square (rms)

2

)(

cos)(

02

0

ItII

tItI

rms

avg

Example : Average powerP = I2R

Resistance and Reactance  

)2cos()cos()(

)2cos()(

)(

coscos)()(

cos)(

00

0

00

0

tC

Itt

C

ItV

tLIt

tILtV

tVtRIRtItV

tItI

C

L

RR

RXC

XLX RCL

1

Reactance & Phase

Low-pass High-pass

Series R-L-C Circuit: Impedance  

reactance) called

Impedance

CL

CL

CL

CL

CLR

XXX

XRXXRZ

XXRI

IXIXIR

VVVV

(

)(

)(

)()(

)(

2222

22

22

22

VL

VR

VC

V

Series R-L-C Circuit: Phase

VL

VR

VC

V

R

CLR

X

R

XXIR

XXI

V

VV

CL

CL

R

CL

/1tan

)(

tan

1

Power in AC: Pure Resistor

power) peak of half (one

0000

2

1

22VI

VIVIP rmsrms

Power in AC: General Case

inductors) pure and capacitors purefor (Zero

factorpower :cos

cos2

1

22cos 00

00

VIVI

VIP rmsrms

Series Resonance: Frequency   

22

2222

1

)(

series C-L-R ain Impedance

CLR

XRXXRZ CL

When XL = XC , Z = Zmin = R, which occurs at

LCCL

110

00

i.e. (resonance frequency)

Resonance & Tuning 

Z

VI

Summary: Phasor & AC

Summary: Resistance & Reactance

RXC

XLX RCL

1

Summary: R-L-C Circuit (series)

LCC

L

CLRXXRZ CL

11

1)(

0

2222

resonance ,R

tan

-1

Summary: Power in AC

cos2

1cos 00VIVIP rmsrmsavg

HomeworkProblems: 3, 8, 10, 16, 21, and 22

P3-Resitance & Reactance

P 7&8 Voltage & Current in C & L

P 10-RLC in Series

P 16-Power in AC

P 21&22-Series Resonance

Schedule (MWF)

WednesdayMar 3

FridayMar 5

MondayMar 8

WednesdayMar 10

FridayMar 12

Review Test 2

Lab DemoRC-const

Test 2Ch19~21

Lab MidtermLabs done so far

LabInduction

Schedule (ThTr)

ThursdayMarch 4

TuesdayMarch 9

ThursdayMarch 11

Review T2Test 2

Lab DemoRC-const

Test 2Ch19~21

Lab MidtermLabs done so far

LabInduction