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‐ 2 -

אאWאא 1-1 IntroductionW

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אאאאאאFSinusoidalEאSine waveK

אאאאאאאאאאאK

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1 J2אאאMagnetic Effects of Electrical Current

1 J2 J1אאGeneration & Concentration of Magnetic Field

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‐ 3 -

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אאאF2EאאF1EאאF1 J3KE


‐ 4 -

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1 J3אאBasic Concepts of Electrical Generator

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אאאאאWאא،אאאאאאK


‐ 5 -

1 J3 J1אאGeneration of Sine Wave

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F1 J6Eאא

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F3E אCאאאאK

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אK אאאאאאאאאאאא،אאא

F1 J7KE


‐ 6 -

F1 J7Eאא

1 J3 J2אאאEvaluation of Sine Wave

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F1 J8Eאא

1 J3 J3אאאRepresentation of Sine Wave

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‐ 7 -

1 J3 J4אאMathematical Representation of Vectors

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‐ 8 -

F1 J3E )aa(A 22

21

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Alternating Current and Voltage as a Sine Wave 1 J4 J1אאא

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F1 J13Eאאאא

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1K אאאאK 2K ،אאאאW

F1 J14Eאאאא


‐ 9 -

1 J4 J2אאאאW WאאW

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F1 J15Eאאאאא

אאאא،אא

אאאFאאEHFאאF JEEKאאאK

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F1 J16Eאאאא

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אאאאKאאאאאאאK

אאKאאK


‐ 10 -

1 J4 J3אאFאESine wave Voltage Sources אאאW

1KאאאRotating Electrical machines אאAC Generator

2KאאאElectronic Oscillator Circuits אאאSignal Generators


‐ 11 -

אאWאאא

1 J5אאאFACEאW Alternating Current & Voltage Values of a Sine Wave

1 J5 J1אאאW אאא،א

W 1K אאInstantaneous Value

2K FאאEPeak Value

3K אאRoot Mean Square (RMS Value)

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1 J5 J2אאInstantaneous Value

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1 J5 J3FאאEPeak Value

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W Peak Value = Amplitude =Magnitude


‐ 12 -


‐ 13 -

F1 J1E אאאאW

F1 J18EאאF1 J1E

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1 J5 J4אאאPeak to Peak Value

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1 J5 J5אאאEffective value of sine wave

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א،אאאאאא،אאאא،

אאאאאאא


‐ 14 -

אאאאאאאאאאאKאR.M.S

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אאאאא PP IV ,אאא PPPP IV ,W

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אK

F1 J20Eאאאא


‐ 15 -

אאאאאאא،W

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avgrmsPPP VVVV ,,,אאW

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VVPP 10

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‐ 16 -

אאWאאאא

1 J6אאאאW Ohm's Law and Kirchhoff's Laws in AC Circuits

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אאאDCאאאאא،אאKאאאאאPhase Angleא

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‐ 17 -

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1 J6 J3אאאא Kirchhoff's Voltage & Current Laws in AC Circuits

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EאK?אאאא


‐ 18 -

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Kirchhoff's Voltage Law in AC Circuits אא،אאW

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‐ 19 -

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‐ 20 -

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Superimposed DC and AC voltage 1 J7 J1W

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‐ 21 -

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‐ 22 -

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אאאRW VVVVVV PDC 221012max

אאאRW VVVVVV pDC 21012min

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‐ 23 -

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F1 J34EאאאF1 J7E

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אא VVVV PDC 4min

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‐ 24 -

אאאWאא

1 J8אאNon Sinusoidal Wave Forms 1 J8 J1W א،אאKא

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1K FאERepetitive Pulse Wave Form

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F1 J36Eא

אאTא،אPeriodKא

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‐ 25 -

F1 J37Eאא

אK W

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‐ 26 -

4K אThe duty Cycle

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5K אאAverage Value

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F1 J8E AmplitudeT

TwVV baselineovg *

F1 J8EW אאW

F1 J41EאאF1 J8E


‐ 27 -

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F1 J43 JE


‐ 28 -

F1 J43 JE

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skV

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t

vslope

/2

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410

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‐ 29 -

1 J8 J5אSaw tooth Wave Form

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‐ 30 -

אSummary 1K אאאאK

2K אאאאאאEmאK

3K אאFאWE

אאא

אאא

4K ،אאאW

אאInstantaneous Value

FאאEPeak Value

אאRoot Mean Square (RMS Value)

אאAverage Value 5K W..........321 vvvvs 6K W LeavingEntering II

7K אאאאאK 8K אאאאא

א،אאFאאאאEאK

9K ،אW

FאERepetitive pulse wave form

אאSquare Wave

אאTriangular Wave Form

אSawtooth Wave Form


‐ 31 -

אא WאW

K אאאאא

K אאא

K אא

K אאאאK

WאW 1 .אאV12

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RMS

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3K אא3RRMS

F1 J48E

167

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אאJJ22

א

א

2

א 116 אא א א J2 אא

‐ 33 -

אא אא

אאWאאאאK

אאWאאאW

אאK

אאאWאאא90٪

אאאאW3

אאW J K J אאK

אאאWאאאאאאאאאK


‐ 34 -

2 J1Introduction

אאאאאKאאאTransformersא،

W 1K אאFאEMutual Inductance

2K אאThe Basic Transformer

3K א Step up – Transformer

4K א Step –down Transformer

2 J2אא Mutual Inductance ،אאאא

אInductor אאא،אאאKאא

אא،אאW

F2 J1Eאא

W

אאאאאאאאKאאאK

2 J3אאThe Basic Transformer

2 J3 J1Structure אאK

אW


‐ 35 -

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W אאאאאאאPrimary Windingא

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K W

אאThe Core אאאאאK

2 J3 J2אW

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F2 J3Eאאאא

2K Ferrite CoreאW

F2 J4Eא


‐ 36 -

3K Iron Core אW

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אאאאאאאHigh Frequency Applications ،אאIron Core אאאאPower Applications

אאאאאAudio Frequency ApplicationsK

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F2 J6 JEא

W אאא،VarnishK

12-4 אFאEאW 2 J4 J1אאTurns Ratio

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‐ 37 -

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Sec

N

NN

Pr

F2 J1EW אאW

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100Pr iN 400sec N

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100

400

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i

Sec

N

NN

אאW

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אאאא4אאK

2 J4 J2אאDirection of Winding

אאאאאאא،אW


‐ 38 -

אאW א،אא،אאאאאא

אPrimary and Secondary are in phase KאW

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אאW

F2 J10Eאאאא

W אאאאK

אאW ،אאאאא

אאW

F2 J11Eאא

אאאאאא0180Tא،W


‐ 39 -

F2 J12Eאאאאא

אאW

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2 J5אאאInductance Voltage and Current Relationship

2 J5 J1אאאאאא Primary and Secondary Voltage Relationship א،אאאאאאא

אאאאאאאאאFאאאEאאFאאEW

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N

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PRI

SEC

PRI

SEC

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SECSEC VNV

N

NV *

2 J5 J2אאאאאא Primary and Secondary Current Relationship

אFאאEאאאאאאFאאE،

אW


‐ 40 -

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N

I

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PRI

1

sec

sec

W

F2 J5E N

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secsec

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1K upstep אאK 2K downstep אאK

2 J6אאTransformer Types

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F2 J6E PRISEC NN 1N،F2 J2EW

F2 J7E PRISEC VV ،אאאאאF2 J5EPRISEC II ،

אאאאא


‐ 41 -

2 J6 J2Step–down Transformer אא،אאאFאאE

אאאFאאאKEא1KאאאאKאאאW

F2 J8E PRISEC NN 1NאאאאאPRISEC VV אא،

אאאPRISEC II K

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200

600*

, where N=3 VVN rmsPRI 360120*3*

AIN

NI rmsPRI

SEC

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600

200*

אאא،אאא

Step– up TransformerKאאאאאK


‐ 42 -

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F2 J16EאאאF2 J3E

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SEC

PRIrmsSEC 306*

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אאאStep– down TransformerKאאK

2 J7אאאTransformer Current Direction

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F2 J17 JEאאאאאאאא



‐ 43 -

2K אאFאאEא،W




‐ 44 -

אSummary 1K אאאאK

2K אאאאאאאאKאאאK

3K אאאWאאאPrimary WindingאK

4K אאWאאSecondary Winding אאK 5K אFNEאאאאsecNאאא

priNK

6K אאאאאאאאאאFאאאEאאFאאEW

NN

N

V

V

PRI

SEC

PRI

SEC

7K אאאאאPRIIאאsecIW

NN

N

I

I PRI

PRI

1

sec

sec

8K אאאאאW

K upstep אאK K downstep אאK


‐ 45 -

אא

1K אא،אאאW

F2 J19E

2K אW

F2 J20E

1K אאא avgVsec 2K אאFאE،אאאאאא

אא؟


‐ 46 -

3K אW

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1K אאאK

2. אאאKאאאאאאאאK

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3

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‐ 47 -

אא אאא

אאWאאאאאK

אאWאאאW

אאאK

אאאWאאא90٪

אאאאW9

אאW J K J אאK

אאWאאאאאאאאאאK


‐ 48 -

3 J1Introduction

א،אאאאאאאאאK،אא

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CapacitanceK

3 J2אאCXCapacitive Reactance אאCXאא،W

אא אא،א

א،אאאאW

F3 J1Eאאאא

אאFאא،Kא؟

F3 J2Eא


‐ 49 -

F3 J2Eא،F1EאאF2KE،t אאאאא12א VV K

V

QC CVQ א،א12 II Kאאאאא

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אאCXא)(OhmK

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א،אאW

F3 J3Eאאאא

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F3 J1E CF

X C ..2

1

F3 J1EW אאאW

F3 J4EאאאF3 J1E


‐ 50 -

אאCX،אאkHzf 1K אW

kCF

X C 8.3110*005.0*10*1*2

1

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163

3 J3אאאאOhm's Law in Capacitive AC Circuits ،אא

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VI

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אאאאW


‐ 51 -

F3 J6Eא

W א،אאאאאאRMSPeak

PeaktoPeak K

F3 J2EW אאאF3 J1E،א5אV،W

F3 J7EאאאF3 J2E

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kFC

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rmsrms 57.1

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‐ 52 -

3 J4אאאאW Current & Voltage Relationship in Capacitive Circuits

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אאאאאFאEאאאאאאKאאאW

F3 J9Eאא


‐ 53 -

W 1K אאאאK

2K אאZ،אI=0AV=0VK

3K minmax VI K 4K אאK

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אאאא،אאאאKא،אאאא

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אאKאאאאאאW

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rms

r X

VP

2

F3 J10E Crmsr XIP *2


‐ 54 -

W 1KאאtruePאאwattK 2KאאrPVolt – Ampere –ReactiveאאVAR

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3

2

3 J6אאאאאSeries & Parallel Capacitive AC Circuits

אאאאאא،אאאKאאאאאאא

،אW 3 J6 J1אאאSeries Capacitors

אאאאאW

F3 J11Eאאא


‐ 55 -

אאאW F3 J11E

N

T

CCC

C1

....11

1

21

،W F3 J12E

NT CCCC XXXX 2!

3 J6 J2אאאParallel Capacitors אאאאאW

F3 J12Eאאא

אאאW F3 J13E NT CCCC 21

،W F3 J14E

N

T

CCC

C

XXX

X1

....11

1

2!

3 J7אאאאאSeries RC Circuits 3 J7 J1אאאאאאCharacteristics of RC Circuits

אאאא،אאאאW

F3 J13Eאאאאא


‐ 56 -

אאאאאCIאאCVKאאא،אRIאRV،אאא

אאאאK ،אCICVאאo90،

אאRVאCVאאo90Kאאא،אאo90אW

F3 J14Eאאאאאאא

RVCVאאRC VV 3 J7 J2אImpedance Z

אא،אאאאאאאFאEאTR،אF

אאאאTCXאאא،

ZOhmK אאאאSeries R – C אW

F3 J15Eאאאא

אאPythagorasW

F3 J15E 222CXRZ

אRCאאW


‐ 57 -

F3 J16E 22CXRZ

3 J7 J3אאPhase Angle

אאאאאאאאKאאאאאאאאא

W


אאFtanEאאאא،אW

F3 J17 JE

R

C

R

C

V

V

V

V 1tantan

F3 J17 JE

R

X

R

X CC 1tantan

אא 1tan אאאאא tan

א

R

C

V

V1tanאאאR

C

V

VK

אPythagorasW F3 J18E 222

CRS VVV אאאW

F3 J19E 22CRS VVV

F3 J20E F3 J21E 22

RSC VVV

3 J7 J4אאאאOhm's Law

،אא،אW


‐ 58 -

F3 J17EאRCאא

אאאאRVאאW F3 J22E RIVR .

אאCVא،אCX،אאאאCVW

F3 J23E CC XIV . אאאאאVFאאE،

אZאRCאאאW F3 J24E ZIV .

אאאW F3 J25E

Z

VI

F3 J26E I

VZ

אאאא،W

F3 J18Eאאא

3 J7 J5אאאאRCFrequency Effect on

אאאאאא،א،אא،אKאאאא

אאאאאW 1K אאFאאאCX،

FCX C 2

1KW


‐ 59 -

אW

22

CXRZ

אאWZ

VI FאאKE

אRV אCV 222

CRS VVV K

2K אFXZ C IVV RC

F3 J4EW

אkHzfmAIFCkR rms 5.1,2.0,02.0,2.2 אאא،W

F3 J19EאאאF3 J4E

אאCX

k

ncnfX C 3.5

10*02.0*10*5.1*2

1

.2

133

K אZ

kXRZ C 73.522

K אRV VRIVR 44.010*2.2*10*2.0. 33

K אCV VXIV CrC rmsrms

06.110*3.5*10*2.0 33

K אSV

VVVV rmsCrmsRSrms15.106.144.0 222

)(2

)( a Or,

VZIV rmsSrms15.110*73.5*10*2.0* 33 b

K אא


‐ 60 -

o

R

C

V

V45.67tan 1

a

Or,

oC

R

X45.67tan 1

b

3 J8אאאאאParallel RC Circuits 3 J8 J1אאאאאאCharacteristics of RC Circuits

אא،אאאאאאאW

F3 J20Eאאאאא

W SRC VVV

RIRVא

CICVאאo90،CIRIאo90K

אאאאאאאאאRCאאאאRCאאאאK

F3 J21EאאאאאRCאא

אCIRIאאo90KRI،RVאTIאא،RIRVא،אא

אTIאאPhase AngleK


‐ 61 -

3 J8 J2אImpedance Z

א،אאאאא،אאאZOhmK،אא

אאאאאאW

F3 J22EאאRCאא

W C

CC X

VI

אאאאParallel R – C ،אאAdmittance triangleW

F3 J23EאאRCאא

W אadmittanceא،א،א

R

1،CX

1،Z

1،

אאK

אאאW F3 J27E

222

111

CXRZ

F3 J28E 22

22

2 *

1

C

C

XR

RX

Z

W

F3 J29E2222

222 **

C

C

C

C

XR

XRZ

XR

XRZ


‐ 62 -


אאאאאאאאאאW

F3 J24EאאאRCאא

אאFtanEאאא،אאW

F3 J30ER

C

I

Itan

Wאא 1tan אאאאא tan

א

R

C

I

I1tanאאאR

C

I

IK

3 J8 J4אאאאRCאאCurrents Relationships אF3 J24 JE،אאאא

אTIאRIאאאCIW F3 J31E 222

CRT III


א،،אאW

F3 J25EאRCאא


‐ 63 -

W F3 J32E ZIV *

אאאW F3 J33E

Z

VI

F3 J34E I

VZ

3 J8 J6אאRCאRCאW

Conversion From Parallel to Series Formא،אRCאאאRC

א،אאRCאאאRCאא،אאא،אאאRCאא

RCאאאאW

F3 J26EאאאאRCאא

W

אאאאאeqRceqXeqCW F3 J38E cos.ZReq F3 J39E

sin.Zxceq

F3 J40E sin.2

1

fZCeq

W

CX

R1tan


‐ 64 -

F3 J5EW אאאW

F3 J27EאאאF3 J5E

K אאCX

kCf

XC 6.1..2

1

K אZ

5.843.

22C

C

XR

XRZ

K אאאRI

mAR

VI rmsS

rmsR 10)()(

K אאאCI

mAX

VI

C

rmsSrmsC 25.6)(

)(

K אאTI

mAIIIa rmsCrmsRrmsT 8.112)(

2)()(

mAZ

VIb rmsS

Trms 8.115.843

10)(

K אא

01 32tan

CX

Ra

0

)(

)(1 32tan

rmsR

rmsC

I

Ib

K אאRCאאאאאא

3.71532cos*5.843cos. oeq ZR


‐ 65 -

3.45232sin*5.843sin. oCeq ZX

FXf

CCeq

eq

035.0*2

1


‐ 66 -

SummaryאאאאW

אRCאא אRCאא 22א

CRS VVV 22אCRT III

22אCXRZ א

22

.

C

C

XR

XRZ

אא

R

C

C

V

V

R

X

1

1

tan

tan

אא

R

C

C

I

I

X

R

1

1

tan

tan

3 J9אאFא JאEאאאSeries-Parallel RC Circuits

אאאאאK F3 J6EW

אאאאאאאאW

F3 J28EאאאF3 J6E

1אאK 2אא 3אאאSVאI

אW WאאW

318.2

1

11 Cf

XC

637.2

1

22 Cf

XC


‐ 67 -

WאאRCאאאאFRCאאEאW

אאW

465

*22

2

222

2CXR

CRZ

אאאW o

CX

R9.46tan

2

21

אאW 318cos2 ZReq אאאW 340sin2 ZX

eqC ،אאאאאאW

F3 J29Eאאא

אאאK

W אא،אאK

אאW kRRR eqT 32.11 אאW 658

1 CeqCC XXXT

אאW


‐ 68 -

F3 J30Eאאאא

W אא JאאRCאאK

אאTZW kXRZ

TCTT 47.122

K אא،TIW mA

k

V

Z

VI

T

Srmsrms 8.6

47.1

10

K אא

o

T

CT

R

X50.26tan 1

F3 J7EW

אאאW

F3 J31EאאאF3 J7E

Kא1R1C1Z אאmAI rms 8.6

11 * ZIV rmsrms 105022

11 !CXRZ VkmAV rms 13.705.1*8.61

Kא2Vא2ZW VmAZIV rmsrms

16.3465*8.6* 22 Kא1Rא1C

VRIV rmsRrms8.6* 1

VXIV CrmsCrms16.2*

1


‐ 69 -

Kאא2Rאא2C mA

R

VI R 64.4

680

16.3

2

22

mAX

VI

CC 9.4

340

16.3

2

22

3 J10אאאאPower in RC Circuits

3 J10 J1אPower Triangle א،RCאאRC،אא

אאאאאאאKאאRCאאאRCא،אאW

F3 J32EאRCאא

אאאאאאאאאאrmsIW

F3 J33Eאא

W

rmsICrmsR

VאאאאK rmsIC

rmsCVאאK rmsIC

rmsSVאאApparent PowerK

א،אW


‐ 70 -

F3 J34EאאRCאא

3 J10 J2אאPower Relationships and Measurement Units אאApparent PowerAmpereVott VAW

F3 J41E ZIZ

VIVP rms

SrmsrmsSrmsa ** 2

2

אאTrue PowerאWatt WW

F3 J42E cos.atrue PP אאReactive PoweractiveAmpereVolt Re VARW

F3 J43E sin.ar PP

3 J10 J3אאThe Significance of apparent Power

אאApparent PowerFE،אאאאאאאאKאאא

אאא،אאאK אאאFאאE

אאאא،KאאK

W אאאאאאאאאא

א،אאctorthePowerFaPF :


‐ 71 -

3 J10 J4אThe Power Factor (PF) אPower Factor،אאא،

אאPFאאאאאא،KאאאאאW

F3 J44E cosa

true

P

PPF

W F3 J45E cosPF

Wאאאא،אאאK אאאא،א،אא

אאאאאKאאאאאאW

Wא א،אא،אאo0K

W 0)0sin( o،1)0cos( o

W

0

*)(

r

rmsrmsSatrue

P

IVPP

،W1PF

Wא אא،אאא90،o90K

1)90sin( o،0)90cos( o

W

rmsrmsSar

true

IVPP

P

*

0

)(

،W0PF


‐ 72 -

WאRC

،אאא،אא10 PFKאאאאK

F3 J8EW אאא،אאאאא؟

F3 J35EאאאF3 J8E

אW

kCF

X C 18.3.2

1

kXRZ C 33.322 mVAVA

Z

VP srms

a 5.6710*5.67 32

אאW

oC

R

X5.72tan 1

אאWmWPP atrue 3.20cos. אW301.0cos PF


‐ 73 -

אSummary

1K ،אאאאאא)are in Phase)RIandRVKEE

2K אאא،Leadsאo90،FF13–6EE

3K אאאאאFאEאאאאאאK

4K אאאאKאאאאאאW

0trueP 5K ،אאאא

אאאW

rmsrmsr IVP *

6K אאאאאW

N

T

CCC

C1

....11

1

21

،W

NT CCCC XXXX 2!

7K אאאאW

NT CCCC 21 ،W

N

T

CCC

C

XXX

X1

....11

1

2!

8K ،אאאאW 22

CXRZ

R

C

V

V1tan


‐ 74 -

22CRS VVV

9K ،אאאאאW

22

*

CXR

CRZ

R

C

I

I1tan 22

CRT III 10K אRCאאRCאאאאW

sin.

cos.

Zx

ZR

ceq

eq

sin.2

1

fZCeq

11K Summary אאאא

אRCאא אRCאא

22אCRS VVV 22א

CRT III

22אCXRZ א

22

.

C

C

XR

XRZ

אא

R

C

C

V

V

R

X

1

1

tan

tan

אא

R

C

C

I

I

X

R

1

1

tan

tan


‐ 75 -

אא 1K אאאאאW

2K אאאאאאאW

3K אאאW

אאאK

؟אאאאא

אאא؟


‐ 76 -


‐ 77 -

4K אאTrmsIאאTavgIאא،W

5K אאאאW

6K אאאW

1oאאTI 2oאאא1:

1CIc

3oאאא2:2

CIC 4oאאאRI R :

7K אאאאRCאאW


‐ 78 -


‐ 79 -

8K 312

,,,,, RCTRR VVIVV

9K TI،אא12 , IIאאאW

،אאאאא؟

10K אRCW

אאTruePowerWWPtrue 2

אאractivePoweReWRAVPr ..5.3 אאאrPwerApperentPoK

11K ،אאא،אאאאPower

Factorאא،W

167

אאאאאא

אא-2

א

אא

4

א 116 אאא א א J2 אאא

‐ 80 -

אאא אאא

אאWאאאאאK

אאWאאאW

אאאK

אאאWאאא90٪

אאאאW9

אאW J K J אאK

אאWאאאאאאאאאאK


‐ 81 -

4 J1Introduction

،אאאאאאאאאאא

א،אאאאאאאאאאאא

אאOpen Circuitא،،אK

אא،אאאFאEאאFאאאKEאא

אאShort Circuit،אK

4 J2אאLXInductive Reactance אאLXאא،W

אא אא،אא

Wא،אאא

F4 J1Eאאאא

אאאK

אאFא،Kאאא؟אאאאא،א


‐ 82 -

אK،אאאאאאאאאאאK

W 1K אאאLXאFX L K

2K אאאאLXInductive Reactance،א)(OhmK

אא אאא0f

א،אאW

F4 J2Eאאאא

א0fK

אאאאאKא،אאאאאאא

אאאKאאLXאKא،א،א،אא

Inductive Reactance Formula،W F4 J1E LFX L .2


‐ 83 -

F4 J1EW אאאW

F4 J3EאאאF4 J1E

אאLX

אW 4.3110*5*10*1*2.2 33 LFX L

4 J3אאאאOhm's Law in Inductive AC Circuits א،،אאא

אF4 J4Eא،KאLmAmp /K

F4 J4Eאאאא

אאאאאא

אאאא،K،W

F4 J2E LXIV . F4 J3E

LX

VI

F4 J4E I

VX L אאאאW


‐ 84 -

F4 J5Eא

W

א،אאאאאאRMSPeakPeaktoPeak K

F4 J2EW

אאאW

F4 J6EאאאF4 J2E

אא؟ אW

4 J4אאאאCurrent & Voltage Relationship in Inductive

Circuits ،אאאאא،אare in Phase)RIandRVKEאאא،

Lagsאo90אאאא،Phase Shift)KE


‐ 85 -

F4 J7Eאאא

אאאאא

אאK،אאאאאאאFEא090K

4 J5אאאPower in an Inductor

אאאא،DCאאIVP .א،K،אאאא

Kא،אאאאאW


‐ 86 -

4 J5 J1אאInstantaneous Power אאאאאFאE

אאאאאאKאאאW

F4 J8Eאא

W

1K אאאאK 2K אאאאK

3K אאאאK

4K אא،אאאאאW KאאK

KאאK

5K אאאאאאאW

KאאK

KאאK 4 J5 J2אאtruePTrue Power

אאא،אאא،אאאKאאאא

،אW


‐ 87 -

F14-5E 0trueP אK،אא،אאא

אאאWRKאא،W

F4 J6E Wrmstrue RIP 2

4 J5 J3אאrP Reactive Power ،אאאא

אאאW F4 J7E rmsrmsr IVP * F4 J8E

L

rmsr X

VP

2

F4 J9E Lrmsr XIP *2 WrmsVWאאאK

rmsIWאאאK rPאא(VAR) Volt- Ampere – ReactiveK

F4 J3EW אאאW

F4 J9EאאאF4 J3E

אאK

אW

L

rmsr X

VP

2

VARX

VPLFX

L

rmsrL 59.18.62.2

2


‐ 88 -

F4 J4E ،אא،א 5WRKאא

אtrueP؟ א

אאאאFאE mA

X

VI

L

rmsrms 159

אאW mwRIP Wrmstrue 126*2


‐ 89 -

4 J6אאאאאSeries & Parallel Inductive AC Circuits

אאאאאא،אאאK،אאאאאאאא

W 4 J6 J1אאאInductors in Series

אאאאאW

F4 J10Eאאאא

،אאאW

F4 J10ENT LLLL ....21 Wא،אא

F4 J11E NT LLLL XXXX ...

21

4 J6 J2אאאParallel Inductors

אאאאאW

F4 J11Eאאאא

،אאאW

F4 J12E N

T

LLL

L1

....11

1

21

،W


‐ 90 -

F4 J13E NLLL

L

XXX

XT 1

...11

1

21

אאאאאSummaryW

אCapacitors אFאEInductors

אCapacitance

1210*85.8** rd

AC

אInductance

ANL

.2

Kאא 2

2

1CVW

אא 2

2

1LIW

אאCapacitive Reactance

CfXC ..2

1

אאInductive Reactance

LfX L ..2

CXIV .

LXIV .


‐ 91 -


אאאאאאo90

אאאאאאo90

Kאא

N

T

CCC

C1

...11

1

21

NT CCCC XXXX .....21

אא

NT LLLL ...21

NT LLLL XXXX ...21

אא

NT CCCC .....21

CNCc

CT

XXX

X1

...11

1

21

אא

N

T

LLL

L1

...11

1

21

N

T

LLL

L

XXX

X1

...11

1

21

אא

21

21

CC

CCCT

21 CCCT XXX

אא

21

21

LLL

T

XXX

LLL

T

אא

21

21.

21

CC

CCC

T

XX

XXX

CCC

T

אא

21

21.

.

21

21

Ll

LL

LT

T

XX

XXX

LL

LLL


‐ 92 -


אאאC

N

CCT

CC XNXT

.

אאאL

LL

T

XNX

LNL

T.

.

KאאאC

N

XX

CNC

CC

T

T

.

אאאL

N

XX

N

LL

LL

T

T


‐ 93 -


אא

NT CCCC .....21

CNCc

CT

XXX

X1

...11

1

21

אא

N

T

LLL

L1

...11

1

21

N

T

LLL

L

XXX

X1

...11

1

21

אא

21

21

CC

CCCT

21 CCCT XXX

Kאא

21

21

LLL

T

XXX

LLL

T

אא

21

21.

21

CC

CCC

T

XX

XXX

CCC

T

אא

21

21.

.

21

21

Ll

LL

LT

T

XX

XXX

LL

LLL

אאאC

N

CCT

CC XNXT

.

אאאL

LL

T

XNX

LNL

T.

.

KאאאC

N

XX

CNC

CC

T

T

.

אאאL

N

XX

N

LL

LL

T

T


‐ 94 -

4 J7אאאאאSeries RL Circuits

4 J7 J1אאאאאאCharacteristics of RL Circuits אאאא،אאאאW

F4 J12Eאאאאא

אאאאאLIאאLVK

אאאRIאRVאאK،אLILVאאo90،אאRVא

LVאאo90א،W

F4 J13Eאא

RVLVאאRL VV K


،א،אאאאאאאאFאEאTRא،

FאאאאTLXאא،

אZOhmK אאאאSeries R – L אW


‐ 95 -

F4 J14Eא

אאPythagorasW F4 J14E 222

LXRZ אRLאאW

F4 J15E 22LXRZ


אאאאאאאאKאאאאאאאאאW

F4 J15Eאאאא

W

F4 J16E

R

L

V

V1tanand

R

X L1tan


F4 J17E R

L

V

Vtan

א

R

L

V

V1tanאאאR

L

V

VK

4 J7 J4אאאRLאאVoltages Relationships אSVאאRVאאLV

אאW


‐ 96 -

F4 J16EאאRL אא

אאאאאW

F4 J17EאאRL אא

אאK

PythagorasW F4 J18E222

LRs VVV אאאאW

F4 J19E22LRS VVV

F4 J20E22LSR VVV

F4 J21E22RSL VVV


،،אאאW

F4 J18EאRL אא

אאאאRVאאW

F4 J22ERIVR . אאLVאא،LX،

אאאאLVW F4 J23E LL XIV .


‐ 97 -

אאאאאVFאאE،אZאRLאאאW

F4 J24E ZIV . אאאW

F4 J25E Z

VI

F4 J26E I

VZ

אאאא،W

F4 J19Eא

4 J7 J6אאאא CircuitRLFrequency Effect on

א،א،אא،אאאאאKאאאאאא

אאאW 1K אאfאאLX، fLX L 2KW אW

22

LXRZ

אWZ

VI FאאKE

אRVKVL אLV 222

LRS VVV K

2K אאfXZ L IVV RL

אW

אאf LX Z I RVLV

fאא LX

Z

I

RV

LV


‐ 98 -

F4 J5E אאאW

F4 J20EאאאF4 J5E

K אאLX

kfLX L 28.62 K א Z

kXRZ L 8.1122 K א

VRIVR 2. K א

VXIV LL 256.1* K א

VZIVb

VVVVa

S

LRS

36.2.)(

36.2)( 22

K אא

01

01

32tan

32tan

R

L

L

V

V

R

X

4 J8אאאאאParallel RL Circuits

4 J8 J1אאאאאאCharacteristics of RL Circuits אאאא،אאאאאW


‐ 99 -

F4 J21EאRLאא

W SRL VVV

RIRVא

LIRIאאo90K

אאאאK

F4 J22EאאRLאא


،אאאאא،אאאאZOhmK،אא

אאאאאאW

F4 J23EאאRLאא

W

F4 J27E R

VI R

R


‐ 100 -


אאאאאאאאאאW


W

F4 J30E

R

L

I

I1tanand

R

X L1tan


F4 J31E R

L

I

Itan

Wא

R

L

I

I1tanאאאR

L

I

IK

4 J8 J4אאאאRLאאCurrents Relationships אאTIאRIאאאLI

אאW

F4 J25EאאאאRLאא

،אW F4 J32E 222

LRT III W

F4 J33E 222222RTLLTRLRT IIIIIIIII


‐ 101 -


א،،אאW

F4 J26EאRLאא

W F4 J34E ZIV *

אאאW F4 J35E

I

VZ

Z

VI

אאאא،W

F4 J27Eא

4 J8 J6אאRLאRLאConversion From Parallel to Series Form

،אאRLאאאRL،אא אRLאאאRLאאא،אא

אאא،،אאW

F4 J28EאאאאRLאא

אאאאאeqReqLX،eqRLeqXאאאW


‐ 102 -

F4 J36EcosZReq F4 J37E

F

Z

F

XLZX Leq

eqLeq

2

sin.

2sin

F4 J6EW אאאW

F4 J29EאאאF4 J6E

K אאLX kLfX L 41.1..2

K אZ

kXR

RXZ

L

L 19.122

K אאאRI

mAR

VI rmsS

rmsR 54.4)()(

K אאאLI

mAX

VI

L

rmsSrmsL 1.7)(

)(

K אאTI

mAIIIa rmsLrmsRrmsT 42.82)(

2)()(

mAZ

VIb rmsS

Trms 42.8)( K אא

01 3.57tan

LX

Ra

0

)(

)(1 3.57tan

rmsR

rmsL

I

Ib

K אאRLאאאאאא


‐ 103 -

F4 J30Eאאאאאא

mH

F

XLkZX Leq

eqLeq 25.1062

1sin.

And 643cos. ZReq

4 J9אאFא JאEאאאSeries -Parallel RL Circuits אאאאאK

F4 J7EW אאאW

F4 J31EאאאF4 J7E

1אאTZK 2אאTIK 3אאאSVאI

אW WאאW

kfLX

kfLX

L

L

14.32

85.72

2

1

2

1

Wאאאאאאא

F4 J32Eאאאאאא


‐ 104 -

אאאאK

kZX

kZR

eqL

eq

65.1sin.

57.1cos

22

22

021

2

222

222

4.46tan

28.2.

2

L

L

L

X

R

kXR

XRZ

אא،אאW

אא

kRRR eqT 27.61 אאא

kXXX LeqLTL 5.91 אאא kX

TL 5.9אא kRT 27.6،W

.877

6.56tan

4.11

1

22

AZ

VI

R

X

kXRZ

T

ST

o

T

L

LTT

T

T

4 J10אאאאPower in RL Circuits

4 J10 J1אPower Triangle א،RLאאRL،אא

אאRLאאאאאK

F4 J33EאRLאא


‐ 105 -

אאאאאאאאאאrmsIW

F4 J34Eאא

W rmsIC

rmsRVאאאאK

rmsICLrmsVאאK rmsIC

rmsSVאאApparent PowerK

אPower Triangleא،W

F4 J35Eא

4 J10 J2אאPower Relationships and Units

אאApparent PowerAmpereVott VAW F4 J38E ZI

Z

VIVP rms

SrmsrmsSrmsa ** 2

2

אאTrue PowerאWatt WW

F4 J39E cos.atrue PP אאReactive PoweractiveAmpereVolt Re VARW

F4 J40E sin.ar PP


‐ 106 -

4 J10 J3אאThe Significance of apparent Power

אאApparent PowerFE،אאאאאאKאאא

אאא،אאאK אאאFאאE

א،אאאKאאK

W

אאאאאאאאאאא،אאctorthePowerFaPF :،א

אאאאאאאאK 4 J10 J4אThe Power Factor FPFE

אאאאאW F4 J41E cos

a

true

P

PPF

W F4 J42E cosPF

Wאאאא،אאאK

אאאא،א،אאאאאאאKאאאא

K


‐ 107 -

F4 J8EW אאאW

F4 J36EאאאF4 J8E

א2,1אאאאw20אאאאKאאא

אKאאא 75.0PFאאא 95.0PFאאא،

אK


‐ 108 -

Summaryאאאאאא

אאאRC אאאRL

אRCאא

אאא

22אCXRZ

אא

R

C

C

V

V

R

X

1

1

tan

tan

222CRS VVV

אRLאא

אא

א 22א

LXRZ

אא

R

L

L

V

V

R

X

1

1

tan

tan

222LRS VVV


‐ 109 -

אאאRC אאאRL

אRCאא

אא

א א

22C

C

XR

RXZ

אא

R

C

C

I

I

X

R

1

1

tan

tan

222CRT III

אאאאאW

sin...2

1

..2

1

sin.

cos.

ZFXFC

ZX

ZR

Ceqeq

Ceq

eq

אRLאא

אא

א א

22

.

L

L

XR

XRZ

אא

R

L

L

I

I

X

R

1

1

tan

tan

222LRT III

אאאאאW

F

Z

F

XL

ZX

ZR

Leqeq

L

eq

eq

2

sin.

2

sin.

cos.


‐ 110 -

אאא 1K mH100אאאא،A1؟

2K אאB,A אא،W

3K אאאW

K אאאאאK

K אא23 , LLK

4K אImpedanceאאא،W


‐ 111 -

5K אאאW

K אאI

K אא

K RL VV ,

6K אאאW

K א

K אאאאTI

K אLR II ,2

K אאtruePאאrP

K אאaPאPF

167

אאאאאאאא

אאJJ22

א

א

אא

5

א 116 אא א א J2 אאאא

‐ 112 -

אא אאאא

אאWאאאאאאK

אאWאאאW

אאאאK

אאאWאאא90٪

אאאאW9

אאW J K J אאK

אאWאאאאאאאאאאאK


‐ 113 -

5-1 Introduction אאאאא

W

K אאאאאאSeries RLC Circuits K אאאאאאParallel RLC Circuits

אאאא،אאאResonance CircuitsK

5 J2אאאאRLCאאSeries RLC Circuit 5 J2 J1אאאאאאאRLC Circuits Characteristics

،אאאאW

F5 J1EאRLCאא

אאאאאאאW

F5 J2EאאאאאאRLCאא

W RLC III ,,אIK

WIVR ,אK

אFאWEILVאאo90K

אWICVאאo90K


‐ 114 -

אF5 J2Eאאא،o180אאאK

5 J2 J2אאTotal Reactance

،אאאאאאאאאW

F5 J3EאאאRLCאא

W F5 J1E

אW CL XX אא LC XX אא LC XX אאאא

5 J2 J3אאTotal Impedance

אאW

F5 J4EאאאRLCאא

אאאאאW F5 J2E 2222 )( CLTT XXRXRZ


‐ 115 -


אאאאאאאW F5 J3E

R

X T1tan

אאאCL XX אאKאאאLC XX אאK

F5 J1EW אאאW

F5 J5EאאאF5 J1E

אאאאK אW

28.6.2

18.3.2

1

LfX

CfX

L

C

LC XX אאK אאW

1.3CLT XXX אW

4.622TT XRZ

אאW 01 29tan

R

XT

LC XX אאאא029


‐ 116 -

F5 J6EאאאVR,VL,VC

א،FאEאLCVאאאא،אאLCVאא

אo90،SVIאo29K

5 J2 J5אאאאאאAnalysis of Series RLC Circuits

אFאEאאRLCאאא،אאא0180K

F5 J2E אאאW

F5 J7EאאאF5 J2E

K אאאאאאאK

K אאאLCVK אW FE ،אW

8.8222CL XXRZ

W mA

Z

VI S 121


‐ 117 -

FE ،אW

VXIV

VXIV

VRIV

LL

CC

R

03.3.

26.7.

08.9.

FE אאאCLV،W

VVVV LCLC23.4

אאאCVK אאW

01 25tan

R

X T

אCL XX אאאאאא025K W

F5 J8Eאאא

5 J2 J6אאSeries Resonance

،אאאאאאאאאאאא،אCX

אאLXאW


‐ 118 -

F5 J9Eאאאא

W F5 J4E

CfXC .2

1

F5 J5ELfX L .2 א،אאאאW

fXX CL , אאLC XX אאאאאא،

אאאאאאKאאאKאא،אW

F5 J6ECLCL VVXX F5 J7ERZ r

אW



‐ 119 -

5 J2 J7אאrFSeries Resonant Frequency ،אW

F5 J8ECL XX F5 J9E

CFLF

rr ..2

1..2

F5 J10E CL

Fr..2

12

2

F5 J11E CL

Fr.2

1

אאאאW F5 J12E

CLFr

.2

1

F5 J3E

אאאאW

F5 J11EאאאF5 J3E

אW kHz

LCFr 318

2

1

،אLC XX אאאאאאאאאאאא

א0180א،W

F5 J12Eאאא


‐ 120 -

אאאאKאאTXאאאK

F5 J4EW

CXZ ,אW

F5 J13EאאאF5 J4E

אW א 50LC XX

א 100RZ

5 J2 J8אאאא Voltage, Current and Impedance Variation with Frequency

WאFFr W אHzF 0א،אאאF

DCEאאאאKאאאאLC XX ،

אאאאאאאאאKאאא

،W IZXXXXF LCLC

W CLR VVV

W CL VV


‐ 121 -

אאW

F5 J14Eאאאא

WאrFF

אאאאCL XX אא،אאLC VV אא،FאאKE

אאאאא،אW

0 CLLCCLr VVVXXFF W

RSS VV

R

VIRZ

WאrFF W אאאאאאאאאא

אאאאא،Kאאא،אאאאKאאאאRV

אCVאאSVאאא،W


‐ 122 -


5 J2 J9אאאPhase Angle Variation with Frequency

אאאאא،אW

F5 J13ELCr XXFF אא،אאאא

אrFF ،F5 J16 JKEאאא،אאאאא

00א،F5 J16 JKEאאאאא،אאאא

،אF5 J16 JWE

F5 J16Eאאא

W F5 J14E

CL

CLT XX

XXX

.


‐ 123 -

W CL XX ،אאTX،אW

F5 J17Eאאא

5 J3אאאאאאRLCParallel RLC Circuit 5 J3 J1אאאאאאאRLC Circuits Characteristics

אאא،אאאאאאW

F5 J18EאRLCאא

W SLCR VVVV

אאאאאאאW WRR IV ,אאK

אFאWELILVאאo90K אWCICVאאo90K


‐ 124 -

F5 J19Eאאאאאאאא

אאא،א0180،W F5 J15ECLLC III

5 J3 J2אאTotal Reactance

،אאאאאאאאW

F5 J16ECL

CLT

CLT XX

XXX

XXX

.111

5 J3 J3אאTotal Impedance

אאאRLCאא،אאאW

F5 J17E22

.

T

TT

XR

XRZ


אא،W

F5 J18E

TX

R1tan

F5 J5EW אא،אאאאW


‐ 125 -

F5 J20EאאאאF5 J5E

אW

07.71010

10*10.

105

10*5.

2222T

TT

CL

CLT

XR

XRZ

XX

XXX

،אאW

o

TX

R45tan 1

5 J3 J5אאParallel Resonance

،אאאא،אאW CL XX

אאאאאאאאאאאאאא

א0180،א،אאאאאAI LC 0KאאאW

F5 J21Eאאאא

אאאאK،אא0LCIאאאא


‐ 126 -

אOpen Circuitsאאא،אK،אאאאW

F5 J19ECL

CLT XX

XXX

CL XX אTXאא،،،אW


אאאIאSVא،o0K

5 J3 J6אאThe Parallel Resonant Frequency

אאאrfאאא،W F5 J20E

LCfr 2

1

אאW 1K אאWrff W

LC XX

11אאK

2K אאWrff WLC XX

11אא

K

3K אאWrff CL XX

11אאK


‐ 127 -

F5 J23EאאRLCא W

F5 J21ECf

XC .2

1

F5 J22ELfX L .2 F5 J6EW

אאאW

F5 J24EאאאF5 J6E

אאא،א،אK אW

אאא،W kHz

LCfr 25.2

2

1

אא TX

א 100RZ

אא A

R

VI S

T 1.0


‐ 128 -

אSummary 1K אאאא،אאאאאא

אאאW

2K אאאאא،אאאW

3K אW CL XX אא LC XX אא LC XX אאאא 4K אאאאאW

2222 )( CLTT XXRXRZ

5K אאאאאאאW

R

X T1tan

6K ،אאאאאאW

7K אאאאW

LCfr 2

1


‐ 129 -

8K אאאאאאא،00K

9K ،אאאאאאSLCR VVVV

10K אאאאאאאW

11K אא

CL

CLT

CLT XX

XXX

XXX

.111

12K אאאRLCא،אאאאW

22

.

T

TT

XR

XRZ

13K אא،W

TX

R1tan

14K אאאrfאאא،W

LCfr 2

1


‐ 130 -

אא

1K אאאאאK

2K אאאW

K אאTI

K אאtrueP RIP rmstrue *2

K אאrP Trmsr XIP *2

K אאאaP rmsSa IVPrms

.

K אא1Rאא2R

K אא1R2Rאא1Lאא2Lאא12 ,CC

K אאFאאאE 3K KאאאW

אK

LC XXZ ,,אIאאK


‐ 131 -

4K אאאW

K אאTZK K א؟؟אא

אRLC III ,,אאאאLCIK

א 116 א א J2

אא

אאFReferencesE Wאאא

1K א،אאאאK

2K א،אאK،K،אKK

Wאאא

[1] Thomas L. Floyed, Electrical Engineering Fundamentals, Prentice, Inc, sixth edition, 2000.

[2] B. L. Theraja, A. K. Theraja, " Electrical Technology", published by Ninja Construction development Co. Ltd. Ram Nagar, New Delhi, 110055, 1995.

[3] M. A. PAI, "Introduction to Electric Circuits and Machines", Affiliated east west presses private limited, 1975.

[4]

א 116 א א J2

א

א

אאWمقدمة للتيار المتردد)1 )الموجة الجيبية: الموضوع الأول 1 J1Introduction K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K2 1 J2אאאMagnetic Effects of Electrical Current K K K K K K K K K K K K K2

1 J2 J1אאGeneration & Concentration of Magnetic Field K K K K K K K K2 1 J3אאBasic Concepts of Electrical Generator K K K K K K K K K K K K K K K4

1 J3 J1אאGeneration of Sine Wave K K K K K K K K K K K K K K K K K K K K5 1 J3 J2אאאEvaluation of Sine Wave K K K K K K K K K K K K K K K K K6 1 J3 J3אאאRepresentation of Sine Wave K K K K K K K K K K K K K K K6 1 J3 J4אאMathematical Representation of Vectors K K K K K K K K K K K K7

1 J4אאFACEאאאאא K K K K K K K K K K K K K K K K K K K K8 1 J4 J1אאא K K K K K K K K K K K K K K K K K K K K K K K K K K K K K8 1 J4 J2אאאא K K K K K K K K K K K K K K K K K K K K K K K9 1 J4 J3אאFאESine wave Voltage Sources K K K K K K K K K K K K K K K K10

אאWאFאאWאאאFACEאE 1 J5אאאFACEא K K K K K K K K K K K K K K K K K K K K K K K K K K11

1 J5 J1אאא K K K K K K K K K K K K K K K K K K K K K K K K K K11 1 J5 J2אאInstantaneous Value K K K K K K K K K K K K K K K K K K K K K K K11 1 J5 J3FאאEPeak Value K K K K K K K K K K K K K K K K K K K K K K11 1 J5 J4אאאPeak to Peak Value K K K K K K K K K K K K K K K K K K K K12 1 J5 J5אאאEffective value of sine wave K K K K K K K K K K K K K K K12 1 J5 J6אאאAverage value of sine wave K K K K K K K K K K K K K K K13

אאWאFאאWאאאאE 1 J6אאאא K K K K K K K K K K K K K K K K K K K K K K K K K15

1 J6 J1 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K15 1 J6 J2אאאOhm's Law in AC Circuits K K K K K K K K K K K K K K K K15 1 J6 J3אאאא K K K K K K K K K K K K K K K K K K K K K16

Wאאא K K K K K K K K K K K K K K K K K K K K K K K K K17 Wאאא K K K K K K K K K K K K K K K K K K K K K K K K17

1 J7FאE K K K K K K K K K K K K K K K K K K K K K19 1 J7 J1 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K19 1 J7 J2אאאאPDC VV K K K K K K K K K K K K K K K K K K20

א 116 א א J2

א

1 J7 J3אאאאPDC VV K K K K K K K K K K K K K K K K K K20 אאWאFאאאWאאE

1 J8אאNon Sinusoidal Wave Forms K K K K K K K K K K K K K K K K K K K K23 1 J8 J1 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K23 1 J8 J2FאERepetitive Pulse Wave Form K K K K K K K K K K K K K K K23 1 J8 J3אאSquare Wave K K K K K K K K K K K K K K K K K K K K K K K K K K26 1 J8 J4אאTriangular Wave Form K K K K K K K K K K K K K K K K K K K K K K K26 1 J8 J5אSaw tooth Wave Form K K K K K K K K K K K K K K K K K K K K K K28 אSummary 29

א30 الأولى אאWא33 א

2 J1Introduction K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K34 2 J2אא Mutual Inductance K K K K K K K K K K K K K K K K K K K K K K K K K34 2 J3אאThe Basic Transformer K K K K K K K K K K K K K K K K K K K K K K K K34

2 J3 J1Structure K K K K K K K K K K K K K K K K K K K K K K K K K K K K K34 2 J3 J2א K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K35 2 J3 J3 K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K36

2 J4אאTurns Ratio K K K K K K K K K K K K K K K K K K K K K K K K K36 2 J4אאDirection of Winding K K K K K K K K K K K K K K K K K K K K K K K K K K37 2 J5אאאInductance Voltage and Current Relationship K K K K K K K K K K K39

2 J5 J1אאאאאא K K K K K K K K K K K K K K K K K K K K K K K39 2 J5 J2אאאאאא K K K K K K K K K K K K K K K K K K K K K K K39

2 J6אאTransformer Types K K K K K K K K K K K K K K K K K K K K K K K K K K40 2 J6 J1Step–up Transformer K K K K K K K K K K K K K K K K K K K K K K K K40 2 J6 J2Step–down Transformer K K K K K K K K K K K K K K K K K K K K K K41

2 J7אאאTransformer Current Direction K K K K K K K K K K K K K K K K K K K42 אSummary 44

אא 45 אאWאאא 46

3 J1Introduction K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K47 3 J2אאCXCapacitive Reactance K K K K K K K K K K K K K K K K K K K K K K47 3 J3אאאא K K K K K K K K K K K K K K K K K K K K K K K49 3 J4אאאא K K K K K K K K K K K K K K K K K K K K K K K K K K K K51 3 J5אאאPower in Capacitor Circuits K K K K K K K K K K K K K K K K K K K K51

א 116 א א J2

א

3 J5 J1אאInstantaneous Power K K K K K K K K K K K K K K K K K K K K K K K51 3 J5 J2אאtrvePTrue Power K K K K K K K K K K K K K K K K K K K K K K K K52 3 J5 J3אאrP Reactive Power K K K K K K K K K K K K K K K K K K K K K K K52

3 J6אאאאאSeries & Parallel Capacitive AC Circuits K K K K K K K K K K K K53 3 J6 J1אאאSeries Capacitors K K K K K K K K K K K K K K K K K K K K K K53 3 J6 J2אאאParallel Capacitors K K K K K K K K K K K K K K K K K K K K K K54

3 J7אאאאאSeries RC Circuits K K K K K K K K K K K K K K K K K K K K K54 3 J7 J1אאאאאאCharacteristics of RC Circuits K K K K K K K K K K K54 3 J7 J2אImpedance Z K K K K K K K K K K K K K K K K K K K K K K K K K K K K55 3 J7 J3אא Phase Angle K K K K K K K K K K K K K K K K K K K K K K K K K K56 3 J7 J4אאאאOhm's Law K K K K K K K K K K K K K K K K K K K56 3 J7 J5אאאאRCFrequency Effect on K K K K K K K K K K K57

3 J8אאאאאParallel RC Circuits K K K K K K K K K K K K K K K K K K K K59 3 J8 J1אאאאאאCharacteristics of RC Circuits K K K K K K K K K K K59 3 J8 J2אImpedance Z K K K K K K K K K K K K K K K K K K K K K K K K K K K K60 3 J8 J3אאPhase Angle K K K K K K K K K K K K K K K K K K K K K K K K K K61 3 J8 J4אאאאRCאאCurrents RelationshipsError! Bookmark not defined.61 3 J8 J5אאאאOhm's Law K K K K K K K K K K K K K K K K K K K61 3 J8 J6אאRCאRCא K K K K K K K K K K K K K K K K K K K K K K62

Summaryאאאא K K K K K K K K K K K K K K K K K K K K K K65 3 J9אאFא JאEאאאSeries-Parallel RC Circuits K K K K K K K K K K65 3 J10אאאאPower in RC Circuits K K K K K K K K K K K K K K K K K K K K68

3 J10 J1אPower Triangle K K K K K K K K K K K K K K K K K K K K K K K K K68 3 J10 J2אאPowers Relationship K K K K K K K K K K K K K K K K K K69 3 J10 J3אאThe Significance of apparent Power K K K K K K K K K K K K K K69 3 J10 J4אThe Power Factor (PFE K K K K K K K K K K K K K K K K K K K K K K70 אSummary 72

אא 74 אאאWאאא 76

4 J1Introduction K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K77 4 J2אאLXInductive Reactance K K K K K K K K K K K K K K K K K K K K K K K77 4 J3אאאאOhm's Law in Inductive AC Circuits K K K K K K K K79 4 J4אאאא K K K K K K K K K K K K K K K K K K K K K K K K K K K K80 4 J5אאאPower in an Inductor K K K K K K K K K K K K K K K K K K K K K K K81

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3 J5 J1אאInstantaneous Power K K K K K K K K K K K K K K K K K K K K K K K82 4 J5 J2אאtruePTrue Power K K K K K K K K K K K K K K K K K K K K K K K K82 4 J5 J3אאrP Reactive Power K K K K K K K K K K K K K K K K K K K K K K K83

4 J6אאאאאSeries & Parallel Inductive AC Circuits K K K K K K K K K K K K K85 4 J6 J1אאאSeries Inductors K K K K K K K K K K K K K K K K K K K K K K K85 4 J6 J2אאאParallel Inductors K K K K K K K K K K K K K K K K K K K K K K K85

אאאאאSummaryW K K K K K K K K K K K K K K K K K K K K K87 4 J7אאאאאSeries RL Circuits K K K K K K K K K K K K K K K K K K K K K91

4 J7 J1אאאאאאCharacteristics of RL Circuits K K K K K K K K K K K K91 4 J7 J2אImpedance Z K K K K K K K K K K K K K K K K K K K K K K K K K K K K91 4 J7 J3אא Phase Angle K K K K K K K K K K K K K K K K K K K K K K K K K K92 4 J7 J4אאאRLאאVoltages Relationships K K K K K K K K K K K K K92 4 J7 J5אאאאOhm's Law K K K K K K K K K K K K K K K K K K K K93 4 J7 J6אאאאRLFrequency Effect on K K K K K K K K K K K K94

4 J8אאאאאParallel RL Circuits K K K K K K K K K K K K K K K K K K K K95 4 J8 J1אאאאאאCharacteristics of RL Circuits K K K K K K K K K K K K95 4 J8 J2אImpedance Z K K K K K K K K K K K K K K K K K K K K K K K K K K K K96 4 J8 J3אא Phase Angle K K K K K K K K K K K K K K K K K K K K K K K K K K97 4 J8 J4אאאאRLאאCurrents Relationships K K K K K K K K K K K K K97 4 J8 J5אאאאOhm's Law K K K K K K K K K K K K K K K K K K K K98 4 J8 J6אאRLאRLא K K K K K K K K K K K K K K K K K K K K K K K98

4 J9אאFא JאEאאאSeries -Parallel RL Circuits K K K K K K K K K K100 4 J10אאאאPower in RL Circuits K K K K K K K K K K K K K K K K K K K K101

4 J10 J1אPower Triangle K K K K K K K K K K K K K K K K K K K K K K K K K101 4 J10 J2אאPowers Relationship K K K K K K K K K K K K K K K K K K102 4 J10 J3אאThe Significance of apparent Power K K K K K K K K K K K K K K103 4 J10 J4אThe Power Factor FPFE K K K K K K K K K K K K K K K K K K K K K K103

Summaryאאאאאא 105 אאא 107

אאWאאאא 109 5 J1Introduction K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K110 5 J2אאאאאאRLCSeries RLC Circuit K K K K K K K K K K K K K K K K110

5 J2 J1אאאאאאאRLC Circuits Characteristics K K K K K K K K K K110 5 J2 J2אאTotal Reactance K K K K K K K K K K K K K K K K K K K K K K K K111

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5 J2 J3אאTotal Impedance K K K K K K K K K K K K K K K K K K K K K K K111 5 J2 J4אאPhase Angle K K K K K K K K K K K K K K K K K K K K K K K K K K K112 5 J2 J5אאאאAnalysis of Series RLC Circuits K K K K K K K K K K K K113 5 J2 J6אאSeries Resonance K K K K K K K K K K K K K K K K K K K K K K K K K114 5 J2 J7אא K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K K116 5 J2 J8אאאא K K K K K K K K K K K K K K K K K K K K K K K K K117 5 J2 J9אאאPhase Angle Variation with Frequency K K K K K K K K K K K K119

5 J3אאאאאאRLCParallel RLC Circuit K K K K K K K K K K K K K K K K120 5 J3 J1אאאאאאאRLC Circuits Characteristics K K K K K K K K K K120 5 J3 J3אאTotal Impedance K K K K K K K K K K K K K K K K K K K K K K K121 5 J3 J4אאPhase Angle K K K K K K K K K K K K K K K K K K K K K K K K K K K121 5 J3 J5אאParallel Resonance K K K K K K K K K K K K K K K K K K K K K K K K122 5 J3 J6אאThe Parallel Resonant Frequency K K K K K K K K K K K K K K K K K123

SummaryKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKKK 124 אא.......................................................................... 127

אאFReferencesE............................................................................. 129

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