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אאאאJJ22
FFEE
111166
א 116 א א J2
א
،،אא،אW
אא א א א א א אאאא،אאאאאאא
אאאא אאאאאאאWא
אאK אאאאאאא
א ،א אא א א אא א א ، א
א،אאאאאאאאאאאאאאאא
אא،אאאא،אK
א א ? א2 ? ?א ?א אאאאאאאK
אאאאאאא،א،אאאא
אאאאאK א א אא،אK
אאאא
א 116 א א J2
אאאא،KKKW
אאא،אאאאאאאK
אאאאאא،אאאאאאאאא
אאאאאKאאאא،אאאא
אאאאאא،אאאאאאאאK
אאאאאאאאאאאאK
אא،אאאאא،א،אאאK
אא،،אאא،אאאא
אאK ،אKKKKKK
א
167
אא
אאJJ22
א
1
א 116 אא א א J2 א
‐ 1 -
אא א
אאWאא אאWאאאאאKאאK
אאWאאאW
אא אאא אאאא
אאאא
אא
אאאWאאא90٪
אאאאW9
אאW
J K J אאK
אאWאאאאאאאאאK
א 116 אא א א J2 א
‐ 2 -
אאWאא 1-1 IntroductionW
אאאאאא،אאאאאאאFDCKE
אאAlternating Current FACEאאא،אאאאK
אאאאאאFSinusoidalEאSine waveK
אאאאאאאאאאאK
אאאאאאאא،אאאאאאאאא
K
1 J2אאאMagnetic Effects of Electrical Current
1 J2 J1אאGeneration & Concentration of Magnetic Field
אאא،אאא(Magnetic Field)אאאFא
אFאאE،φEאאא،F1 J1KE
F1 J1Eאאא
א 116 אא א א J2 א
‐ 3 -
אאא،אאאאWאאאא
אאK
W
1K אאאאF1 J2KE
F1 J2Eאאא
2K אאF1Eא،א،אאאאאא،אא
אאאאאFEא،אאאאאא
אK
F1 J3Eאאאא
אא،אאאאאאאFאאE
אא،אאאאאאאאאאאאאאKא
אאאF2EאאF1EאאF1 J3KE
א 116 אא א א J2 א
‐ 4 -
،אאאאאאאאF1 J4KE
F1 J4E
W F1 J1E1<2<3
אאאאאא،אאאאאאאK
1 J3אאBasic Concepts of Electrical Generator
F1 J4Eאאאא،אאאא،אאא
אאאאאאאאאאא،א
،אF1 J5KE
F1 J5Eאאאאא
אאאאאWאא،אאאאאאK
א 116 אא א א J2 א
‐ 5 -
1 J3 J1אאGeneration of Sine Wave
אאאאא،אאאאF1 J6Eאאא،
אאאאאאאאFEאאK
F1 J6Eאא
אאאF1 J6Eאא،ABCDAא،W
F1E אAאאאאK
F2E אBאאאאאאFאאEאא
אF1 J6Eאאא،אאאאאאאאK
F3E אCאאאאK
)4( אDאאאאאאFאאEאאא
אK אאאאאאאאאאאא،אאא
F1 J7KE
א 116 אא א א J2 א
‐ 6 -
F1 J7Eאא
1 J3 J2אאאEvaluation of Sine Wave
אאאאF1 J8E،אK
F1 J8Eאא
1 J3 J3אאאRepresentation of Sine Wave
אאאאאאEmאאאאאא،אא
אאtאאאאאאאF1 J9KE
F1 J9Eאאא
א 116 אא א א J2 א
‐ 7 -
1 J3 J4אאMathematical Representation of Vectors
אאW 1K אאאK 2K אאK
א،אאAW F1 J2E 21 jaaA
jWאאאאZ1K אאאא
אF1 J10KE
F1 J10Eאאא
אXאא،j
W XjjX
אאאFF–KEE אאjאאאא،
90א،jאאאא90KאאאאאאאאאאאאאאF1 J11KE
F1 J11Eאאאא
א 116 אא א א J2 א
‐ 8 -
F1 J3E )aa(A 22
21
F1 J4E
1
21
a
atan
1 J4אאFACEאאאאא
Alternating Current and Voltage as a Sine Wave 1 J4 J1אאא
א،אאאאאW
F1 J12Eאא
،אאא،אאאאאאW
F1 J13Eאאאא
אאאאאK W
1K אאאאK 2K ،אאאאW
F1 J14Eאאאא
א 116 אא א א J2 א
‐ 9 -
1 J4 J2אאאאW WאאW
אF1 J12EאאאF1 J15EW
F1 J15Eאאאאא
אאאא،אא
אאאFאאEHFאאF JEEKאאאK
WאאW
F1 J16EW
F1 J16Eאאאא
،אאWאאאא
،אאFאאאאKEאאאאא
אאאאKאאאאאאאK
אאKאאK
א 116 אא א א J2 א
‐ 10 -
1 J4 J3אאFאESine wave Voltage Sources אאאW
1KאאאRotating Electrical machines אאAC Generator
2KאאאElectronic Oscillator Circuits אאאSignal Generators
א 116 אא א א J2 א
‐ 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)
4K אאAverage Value
1 J5 J2אאInstantaneous Value
אאFאEאFאE،אאF1 J17KE
F1 J17Eאאא
1 J5 J3FאאEPeak Value
אאאאאאאאאאאאא
אKאאאאK
W Peak Value = Amplitude =Magnitude
א 116 אא א א J2 א
‐ 12 -
א 116 אא א א J2 א
‐ 13 -
F1 J1E אאאאW
F1 J18EאאF1 J1E
אW VVP 8
1 J5 J4אאאPeak to Peak Value
אאאאאאאאאא W
F1 J5EPPP II 2PPP VV 2 אאW
F1 J19Eאאא
1 J5 J5אאאEffective value of sine wave
אאRoot Mean Square (RMS Value)
א،אאאאאא،אאאא،
אאאאאאא
א 116 אא א א J2 א
‐ 14 -
אאאאאאאאאאאKאR.M.S
אRoot Mean SquareאאאאאאאאאKא،אא
אאאאא PP IV ,אאא PPPP IV ,W
F1 J6EPrms II 707.0orPrms VV 707.0
F1 J7E rmsP II 414.1orrmsP VV 414.1 F1 J8E rmsPP II 828.2orrmsPP VV 828.2
W 1Kאאא،אא
אאאאאאאK 2KאאאEffective valueאKאאאK
1 J5 J6אאאAverage value of sine wave
אאאאאאא(T)אא،ZKאאאT/2
אא،אאאאאאאאאT/2אאא
F1 J20E،WאאאאT/2אאאאאKאא
אK
F1 J20Eאאאא
א 116 אא א א J2 א
‐ 15 -
אאאאאאא،W
F1 J9ErmsPavg III 9.0637.0 rmsPavg VVV 9.0637.0
F1 J21Eאאאא
F1 J2EW
avgrmsPPP VVVV ,,,אאW
F1 J22EאאF1 J2E
אW VVp 5
VVPP 10
VVV Prms 535.3*707,0 VVV Povg 535.3634,0
א 116 אא א א J2 א
‐ 16 -
אאWאאאא
1 J6אאאאW Ohm's Law and Kirchhoff's Laws in AC Circuits
1 J6 J1W אאאאאAC אא
אאאDCאאאאא،אאKאאאאאPhase Angleא
K
1 J6 J2אאאOhm's Law in AC Circuits א،Current،א
FEא،Voltageאא،אResistorKאאאאW
F1 J10E I
VRRIV
R
VI .
F1 J23E
W
1K אאאאK 2K אאאFאESame Phase angle
3K אאACאאאאWאאPeak Value Average ValueRMS Value
א 116 אא א א J2 א
‐ 17 -
F1 J3E אאאW
F1 J24EאאאF1 J3E
1E אK
2E אאאK
אW אאאW kRRRT 56.121
אאא
T
rmssrms R
VI
،אאאאאW VVV PrmsS 7.70707.0
W mAIrms 3.45
א12 , RRW VRIV rmsrms 32.4511
VRIV rmsrms 38.2522
1 J6 J3אאאא Kirchhoff's Voltage & Current Laws in AC Circuits
،אאאאאאאK?אאאF
EאK?אאאא
א 116 אא א א J2 א
‐ 18 -
אאאא،אK?אאאאאW
W F1 J11E ..........321 vvvvs
W F1 J12E LeavingEntering II
W
אאאאאK WאאאW
Kirchhoff's Voltage Law in AC Circuits אא،אאW
F1 J25Eאאא
אאאW
F1 J13E )()(2)(1)( ..... rmsNrmsrmsrmss VVVV F1 J14E )()(2)(1)( ..... PNPPPs VVVV
אאאאאאאK
WאאאW Kirchhoff's Current Law in AC Circuits
אא،אאW
א 116 אא א א J2 א
‐ 19 -
F1 J26Eאאא
אאאW
F1 J15E )()(2)(1)( .... rmsNrmsrmsrms IIII F1 J16E)()(2)(1)( .... PPNPPPPPP IIII אאאאאאאK
F1 J4EW אאPeak Valueא3R؟
WאאאאאR.M.S ValueK
F1 J27EאאאF1 J4E
אW א3VW
321 VVVVS )(3)(2)(1)( rmsrmsrmsrmsS VVVV
אאא3V VV rms 4)(3
אא3VW VVV rmsP 66.5414.1 )(3)(3
א 116 אא א א J2 א
‐ 20 -
F1 J5EW אאאW
F1 J28EאאאF1 J5E
אאRMSאא،avgI
א א)(rmstotIW
AIII rmsrmsrms 13310)(2)(1)( אאאF)(PI E
AII rmstP 382.18414.1 )()( אאאFE)(avgtI
AII Pavg 7.11*637.0 )()( 1 J7FאEW
Superimposed DC and AC voltage 1 J7 J1W
א،אWאKא،א،א
F1 J29Eא
א 116 אא א א J2 א
‐ 21 -
אאאאאא،אאFאאאאE
אא،אW
1 J7 J2אאאאPDC VV אא،אW
F1 J30EPDC VV
אא،אWpDC VV K
אאWPDC VV K אאאא
אא،אK 1 J7 J3אאאאPDC VV
אא،אW
F1 J31EPDC VV
אאא،WpDC VV K אאWPDC VV K
א 116 אא א א J2 א
‐ 22 -
אאא،אאאאאא
K
F1 J6EW אאא،אאאW
F1 J32EאאאF1 J6E
Wא
אאאRW VVVVVV PDC 221012max
אאאRW VVVVVV pDC 21012min
א،אאאאאK
F1 J33EאאאPDC VV
א 116 אא א א J2 א
‐ 23 -
F1 J7EW אאאR
F1 J34EאאאF1 J7E
אW
אא vVVV pDC 16max
אא VVVV PDC 4min
אאא،אאאW
F1 J35EאאאPDC VV
א 116 אא א א J2 א
‐ 24 -
אאאWאא
1 J8אאNon Sinusoidal Wave Forms 1 J8 J1W א،אאKא
אאא،אאאאאאKאאאW
1K FאERepetitive Pulse Wave Form
2K אאSquare Wave Form
3K אאTriangular Wave Form
4K אSaw tooth Wave Form 5K אאHarmonics
א،K
1 J8 J2FאERepetitive Pulse Wave Form אאאאW
F1 J36Eא
אאTא،אPeriodKא
BaselineאאאW
א 116 אא א א J2 א
‐ 25 -
F1 J37Eאא
אK W
אאאאFE،אאKאאאא،אאאאאPractical Pulse Wave FormK
F1 J38Eאא
،אW
1K א rTRise TimeWאא%10א%90אאAmplitudeK
2K א FTFall TimeWאא%90א%10אאK
3K א WTPulse Width WאאN, M א%50אאAK
אW
א 116 אא א א J2 א
‐ 26 -
4K אThe duty Cycle
F1 J39Eאא
אאאFאEאא
אאW F1 J17E %100*..
T
TCDP w
FCDP ..EאאPercent Duly CycleK
5K אאAverage Value
F1 J40Eאאא
F1 J8E AmplitudeT
TwVV baselineovg *
F1 J8EW אאW
F1 J41EאאF1 J8E
א 116 אא א א J2 א
‐ 27 -
אT،אF،אאCDP ..אא،K א
ZkHsT
FsT 10010
1110
%10%100*10
1%100
T
TWPercent duty Cycle=
W א%10אK
VVVs
sV
amplitudeT
TVV W
baselineavg
4.115*10
11
*
1 J8 J3אאSquare Wave אאאאא
%50אZאT،W F1 J19E
2
TTW
אאאW
F1 J42Eאא
W
2
TTW
1 J8 J4אאTriangular Wave Form
אW
F1 J43 JE
א 116 אא א א J2 א
‐ 28 -
F1 J43 JE
אא،אאאאא
א،אW
F1 J44Eאא
F1 J9EW אFאאEW
F1 J45EאאF1 J9E
אW
skV
msV
ms
vv
t
vslope
sVs
v
t
vslope
/2
/3
63
410
/25
10
א 116 אא א א J2 א
‐ 29 -
1 J8 J5אSaw tooth Wave Form
،אאא،אאW
F1 J46Eא
،אאאא
אאאאאאKאאאאאאא
אK
א 116 אא א א J2 א
‐ 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
א 116 אא א א J2 א
‐ 31 -
אא WאW
K אאאאא
K אאא
K אא
K אאאאK
WאW 1 .אאV12
אRMSאאאPPV אאAVGV 2Kאא21RRאאא
RMS
F1 J47E
3K אא3RRMS
F1 J48E
167
אאאא
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
א 116 אא א א J2 אא
‐ 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
א 116 אא א א J2 אא
‐ 35 -
F2 J2Eאא
W אאאאאאאPrimary Windingא
K אאאאאSecondary Winding א
K W
אאThe Core אאאאאK
2 J3 J2אW
،אאW 1K אAir Core אאW
F2 J3Eאאאא
2K Ferrite CoreאW
F2 J4Eא
א 116 אא א א J2 אא
‐ 36 -
3K Iron Core אW
F2 J5Eאא
אאאאאאאHigh Frequency Applications ،אאIron Core אאאאPower Applications
אאאאאAudio Frequency ApplicationsK
2 J3 J3W א،אאW Wאא،Core –type א،W
F2 J6 JEא
WאאאאShell – type א،W
F2 J6 JEא
W אאא،VarnishK
12-4 אFאEאW 2 J4 J1אאTurns Ratio
אFNEאאאאsecNאאאpriNאא،W
א 116 אא א א J2 אא
‐ 37 -
F2 J1E i
Sec
N
NN
Pr
F2 J1EW אאW
F2 J7EאאאF2 J1E
100Pr iN 400sec N
W 4
100
400
Pr
i
Sec
N
NN
אאW
F2 J8Eא
אאאא4אאK
2 J4 J2אאDirection of Winding
אאאאאאא،אW
א 116 אא א א J2 אא
‐ 38 -
אאW א،אא،אאאאאא
אPrimary and Secondary are in phase KאW
F2 J9Eאאא
אאW
F2 J10Eאאאא
W אאאאK
אאW ،אאאאא
אאW
F2 J11Eאא
אאאאאא0180Tא،W
א 116 אא א א J2 אא
‐ 39 -
F2 J12Eאאאאא
אאW
F2 J13Eאאאא
2 J5אאאInductance Voltage and Current Relationship
2 J5 J1אאאאאא Primary and Secondary Voltage Relationship א،אאאאאאא
אאאאאאאאאFאאאEאאFאאEW
F2 J2E NN
N
V
V
PRI
SEC
PRI
SEC
W
F2 J3E PRIPRIPRI
SECSEC VNV
N
NV *
2 J5 J2אאאאאא Primary and Secondary Current Relationship
אFאאEאאאאאאFאאE،
אW
א 116 אא א א J2 אא
‐ 40 -
F2 J14Eאאאאא
אאאאאPRIIאאsecIW
F2 J4E NN
N
I
I PRI
PRI
1
sec
sec
W
F2 J5E N
II
N
NI PRI
PRIPRI
*
secsec
WאאאאאW
1K upstep אאK 2K downstep אאK
2 J6אאTransformer Types
2 J6 J1Step–up Transformer אאא،אאאFאאE
אאאFאאאKEא1KאאאאKאאאW
F2 J6E PRISEC NN 1N،F2 J2EW
F2 J7E PRISEC VV ،אאאאאF2 J5EPRISEC II ،
אאאאא
א 116 אא א א J2 אא
‐ 41 -
2 J6 J2Step–down Transformer אא،אאאFאאE
אאאFאאאKEא1KאאאאKאאאW
F2 J8E PRISEC NN 1NאאאאאPRISEC VV אא،
אאאPRISEC II K
F2 J2EW אאאא200אא،600א،
אאאאW
F2 J15EאאאF2 J2E
אW
VVN
NV rmsPRI
PRI
SECrmsSEC 360120*
200
600*
, where N=3 VVN rmsPRI 360120*3*
AIN
NI rmsPRI
SEC
PRIrmsSEC 26*
600
200*
אאא،אאא
Step– up TransformerKאאאאאK
א 116 אא א א J2 אא
‐ 42 -
F2 J3EW אאאאאW
F2 J16EאאאF2 J3E
אW
VVN
NV rmsPRI
PRI
SECrmsSEC 24120*
50
10* )(
AAIN
NI rmsPRI
SEC
PRIrmsSEC 306*
10
50*
אאאStep– down TransformerKאאK
2 J7אאאTransformer Current Direction
،אאW 1K אאFאאEא،W
F2 J17 JEאאאאאאאא
F2 J17 JEאאאאאאאא
א 116 אא א א J2 אא
‐ 43 -
2K אאFאאEא،W
F2 J18 JEאאאאאאאא
F2 J18 JEאאאאאאאא
א 116 אא א א J2 אא
‐ 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
א 116 אא א א J2 אא
‐ 45 -
אא
1K אא،אאאW
F2 J19E
2K אW
F2 J20E
1K אאא avgVsec 2K אאFאE،אאאאאא
אא؟
א 116 אא א א J2 אא
‐ 46 -
3K אW
F2 J21E
1K אאאK
2. אאאKאאאאאאאאK
167
אאאאאא
אאJJ22
א
אא
3
א 116 אא א א J2 אאא
‐ 47 -
אא אאא
אאWאאאאאK
אאWאאאW
אאאK
אאאWאאא90٪
אאאאW9
אאW J K J אאK
אאWאאאאאאאאאאK
א 116 אא א א J2 אאא
‐ 48 -
3 J1Introduction
א،אאאאאאאאאK،אא
sKאאאACאאא،،אאאFrequencyא
CapacitanceK
3 J2אאCXCapacitive Reactance אאCXאא،W
אא אא،א
א،אאאאW
F3 J1Eאאאא
אאFאא،Kא؟
F3 J2Eא
א 116 אא א א J2 אאא
‐ 49 -
F3 J2Eא،F1EאאF2KE،t אאאאא12א VV K
V
QC CVQ א،א12 II Kאאאאא
אאאאאאאאאFEא،אאאK
W אאאאCXCapacitive Reactance،
אאCXא)(OhmK
אא אאא
א،אאW
F3 J3Eאאאא
א،אאאKאאאCapacitive Reactance Formula،W
F3 J1E CF
X C ..2
1
F3 J1EW אאאW
F3 J4EאאאF3 J1E
א 116 אא א א J2 אאא
‐ 50 -
אאCX،אאkHzf 1K אW
kCF
X C 8.3110*005.0*10*1*2
1
.2
163
3 J3אאאאOhm's Law in Capacitive AC Circuits ،אא
אF3 J3E،אא،אKW
F3 J2E VQ
F3 J3E CVQ
אאאCאאאא،א
FaradK
F3 J5Eאאאא
אאאאאאאאאא،K
،W F3 J4E CXIV * F3 J5E
CX
VI
F3 J6E I
VX C
אאאאW
א 116 אא א א J2 אאא
‐ 51 -
F3 J6Eא
W א،אאאאאאRMSPeak
PeaktoPeak K
F3 J2EW אאאF3 J1E،א5אV،W
F3 J7EאאאF3 J2E
אPeakPIK אW 1K PI،CXאאW
kFC
X C 18.310*005.0*10*102
1
2
163
2K smrI ..W
mAX
VI
C
rmsrms 57.1
10*18.3
53
3K אsmrI ..PIW mAII rmsP 22.2*414.1
א 116 אא א א J2 אאא
‐ 52 -
3 J4אאאאW Current & Voltage Relationship in Capacitive Circuits
אאאאא،،אare in Phase)RIandRVKEאא،
אLeadsאo90אאא،אPhase Shift)EK
F3 J8Eאאאא
3 J5אאאPower in Capacitor Circuits א،אאאDCא
אIVP .א،K،אאאאK،אאא
אאאW 3 J5 J1אאInstantaneous Power
אאאאאFאEאאאאאאKאאאW
F3 J9Eאא
א 116 אא א א J2 אאא
‐ 53 -
W 1K אאאאK
2K אאZ،אI=0AV=0VK
3K minmax VI K 4K אאK
אאאאאאאאKאאא
אאאא،אאאאKא،אאאא
אאאא،אאאK
3 J5 J2אאtruePTrue Power אאא،אאאא،
אאKאאאאאאW
F3 J7E 0trueP אא،אאאLeakage،אאאאK
אאK
3 J5 J3אאrP Reactive Power אאא،א
אאאW F3 J8Ermsrmsr IVP * F3 J9E
C
rms
r X
VP
2
F3 J10E Crmsr XIP *2
א 116 אא א א J2 אאא
‐ 54 -
W 1KאאtruePאאwattK 2KאאrPVolt – Ampere –ReactiveאאVAR
F3 J3E אאאW
F3 J10EאאאF3 J3E
אאאאK אW
WPtrue 0
C
rmsr X
VP
2
kFC
X C 96.7.2
1
VARVARPr 50310*50310*96.7
2 6
3
2
3 J6אאאאאSeries & Parallel Capacitive AC Circuits
אאאאאא،אאאKאאאאאאא
،אW 3 J6 J1אאאSeries Capacitors
אאאאאW
F3 J11Eאאא
א 116 אא א א J2 אאא
‐ 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
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....11
1
2!
3 J7אאאאאSeries RC Circuits 3 J7 J1אאאאאאCharacteristics of RC Circuits
אאאא،אאאאW
F3 J13Eאאאאא
א 116 אא א א J2 אאא
‐ 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
א 116 אא א א J2 אאא
‐ 57 -
F3 J16E 22CXRZ
3 J7 J3אאPhase Angle
אאאאאאאאKאאאאאאאאא
W
F3 J16Eאאאאאאא
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
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V1tanאאאR
C
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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
א 116 אא א א J2 אאא
‐ 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
א 116 אא א א J2 אאא
‐ 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
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ncnfX C 3.5
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1
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133
K אZ
kXRZ C 73.522
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K אCV VXIV CrC rmsrms
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א 116 אא א א J2 אאא
‐ 60 -
o
R
C
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3 J8אאאאאParallel RC Circuits 3 J8 J1אאאאאאCharacteristics of RC Circuits
אא،אאאאאאאW
F3 J20Eאאאאא
W SRC VVV
RIRVא
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אאאאאאאאאRCאאאאRCאאאאK
F3 J21EאאאאאRCאא
אCIRIאאo90KRI،RVאTIאא،RIRVא،אא
אTIאאPhase AngleK
א 116 אא א א J2 אאא
‐ 61 -
3 J8 J2אImpedance Z
א،אאאאא،אאאZOhmK،אא
אאאאאאW
F3 J22EאאRCאא
W C
CC X
VI
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F3 J23EאאRCאא
W אadmittanceא،א،א
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F3 J28E 22
22
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F3 J29E2222
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א 116 אא א א J2 אאא
‐ 62 -
3 J8 J3אאPhase Angle
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F3 J24EאאאRCאא
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F3 J30ER
C
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3 J8 J4אאאאRCאאCurrents Relationships אF3 J24 JE،אאאא
אTIאRIאאאCIW F3 J31E 222
CRT III
3 J8 J5אאאאOhm's Law
א،،אאW
F3 J25EאRCאא
א 116 אא א א J2 אאא
‐ 63 -
W F3 J32E ZIV *
אאאW F3 J33E
Z
VI
F3 J34E I
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Conversion From Parallel to Series Formא،אRCאאאRC
א،אאRCאאאRCאא،אאא،אאאRCאא
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F3 J26EאאאאRCאא
W
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sin.Zxceq
F3 J40E sin.2
1
fZCeq
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CX
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א 116 אא א א J2 אאא
‐ 64 -
F3 J5EW אאאW
F3 J27EאאאF3 J5E
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K אZ
5.843.
22C
C
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K אאאCI
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rmsSrmsC 25.6)(
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2)()(
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‐ 65 -
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א 116 אא א א J2 אאא
‐ 66 -
SummaryאאאאW
אRCאא אRCאא 22א
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22אCXRZ א
22
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C
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R
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1
1
tan
tan
אא
R
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C
I
I
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1
1
tan
tan
3 J9אאFא JאEאאאSeries-Parallel RC Circuits
אאאאאK F3 J6EW
אאאאאאאאW
F3 J28EאאאF3 J6E
1אאK 2אא 3אאאSVאI
אW WאאW
318.2
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א 116 אא א א J2 אאא
‐ 67 -
WאאRCאאאאFRCאאEאW
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222
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CX
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2
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א 116 אא א א J2 אאא
‐ 68 -
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k
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o
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אאאW
F3 J31EאאאF3 J7E
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11 * ZIV rmsrms 105022
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Kא2Vא2ZW VmAZIV rmsrms
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VXIV CrmsCrms16.2*
1
א 116 אא א א J2 אאא
‐ 69 -
Kאא2Rאא2C mA
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VI R 64.4
680
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340
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2
22
3 J10אאאאPower in RC Circuits
3 J10 J1אPower Triangle א،RCאאRC،אא
אאאאאאאKאאRCאאאRCא،אאW
F3 J32EאRCאא
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rmsICrmsR
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rmsCVאאK rmsIC
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‐ 70 -
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3 J10 J2אאPower Relationships and Measurement Units אאApparent PowerAmpereVott VAW
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אאTrue PowerאWatt WW
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3 J10 J3אאThe Significance of apparent Power
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אאא،אאאK אאאFאאE
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W אאאאאאאאאא
א،אאctorthePowerFaPF :
א 116 אא א א J2 אאא
‐ 71 -
3 J10 J4אThe Power Factor (PF) אPower Factor،אאא،
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F3 J44E cosa
true
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r
rmsrmsSatrue
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،W1PF
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rmsrmsSar
true
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0
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א 116 אא א א J2 אאא
‐ 72 -
WאRC
،אאא،אא10 PFKאאאאK
F3 J8EW אאא،אאאאא؟
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אW
kCF
X C 18.3.2
1
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a 5.6710*5.67 32
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א 116 אא א א J2 אאא
‐ 73 -
אSummary
1K ،אאאאאא)are in Phase)RIandRVKEE
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3K אאאאאFאEאאאאאאK
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rmsrmsr IVP *
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N
T
CCC
C1
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1
21
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NT CCCC XXXX 2!
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א 116 אא א א J2 אאא
‐ 74 -
22CRS VVV
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CRT III 10K אRCאאRCאאאאW
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tan
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R
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1
tan
tan
א 116 אא א א J2 אאא
‐ 75 -
אא 1K אאאאאW
2K אאאאאאאW
3K אאאW
אאאK
؟אאאאא
אאא؟
א 116 אא א א J2 אאא
‐ 76 -
א 116 אא א א J2 אאא
‐ 77 -
4K אאTrmsIאאTavgIאא،W
5K אאאאW
6K אאאW
1oאאTI 2oאאא1:
1CIc
3oאאא2:2
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א 116 אא א א J2 אאא
‐ 78 -
א 116 אא א א J2 אאא
‐ 79 -
8K 312
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،אאאאא؟
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אאTruePowerWWPtrue 2
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167
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א
אא
4
א 116 אאא א א J2 אאא
‐ 80 -
אאא אאא
אאWאאאאאK
אאWאאאW
אאאK
אאאWאאא90٪
אאאאW9
אאW J K J אאK
אאWאאאאאאאאאאK
א 116 אאא א א J2 אאא
‐ 81 -
4 J1Introduction
،אאאאאאאאאאא
א،אאאאאאאאאאאא
אאOpen Circuitא،،אK
אא،אאאFאEאאFאאאKEאא
אאShort Circuit،אK
4 J2אאLXInductive Reactance אאLXאא،W
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א 116 אאא א א J2 אאא
‐ 82 -
אK،אאאאאאאאאאאK
W 1K אאאLXאFX L K
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א،אאW
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אאאKאאLXאKא،א،א،אא
Inductive Reactance Formula،W F4 J1E LFX L .2
א 116 אאא א א J2 אאא
‐ 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
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אאאאאא
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F4 J2E LXIV . F4 J3E
LX
VI
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א 116 אאא א א J2 אאא
‐ 84 -
F4 J5Eא
W
א،אאאאאאRMSPeakPeaktoPeak K
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אאאW
F4 J6EאאאF4 J2E
אא؟ אW
4 J4אאאאCurrent & Voltage Relationship in Inductive
Circuits ،אאאאא،אare in Phase)RIandRVKEאאא،
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א 116 אאא א א J2 אאא
‐ 85 -
F4 J7Eאאא
אאאאא
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4 J5אאאPower in an Inductor
אאאא،DCאאIVP .א،K،אאאא
Kא،אאאאאW
א 116 אאא א א J2 אאא
‐ 86 -
4 J5 J1אאInstantaneous Power אאאאאFאE
אאאאאאKאאאW
F4 J8Eאא
W
1K אאאאK 2K אאאאK
3K אאאאK
4K אא،אאאאאW KאאK
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KאאK 4 J5 J2אאtruePTrue Power
אאא،אאא،אאאKאאאא
،אW
א 116 אאא א א J2 אאא
‐ 87 -
F14-5E 0trueP אK،אא،אאא
אאאWRKאא،W
F4 J6E Wrmstrue RIP 2
4 J5 J3אאrP Reactive Power ،אאאא
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L
rmsr X
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2
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rmsIWאאאK rPאא(VAR) Volt- Ampere – ReactiveK
F4 J3EW אאאW
F4 J9EאאאF4 J3E
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rmsr X
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2
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VPLFX
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rmsrL 59.18.62.2
2
א 116 אאא א א J2 אאא
‐ 88 -
F4 J4E ،אא،א 5WRKאא
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אאאאFאE mA
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rmsrms 159
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א 116 אאא א א J2 אאא
‐ 89 -
4 J6אאאאאSeries & Parallel Inductive AC Circuits
אאאאאא،אאאK،אאאאאאאא
W 4 J6 J1אאאInductors in Series
אאאאאW
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،אאאW
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F4 J11E NT LLLL XXXX ...
21
4 J6 J2אאאParallel Inductors
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T
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21
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א 116 אאא א א J2 אאא
‐ 90 -
F4 J13E NLLL
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1
21
אאאאאSummaryW
אCapacitors אFאEInductors
אCapacitance
1210*85.8** rd
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אInductance
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1
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א 116 אאא א א J2 אאא
‐ 91 -
אCapacitors אFאEInductors
אאאאאאo90
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T
CCC
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...11
1
21
NT CCCC XXXX .....21
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X1
...11
1
21
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N
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21
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א 116 אאא א א J2 אאא
‐ 92 -
אCapacitors אFאEInductors
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א 116 אאא א א J2 אאא
‐ 93 -
אCapacitors אFאEInductors
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1
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א 116 אאא א א J2 אאא
‐ 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
4 J7 J2אImpedance Z
،א،אאאאאאאאFאEאTRא،
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אZOhmK אאאאSeries R – L אW
א 116 אאא א א J2 אאא
‐ 95 -
F4 J14Eא
אאPythagorasW F4 J14E 222
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F4 J15E 22LXRZ
4 J7 J3אאPhase Angle
אאאאאאאאKאאאאאאאאאW
F4 J15Eאאאא
W
F4 J16E
R
L
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X L1tan
אאFtanEאאא،אאW
F4 J17E R
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א
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4 J7 J4אאאRLאאVoltages Relationships אSVאאRVאאLV
אאW
א 116 אאא א א J2 אאא
‐ 96 -
F4 J16EאאRL אא
אאאאאW
F4 J17EאאRL אא
אאK
PythagorasW F4 J18E222
LRs VVV אאאאW
F4 J19E22LRS VVV
F4 J20E22LSR VVV
F4 J21E22RSL VVV
4 J7 J5אאאאOhm's Law
،،אאאW
F4 J18EאRL אא
אאאאRVאאW
F4 J22ERIVR . אאLVאא،LX،
אאאאLVW F4 J23E LL XIV .
א 116 אאא א א J2 אאא
‐ 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
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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
א 116 אאא א א J2 אאא
‐ 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
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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
א 116 אאא א א J2 אאא
‐ 99 -
F4 J21EאRLאא
W SRL VVV
RIRVא
LIRIאאo90K
אאאאK
F4 J22EאאRLאא
4 J8 J2אImpedance Z
،אאאאא،אאאאZOhmK،אא
אאאאאאW
F4 J23EאאRLאא
W
F4 J27E R
VI R
R
א 116 אאא א א J2 אאא
‐ 100 -
4 J8 J3אאPhase Angle
אאאאאאאאאאW
F4 J24Eאאאאאאא
W
F4 J30E
R
L
I
I1tanand
R
X L1tan
אאFtanEאאא،אאW
F4 J31E R
L
I
Itan
Wא
R
L
I
I1tanאאאR
L
I
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4 J8 J4אאאאRLאאCurrents Relationships אאTIאRIאאאLI
אאW
F4 J25EאאאאRLאא
،אW F4 J32E 222
LRT III W
F4 J33E 222222RTLLTRLRT IIIIIIIII
א 116 אאא א א J2 אאא
‐ 101 -
4 J8 J5אאאאOhm's Law
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
א 116 אאא א א J2 אאא
‐ 102 -
F4 J36EcosZReq F4 J37E
F
Z
F
XLZX Leq
eqLeq
2
sin.
2sin
F4 J6EW אאאW
F4 J29EאאאF4 J6E
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K אZ
kXR
RXZ
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L 19.122
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rmsR 54.4)()(
K אאאLI
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rmsSrmsL 1.7)(
)(
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2)()(
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rmsL
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א 116 אאא א א J2 אאא
‐ 103 -
F4 J30Eאאאאאא
mH
F
XLkZX Leq
eqLeq 25.1062
1sin.
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4 J9אאFא JאEאאאSeries -Parallel RL Circuits אאאאאK
F4 J7EW אאאW
F4 J31EאאאF4 J7E
1אאTZK 2אאTIK 3אאאSVאI
אW WאאW
kfLX
kfLX
L
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14.32
85.72
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1
2
1
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F4 J32Eאאאאאא
א 116 אאא א א J2 אאא
‐ 104 -
אאאאK
kZX
kZR
eqL
eq
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22
22
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28.2.
2
L
L
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R
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kXXX LeqLTL 5.91 אאא kX
TL 5.9אא kRT 27.6،W
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1
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4 J10אאאאPower in RL Circuits
4 J10 J1אPower Triangle א،RLאאRL،אא
אאRLאאאאאK
F4 J33EאRLאא
א 116 אאא א א J2 אאא
‐ 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
א 116 אאא א א J2 אאא
‐ 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
א 116 אאא א א J2 אאא
‐ 107 -
F4 J8EW אאאW
F4 J36EאאאF4 J8E
א2,1אאאאw20אאאאKאאא
אKאאא 75.0PFאאא 95.0PFאאא،
אK
א 116 אאא א א J2 אאא
‐ 108 -
Summaryאאאאאא
אאאRC אאאRL
אRCאא
אאא
22אCXRZ
אא
R
C
C
V
V
R
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1
1
tan
tan
222CRS VVV
אRLאא
אא
א 22א
LXRZ
אא
R
L
L
V
V
R
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1
1
tan
tan
222LRS VVV
א 116 אאא א א J2 אאא
‐ 109 -
אאאRC אאאRL
אRCאא
אא
א א
22C
C
XR
RXZ
אא
R
C
C
I
I
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R
1
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tan
tan
222CRT III
אאאאאW
sin...2
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..2
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sin.
cos.
ZFXFC
ZX
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Ceq
eq
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.
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tan
222LRT III
אאאאאW
F
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F
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ZX
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Leqeq
L
eq
eq
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2
sin.
cos.
א 116 אאא א א J2 אאא
‐ 110 -
אאא 1K mH100אאאא،A1؟
2K אאB,A אא،W
3K אאאW
K אאאאאK
K אא23 , LLK
4K אImpedanceאאא،W
א 116 אאא א א J2 אאא
‐ 111 -
5K אאאW
K אאI
K אא
K RL VV ,
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K א
K אאאאTI
K אLR II ,2
K אאtruePאאrP
K אאaPאPF
167
אאאאאאאא
אאJJ22
א
א
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5
א 116 אא א א J2 אאאא
‐ 112 -
אא אאאא
אאWאאאאאאK
אאWאאאW
אאאאK
אאאWאאא90٪
אאאאW9
אאW J K J אאK
אאWאאאאאאאאאאאK
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 115 -
5 J2 J4אאPhase Angle
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
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XT
LC XX אאאא029
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 117 -
FE ،אW
VXIV
VXIV
VRIV
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CC
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03.3.
26.7.
08.9.
FE אאאCLV،W
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אאאCVK אאW
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R
X T
אCL XX אאאאאא025K W
F5 J8Eאאא
5 J2 J6אאSeries Resonance
،אאאאאאאאאאאא،אCX
אאLXאW
א 116 אא א א J2 אאאא
‐ 118 -
F5 J9Eאאאא
W F5 J4E
CfXC .2
1
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fXX CL , אאLC XX אאאאאא،
אאאאאאKאאאKאא،אW
F5 J6ECLCL VVXX F5 J7ERZ r
אW
F5 J10Eאאאאאאא
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 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
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W CLR VVV
W CL VV
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 122 -
F5 J15Eאאאאאאא
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
.
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 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
5 J3 J4אאPhase Angle
אא،W
F5 J18E
TX
R1tan
F5 J5EW אא،אאאאW
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 126 -
אOpen Circuitsאאא،אK،אאאאW
F5 J19ECL
CLT XX
XXX
CL XX אTXאא،،،אW
F5 J22Eאאאאאאא
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
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 129 -
8K אאאאאאא،00K
9K ،אאאאאאSLCR VVVV
10K אאאאאאאW
11K אא
CL
CLT
CLT XX
XXX
XXX
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12K אאאRLCא،אאאאW
22
.
T
TT
XR
XRZ
13K אא،W
TX
R1tan
14K אאאrfאאא،W
LCfr 2
1
א 116 אא א א J2 אאאא
‐ 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
א 116 אא א א J2 אאאא
‐ 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
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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 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