Embed Size (px)
Citation preview
JJ١١
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
١٤٠١٤٠
١٤٠ א א
-١
،،אא،אW
אאאאאאאאאא א א א א א א א ،א
אאאאאא،אאאאאא
אאאK
אאאאאאא א ،א אא
א א א ، אא א אא،אאאאאאאאאאאאאאאאא
א א א ،אא،אאK
א א ? J١ ? ?
?אאאאאאאK
אאאאאאא،א،אאאא
אאאאאK
، א אאאאK
אאאא
١٤٠ א
-١
אאאא،KKK،א،אאאאאא
אאאKאאאאאא
א،אאאאאאאאאאאאאאKאאא
،אאאאאאאא،אאאאאאאאאאאK
אאJ١אאאאאאאאאK
אא،אאאאאאאא،א،אאK
א،،אאאא،אאאא
אאK،אKKKKKK
אאאאאא
JJ١١
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
א
א
א
١
אא ١٤٠ א א
אא -١ אא
- ١ -
אאאא
،אאאאאW• אאאK • אאאK
אא ١٤٠ א א
אאא -١
- ٢ -
١J١ אאאאאאא،
אאאK١J٢ אאאThe International System of Units
אאאאאאאאKאאאא
אKK١J٢J١ אאThe Measurement Units אאא،אא
אאW
אQuantity אUnit אSymbol
אLengthMeter m
אMass אKilogram kg
אCurrent Ampere A
אTime Second s
אאTemperature Kelvin K
אLuminous Intensity Candle cd
F١-١EאאThe Measurement Units
אאTemperatureא Luminous IntensityאאאKאאאאאאאאאאא
אא،אאForceNא
א2skgKאאElectric PowerאWatt
אא ١٤٠ א א
אאא -١
- ٣ -
Ws
NmKאאElectric Energy
אJoule JNmK١J٢J٢ אאאאאא
Power of ten units، prefixes، which attached to the measurement unitsאאאאThe International System of Unitsאpower
of tenאאא،אאאאאW
אPrefixes to the Units
אSymbol
אPower of ten
Attoa1810*1 −Femto f1510*1 −
Pico p1210*1 −Nano n910*1 −
Micro µ610*1 −Milli m310*1 −Centi c210*1 −Deci d110*1 −Deka da110*1Hecto h210*1Kilo k310*1Mega M610*1
Giga G910*1אTera T1210*1
F١J٢Eאאאאאא
١J٣ אאאThe Basic Electrical Quantities אאאאChargeא،Currentא،Voltageא،
אאElectrical ResistanceKאא
אא ١٤٠ א א
אאא -١
- ٤ -
אאאאאא،AtomsKאאאElectronsFאJE،
אProtonsFאEHא،NeutronsFאKE١J٣J١ אCharge
Qאא،ElectronאProton،אאאאK،א
אK،אאא
אאא،אאאאCoulombאCK
١J٣J٢ אCurrent אאאאאI،
אאאאאאKאאFאEאאCurrentKW
dtdQI = F١J١E
אAmpereא،W
sCA ≡ F١J٢E
WIאAKQWאChargeCKtWאtimesK
א،אElectronsא،אאK
אא ١٤٠ א א
אאא -١
- ٥ -
F١J١Eא אאאאאאא
אvoltage sourceאא،א،אאאאKאאאאא
KאאאאW١K Pure D.C. Current
،אאאאF١J٢KE
time (t)
Cur
rent
(I)
F١J٢E
٢K Pulsating Current ،אF٣J١KE
time ( t )
curre
nt (
I )
E
I
Load
אא ١٤٠ א א
אאא -١
- ٦ -
time ( t )cu
rrent
( I )
time ( t )
curre
nt (
I )
F١J٣EPulsating Current
٣K Alternating Current אאKאאsin wave
אאAlternating CurrentK
time ( t )
curre
nt (
I )
F١J٤EAlternating Current
١J٣J٣ אVoltage אא(Work)،אאVolt
אW
CJV ≡ F١J٣E
W
dQdWV = F١J٤E
W
אא ١٤٠ א א
אאא -١
- ٧ -
VWאVKWWאJKQWאChargeCK
١J٣J٤ אResistance ،אאאאאא
אאאאא،Electric PowerאאאאKאאא،אאאאOhmKא
אא،אאOhmΩ،אא،אאאאאאא،אאאאא
אאאאאKא،אאאאאאאא
אאW
Resistance (R)
Cur
rent
(I)
F١J٥Eאאא
١J٣J٥ אאResistance of a wire אWiresאW
١K אLength،LK٢K אCross-section Area،AK
אא ١٤٠ א א
אאא -١
- ٨ -
٣K אFאאEMaterial،ρ،KאK
٤K אאTemperature،TK אאאW
AL.R ρ
= F١J٧E
WRWאResistanceΩKρWאאm.ΩKLWאLength،mAWאCross-section Area،א2mK
F١J١Eאא٥mmא،٥mKא
אC20oאא،m10*72.1 8Ω−
א
אRאF١J٧E،W
AL.R ρ
=
( )Ω=⎟
⎟
⎠
⎞
⎜⎜
⎝
⎛
∗π∗∗=∴
−
− 38.42105
51072.1R23
8
אא ١٤٠ א א
אאא -١
- ٩ -
אאTypes of Resistors אW
١K אאWOpto-photo-Resistorsאאא،א،א
אאK ٢K אאאWThermal-Resistors،אאא
אאKאאאאאאאKאאא
1
10
100
1000
10000
0 40 80 120 160 180 200درجة مئوية
ومأ
F١J٦Eאאאאאא
אאאאאא
אאאK٣K אאאVoltage Dependent ResistorsWא
VDR،אאאK ٤K אאLinear ResistorsWאאאאW
K אאWK
אא ١٤٠ א א
אאא -١
- ١٠ -
K אאWאאאאאאKאאא
W ١EאPotentiometerWא
Voltage Divider،א١،٢،٣F١J٧FEEא،אאMega OhmK
٢ERheostatWאאאאKilo
Ohmאא،אא،אאאא،
אאאאKאF١J٧FEE
KאאWאאאאאאאאאא،אאK
אאאאאאK
FEFEF١J٧Eאא
٣
+
-
١
٢+
-V٢٣
V١٣١
٢٣
אא ١٤٠ א א
אאא -١
- ١١ -
١J٣J٦ אConductanceאא،אאאG
SiemensאAmpere per Voltא،W
R1G = F١J٥E
SiemensKW
G1R = F١J٦E
.OhmאGאאK
אא ١٤٠ א א
אאא -١
- ١٢ -
אא
١K אאאאאא: E٢٩٠٠٠ kW
EΩ ٧٠٠٠E٠٠٠٣٠ msE٠٥٠ A
E٠٠٠٠٩٠ V E٧٠٠٠٠٠٠ V E٠٠٠٠٠٠٠٠٨٠ s E٩٠٠٠ kW
٢K W E١٥mAA
E١٠ nssEAµ ٨٠٠mAE١٣ nAA
٣K אW E١٥mAHAµ ٨٠٠
E١٠ nsH١٣ msEAµ ٨٠٠+ ١A E١٣ nA+٧٠٠٠ µA
٤K אA - BW
EA=١٥mA،Aµ B=٨٠٠EB=١٣ ns A=١٠ msEAµ A=٨٠٠، B= ١٠٠٠ nA EA=١٣mV،B=٧٠٠٠ µV
אא ١٤٠ א א
אאא -١
- ١٣ -
٥K א
BAW
EA=١٥mA،Aµ B=٨٠٠EB=١٣ ns A=١٠ msEAµ A=٨٠٠، B= ١٠٠٠ nA EA=١٣mV،B=٧٠٠٠ µV
JJ١١
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
٢
א١٤٠ א א א
-١
- ١٤ -
אאאא
،אאאאאW• אאאK • אאאK • אאאK • אאא
א١٤٠ א א א
-١
- ١٥ -
٢J١אאאFundamental Lawאאא
،אאאKאאאא
א،אאאKאאאאאא
אאאאKאאאאאאאGeorge Simon Ohm
Ohm’s Law١٨٢٦Kאאא،אאאא،אאאא
אא،אאאW
F٢J١Eאא
٢J٢Ohm’s Law ،אאאאא
אK٢J٢J١ FEאCurrent Formula
אאאא
RVI ,
REI
T== F٢J١E
WIאAK
EאVoltage SourceVKVאאVoltage Drop،VK
I R
+ − V
I
t
Slope = R
א١٤٠ א א א
-١
- ١٦ -
F٢J١EאΩ100،א٥٠V،
אאא؟
F٢J٢EאאאF٢J١E
אאאW
A5.010050
RVI ===
٢J٢J٢ אResistance Formula
אאאאKאאאW
TT I
ER , IVR == F٢J٢E
WTRW،אאאΩIאAK
TIאאאאKEאVKVאאVK
AI
V Ω100
א١٤٠ א א א
-١
- ١٧ -
F٢J٢Eא ١٥٠mVא،A75µ،
א؟
F٢J٣EאאאF٢J٢Eא
אW
Ω=Ω===−
−K210*2
10*7510*150
IVR 3
6
3
NoteW
،אאאאאאאK
F٢J٣Eאא א٥٠ mAאא٣٠VK
Kאאאאא
אW
Ω=Ω===−
k6010*6010*5.0
30IER 3
3T
T
AA75I µ=
V mV150
-
+
א١٤٠ א א א
-١
- ١٨ -
F٢J٤E
אאאאאR١١٠mA،אא٢٥ V؟אא،
F٢J٤EאאאF٢J٤E
א
Ω=Ω===−
k5.210*5.210*10
25IVR 3
31
٢J٢J٣ Voltage Formula
אאאאאKאאאK
٢J٢J٣J١ אVoltage Drop
א،אאאאאאאFאאE
אאאאאאאא،אאאאא
אK
R.IV = F٢J٣E
V25V =
V
A mA10I =
1R
א١٤٠ א א א
-١
- ١٩ -
٢J٢J٣J٢ אVoltage Source אאאאא
אאTR،
TT R.IE = F٢J٤E
F٢J٥E،אאא אΩ500אא
١٠אAא
V50500*1.0R.IE TT ===
F٢J٦E
א،אאΩK27אא٣mAא
V 8110*27*10*3R.IE 33TT === −
F٢J٧E
אΩk28אאא،٨٠mA
א
V 4.2210*28*10*8.0R.*IV 33 === −
NoteWאא
אאא،א،אאאאאאW
א١٤٠ א א א
-١
- ٢٠ -
F٢J٥E
א،אאאאאW
R*IV =F٢J٥E
RVI = F٢J٦E
IVR =F٢J٧E
אK
אSummary١K אאאאK٢K אCurrent،א،א،א
WRVI =K
٣K ،אאאW
R*IV = ٤K אאאאTIאאא
אאאTRאא،K ٥K אאא
אאאK
VI R
א١٤٠ א א א
-١
- ٢١ -
אא
١K אאאאW
FE אKFE א٧٥٪K FE אK FE א٣٥٪K FE אאאאK FE אאאאK
٢K א،אאW
FE Ω== 1R , V5VFE Ω== 10R , V15V FE Ω== 100R , V50VFE Ω== K15R , V30VFE Ω== M6.5R , V250V
٣K ΩK10١٢V؟אאא، ٤K אאאWJJJ،
אאאא،١٢VK
٥K ٢٥V،אאאאאאאWJJJK
٦K אאאאאאא
אא،אאאΩ8אW
א١٤٠ א א א
-١
- ٢٢ -
אFuse،אאאאאא١٠٠ V؟
٧K אאIאRאאW FEΩ== 18R ,A2IFEΩ== 680R ,A5.2IFEΩ== 56R ,A5I
٨K אאΩ27٣Aא،
K؟א ٩K אאVא،IאאW FEV10V ,A2I ==FEV90V ,A45I ==FEV50V ,A5I ==
١٠K א،אאאאΩ= 100R
Variable Voltage Sourceאאא،אאאאאאאVK ١٠٠אא
V V100V120
Fuse
R
א١٤٠ א א א
-١
- ٢٣ -
KאאVאIKאא؟؟אאא
١١K אאmA5I =אV1V =K
אאאאאאW FE V5.1V =FE V2V = FE V3V =FE V4V =FE V10V =
א،אVאIאא،K
١٢K אאאא،אא،K
V50
Ω= k3.3R Ω= k9.3R
V75
Ω= k7.4R
V100
אאאא
JJ١١
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
א
א
٣
אא ١٤٠ א א
אא -١
- ٢٤ -
אאאא
،אאאאאW• אאאK • אאאאאK • אאאאאאאK
אא ١٤٠ א א
אא -١
- ٢٥ -
٣J١ Introduction א،אאאאאא
א אא א א K א א אאאאPower K
אאאאאאאK
٣J٢ אPower אאאKאאWatt،PK
אאtאאW
timeEnergyPower = F٣J١E
tEP = F٣J٢E
WאZאLא
WPWאPowerאWattKEWאEnergyJאא⋅secondWatt ⋅KtWאtimesecondK
Note،אאאאאאאWWatt
אJouleאאאא،אW
ondsecJouleWatt = F٣J٣E
אא ١٤٠ א א
אא -١
- ٢٦ -
F٣J١Eאא١٠٠ Jא٥ sec؟אא،
א
אW
Watt 20sec 5
J 100tE
timeEnergyPower ====
F٣J٢E
אאP = ١٠٠ Wאאא،t = ٣٠ secKא؟א
time*Power Energy time
EnergyPower =⇒= kJ3J300030*100 t*PE ====
NoteWאאEnergyEWK
F٣J٣EאאאאאאאW
FE ٠٤٥٠ WFE ٠٠٠٠١٢٠ W FE ٣٥٠٠ W FE ٠٠٠ ،٠٠٠ ،١٠ W
א אאmWWkWMWKאאא
אאאאאא،mWאא،אאאאאKWKאאאא
אאאMWK
FE P=٠٤٥٠ W،אאא،אmW
אא ١٤٠ א א
אא -١
- ٢٧ -
W
mW4510*45W10*10*045.0W045.0P 333 ==== −−
FE P=٠٠٠٠١٢٠ W،،אאאאאאא،אWµא،
W
W12W10*10*000012.0W000012.0P 66 µ=== −
FE P=٣٥٠٠ W،kWאW
kW5.3W10*10*3500W3500P 33 === −
FE P=٠٠٠٠٠٠١٠ WאMWW
MW10W10*10*10,000,000W10,000,000P 66 === −
NoteWאאאW
JאאאאאאKJאאאאאאK
Jאאאאאאא،אאאKJאאאאאאא،אאאK
F٣J٤EאאאW
FE١٤٠٠ WאKFE٢٥٠٠ WKFE٠٠٠١٠٠٠ WK
א
אאאאאאW
אא ١٤٠ א א
אא -١
- ٢٨ -
kW4.1101400W1400
3== FE
kWh4.1h1*kW4.1t*PW ===
kW5.2102500W2500
3== FE
kWh5h2*kW5.2t*PW ===
kW100010
1000000W10000003
== FE
kWh5000h5*kW1000t*PW ===
٣Jא ٣אאאPower in Electric Circuit אPowerא،אא
،א،א،אאאאאאאאאאאOhm’s LawK
אאאWI.VP = F٣J٤E
WPWאPowerא،WattKIWאAK
VW،אVK
אא ١٤٠ א א
אא -١
- ٢٩ -
F٣J١Eא
אאאR.IV =אאW
R.II.R.II.VP 2=== F٣J٥E
א،RVI =א
אW
RV
RV.VI.VP
2=== F٣J٦E
TT I
ER , IVR == F٣J٧E
F٣J٥EאאΩ10אא،W
FEI=٧٠A FEI=٤١AFEI=١٢A
I
V R
+
אא ١٤٠ א א
אא -١
- ٣٠ -
אאאW
W9.410*)7.0(R.IP 22 === FE
W6.1910*)4.1(R.IP 22 === FE
W1.4410*)1.2(R.IP 22 === FE
אא،אאאPIKW
2IP α F٣J٨E
אאאאאאאאאאאW
FEA7.0IWatt9.4P =←= FEA4.1IWatt6.19P =←=
FEאFEאFKE
F٣J٦EאF٣J٢Eאא،Ωk10١٥ V،
אאΩk12؟
F٣J٢EאאאF٣J٦E
١٥V
I
Ωk10
+ V
Ωk12
+
−
-
אא ١٤٠ א א
אא -١
- ٣١ -
אאאאאW
mA 5.11015
10*1015
RVI
43====
אאאΩk12W
R*IV =
V1210*12*10*5.1 33 == −
אאΩk12V=١٢ V K
אSummary
• אאאא،Wondsec
JouleWatt =K
• אK • אאאא
אK • אאאאאאאK • אאאK • אאאאאאopen circuitK • אאאאא
K • אxAmpere. HourK • אx١١K
אא ١٤٠ א א
אא -١
- ٣٢ -
אא١–אאאs
j350؟٢–אאj7500h5؟٣–אאאj1000ms500٤–אאאkw
FEw1000FEw3750FEw50000FEw500
٥–אF610*5אxEאxK٦–אאאV75A2א
אLR؟٧–V120אA3אא
؟א٨–אאאΩk10A100µ؟
JJ١١
אאאאאאאאאאאא
אאאÃj×Ö<íÚ^ÃÖ]<퉉ö¹]ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×
אאאא
א
אא
א
א
א
٤
אא١٤٠ א א א
אאאאאא -١
- ٣٣ -
אאאאא
،אאאאאW• אאאאK • אאאK • אאאK • אאאאK • אאאK • אאאאK • אאאאאאK
אא١٤٠ א א א
אאאאאא -١
- ٣٤ -
٤J١ Introduction ،אאאאאא
אא،אאאאאאKאאאאאאKאאאא
אאאא،אאאאאאאאאאא
אאKאאאאאאאK
٤J٢ אאאSeries Connection
א،אאאאאאא،אאאא،אא
אK،אאאאאאK
F٤J١Eאאא
b
a
R٢
R١
R٣
b
a
R٢
R١
R٣
R٤b
a
R٢
R١
R٣
I
II
אא١٤٠ א א א
אאאאאא -١
- ٣٥ -
٤J٢J١ אTotal Resistance (RT) אאאאאאW
n321T RRRRR ++++= KF٤J١E F٤J١E
אאאאאאאW
F٤J٢EאאאF٤J١Eא
אאאאאאא
Ω+Ω+Ω+Ω+Ω= 6.5102710056R T
Ω= 6.198 Ω=∴ 6.198R T
F٤J٢EאאאאKאאא
Ω22K
אאאאאאאא
nRR T =Q F٤J٢EΩ==∴ 17622*8R T
WnאK
I
SV
Ω= 56R1 Ω=100R 2
Ω= 6.5R 5 Ω=10R 4
R٢٧ = ٣ Ω
אא١٤٠ א א א
אאאאאא -١
- ٣٦ -
٤J٣ אאאOhm's Law in Series Circuits אאא،אאא
אKF٤J٣E
אאאאאΩk6.12،אVoltage DropאΩk9.3אאאW
F٤J٣EאאאF٤J٣E
אאאאאR١، R٢א،אI
אאאW
mA59.110*6.12
20RVI 3
T
S ===
V19.610*9.3*10*59.1R*IV 333 === −
∴אאR٣١٩٦ V
F٤J٤Eאא،אאVsK
א VsאFuse mA5K
1R 2R
_?V =
+Vs = ٢٠ V R٣٫٩= ٣ kΩ
אא١٤٠ א א א
אאאאאא -١
- ٣٧ -
F٤J٤EאאאF٤J٤Eא
אאW
( ) ( ) V110*10*1K1mA1IRV 3311 ==Ω⋅== −
V1V1 =∴
( ) ( ) V3.310*3.3mA1IRV 322 =⋅==
V3.3V 2 =∴ ( ) ( ) V7.410*7.4*10*110*7.4mA1IRV 333
33 ==Ω⋅== V7.4V3 =∴
אVSRTK
Ω=++=∴ K97.43.31R T
V910*9*10*1V 33S == −
V٣ ،V٢ ،V١VSWV9VVVV 321S =++=
אFKirchhoff’s Voltage LawEאFEאVSא
אאאK NoteW
FKVLEאאאK
−
+
SV
Ω= k1R1 Ω= k3.3R 2
Ω= k7.4R3
Fuse mA5
mA1I =
אא١٤٠ א א א
אאאאאא -١
- ٣٨ -
אא٥mAאW
Ω= K9*mA5VS
V4510*9*10*5V 33S == −
F٤J٥EאאאאאmA1א،VS؟
F٤J٥EאאאF٤J٥E
אאVS،אאRT
Ω=+++= k5.95.12.16.52.1R T Ω=∴ k5.9R T
אVS
( ) ( ) 33TS 10*5.9*10*1k5.9mA1IRV −=Ω⋅==
V5.9VS =∴
+− V S
Ωk2.1
Ωk6.5Ωk2.1
Ωk5.1I
אא١٤٠ א א א
אאאאאא -١
- ٣٩ -
٤J٤ אאאVoltage Sources in Series אאאאאאא
אאאא،אאKאאאאאאאא
אאאאאאאאKאאאKא
F٤J٦EאאאWאE١، E٢אאאאא،אא
RTK
F٤J٦EאאאF٤J٦E
אאE٢، E١אא،אא
אW
21T EEE +=V502030ET =+=
W
A25.020050
RE
IT
T ===∴
A25.0I =∴
1EΩ= 200R T
−
+V30
−
+V20 2E
אא١٤٠ א א א
אאאאאא -١
- ٤٠ -
אאFSeries–OpposingEאא،אאאאאאאא
Wאאאאאאאאא
F٤J٧E؟אאאא
F٤J٧EאאאF٤J٧Eא
אE٢، E١אאאא،אאאאאאאH–א
אKאאאאאאאאאאKאאאW
21 EEE −= V101525E =−=
1ETR−
+V25
−
+V15
2E
אא١٤٠ א א א
אאאאאא -١
- ٤١ -
F٤J٨Eאאאאא،א
؟אא
F٤J٨EאאאF٤J٨E
אV65.1*4ET ==
٤J٥ Kircchoff's voltage law (KVL) אאאאא?
אאאFEאK?W
אאאVoltage Dropsאאא?
אאVoltage Dropsאאאא،אאאאא
אאאKאאאאאאK
+− 1E
V5.1
+− 2E +− 3E +− 4E
V5.1 V5.1 V5.1
TE
אא١٤٠ א א א
אאאאאא -١
- ٤٢ -
F٤J٩Eאאאאא
4321s vvvvv +++=
אVoltage DropsאאK
..........vvvv 321s +++=F٤J٩E
אSVאאאאW
F٤J١٠EאאאF٤J٩E
אK
21s vvv += v15105vs =+= v15vs =∴
−
+
SV- 5V +
−
+V10
1R 3R2R
+− 1V +− 2V +− 3V
SV
R٤
+− 4V
אא١٤٠ א א א
אאאאאא -١
- ٤٣ -
F٤J١٠Eאאאאאאא،אאmA200I =א،
א1R،2R،3R4R؟
F٤J١١EאאאF٤J١٠E
אאאOhm’s Law
Kirchhoff's Voltage LawKאVoltage Drops
V210*10*200IRV 311 === −
V4.947*10*200IRV 322 === −
V20100*10*200IRV 333 === −
4vFא4אREW
( ) 0vvvvv 4321s =+++−
0v204.92100 4 =−−−−0v6.68 4 =−
V6.68v4 =∴
Ω=100R 3 Ω= 47R 2
4R
E=١٠٠ V mA200I =
Ω=10R1
אא١٤٠ א א א
אאאאאא -١
- ٤٤ -
٤J٦ Kirchhoff's Current Law (KCL) אW
?FNodeEאאאאאאאאאאאאא?
אNodeאאK
F٤J١٢Eאאא
W
321 III +=אKCLאW
?אאאאNodeאאאא?אאאאW
0III 321 =−−
KCLאאאאאאאאאא،אאNodsאאא
KCLאאאאאאאKאאK
٤J٧ אVoltage Divider אאא،אאאאא
אאאאאאאאVoltage DividersאאאאאאK
4RR٢
R١
R٣
2I3I
Node
אא١٤٠ א א א
אאאאאא -١
- ٤٥ -
F٤J١٣Eאאאאאא
אא1R،2Rאא
אא
11 IRV =
22 IRV =
אא1V،2V21 R,RK،אV10VS =،Ω= 50R1،Ω= 100R2W
Ω=+= 15010050R T
A151
150V10
I =Ω
=
V10*3150*
151IRV 11 ===
( )V1031V1 =∴
( )V2031100*
151IRV 22 ===
( )V1032V2 =∴
−
+
SV
1R
_V2
+I
R٢
+− 1V
אא١٤٠ א א א
אאאאאא -١
- ٤٦ -
1אVא2VאKאאאאאK
٤J٧J١ אאאVoltage Divider Formula אאאאאאאאא
אאאKאאאW
F٤J١٤Eאא
אאXVX،א
XX IRV = Wxא٤ ،٣ ،٢ ،١
אאאW
T
S
RVI =
אIאXV
XT
SX R
RVV ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
אXVW
ST
XX V
RRV ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
R٤
I− V١ + − V٢ + − V٣ + − V٤ +
R١ R٢ R٣
− VS +
אא١٤٠ א א א
אאאאאא -١
- ٤٧ -
F٤J١١Eא1Vא2Vאא؟א
F٤J١٥EאאאF٤J١١E
א1V،2Vאא
ST
XX V
RRV ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
אאTRΩ=+= 15656100R T
V41.610*156100V
RR
V ST
11 ==⎟⎟
⎠
⎞⎜⎜⎝
⎛=
V41.6V1 =∴
2V
V59.310*15656V
RRV S
T
22 ==⎟⎟
⎠
⎞⎜⎜⎝
⎛=
א
V59.341.610VVV 1S2 =−=−=
Ω=100R1
Ω= 56R 2
−
+
1V
−
+
2V−
=+
V10VS
אא١٤٠ א א א
אאאאאא -١
- ٤٨ -
F٤J١٢EWאאאאאאא
(a)B toA (b)CtoA (c)CtoB(d)DtoB(e)D toC אW
(a)ABV (b)ACV (c)BCV(d)BDV(e)CDV
F٤J١٦EאאאF٤J١٢E
אאאTR
321T RRRR ++=
3.32.81R T ++=Ω= K5.12R T
אאאW
ST
1AB V
RR
V ⎟⎟⎠
⎞⎜⎜⎝
⎛=
V225*5.12
1VAB ==
V2VAB =∴
VS = ٢٥V
R١ = ١kΩ
R٨٫٢ = ٢kΩ
R٣٫٣ = ٣kΩ
A B
C
D
אא١٤٠ א א א
אאאאאא -١
- ٤٩ -
S3
21AC V
RRR
V ⎟⎟⎠
⎞⎜⎜⎝
⎛ +=
V4.1825*5.122.9VAC =⎟⎠⎞
⎜⎝⎛=
V4.18VAC =∴
אאB، C
ST
2BC V
RR
V ⎟⎟⎠
⎞⎜⎜⎝
⎛=
V4.1625*5.122.8VBC =⎟⎠⎞
⎜⎝⎛=
V4.16VBC =∴
25*5.12
3.32.8VBD ⎟⎠⎞
⎜⎝⎛ +
=
V2325*5.125.11VBD =⎟⎠⎞
⎜⎝⎛=
V23VBD =∴
אCDV
6.625*5.123.3VCD =⎟⎠⎞
⎜⎝⎛=
V6.6VCD =∴
٤J٨ אאאאPower in a Series Circuit אאאאאאאא
W
n21T P...........PPP +++=TPאאאK
WאאאאIVP )1 ST =
אא١٤٠ א א א
אאאאאא -١
- ٥٠ -
T2
T RIP )2 =
T
2S
T RV
P )3 =
F٤J١٣EאאאאאW
F٤J١٧EאאאF٤J١٣E
אאאK
Ω=+++= 10622561810R T
אאאאF٣EאW
( ) W12.210615
RV
P2
T
2S
T ===∴
W12.2PT =∴
R١٨ = ٢ Ω
R٥٦ = ٣ Ω
R٢٢ = ٤ Ω
VS = ١٥ V
אא١٤٠ א א א
אאאאאא -١
- ٥١ -
F٤J١٤Eאאאאאא٥٠ W،
אאא؟
F٤J١٨EאאאF٤J١٤Eא
אא
4321T RRRRR +++=
Ω=+++= k91.73.391.07.21R TΩ= k91.7R T
אאאאא
mA2.1591.7
120RV
IT
S ===
אW
( ) ( ) mW231k1mA2.15RIP 21
21 =Ω==
( ) ( ) W62.0mW624k7.2mA2.15RIP 22
22 ==Ω==
( ) ( ) W21.0mW210910mA2.15RIP 23
23 ==Ω==
( ) ( ) W762.01000762mW762k3.3mA2.15RIP 2
42
4 ===Ω==
R١ = ١kΩ R٢٫٧ = ٢kΩ
R٩١٠ = ٣Ω
R٤ = ٣٫٣kΩVS = ١٢٠ V
אא١٤٠ א א א
אאאאאא -١
- ٥٢ -
אא2R،4RאאmW2.15،אאW
W21W62.0P2 >=
W21W762.0P4 >=
אאא١wאK
٤J٩ אVoltage With Respect to Ground אאאFאE
Reference Point.אאאא،אKאאא١٠٠Vא،
אא١٠٠אVאאאCircuit GroundKאאאאאא
אאאאGround،אF٤J١٩KE
אא١٤٠ א א א
אאאאאא -١
- ٥٣ -
F٤J١٩EאאNote
אאaF٤J١٥E
،אאאאאאאVoltage Dropped ٢٥ VK
(b) (a)
F٤J٢٠E(a، b)אאאF٤J١٥E
1R
2R
−
+
1V
−
+
2V
−
+
2V
V
a
−
+V100
−+ −+
−
+
+−
ba c
de−
+V100
−+ −+
−
+
+−
ba c
de
אא١٤٠ א א א
אאאאאא -١
- ٥٤ -
(c) F٤J٢٠E(c)אאאF٤J١٥E
אאאW
אאFaEא،אאאאאאaVא،אaא،aV
אaאאaאKאאFaEאאאאאW
0Ve = V25Vd += V50Vc += V75Vb += V100Va +=
אאFb EאdאאW
V25Ve −=
V0Vd =
V25Vc +=
50Vb +=
−
+V100
−+ C
−
+
+−
ba
c
de
אא١٤٠ א א א
אאאאאא -١
- ٥٥ -
V75Va +=אאFcEא،cאא،W
V50Ve −=
V25Vd −=
V0Vc =
V25Vb +=V50Va +=
אאאאאאאאאaא،
אKאאW
אאאaאאb،c،d،←eK،אאאאאאH،JK
אאFaEAVWV100VV Sa == V7525100Vb +=−= V502525100Vc +=−−= V25252525100Vd +=−−−=
אeא
edcbse VVVVVV ++++= 025252525100Ve =−−−−= 0Ve =∴
Note אאאאW
אא١٤٠ א א א
אאאאאא -١
- ٥٦ -
١E אאWאאאאאאאאאאאאאFאאKE
٢E אאWאאאא،אאאאאא
אאאאאא1RW
1sb IRVV −=
אאאאa،b،cK
٤J١٠ אאTroubleshooting א،אאאאW
F١EאאאאאOpen Circuit KF٢EאאאאאShort CircuitK
אאא،אאאאאאאא
אאOpen Circuitאאאאאאא،KאאאאאאאW
١K אאאא
0IRV == אאאאא
אK٢K אאCheek For Burned Resistor
אאאאאאאאאאאאאאK
אא١٤٠ א א א
אאאאאא -١
- ٥٧ -
F٤J٢١EאאShort Circuit אאאShortKאא
אאאאאKאאאאאא
אאאאK
F٤J١٦EאאאאאאK
V100VS =א،WEאאאאאKEאShortאB,A،אא؟א؟א
F٤J٢٢EאאאF٤J١٦E
V0 −+ V10
1R
V0
2R 2R
V10VS =
+=
−V100VS
Ω10 Ω18
Ω33
Ω39
a
bc
אא١٤٠ א א א
אאאאאא -١
- ٥٨ -
אWאTRK
Ω=+++= 10039331810R T
A1100100I ==
WShortאB,AKאאאאB,AאאאK
אאאΩ=+= 281018R T
F٤J٢٣EאאאF٤J١٦E
A57.328
100RVI
T
S ===
אWאB,A،אאA1A57.3K
אאאאא،אאאCA,
אאאΩ39،Ω33،Ω18אאאאאאK
+=
−V100VS
Ω10
a
bΩ18
C
Ω33
Ω39
I
אא١٤٠ א א א
אאאאאא -١
- ٥٩ -
Ω=10R T
A1010
100RV
IT
S ===
אאA10
אSummary אאאאאK אאאאאאאא
אאאאK אאאאאKVLK אאאאאא
אאאאK אאאSeries-Opposition
אאאאK אVoltage DropsאאאK אאאאאאא
אאאאאאK אאK אאאאאאאK אאאאK אGroundאאאאK אאNegative GroundאK אאPositive Groundאאאאא
K אאאאOpen circuitאאאאא
אK
אא١٤٠ א א א
אאאאאא -١
- ٦٠ -
אאא
١K אאאאאB,AK
٢K אאא،אאאאV12
אאΩ120 ٣K אאאאאאmA5א،א
אאא؟
A
1R
2R
A
A
mA5
−
+
SV
R٣
A
B
R١
R٢
R٣
A B
R١ R٢ R٣
A
B R٢
R٣R١
R٤
R٥
אא١٤٠ א א א
אאאאאא -١
- ٦١ -
٤K אאTRאאאW
FEΩ500،Ω1000FEΩ47،Ω56FEΩk5.1،Ωk2.2،Ωk10
FEΩM1،Ωk470،Ωk1،ΩM2.2
٥K א؟אאאאא
Ω=10R 2
Ω= k6.25R1
Ω= k2.2R 3
)a(
Ω= 10R 2
Ω=12R 3
Ω=1R 4
)b(
Ω= 7.4R1
)c(
Ω= M1R1
Ω= M1R 1
Ω= M6.5R3
Ω= M10R 5
Ω= k560R 2
אא١٤٠ א א א
אאאאאא -١
- ٦٢ -
٦K אאאאאmA100א، אא؟
٧K אאא א1אRmA25א،2RV25،
2R؟
٨K אאאV48VS =א،Ω= 10R1،Ω= 96R2،Ω== 47RR ؛אא؟43
٩K אאΩ= k7.4R1،Ω= k6.5R 2אV24VS =،
א؟
١٠K אאאאאאאאא،SV؟W
Ω=100R1، Ω= 56R 2، Ω= 330R 3،
Ω= 45R1
Ω=15R 2
Ω= 90R3
+
−
SV
A
V
1R
2R
3R+
−
SV
A
אא١٤٠ א א א
אאאאאא -١
- ٦٣ -
Ω= 220R 4، Ω= 47R 5 & V124.1V5 =
١١K אאאV15VS =אא1RV69.4V1 =،2RΩ= k5.1R1؟
V69.4V,k5.1R 11 =Ω=
١٢K אאאאאאאאmA43.1I =V15VS =אא،21 V2V =،
32 V2V =،1R،2R،3R؟
١٣K ؟א،אאאאאא
−=
+V15VS
1R 2R
V
SV
1R 2R
5R
3R
4R
I
V
אא١٤٠ א א א
אאאאאא -١
- ٦٤ -
Ω= K15R1، Ω= K10R 2،
Ω= K8.6R 3، Ω= K2.2R 4
١٤K אאאאאא1SV
אאa؟אא،١٥K אאא،אאא1RV16.2W
FV16.2V1 =Eא،3VFא3אRE،KW
Ω= 390R1 ، Ω= K1R 2، Ω= 560R 3 & Ω= K220R 4
V24V 1S =
1Ra 2R
3R
4RV12V 2S =
1SV
Ω= 390R1AΩ= k1R 2
Ω= 560R 3
Ω= 220R 4
2SV
I
אא١٤٠ א א א
אאאאאא -١
- ٦٥ -
١٦K אאאF١٥EאV15V1S =،
2SVאא1אRV77.3FWV77.3V1 =KE
١٧K א
2SVאא1Rאא2RFאאF١٥EEא
2SVאאאF١٦Eאא،1V،2V،3V،4Vא؟אא
١٨K אאאאאאאFאEאאאאאD,C,B,A
؟WΩ=Ω=Ω=Ω= k15R&k47R,k22R,k12R 4321
١٩K אאאאΩ560אאאאאΩ= 27R؟
٢٠K אאB,AאאאW
1R
3R
2R
−
+
1V
−=
+V48VS
4R
a
b
cd
אא١٤٠ א א א
אאאאאא -١
- ٦٦ -
−
+V12
A
Ω100
Ω56
B
Ωk3.3
Ωk1
Ωk2.2
−
+V8
A
B
b
אאאאאאאאאאאא
JJ١١
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
א
אא
א
א
א
٥
א١٤٠ א א א
אאאאאא -١
- ٦٧ -
אאאא
،אאאאאW• אאאK • אאאאאK • אאאK • אאאאאK • אאאK • אK • אאאאאאK
א١٤٠ א א א
אאאאאא -١
- ٦٨ -
٥J١Introduction א،אאאאאא،א
אאVoltage DropKאאאאVoltage DividerK
אא،אאאאאאאאאא،א،
אאאKאאאKCL،אאאאא،
אCurrent DividerאאKאאאParallel Circuit
אאאFEאאאFאEאאFאE
אאK،אאאאKאאאF٥J١E
אאאK
F٥J١JEאאאK
I
2R
A
1R
2I1I
B
I
2R
A
1R
2I1I
B
2R
A
1R
2I1I
B
I
2R
A1R
B
1I
2I
I
א١٤٠ א א א
אאאאאא -١
- ٦٩ -
F٥J١JEאאאK
٥J٢אאאאאVoltage Drop in Parallel Circuit אאאאאאאאאא
אאאאאאאKאאאK
F٥J١EאאF٥J٢E
F٥J٢EאאאF٥J١KEא
אאאאאאאאW
V25VVVVVV S54321 ======
Ω=
k1R 2
FΩ=
k8.1R1
Ω=k2.2
R 3
Ω=
k2.2R 4
Ω=
k3.3R 5
V25VS =
2R
A
1R
2I
1I
B
I2R
A
1R
B
3R
1I 2II
I٢
א١٤٠ א א א
אאאאאא -١
- ٧٠ -
٥J٣Kirchhoff’s Current Lawאאאאא
NodeאאאאאאאKאאאאK
F٥J٢EאאאאאF٥J٣E،
אאאאאAK
F٥J٣EאאאF٥J٢KE
אאאאAאאmA5אא1R א
mA12אא2RאאאAW
21T III +=
mA17mA12mA5 =+=
mA17IT =∴
2R1R
mA12I2 =mA5I1 =TI
TI
A
B
−
+
SV
א١٤٠ א א א
אאאאאא -١
- ٧١ -
F٥J٣Eאאא2RאF٥J٤KE
F٥J٤EאאאF٥J٣KE
אאאאאאATI
321T IIII ++=
mA20ImA30mA100 2 ++=∴
mA50mA50mA100I 2 =−=∴
F٥J٤E21אאאא A,Aא
אW
F٥J٥EאאאF٥J٤KE
2R1R2I
mA30I1 =
mA100IT =
TI
A
B
−
+
SV 3R
mA20I3 =
2R1R
A1I2 =A5.1I1 =TI
x
−
+
SV3R
3IA5 y
א١٤٠ א א א
אאאאאא -١
- ٧٢ -
א אאאאאxA5W
1AIA5.1A5 +=
W1AIאאא1AKA5.35.15I 1A =−=∴
אאyאאאA5.3K
2AIA1A5.3 +=∴ A5.215.3I 2A =−=∴
∴אאאWA5.3I 1A = A5.2I 2A =
٥J٤אאאאאTotal Parallel ResistorsWאאTRאא
אאאאאאאאאאאאאאK
F٥J٦Eאא21 R,R
2R
1R
2I
1I
TI
−+ V S
א١٤٠ א א א
אאאאאא -١
- ٧٣ -
אאא21א R,Rאא،אאFאאETRאW
א،W
21T III += F٥J١E
אאאאW
2
S
1
S
T
S
RV
RV
RV
+= F٥J٢E
אאאSVK
21T R1
R1
R1
+= F٥J٣E
אF٥J٣Eאאאאאא،אאאאא
אאW
21
21
T RRRR
R1
∗+
= F٥J٤E
W
21
21T RR
RRR+∗
= F٥J٥E
TR אאאKWTRאא
א١٤٠ א א א
אאאאאא -١
- ٧٤ -
F٥J٧Eאא321 R,R,R
W321T IIII ++= F٥J٦E
אW
3
S
2
S
1
S
T
S
RV
RV
RV
RV
++= F٥J٧E
SVאW
321T R1
R1
R1
R1
++= F٥J٨E
W
323121
321T RRRRRR
RRRR++∗∗
= F٥J٩E
אאTRאאאאאK
2R
1R
2I
1I
TI
−+ V S
3R3I
א١٤٠ א א א
אאאאאא -١
- ٧٥ -
אאאTRאאאאW
)R1()
R1()
R1()
R1(
1R
n321
T++++
=K
F٥J١٠E
F٥J٥EWאאB,AאTRאאא
F٥J٨EאאאF٥J٥KE
אאאאF٥J٩EW
323121
321T RRRRRR
RRRR++∗∗
=
Ω=∗+∗+∗
∗∗= 13
224722100471002247100RT
٥J٤J١אאאא אא،אאאאא
W
RRRRR n321 ===== KQ F٥J١١E
Ω= 47R 2Ω=100R1
A
Ω= 22R 3
B
א١٤٠ א א א
אאאאאא -١
- ٧٦ -
Rn1R T =∴ F٥J١٢E
nRR or T = F٥J١٣E
WRאאאאאK
אא،אאאאK
F٥J٦EΩ8אאאאTRK
א
אאW
Ω=== 248
nRRT
٥J٥אאאDetermining an unknown Parallel Resistor،אאאאאאאאאאא
אKאאאאא،אאאאאTRאאא
אאאאאאFF٥J٥WEE
21
21T RR
RRR+
=
אאARאXRאאW
א١٤٠ א א א
אאאאאא -١
- ٧٧ -
F٥J٩EאK
אאאאאאאXRW
XA
XAT RR
RRR
+= F٥J١٤E
XAXAT RR)RR(R =+ F٥J١٥E
XAXTAT RRRRRR =+ F٥J١٦E
)RR(RR TAAT −= F٥J١٧E
TA
ATX RR
RRR
−=∴ F٥J١٨E
F٥J٧EאאΩ150אאא
אΩ330Kאאא؟
F٥J١٠EאאאF٥J٧KE
XR
AR
TR
XR
Ω= 330RA
א١٤٠ א א א
אאאאאא -١
- ٧٨ -
אאאאאאאΩ330א
אאאאאW
XA
XAT RR
RRR
+=
X
X
R330R330
150+
=
XX R330)R330(150 =+
XX R150R330330*150 −=
Ω==∴ 275180
330*150R X
F٥J٨EאאאאאF٥J١١KE
F٥J١١EאאאF٥J٨KE
אאא،אאאאTR
W
323121
321T RRRRRR
RRRR
++∗∗
=
Ω= 560R 2Ω= 220R1
−
+
SV Ω= k1R 3
mA10
א١٤٠ א א א
אאאאאא -١
- ٧٩ -
Ω=∗+∗+∗
∗∗= 136
100056010002205602201000560220R T
V36.1136*mA10R*IV TT =Ω==∴
F٥J٩E אאאΩ= 680R3אΩk1א،
mA10IT =K
אאאאאTRW
323121
321T RRRRRR
RRRR
++∗∗
=
Ω=∗+∗+∗
∗∗= 128
680560680220560220680560220R T
V28.1128*mA10R*IV TT =Ω==∴
٥J٦FEאאאאCurrent Division in Parallel CircuitsאאאאTR،אאאא
אאאאאאBranchesKאאאCurrent Divider Lawאאאאא
،אאאאא،אאאאאאאF٥J١٢Eא،W
א١٤٠ א א א
אאאאאא -١
- ٨٠ -
F٥J١٢EאאאאK
אאא21 I,IאIW
TR*IV = F٥J١٩E
11 R*IV = F٥J٢٠(
22 R*IV = F٥J٢١E
אF٥J١٩EאF٥J٢٠E،אא،W
11T R*IR*I = F٥J٢٢E
1
T1 R
RII = F٥J٢٣E
אF٥J١٩EF٥J٢١E،אא،W
2
T2 R
RII = F٥J٢٤E
אאאאאאאאאאאNode،אאא
אאאW
2R
1R
2I
1I
I
−+ V S
א١٤٠ א א א
אאאאאא -١
- ٨١ -
X
TX R
RII = F٥J٢٥E
Wn,,3,2,1X K=KTRWאאאאאKXRWאאאאKXIWאאXאXאאא
אK
א١٤٠ א א א
אאאאאא -١
- ٨٢ -
F٥J١٠EאBranchאF٥J١٣KE
F٥J١٣EאאאF٥J١٠KE
אאאאאA10אאא،
אאTRאK
323121
321T RRRRRR
RRRR
++∗∗
=
Ω=∗+∗+∗
∗∗= 111
220330220680330680220330680R T
A63.168011110
RR
II1
TT1 =∗==
A36.333011110
RR
II2
TT2 =∗==
A05.522011110
RR
II3
TT3 =∗==
Ω= 330R2
Ω= 680R1
2I
1I
A10
Ω= 220R33I
א١٤٠ א א א
אאאאאא -١
- ٨٣ -
21 I,Iא3IW
321T IIII ++=
3I36.363.110 ++=
)36.363.1(10I3 +−=
A05.5I3 =∴
אאאאKאאאΩ= 680R1A63.1I1 =K
אΩ= 220R3A05.5I3 =KאאK
א١٤٠ א א א
אאאאאא -١
- ٨٤ -
אאאאאאW
F٥J١٤EאאאאK
אאF٥J٢٣EאF٥J٥WE
1
TT1 R
RII = F٥J٢٣E
21
21T RR
RRR
+= F٥J٥E
TRאF٥J٢٣EW
21
1T1 RR
RII
+= F٥J٢٦E
2IאאW
RR
RII
21
2T2 +
= F٥J٢٧E
אאאF٥J٢٦E،F٥J٢٧Eאאא21א I,I
321 R,R,Rאאא،א321 I,I,IאאאאW
2R1R
TI
1I 2I
א١٤٠ א א א
אאאאאא -١
- ٨٥ -
F٥J١٥EאאאאK
א1I אא1RאW
1
TT1 R
RII = F٥J٢٣E
אאTRאא
323121
321T RRRRRR
RRRR++∗∗
= F٥J٢٨E
TRאאW
323121
32T1 RRRRRR
RR.II++
∗= F٥J٢٩E
32 I,IW
323121
31T2 RRRRRR
RR.II
++∗
= F٥J٣٠E
323121
21T3 RRRRRR
RR.II
++∗
= F٥J٣١E
2R
1R
2I
1I
TI
−+ V S
3R3I
א١٤٠ א א א
אאאאאא -١
- ٨٦ -
٥J٧אאאאPower in Parallel Circuits אאאאאTPאאאFאאאEW
n321T PPPPP ++++= K F٥J٣٢E
F٥J١٦EאאאאK
T
2
T2TT R
VR.II.VP === F٥J٣٣E
אW
1211 R.IP = F٥J٣٤E
2222 R.IP = F٥J٣٥E
3233 R.IP = F٥J٣٧E
321T PPPP ++= F٥J٣٨E
אWattK
2R1R
TI
1I 2I
1P 2P 3R
3I
3P nR
nI
nPTP
א١٤٠ א א א
אאאאאא -١
- ٨٧ -
F٥J١١Eאאאאאאא
F٥J١٧EאאאF٥J١١KE
אאא
323121
321T RRRRRR
RRRR
++∗∗
=
Ω=++
∗∗= 1.11
22*3322*6833*68223368
T2TT R.IP =Q
W44.411.1*(2) 2 ==
W4.44PT =∴
אאאKאאK
V2.221.11*2R.IV TS ===
W25.768
)2.22(RV
P2
1
2S
1 ===
Ω= 33R 2Ω= 68R1 Ω= 22R 3
א١٤٠ א א א
אאאאאא -١
- ٨٨ -
W9.1433
)2.22(RV
P2
2
2S
2 ===
W4.2222
)2.22(RV
P2
3
2S
3 ===
321T PPPP ++=Q
4.229.1425.7 ++=
W6.44PT =∴
אאאאאאאFאKE
א١٤٠ א א א
אאאאאא -١
- ٨٩ -
אאF١EאאאWFEאFEאFEאFE
F٢EאΩk2.1אΩ100א،אא
אTRFEΩk2.1FEΩ100Ωk2.1FEΩ100Ω90FEEΩ90
F٣EΩ330Ω270،Ω68אא،אאFEΩ668FEΩ47FEΩ68FEΩ22
F٤EאאאΩk1،
אאFEΩk8FEΩk1FEΩk1FEΩ500
F٥EאאאאFEFEFEFEאא
F٦EאאאאאFEאאFEFEFE
א١٤٠ א א א
אאאאאא -١
- ٩٠ -
F٧EאאאA5א،A3KאאאW
FEA2FEFE A8FEאK
F٨EאאΩΩΩ 820,560,390א،אאא
FEΩ390FEΩ560FEΩ820FEאK
F٩EאאאאאFEFEאFEאאFEאFEFE
F١٠EאאאאאWFEאאאאאFEאאאאFEאאאאFאאאE
FEאK
F١١EאאאאW1אאא،WFEW1FEW4FEW25.0FEW16
אאאאאא
JJ١١
אאאÖ]<퉉ö¹]ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^Ã
אאאא
אא
א
٦
א١٤٠ א א א
אאא -١
- ٩١ -
אאאא
،אאאאאW• אאאK • אאאK • אאאאK • אאאאK
א١٤٠ א א א
אאא -١
- ٩٢ -
٦J١ אאאאאאאאאא،אאאאאאאאאאאאא
אאאא،אאאאאאאאK
אאא–אאWאא،אאאאאF٦J١Eאאא–אאK
٦J٢ אא–אאF٦J١E
אאאאאאאF٦J١KE
F٦J١EאאאF٦J١KE
אאא71א R,Rאאאאאא
אKאאאאאאאW
987654321T R//RRR//R//RR//RRR ++++=W
R١
R٢
R٣
R٤R٥R٦
R٨
R٩
R٧
א١٤٠ א א א
אאא -١
- ٩٣ -
98
987
656454
654
32
321T RR
RRR
RRRRRRRRR
RRRR
RR+
++++
++
+=
F٦J٢EאאאF٦J٢Eאאאא،K
F٦J٢EאאאF٦J٢KEא
אאאאאא1אRאA،2Rאא،3RK
אBאא4RKאא41 R,RאאKא32 R,R،אא32 R//R،אאTRW
4321T RR//RRR ++=F٦J٣E
אאאאאאF٦J٣KE
TI
1R
2R3R
4R
3I 2I
TI−
+
SV
A
B
א١٤٠ א א א
אאא -١
- ٩٤ -
F٦J٣EאאאF٦J٣KE
אאאאאF٦J٤KE
F٦J٤EאאאF٦J٣KE
א،אאאאאאאTRאW
1T54321T RR//RR//RRR ++=
1R
2R 3R
−
+
SV
5R4R
1R
2R 3R
−
+
SV
5R4R
א١٤٠ א א א
אאא -١
- ٩٥ -
F٦J٤EאאאאאD,AאF٦J٥KE
F٦J٥EאאאF٦J٤KE
1R 2R 3R
A
5R
4R
D6R
א١٤٠ א א א
אאא -١
- ٩٦ -
אאא
1TRאאאא32 R,Rאאאא4RW
432
432T R)RR(
R)RR(R
1 ++⋅+
=
אא
1TRאא5RF٦J٦KE
F٦J٦EאאאF٦J٤KE
אאאאA,DאאW
)RR//(RRR 5T61T 1++=
F٦J٥EאאאF٦J٧Eאא،אאC,B,AK
F٦J٧EאאאF٦J٥KE
1R
6R1TR
A
D5R
3R
2R
C
1R
A
B
א١٤٠ א א א
אאא -١
- ٩٧ -
אאאאB,A31 R,Rאא
אא2RאאTRW
)RR(R)RR(*R
R312
312TAB ++
+=
אאC,AC,BW
321
321T R)RR(
R*)RR(R
AC +++
=
132
132T R)RR(
R*)RR(R
BC +++
=
٦J٣ אאא–אאAnalysis of Series-Parallel Circuitsאאאאא
א،אאאאאאאאW♦ אאאאאאאאK ♦ אאאאאאאאK ♦ אאאאאאאK
F٦J٦EאאאאאאאאאF٦J٨KE
F٦J٨EאאאF٦J٦KE
A
Ω=100R1
−
+
SV
Ω= 68R 4
Ω= 39R 5
Ω= 47R 2 Ω= 47R 3
Ω= 75R 6
B
א١٤٠ א א א
אאא -١
- ٩٨ -
אא32 R,Rאא
Ω=+= 944747R3,2T
אא54 R,Rאאאאאא6RW
Ω=++
= 8.9975396839*68R
6,5,4T
אΩΩ 94,8.99אאאא
Ω=+
= 41.48948.9994*8.99R
B,AT
F٦J٩EאאאF٦J٦KE
Ω=∴ 41.48R AB
Ω=Ω+Ω=∴ 41.14841.48100R TF٦J٧E
אאא2Rאא3RF٦J١٠KE
Ω94
Ω8.99
AΩ100
−
+
SV
B
א١٤٠ א א א
אאא -١
- ٩٩ -
F٦J١٠EאאאF٦J٧KEא
אא2Rא3RאאאאאאAK
אאאאאאאTRK
32
321T RR
RRRR
++=
Ω+ΩΩΩ
+Ω=k3.3k2.2
)k3.3)(k2.2(k1R T
Ω=Ω+Ω=∴ k32.2k32.1k1R T
Ω=∴ k32.2R T
mA48.9k32.2V22
RV
IT
ST =
Ω==
אא
mA69.5k5.5k3.3*mA48.9I2 =ΩΩ
=
mA79.3k5.5k2.2*mA48.9I3 =ΩΩ
=
Ω= k1R1
−=
+V22VS
Ω= k3.3R 33I
Ω= k2.2R 2
2I
TI
א١٤٠ א א א
אאא -١
- ١٠٠ -
F٦J٨Eאאא4RאאאאV50VS =
F٦J١١EאאאF٦J٨KEא אאאאV50אא،
1אRאאא2Rאאאא43 R,RKא4Iאא4RאאW
Wאאא432 R,R,RKW2Iאאא432 R,R,RKW2IאAא4IאK
432T R//RRR4,3,2
+=
43
432 RR
RRR
++=
Ω=+
+= 538560330560*330 330
Ω=∴ 538R4,3,2T
mA9353850I2 ==
Ω560R1 Ω330
R2
−=
+V50VS
Ω330R3
Ω560R4
4I3I
1I2I
A
א١٤٠ א א א
אאא -١
- ١٠١ -
אאW
mA5.34RR
RII
43
324 =⎟⎟
⎠
⎞⎜⎜⎝
⎛+
=
mA5.34I4 =∴
٦J٤ אאאאאVoltage Drops in Series-Parallel Circuits אא،אאאאאא
אאאאא،אאאאאאK
F٦J٩EאאאאAאאאF٦J١٢Eא،
א1אRK
F٦J١٢EאאאF٦J٩KE
אאא32 R,Rא،אא
אאKW
Ω=+
= 280560560560*560R
3,2T
Ω= 150R1
Ω= 560R 2 Ω= 560R 3
−=
+V80VS
B
A
א١٤٠ א א א
אאא -١
- ١٠٢ -
אאאאאא
( ) Ω== 28056021R
AGT
אΩ280אאא1Rאאאא،W
F٦J١٣EאאאF٦J٩KE
אאאTRWΩ=+= 430280150RT
אאAGV
ST
AGAG V
RRV ⎟⎟
⎠
⎞⎜⎜⎝
⎛=
AGRאאK
V1.5280*430280VAG =⎟
⎠⎞
⎜⎝⎛=
אא1R
AG1S VVV +=
AGS1 VVV −=
27.9V52.1-80 ==
Ω= 150R1
Ω280
−=
+V80VS
A
B
א١٤٠ א א א
אאא -١
- ١٠٣ -
V9.27V 1 =∴F٦J١٠E
אאאאאF٦J١٤KE
F٦J١٤EאאאF٦J١٠KE
א،אאאאאאא
אאא21 R,RאאKאא1Rאא2אRאאW
⎟⎟⎠
⎞⎜⎜⎝
⎛+
=21
2T1 RR
RII
A688k2.2k1
k2.2mA1 µ=⎟⎠⎞
⎜⎝⎛
Ω+ΩΩ
=
A688I1 µ=∴אאא1R
Ωµ== k1*A688R.IV 111
∴= mV688V1
Ω= k2.2R2
mA1IT =
Ω= k9.3R 3
−
+
SV
Ω= 560R 5
Ω= k5.1R 43I4I
Ω= k1R1
1I2I
א١٤٠ א א א
אאא -١
- ١٠٤ -
א3Iא3RאW
⎟⎟⎠
⎞⎜⎜⎝
⎛++
+=
)RR(RRRII
543
54T3
TIאWA346I3 µ=
אא543א R,R,RW
)k9.3)(A346(R.IV 333 Ωµ==
V35.1V3 =∴4Vאא4R،W
3T54 IIII −==
A346-1mA µ=
Am0.346-1mA =
mA654.0I4 =∴
V981.0)k5.1)(mA654.0(V4 =Ω=
mV981V4 =∴
mV366R*IV 555 ==
א١٤٠ א א א
אאא -١
- ١٠٥ -
F٦J١١EF٦J١٥KEאאאאאאא
F٦J١٥EאאאF٦J١١KEא
אאא،אאF٦J١٥Eאא،אאא
אאאRABאאB,AW
Ω=+
= k15.2RR
RRR21
21AB
אאאאRCDאאD,CW
Ω=+++
= 517RRR
)RR(RR654
654CD
אאאאאאF٦J١٦KE
Ω= k3.3R1
Ω= k2.6R 2
Ω= 390R6
−=
+V8VS
Ω= 680R5
Ω= k1R 4
A
Ω= k1R3
B
C
D
א١٤٠ א א א
אאא -١
- ١٠٦ -
F٦J١٦EאאאF٦J١١KE
אאאאW
V69.4VR
RV S
T
ABAB =⎟⎟
⎠
⎞⎜⎜⎝
⎛=
V13.1VR
RV S
T
CDCD =⎟⎟
⎠
⎞⎜⎜⎝
⎛=
V18.2VRR
V ST
33 =⎟⎟
⎠
⎞⎜⎜⎝
⎛=
אאW
V69.4VR
RV69.4VVV ST
AB21AB =⎟⎟
⎠
⎞⎜⎜⎝
⎛===
אCDVא4Rאא)RR( 65 +K
mV718VRR
RV CD
65
55 =⎟⎟
⎠
⎞⎜⎜⎝
⎛+
=
mV412VRR
RV CD
65
66 =⎟⎟
⎠
⎞⎜⎜⎝
⎛+
=
Ω= k15.2RAB
Ω= k1R 3
−=
+V8VS
Ω= 517R CD
א١٤٠ א א א
אאא -١
- ١٠٧ -
F٦J١٢EאאאאF٦J١٧KE
F٦J١٧EאאאF٦J١٢KE
א אאאאאאאא
אאאKאאאאאאאאW
Ld R,RאאLd R//RKאאאCRLdC R//RR +
אא–אאאאאbRא
[ ])R//R(R//R LdCb +אאאאאאaRא،
אאאW[ ])R//R(R//RRR LdCbaT ++=
TI
SVbR
aR
cR
dR LR
A B
C D
א١٤٠ א א א
אאא -١
- ١٠٨ -
אאTRאאא W
F٦J١٨EאאאF٦J١٢KE
אאאאW
Ta II =
CbT III +=
LdC III +=אDאאאאאאאא
אTIW
LdbT IIII ++=
٦J٥ אאאאאאאאאאאאאאK
אאאא–אאKאאאאאאאאאא
aR
bR−
+
SV LRdR
cR
TI
bI cI
dI
LI
A
D
B
C
א١٤٠ א א א
אאא -١
- ١٠٩ -
אאאאאאKאF٦J١٣EאאאK
F٦J١٣EאאאF٦J١٨E؟א،W
V5V,V8V,V8V,V12V 4321 ====
F٦J١٩EאאאF٦J١٢KEא
אאאאאSVW
421S VVVV ++=
25V5812 =++= F٦J١٤E
אאאאF٦J٢٠KE
1R
2R 3R
−
+
SV
4R
Ω=100R 2
Ω= 50R1
Ω= 50R3
Ω=100R 4
Ω= 50R5
Ω=100R 6 Ω=100R 7
א١٤٠ א א א
אאא -١
- ١١٠ -
F٦J٢٠EאאאF٦J١٤KE
א
76 R//RQ
Ω=+
=∴ 50100100100*100R 7,6
5Rאא7,6RאW
Ω=+=+ 1005050RR 7,65
Ω==+ 50100//100)R//RR//(R 7654
אאאא3RאאK
Ω=+=++ 1005050)R//RR//(RR 76543אאאא2אR،W
[ ] Ω=+
=++ 50100100100*100)R//RR//(RR//R 765432
אאאאא1RאTR
Ω=+= 1005050RTF٦J١٥E
אאאWאV2.28V4 =SV،W
Ω=Ω=Ω=Ω=Ω=Ω= 820R,k15R,k10R,k6.5R,k2.2R,k7.2R 654321
TI1R
א١٤٠ א א א
אאא -١
- ١١١ -
F٦J٢١EאאאF٦J١٥KE
א،אW
543T IIII ++=V2.28V4 =אא543 R,R,R،
אא543 I,I,IW
mA82.2k102.28I4 ==
mA88.1k152.28I5 ==
mA04.5k6.52.28I3 ==
mA74.9mA82.2mA88.1mA04.5IT =++=∴
TIאאeqR
543 R,R,RTIW
eq
4T R
VI =
W
2R
3R−
+
SV
5R4R
3I4I
1I2I TI
5I
6R TI
א١٤٠ א א א
אאא -١
- ١١٢ -
Ω=++
= k896.2RRRR,RR
RRRR
545343
543eq
mA74.910*896.2
2.28I3T ==∴
אאKאאאא21 R//R
)R//R(IVV 21T21 ==
)RR
RR(I
21
21T +
=
אאWV8.11VV 21 ==
אא6R33
6T6 10*82.0*10*74.9R.IV −==
V99.7V6 =∴אSV
641S VVVV ++=
48V7.9928.211.8 =++=
V48VS =∴F١ESVאא
אאKFKW٢ESVאאאSV
אW
TTS R*IV =אSummary
א١٤٠ א א א
אאא -١
- ١١٣ -
F١EאאאFא–אEאאאאאK
F٢Eאאאאאאאאאאאא
F٣EאאאאאאאאFאאאאאאאE
F٤EאאאאאאאW
⎟⎟⎠
⎞⎜⎜⎝
⎛=
T
XSX R
RVV
W
XRWאאאXVWאאאSVWאTRWאאאK
F٥EאFאאEא
Common Reference PointאK
א١٤٠ א א א
אאא -١
- ١١٤ -
א
١JאאאאאW
FE21 R,Rאא543 R,R,RFE21 R,RאאKFE543 R,R,RאאFEאא21 R,Rאאאא543 R,R,RFEאFE،FE
٢–אאאאTRאא،WFE54321 R//R//RRR ++FE54321 R//R//RR//R +FE)RRR//()RR( 54321 +++FE
٣–אאאאאB,Aא
אאWFE5RFE543 R,R,RFE21 R,RFEא
1R 2R
3R 4R 5R BA
א١٤٠ א א א
אאא -١
- ١١٥ -
٤–אאאאאא،Ωk1א،אאאאΩk2.2אא،
אאΩk1٦V،
אאאΩk2.2:FE٦VFE٣VFE١٢V FE٢١٣V
٥–אאאΩΩ 470,330אאא،
Ωk1KאאאV100אאאW
Ωk1
V6V1 =
Ωk2.2
Ωk1
Ω330
V100
Ω470
Ωk1
Ωk1
Ωk1
Ωk1
א١٤٠ א א א
אאא -١
- ١١٦ -
אאWFEΩk1FEΩ330FEΩ470
٦JאאאאF٥Eא،FEΩk1FEΩ330FEΩ470
٧JאאאאF٥Eאאאא،אΩk1WFE١٠٠٪FE ٢٥٪FE٥٠٪ FE ٣٣١٪
٨Jאאא٩VאFא
אאEאאאאאאא،WFEFE FEא FE
٩JאΩk10F
אאEאW
−
+
2V
Ωk10
outputΩk10
א١٤٠ א א א
אאא -١
- ١١٧ -
אאאאאאFKEΩM1FEΩk20FEΩk100 FEΩk10
١٠JאאאאאאWFEFE FE FEאא
א١٤٠ א א א
אאא -١
- ١١٨ -
אא
١KאאאאאאאאW
Ω= 56R1
Ω=100R 2 Ω=100R 3
−=
+V5.1VS
Ω= 27R4
)(a
Ω= k2.6R2
Ω= k3.3R3
Ω= k1R1−
+V5
Ω= k10R4
Ω= k6.5R5
)(c
Ω680R2
−=
+V3VS
Ω180R4
Ω330R3
Ω680R1
)(b
א١٤٠ א א א
אאא -١
- ١١٩ -
٢Kאאאא١אאאK
٣Kאאאאאא،אאאאאאא
٤KאאאאW
٥Jאא)B,A(אאW
−
+V100
Ω= 470R 3
Ω= k1R1 Ω= 330R2
Ω= 560R 4
Ω= k1R 5 Ω= k5.1R 6
Ω= 680R 7Ω= 100R8
A B
Ω= k1R2
Ω= k1R1
+
−V1 Ω= k2.2R 3
Ω= k3.3R 4
−
+V100
Ωk10
Ωk8.1
Ωk7.4
Ωk1
Ωk1
Ωk6.5
A B
C
D
E
F
א١٤٠ א א א
אאא -١
- ١٢٠ -
٦JאאW
٧JאאאאאאאאאNo LoadFא)B,A(KEאΩ= k10RLא،
אאאאK
٨JאאWFEאאאTRFEאאאאTIFEאאΩ910FEאB,ABA V,VK
A4
−
+V40
1R
5R 6R
W20P =
3R
V20
7R
8R
4R
2R
W2P =
V5V1
A1
A1
Ω= k10R1
Ω= k6.5R 2
Ω= k7.2R 3
LR
−
+V22 A
B
א١٤٠ א א א
אאא -١
- ١٢١ -
٩JאאאLadder NetworkWFEאאTRFEאאA،AV
אאB،BV
١٠JאאאאB,AאאאאאW
−
+V60
Ω910
Ωk560
A BΩk1 Ωk1
Ωk1 Ωk1Ωk560
Ω56 Ω56
V18 Ω= k2.2R 2
Ω= k6.5R1 Ω= k1R3 Ω= k1R5
Ω= k1R 6Ω= k2.2R 4
A B
א١٤٠ א א א
אאא -١
- ١٢٢ -
١١Jאאאאא١٠אא
אאB,A١٠V،V10VS ؟=
١٢Jאאאא،אאאאאW
Ω=Ω=Ω=Ω=Ω= k5R,k15R,k60R,k20R,k10R 54321
2R
3R
−
+V100
4R
5R
CVAV
BV
A
B
C
R١
−
+Ω= 820R 2
Ω= 100R1 Ω= 220R3
Ω= 820R 4 Ω= 680R 6
Ω= 100R5A
BΩ= 100R7Ω= 220R8
Ω= 100R9
TI
TI
2I 3I 4I 5I
אאאאאא
JJ١١
אאאã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
אאאא
א
אא
٧
אא ١٤٠ א א
אאא -١
- ١٢٣ -
אאאא
،אאאאאW• אאאאאאK • אאאאאאK • אאאאאK • אאאאאאאK • אאאאאאאK
אא ١٤٠ א א
אאא -١
- ١٢٤ -
٧J١ Introduction אאאאאא
אKאאאאאאאאאאאK
אאאאאאאKאאא
א،אאאFJ٢KEא،אאאאאא
K
٧J٢ אאאא אאאVoltage Source
Current Sourceאאאאאאאא،K٧J٢J١ אא Constant Voltage Source אאאאא
אאSRאאאאF٧J١KE
F٧J١E
אאIdeal Voltage Source،SRאאW
SL RR >> F٧J١E
−
+
SVSR
LR
אא ١٤٠ א א
אאא -١
- ١٢٥ -
٧J٢J٢ Constant Current Source אאאאאאSR
אאאאא،F٧J٢KE
F٧J٢JE
F٧J٢JE
אאIdeal Current Source،SRאאW
LS RR ⟩⟩ F٧J٢E
אאאאאאאאאK
٧J٢J٣ אSource Conversions " ? א،אאא
אF٧J٣EאK
SR Si
B
A
A
SRSi LR
A
B
A
אא ١٤٠ א א
אאא -١
- ١٢٦ -
F٧J٣EK
אאאLIW
LS
SL RR
VI+
= F٧J٣E
אאאאאאLIKW
SLS
SL i
RRRI ⎟⎟
⎠
⎞⎜⎜⎝
⎛+
= F٧J٤E
אאF٧J٣EF٧J٤EW
SSS iRV ⋅= F٧J٥E
−
+
SVSR
LR
LiA
B
Si I SR LR
Li
A
B
≡
אא ١٤٠ א א
אאא -١
- ١٢٧ -
F٧J١EאאאאW
Ω= K1R)c( LΩ= 560R)b( LΩ= 100R)a( L
F٧J٤EאאאF٧J١KEא
Ω= 100RLF٧J٣E،LI
SLS
SL i
RRRI ⎟⎟
⎠
⎞⎜⎜⎝
⎛+
=
A99.0mA9901*k1.10
k10IL ==⎟⎠⎞
⎜⎝⎛
ΩΩ
=
Ω= 560RL،W
A947.01*k56.10
k10IL =⎟⎠⎞
⎜⎝⎛
ΩΩ
=
Ω= K1RLLI
A909.01*k11k10IL =⎟
⎠⎞
⎜⎝⎛
ΩΩ
=
אאאאאLI١٠٪SiLRאSRאאאאK
I
Ωk10RSA1
iS
A
B
LR
Li
אא ١٤٠ א א
אאא -١
- ١٢٨ -
F٧J٢E،אאאLRאmA750IL =K
F٧J٥EאאאF٧J٢KE
אאאF٧J٣Eא،W
SLS
SL i
RRRI ⎟⎟
⎠
⎞⎜⎜⎝
⎛+
=
אSR،SiאW
( ) 10R1075.0 L =+
10R75.05.7 L =+
5.2R75.0 L =
Ω== k33.375.05.2R L
I Ω= k10R SA1iS =
A
B
LR
Li
אא ١٤٠ א א
אאא -١
- ١٢٩ -
F٧J٣EאאאF٧J٦EאK
F٧J٦EאאאF٧J٣KEא
A250
100RVi
S
SS ===
−=
+V100VS
Ω= 50RS
A
B
אא ١٤٠ א א
אאא -١
- ١٣٠ -
אאאF٧J٧E،W
F٧J٧EאאאF٧J٣KE٧J٣ אSuperposition Theorem
אאאאא?א?אא
KאאאאאאW
אאאאאאאאא،אאאאאא
אאאW
♦ אא،אאSRאאאאShort CircuitK
♦ אא،אאSR،אאאאOpen-Circuit
אאאF٧J٨Eאאאא،K
Ω= 50R SIA2iS =
A
B
אא ١٤٠ א א
אאא -١
- ١٣١ -
F٧J٨EאK
אאאאabF3אREאאאא
אF٧J٩Eאא،1I،2Iאאאאאאאאאab،א
אאאאאאאabאאK
F٧J٩EאאאK
−
+
1SV
2R
3R −
+
2SV
a
b
R١
+ 2R
3R
+
2SV
a
b
2I
+
1SV2R
3R
a
b
1I
R١ R١
אא ١٤٠ א א
אאא -١
- ١٣٢ -
F٧J٤Eאא2RאאאאאK
F٧J١٠EאאאF٧J٤KE
אאאאא،אאאK
אאאWאא١٠ VF٧J١١KE
F٧J١١Eאא١٠ VאאאF٧J٣KEWאא2Rא
132
32T R
RRR*R
R ++
=
Ω=++
= 150100100100100*100R T
mA7.6615010
RV
IT
ST ===
−
+V10
Ω= 100R1 Ω= 100R3
Ω=100R 2−
+V5
a
b
−
+V10
Ω= 100R1 Ω= 100R3
Ω=100R 2
a
b
אא ١٤٠ א א
אאא -١
- ١٣٣ -
אאאabאאW
mA3.33100100
100*7.66Iab =+
=
אאאWאא٥ VF٧J١٢KE
F٧J١٢Eאא٥ VאאאF٧J٣KE
אאאabאאאTRW
12
213T RR
RRRR
++=
Ω=+
+= 150100100100*100100R T
mA3.33150
5RV
IT
ST ===
אאאabW
⎟⎟⎠
⎞⎜⎜⎝
⎛+
=21
1Tab RR
RII
mA7.16100100
100*3.33Iab =+
=
Ω= 100R1 Ω= 100R3
Ω=100R 2−
+V5
a
b
אא ١٤٠ א א
אאא -١
- ١٣٤ -
אאW
mA507.163.33ITab =+=
אא،אאאאאאאאK
F٧J٥Eאאא2RאאאF٧J١٣KE
F٧J١٣EאאאF٧J٥KEא
אאאKאאאWאא١٠ VF٧J١٤KE
F٧J١٤EאאאאF٧J٥KEאאאאK
אאאאTRW
Ω=+= 320100220R T
mA2.3132010ii
2RT ==↓=
−
+V10
Ω= 220R1
Ω=100R 2
a
b
A mA100iS =
−
+V10
Ω= 220R1
Ω=100R 2
a
b
אא ١٤٠ א א
אאא -١
- ١٣٥ -
∴אאא2RאV10mA2.31KאאאWאא١٠٠ mAF٧J١٥KE
F٧J١٥EאאאאF٧J٥KE
אאabאאW
⎟⎠⎞
⎜⎝⎛
+=↓ 100220
220ii SR 2
2Ri ↓אאא2R،אsiא
א،אW
mA8.68320220100i
2R =⎟⎠⎞
⎜⎝⎛=↓
mA8.68i2R =↓∴
אאא2RאאאאאmA8.68Kאאא2RאאW
mA1008.682.31i =+=
Ω= 220R1
Ω=100R 2
a
b
A mA100iS =
אא ١٤٠ א א
אאא -١
- ١٣٦ -
٧J٤ Thevinen's Theoremאא
FEThevinen's TheoremKאאThVאאThR
F٧J١٦KE
F٧J١٦Eא?K?
אאאאאאThRאאאאIאאrאאאW
rRV
ITh
Th
+= F٧J٦E
אWאאאFEאאאאאW
١E אאאאאאאThVK
٢E אאאאFZEאאShort CircuitאאאThRFThRאאאאאאKE
ThV
ThR
rI
A
B
אא ١٤٠ א א
אאא -١
- ١٣٧ -
٣E FאEThVאאThRאאאאF٧J١٦KEאא
אאאW
rRV
ITh
Th
+=
WאאאComplex CircuitKאאאאאOutputא
אא،אאW١E OpenאFאEאאאא
אThVK ٢E אאאאאFאאEאא
ThRאאK ٣E FאEאאSeries Circuit
ThV،ThRLRאK
F٧J٦Eאאאאאb،aאK
F٧J١٧EאאאF٧J٦KE
−
+V10
Ω= 4R1 Ω= 8R 2
Ω= 6R 3−
+V5
a
b
אא ١٤٠ א א
אאא -١
- ١٣٨ -
אאאWאאabאאאOpenא
אa،bThVK
F٧J١٨EאאאF٧J٦EאabKאאאא،אW
( )84I510 +=−
A125
12510I =
−=∴
aVאאW4*I10Va −=∴
V33.84*12510Va =−=
V33.8VTh =∴
אאaאאאאaאא ٥V אאאאא
אaVW8*I5Va +=
8*1285Va +=
V33.833.35Va ≈+=
−
+V10
Ω= 4R1 Ω= 8R 2
−
+V5
a
b
I
אא ١٤٠ א א
אאא -١
- ١٣٩ -
אאaVאאאKאאWThRShortאK
abTh RR =
אאאאאאF٧J١٩KE
F٧J١٩EאאאF٧J٦EאאKאאאאF٧J٢٠KE
F٧J٢٠EאאאF٧J١٩KE
אRTHW
Ω=+
==∴ 66.2848*4RR abTh
Ω= 4R1 Ω= 8R 2
a
b
Ω= 4R1 Ω= 8R 2
a
b
אא ١٤٠ א א
אאא -١
- ١٤٠ -
אאWאאאאF٧J٢١KE
F٧J٢١EF٧J٦KE
אאabW
A96.0666.2
33.86R
VITh
Thab =
+=
Ω+=
F٧J٧EאאאאאאK
אאאאאאא
אKאאאWאא1E،F٧J٢٢KE
F٧J٢٢Eאא١٠ VאאאF٧J٧KE
אIab١W
V33.8VTh =
Ω= 66.2R Th
Ω6I
A
B
−
+V10
Ω= 4R1 Ω= 8R 2
Ω= 6R 3
a
b
IT١
Iab١
אא ١٤٠ א א
אאא -١
- ١٤١ -
Ω=+
+= 43.7686*84RT
A345.143.7
10i 1T ==
A77.068
8*345.1i 1ab =+
=
אאאWאא2E،F٧J٢٣KE
F٧J٢٣Eאא ٥ VאאאF٧J٧KE
אIab٢W
Ω=+
+= 4.10646*48R T
A48.04.10
5iT ==
A192.064
4*48.0iab =+
=
אאWאאאאאab،אאאאאאW
A962.0192.077.0iab =+=
אאאאK
Ω= 4R1 Ω= 8R 2
Ω= 6R 3−
+V5
a
b
IT٢
Iab٢
אא ١٤٠ א א
אאא -١
- ١٤٢ -
F٧J٨EאאאLRאאאF٧J٢٤EאW
FEאKFEK
F٧J٢٤EאאאF٧J٨KE
אWאאאאאΩK8،ΩK12אא
אאΩK10K
201010*2i
LR +=∴ ↓
mA32
31*2i
LR==↓
Ωk12a
b
Ω= k8R LmA2 Ωk10I
אא ١٤٠ א א
אאא -١
- ١٤٣ -
WאKאאWאLRThVאאF٧J٢٥JKE
F٧J٢٥JEאאאF٧J٨ERLK
V20K10*mA2VTh =Ω=∴
אאWאאאאאאאא
FEאאאF٧J٢٥JKE
F٧J٢٥JEאאאF٧J٨EאK
RThW
Ω=+=∴ K221210RTh
אאWF٧J٢٦KE
Ωk12
open ⇐ThR0I =
a
b
Ωk10
⇐ThV0I =
Ωk12a
b
mA2 Ωk10I
אא ١٤٠ א א
אאא -١
- ١٤٤ -
F٧J٢٦EF٧J٨KE
אאאW
LTH
ThRR
VI+
=∴
mA32
K30V20
82220I =
Ω=
+=
אאאאK
٧J٤J١ אא אאאאאאBridge Circuit،
אאאאאאאאאא،אאThevinen's Theoremא
א،אאאאK אאF٧J٢٧Eאא،WאאA،B
אOutputC،DאLRK
אאאC،DאאאאA،BאאSourceK
V20VTh =
Ω= k22R Th
Ω= k8R LI
A
B
אא ١٤٠ א א
אאא -١
- ١٤٥ -
F٧J٢٧EאאK
F٧J٩EאאאF٧J٢٨Eא،W
FEאאLRאC،DKFEאאאLRK
F٧J٢٨EאאF٧J٩KE
SV
2R
C
1R
3R 4R
A
B
DLR
V24VS =
Ω= 680R 2
Ω= 680R 3 Ω= 560R 4
C
Ω= 330R 3
A
B
DΩ= k1R L
אא ١٤٠ א א
אאא -١
- ١٤٦ -
אאW
אאWאLRאC،DאאאאC،DThVW
DCTh VVV −=
S42
4S
31
3Th V
RRRV
RRRV ⎟⎟
⎠
⎞⎜⎜⎝
⎛+
−⎟⎟⎠
⎞⎜⎜⎝
⎛+
= F٧J٧E
אאאאאLRאאK،F٧J٢٩KE
W
31C RIV =
31
S1 RR
VI+
=
42D RIV =
42
S2 RR
VI+
=
F٧J٢٩EאאF٧J٩EאRLK
ThV−
+V24
Ω= 330R1
Ω= 560R 4
Ω= 680R 2
DC
Ω= 680R 3
1I 2I
CV DV
אא ١٤٠ א א
אאא -١
- ١٤٧ -
VThW
24*560680
56024*680330
680VTh ⎟⎠⎞
⎜⎝⎛
+−⎟
⎠⎞
⎜⎝⎛
+=∴
V32.5838.10158.16VTh =−=
אאWאאאThRאאC،DאאאאF٧J٣٠KE
F٧J٣٠EאRThF٧J٩KERThW
42
42
31
31Th RR
RRRR
RRR+
++
=∴ F٧J٨E
560680560*680
680330680*330R Th +
++
=
Ω=+= 27.529096.307178.222RTh
אאWF٧J٣١KE
1R
4R
2R
D
C3R
B
A
⇐ThR
אא ١٤٠ א א
אאא -١
- ١٤٨ -
F٧J٣١EF٧J٩KE
אאCD،אW
LTh
ThCD RR
VI+
=∴
mA5.3100027.529
32.5ICD =+
=
∴אאאCD٥٣ mA
٧J٥ א–אJ٧J٥J١ אאאאF∆←YE "Star Delta FromConversion" →
אאאאאאא،א∆←YאF٧J٣٢KE
F٧J٣٢E ∆↔YK
V32.5VTh =
Ω= 27.529RTh
Ω= k1R LI
C
D
≡
C
3R
1R
2R
A
B
O
CR AR
BR
A
B C
אא ١٤٠ א א
אאא -١
- ١٤٩ -
א∆A،B،Ca،b،cKאY١،٢،٣Kא(Y←∆)" Conversion From (Y←∆)"
אYאא∆F٧J٣٣E،אK
F٧J٣٣Eאאא
אאאWY=אא∆אא∆KW
CBA
CA1 RRR
RRR++
= F٧J٩E
CBA
CB2 RRR
RRR++
= F٧J١٠E
CBA
AC3 RRR
RRR++
= F٧J١١E
BR
3R
1R
2R
A
B C
O
ARCR
אא ١٤٠ א א
אאא -١
- ١٥٠ -
٧J٥J٢ אאאFY←∆E אאאW
2
3131A R
RRRRR ++= F٧J١٢E
1
3232B R
RRRRR ++= F٧J١٣E
3
2121C R
RRRRR ++= F٧J١٤E
אא∆אYאאאאאאאאK
F٧J١٠Eא∆אF٧J٣٤EאYאK
F٧J٣٤EאF٧J١٠KE
אאYאא∆F٧J٣٥E،
א∆←YK
Ω100
Ω560Ω220
A
B C
אא ١٤٠ א א
אאא -١
- ١٥١ -
F٧J٣٥EאאאF٧J١٠EK
אאאאאF٧J٩EJF٧J١١E،W
Ω=++
= 25560220100
220*100R1
Ω=++
= 6.63560220100
560*100R 2
Ω=++
= 140560220100
560*220R3
Ω100
Ω560
Ω220
3R
1R
2R
A
B C
O
אא ١٤٠ א א
אאא -١
- ١٥٢ -
אאF٧J٣٦KE
F٧J٣٦EאאאF٧J١٠KE
F٧J١١E
אY←∆אאF٧J٣٧KE
F٧J٣٧EאF٧J١١KE
Ω=140R 3
Ω= 25R1
Ω= 5.63R 2
A
B C
O
Ω= k6.5R 3
Ω= k1R1
Ω= k2.2R 2
A
B C
O
אא ١٤٠ א א
אאא -١
- ١٥٣ -
אא∆אY،F٧J٣٨E،
אY←∆K
F٧J٣٨EאאאF٧J١٢KE
א∆=אאאYHאYאKאאF٧J١٢EJF٧J١٤E،W
Ω=++= K15.92.2
6.5*16.51R A
Ω=++= K59.36.5
2.2*12.21R B
Ω=++= K12.201
6.5*2.26.52.2R C
BR
CR
AR
Ωk6.5
Ωk1
Ωk2.2
A
B C
O
אא ١٤٠ א א
אאא -١
- ١٥٤ -
٧J٥J٣ אאא∆←YY←∆אאK
F٧J١٢EאאאLRאאאF٧J٣٩Eא،
Y→∆K
F٧J٣٩EאאאF٧J١٢KE
אאאא∆אאאA،C،D
א∆אאאB،C،DאYאאא∆אאאB،C،Dא
אאYF٧J٤٠KE
F٧J٤٠EאאאF٧J١٢KE
V120VS =
Ω= k9.3R 2Ω= k7.4R1
Ω= k2.2R 3 Ω= k7.2R 4
C
A
B
DΩk18
Ω= k2.2R 3 Ω= k7.2R 4
C
B
DΩk18
o
B
C DR١ R٢
R٣≡
אא ١٤٠ א א
אאא -١
- ١٥٥ -
1R،2R،3RW
Ω=++
= K73.1187.22.2
2.2*18R1
Ω=++
= K12.2187.22.2
18*7.2R 2
Ω=++
= K26.0187.22.2
7.2*2.2R3
אאאא1R،2R،3RF٧J٤١WE
F٧J٤١EאאאאאK
אאאאF٧J٤٢WE
Ωk26.0
Ωk12.2Ωk73.1
V120VS =
Ω= k9.3R 2Ω= k7.4R1
C
A
B
D
o
אא ١٤٠ א א
אאא -١
- ١٥٦ -
F٧J٤٢EאF٧J٤١KE
אאאא∆אΥאאאאאאאאאאא
אאWWTRאK
WאאTIKW1I،2IאאK
אWאאCCVKWאאDDVKWאאאC،DK
DCCD VVV −= WאאCDאאCDVLRK
L
CDCD R
VI =∴
אאאW
( ) ( )( ) ( ) Ω≈+
++++⋅+
= K37.326.012.29.373.17.412.29.373.17.4
R T
Ωk7.4
Ωk12.2
Ωk9.3
Ωk73.1−
+V120
1I 2I
Ωk26.0
A
B
C D
אא ١٤٠ א א
אאא -١
- ١٥٧ -
Ω=∴ K37.3R T
mA6.3537.3
120IT ≈≈
אאW
( )( ) ( )73.17.412.29.3
12.29.3*II T1 ++++
=
mA2.17I1 =∴
mA38.18I2 =
V18.39VC ≈
V32.48VD =
אאC،DK
DCCD VVV −=∴
V14.932.4818.39VCD −=−=
WאFJEאאDאאCCD VV ⟩אאCDIK
mA507.0K18
V14.9ICD =Ω
=∴
٧J٦ אאאאאאFאאKEאאאא
אאאKא،אאאאאאאאאא
אאאאאאאאאאא
אאאאא،אאאאK
אא ١٤٠ א א
אאא -١
- ١٥٨ -
MeshאאאאאאF٧J٤٣Eאא،a،bאK
K
F٧J٤٣EאאאאאאאK
אאאאאאWF١E אאאאMeshKF٢E אא Meshes אKCL
אאK F٣E אKVLאאאK F٤E אאאאאאK F٥E אאאאאMeshes. F٦E אאאאאK
3R
4R5R
a b
a b
c
d
e
R١ R٢
V١ V٢
אא ١٤٠ א א
אאא -١
- ١٥٩ -
F٧J١٣Eאאאאאאאאאא
אF٧J٤٤KE
F٧J٤٤EאאאF٧J١٣KE
אWאאאאאאאא،אאK
אאאאאא1I،2I،3Iאאא1I،2I،3I،4I،5IK
4I،5IאאאFbE
215 III −= (a)
324 III −= (b)
א1אI،2I،3IאאאאK
אאאאאאאאK
אאWאאF١EMesh
51 I20I1010 += (c)
V10Ω10
Ω20
Ω30 Ω20V15V20
a b d
c
f
1I 2I 3I
5I
1I3I
Ω10
4I2I
אא ١٤٠ א א
אאא -١
- ١٦٠ -
5IFaE21 II +KW5I1I،2I
211 I20I20I1010 −+=∴
21 I20I3010 −= (d)
FdEK
אאWאאF٢EMesh 452 I10I20I3020 −+= (e)
א4I،5IFeEW( ) ( )32212 II10II20I3020 −−−+−=
32212 I10I10I20I20I3020 +−−+−=
321 I10I60I2020 +−= (f)
אWאאF٣EMesh 43 I10I2015 +−= (g)
4IFbEW( )323 II10I2015 −+−=
323 I10I10I2015 −+−=
23 I10I3015 +−= (h) אFdE،FfE،FhE1I،2I،3Iא
Wאאא( ) 321 I0I20I3010 −−= (I)
321 I10I60I2020 −+−=− (II) ( ) 321 I30I10I015 +−=− (III)
אא(III, II, I)W
אא ١٤٠ א א
אאא -١
- ١٦١ -
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
⎥⎥⎥
⎦
⎤−−
⎢⎢⎢
⎣
⎡
−−+−−+
=⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−−
3
2
1
III
30100
10060202030
1520
10 (IV)
אאFIVEW
[ ] [ ] [ ]IRV ⋅= F٧J١٥E Jא[ ]Iאאאאא،KJא[ ]VWאאאF١EMesh،F٢EMesh،F٣EMesh
א،אאאאאאאאאאאK
Jא[ ]RWאאאאW
[ ]⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡=
333231
232221
131211
RRRRRRRRR
R F٨J١٦E
אא11R،22R،33Rאאא
،אW11RאאF١EMeshK22RאאF٢EMeshK33RאאF٣EMeshK
אאאא12R
אאF١EMesh،F٢EMeshKא23RאאאF٢EMeshא،F٣EMesh،אאאאK
אF١EMeshאF٣EMeshאאאR١٣אK
אא ١٤٠ א א
אאא -١
- ١٦٢ -
אאאא1I،2I،3IK
אאא١EאW
333231
232221
131211
RRRRRRRRR
=∆ F٧J١٧E
∆אKאאאW
223132211323313321122332332211 RRRRRRRRRRRRRRR −+−−−=∆
אאא∆Kא1IW
33323
23222
13121
1
RRVRRVRRV
1I∆
= F٧J١٨E
א2IW
33331
23221
13111
2
RVRRVRRVR
1I∆
= F٧J١٩E
א3IW
33231
22221
11211
3
VRRVRRVRR
1I∆
= F٧J٢٠E
אא∆א1I،2I،3IאWא∆W
3010010602002030
+−−−+−−−+
=∆
אא ١٤٠ א א
אאא -١
- ١٦٣ -
،אאאאאאאW
( ) ( ) ( ) 390000030*20*)20()10(*)10(30*6030 =+−−−−−−−=∆ KK
1Iאאא،W
30101510602002010
1I1
+−−−+−−−+
∆=
אW
( ) ( ) A05128.010*1530*20*)20(10030*60*1039000
1I1 =−−−−−=∴
W
3015010202001030
390001
3015010202001030
1I2
+−−−−−
++⋅=
+−−−−−−++
∆=
אאאW
))0()30(*)20((*)10())10(*)15()30(*)20((*3039000
1I2 −−−−−−−=
A423.0I2 −=
אאאאאK
W
15100206020102030
1I3
−−−−+−+−+
∆=
אאא∆אI٣W
=−−
−−−−−−−−=
))10(*)10(
)15(*)20((*)20())20(*)10()15(*)60((*3039000
1I3
A641.0I3 −=
אא ١٤٠ א א
אאא -١
- ١٦٤ -
אאאאאK
אאאא1I،2I،3I4I،5IW
A218.0III 324 =−=
A47428.042300.005128.0III 215 =+=−=
WאאאאאאאאK
א"Summary"F١E KCLאאאאKF٢E KVLאא
אKF٣E KF٤E אאאאKF٥E אאאאאאאKF٦E אאאאא
אאא،אאאאאא
אאאאאKF٧E אאאאאאאא
אאאKF٨E אאאאאא
ThVאאThRאאאאK
אא ١٤٠ א א
אאא -١
- ١٦٥ -
אא
F١EV300VS =،Ω= 50RSK
F٢EאאאאאK
F٣EאאmA600iS =،Ω= K2.1RSK
F٤EאאאאK
F٥Eאאאאאא5RאאאK
I Ωk7.2A01.0 I Ωk7.4mA10
kV5Ω100
V12Ω2.2
V2
Ω= k1R1
Ω= k2.2R 2
Ω= k1R3
Ω= k1R 4
V3
5R
אא ١٤٠ א א
אאא -١
- ١٦٦ -
F٦Eאאאאא3RאאW
F٧E אאאאLRK
F٨EאאאLRאא
Ω= 680R1 Ω= 220R 2
Ω= 330R3
V20
Ω= 470R 4mA100 I
V40Ωk1 Ωk2.8
V60
Ω= k5.1R 5IA5.0
Ωk1
Ω560
V12VS =
Ω= k1RL
Ω= 820R 2
C
Ω= k1R1
Ω= k2.2R 3 Ω= k2.1R 4
A
B
D
אא ١٤٠ א א
אאא -١
- ١٦٧ -
F٩EאABאאאW
−
+V10
4R
BA
mA2.0I =
Ω=10R1 Ω= k15R 2
Ω= k12R 3
א١٤٠ א א א
-١
- ١٦٨ -
אא(References)
[١] Thomas L. Floyed, Electrical Engineering Fundamentals, Prentice, Inc, sixth edition, ٢٠٠٠.
[٢] B. L. Theraja, A. K. Theraja, " Electrical Technology", published by Ninja Construction development Co. Ltd. Ram Nagar, New Delhi, ١٩٩٥ ,١١٠٠٥٥.
[٣] M. A. PAI, "Introduction to Electric Circuits and Machines", Affiliated east west presses private limited, ١٩٧٥.
א ١٤٠ א א
-١
א
אא
אאWאאא אאאא
١J١٢١J٢אאא٢١J٢J١אא٢١J٢J٢אאאאאא٣١J٣אאא٣١J٣J١א٤١J٣J٢א٤١J٣J٣א٦١J٣J٤א٧١J٣J٥אא٧١J٣J٦אא٩١J٣J٧א١٠
אא١٢אאW
אאאא١٤٢J١١٥٢J٢١٥٢J٢J١FEא١٥٢J٢J٢א١٦٢J٢J٣١٨
א ١٤٠ א א
-١
٢J٢J٣J١א١٨٢J٢J٣J٢א١٩
אא٢١אאWאא
אאאא٢٤٣J١٢٥٣J٢א٢٥٣J٣אאאא٢٨
אא٣٢אאאWאאאאאא
אאאאא٣٣٤J١٣٤٤J٢אאא٣٤٤J٢J١אא٣٥٤J٣אאא٣٦٤J٤אאא٣٩٤J٥ ٤١٤J٦ ٤٤٤J٧א٤٤٤J٧J١אאא٤٦٤J٨אאאא٤٩٤J٩א٥٢٤J١٠אא٥٦
אאא٦٠אאWאאאאאא
אאאא٦٧
א ١٤٠ א א
-١
٥J١٦٨٥J٢אאאאא٦٩٥J٣٧٠٥J٤אאאאא٧٢٥J٤J١אאאא٧٥٥J٥אאא٧٦٥J٦FEאאאא٧٩٥J٧אאאא٨٦
אא٨٩אאWאאא
אאאא٩١٦J١٩٢٦J٢אא–אא٩٢٦Jא٣אא–אא٩٧٦J٤אאאאא١٠١٦J٥אאאאא١٠٨
אא١١٨אאWאאא
אאאא١٢٣٧J١١٢٤٧J٢אאאא١٢٤٧J٢J١אא ١٢٤٧J٢J٢١٢٨٧J٢J٣א١٢٨٧J٣א١٣٠٧J٤١٣٦
א ١٤٠ א א
-١
٧J٤J١אא١٤٤٧J٥א–אJ١٤٨٧J٥J١אאאאF∆←YE١٥٠٧J٥J٢אאאFY←∆E١٥٠٧J٥J٣אאא∆←YY←∆
אאK١٥٤
٧J٦אאאאאאFאאKE
١٥٧
אא١٦٥אא١٦٨
אאאאאא
אאFאEא
GOTEVOT appreciates the financial support provided by BAE SYSTEMS
