Electrical Engineering

 ‫א‬‫א‬‫א‬ ã¹]...

Author: General Management for Creating and Developing Courses

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 ‫א‬‫א‬‫א‬ ã¹]
 ١ J

 ١٤٠

‫א‬

  ١٤٠

‫א‬

 ١-



 W،،‫א‬‫א‬،‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬ ‫א‬  ،‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬        ،‫א‬ ‫א‬‫א‬   ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬    ،   ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬      ‫א‬  ‫א‬   ،‫א‬     K‫א‬‫א‬،‫א‬‫א‬    ?  ? ١J   ? ‫א‬ ‫א‬    K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬?  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬  K‫א‬

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‫א‬‫א‬‫א‬‫א‬















  ١٤٠

‫א‬

 ١-



 ،KKK،‫א‬‫א‬‫א‬‫א‬  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J  ‫א‬‫א‬  K‫א‬

‫א‬‫א‬  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬،‫א‬،‫א‬‫א‬

  ،‫א‬‫א‬‫א‬ ‫א‬،

‫א‬،‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

 KKKKKK،‫א‬ 

 ‫א‬‫א‬‫א‬ ã¹]
١ J  

 ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

١

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

‫א‬‫א‬

 ١-

‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬،‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬ •

-١-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



  ١J ١ ،  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ The International System of Units‫א‬‫א‬‫א‬ ٢J ١

 ‫א‬  ‫א‬ ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  KK‫א‬

The Measurement Units‫א‬‫א‬

١J ٢J ١

،‫א‬‫א‬   ‫א‬‫א‬‫א‬



 W‫א‬‫א‬

 Symbol‫א‬

Unit‫א‬

Quantity‫א‬

 m

Meter

 kg

Kilogram‫א‬

Mass‫א‬

 A

Ampere

Current‫א‬

 s

Second

Time‫א‬

 K

Kelvin

Temperature‫א‬‫א‬

 cd

Candle

Luminous Intensity‫א‬

 Length‫א‬

 The Measurement Units‫א‬‫א‬E١-١F



K‫א‬‫א‬‫א‬ Luminous Intensity‫א‬Temperature‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬NForce‫א‬‫א‬،‫א‬‫א‬ Watt‫א‬Electric Power‫א‬‫א‬K

-٢-

kg ‫א‬ s2

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



Nm W s  K Nm  JJoule‫א‬

Electric Energy‫א‬‫א‬K

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

٢J ٢J ١

 which attached to the measurement units، prefixes،Power of ten units

power ‫א‬The International System of Units‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬of ten  W‫א‬‫א‬

‫א‬ Power of ten  1 * 10−18

 1 * 10−15

‫א‬ Symbol  a  f

‫א‬ Prefixes to the Units  Atto

Femto

 1 * 10−12

 p

 1 * 10−6

Micro

 1 * 10−3

 µ  m

 1 * 10−2

 c

 1 * 10 −1

 d

Centi

 1 * 10−9

 n

 1 *101

 da

 1 *103

 k

 1 *102

 h

 1 *106

 M

 1 *1012

 T

 1 *109

Pico Nano Milli Deci Deka Hecto Kilo Mega

 G

Giga Tera‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٢J ١F The Basic Electrical Quantities‫א‬‫א‬‫א‬ ٣J ١

‫א‬،Voltage‫א‬،Current‫א‬،Charge‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬KElectrical Resistance‫א‬‫א‬ -٣-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ،EJ ‫א‬FElectrons‫א‬‫א‬‫א‬KAtoms  KE‫א‬FNeutrons‫א‬،EH‫א‬FProtons‫א‬ Charge‫א‬

١J ٣J ١

‫א‬Electron‫א‬‫א‬،Q

،‫א‬K‫א‬‫א‬‫א‬‫א‬،Proton

K  ‫א‬ ‫א‬‫א‬‫א‬، ‫א‬  ‫א‬‫א‬‫א‬،‫א‬‫א‬

 KC‫א‬Coulomb‫א‬ Current‫א‬

٢J ٣J ١

،I‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

 WKCurrent‫א‬‫א‬E‫א‬F‫א‬ I=

dQ dt

A≡

C s

E١J ١F  W‫א‬،Ampere‫א‬ E٢J ١F  KA‫א‬IW

 KCCharge‫א‬WQ  Kstime‫א‬Wt

 ‫א‬،‫א‬

 K‫א‬‫א‬،‫א‬Electrons

-٤-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 I

E

Load 



 ‫א‬E١J ١F

‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬  ‫א‬‫א‬،voltage source‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

 W‫א‬‫א‬‫א‬‫א‬K Pure D.C. Current  K١

Current (I)

 KE٢J ١F،‫א‬‫א‬‫א‬‫א‬

time (t)

 E٢J ١F Pulsating Current  K٢

current ( I )

 KE١J ٣F،‫א‬

time ( t ) 

-٥-

 ‫א‬‫א‬

‫א‬

 ١-



current ( I )

‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

time ( t ) current ( I )



time ( t )



Pulsating CurrentE٣J ١F

Alternating Current K٣

  sin wave‫א‬‫א‬K‫א‬‫א‬

current ( I )

 KAlternating Current‫א‬‫א‬

time ( t )



Alternating CurrentE٤J ١F Voltage‫א‬

٣J ٣J ١

Volt،‫א‬‫א‬(Work)‫א‬‫א‬ V≡

V=

 W‫א‬

J C

E٣J ١F  W

dW dQ

E٤J ١F  W -٦-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 KV‫א‬WV  KJ‫א‬WW

 KCCharge‫א‬WQ Resistance‫א‬

٤J ٣J ١

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬Electric Power‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬KOhm‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬K‫א‬

، Ω  Ohm،‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬ ‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

Current (I)

 W‫א‬‫א‬



Resistance (R)

 ‫א‬‫א‬‫א‬E٥J ١F

Resistance of a wire‫א‬‫א‬

٥J ٣J ١

 W‫א‬Wires‫א‬

 KL،Length‫א‬ K١

KA،Cross-section Area‫א‬ K٢ -٧-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



‫א‬K، ρ ،MaterialE ‫א‬‫א‬F‫א‬ K٣ K

KT،Temperature‫א‬‫א‬ K٤

R=

ρ.L A

 W‫א‬‫א‬‫א‬

E٧J ١F  K Ω Resistance‫א‬

 W WR

 K Ω.m ‫א‬‫א‬

Wρ

 K m 2 ‫א‬،Cross-section Area‫א‬

WA

 m،Length‫א‬

WL

 E١J ١F

‫א‬K٥m‫א‬،٥mm‫א‬‫א‬

1.72 * 10 −8 Ω m ‫א‬‫א‬، 20o C ‫א‬

 ‫א‬  W،E٧J ١F‫א‬R‫א‬ R =  ∴ R = 1.72 ∗ 10

−8

-٨-

ρ.L A

⎛ ⎞ 5 ⎜ ⎟ = 4.38 Ω ∗ 2 ⎜ ⎟ −3 ⎝ π 5 ∗ 10 2 ⎠

(

)

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



Types of Resistors‫א‬‫א‬

 W‫א‬

 ‫א‬‫א‬‫א‬Opto-photo-ResistorsW ‫א‬‫א‬

،‫א‬،‫א‬ K‫א‬‫א‬

، ‫א‬‫א‬‫א‬ Thermal-ResistorsW‫א‬  ‫א‬‫א‬

K١

K٢

K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  ‫א‬‫א‬‫א‬

10000 1000 ‫أوم‬

100 10 1 0

40

80

120

160

180 200 ‫درﺟﺔ ﻣﺌﻮﻳﺔ‬

  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٦J ١F



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

‫א‬WVoltage Dependent Resistors‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬،VDR

W‫א‬‫א‬‫א‬‫א‬WLinear Resistors‫א‬‫א‬

 KW‫א‬‫א‬ K

-٩-

K٣ K٤

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬‫א‬‫א‬W ‫א‬‫ א‬K  ‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬

W

‫א‬WPotentiometer‫א‬E١ J ١F ٣،٢،١‫א‬ ،Voltage Divider

 KMega Ohm‫א‬‫א‬‫א‬،EEF٧

‫א‬‫א‬ ‫א‬WRheostatE٢ Kilo  ‫א‬

‫א‬‫א‬،‫א‬‫א‬،Ohm

‫א‬‫א‬‫א‬‫א‬،

‫א‬K ‫א‬‫א‬‫א‬‫א‬

 EEF٧J ١F

‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬W ‫א‬‫א‬K

K ‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١

+ ٢ ١

٢

V١٣ ٣



V٢٣

 EF

+









 ‫א‬‫א‬E٧J ١F

-١٠-



EF

٣





 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 Conductance‫א‬

٦J ٣J ١

G‫א‬‫א‬،‫א‬‫א‬‫א‬

‫א‬،Ampere per Volt‫א‬Siemens G=

 W

1 R

E٥J ١F  KSiemens

R=

 W

1  G

E٦J ١F  .Ohm

 K‫א‬‫א‬G‫א‬                 -١١-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬‫א‬ 

:‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K١

 ٢٩٠٠٠ kWE 

Ω ٧٠٠٠E

 ٠{٠٠٠٣ msE ٠{٠٥ AE

٠{٠٠٠٠٩ VE

٧٠٠٠٠٠٠ VE ٠{٠٠٠٠٠٠٠٠٨ sE ٩٠٠٠ kWE

W K٢  A١٥mAE  s٠{١ nsE

 mA µA ٨٠٠E  A١٣ nAE 

W‫ א‬K٣

µA ٨٠٠H١٥mAE

 ١٣ msH٠{١ nsE ١A+  µA ٨٠٠E

 ٧٠٠٠ µA+١٣ nAE



WA - B‫ א‬K٤

µA B=٨٠٠،A=١٥mAE

 B=١٣ ns A=٠{١ msE

B= ١٠٠٠ nA ، µA A=٨٠٠E

 B=٧٠٠٠ µV،A=١٣mVE -١٢-

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-





A ‫ א‬K٥ B µA B=٨٠٠،A=١٥mAE

W



 B=١٣ ns A=٠{١ msE B= ١٠٠٠ nA ، µA A=٨٠٠E

 B=٧٠٠٠ µV،A=١٣mVE

-١٣-

 ‫א‬‫א‬‫א‬ ã¹]
١ J

 



٢

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



 ‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬،‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬ • ‫א‬‫א‬‫א‬ •

- ١٤ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



 ١J ٢ ‫א‬‫א‬‫א‬Fundamental Law‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬،

‫א‬‫א‬‫א‬‫א‬ K  ‫א‬ ‫א‬ ‫א‬،‫א‬

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

George Simon Ohm‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K١٨٢٦Ohm’s Law

،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

W‫א‬،‫א‬‫א‬‫א‬‫א‬ I

I

  =R Slope

+

R

−

V



t



 ‫א‬‫א‬E١J ٢F

 Ohm’s Law ٢J ٢ ،‫א‬‫א‬‫א‬‫א‬‫א‬    K‫א‬

Current Formula‫א‬EF

١J ٢J ٢

 ‫א‬‫א‬‫א‬‫א‬ E١J ٢F

I=

E V , I= RT R

 KA‫א‬IW  KVVoltage Source‫א‬E  KV،Voltage Drop‫א‬‫א‬V - ١٥ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



 E١J ٢F ،٥٠V‫א‬ ، 100Ω ‫א‬

 ‫؟‬‫א‬‫א‬‫א‬ 

I



A

 100Ω



V

 

 E١J ٢F‫א‬‫א‬‫א‬E٢J ٢F  ‫א‬

 W‫א‬‫א‬ I=

V 50 = = 0.5A R 100

Resistance Formula‫א‬

٢J ٢J ٢

‫א‬‫א‬K ‫א‬‫א‬ ‫א‬‫א‬

 W‫א‬

E٢J ٢F

R=



V E , RT = I IT

 W

Ω ،‫א‬‫א‬‫א‬ W R T

 KA‫א‬I

 K‫א‬‫א‬‫א‬‫א‬ I T

 KV‫א‬E

 KV‫א‬‫א‬V

- ١٦ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



 E٢J ٢F ، 75µA   ‫א‬،١٥٠mV   ‫א‬

 ‫؟‬‫א‬  

I = 75µA A

 

+ V



150mV

 

-



 E٢J ٢F‫א‬‫א‬‫א‬E٣J ٢F

 ‫א‬

 W‫א‬

R=

V 150 * 10 −3 = = 2 * 10 3 Ω = 2KΩ 6 − I 75 * 10

  WNote ،‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

 E٣J ٢F

K٣٠V‫א‬‫א‬٠{٥ mA‫א‬ ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬  ‫א‬

 W‫א‬

RT =

E 30 = = 60 * 10 3 Ω = 60 kΩ 3 − I T 0.5 * 10

- ١٧ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



 E٤J ٢F ‫א‬،١٠mAR١‫א‬‫א‬‫א‬  ‫א‬‫א‬

‫؟‬‫א‬‫א‬،٢٥ V‫א‬

V = 25 V V A

R1

I = 10 mA

 



 E٤J ٢F‫א‬‫א‬‫א‬E٤J ٢F

R1 =

 ‫א‬

V 25 = = 2.5 * 10 3 Ω = 2.5 kΩ − 3 I 10 * 10 Voltage Formula

٣J ٢J ٢

K ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬ Voltage Drop‫א‬

١J ٣J ٢J ٢

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ E ‫א‬  ‫א‬ F‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬،‫א‬  K‫א‬ E٣J ٢F

V = I.R - ١٨ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



Voltage Source‫א‬

٢J ٣J ٢J ٢

‫א‬‫א‬‫א‬‫א‬‫א‬

 ، R T ‫א‬‫א‬

E٤J ٢F

E = IT .R T

 E٥J ٢F

‫א‬‫א‬ 500 Ω ‫א‬ ‫א‬،‫א‬‫א‬

 ٠{١A‫א‬

 ‫א‬

E = I T .R T = 0.1 * 500 = 50 V

 E٦J ٢F  ٣mA‫א‬‫א‬ 27 KΩ ‫א‬،‫א‬‫א‬

 ‫א‬

E = I T .R T = 3 * 10 −3 * 27 * 10 3 = 81 V

 E٧J ٢F  ٠{٨mA‫א‬‫א‬‫א‬، 28 kΩ ‫א‬  ‫א‬ V = I * .R = 0.8 *10−3 * 28 *103 = 22.4 V

  WNote

‫א‬‫א‬ 

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬  W‫א‬‫א‬‫א‬

- ١٩ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



  

V R

I

 E٥J ٢F



 W‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ E٥J ٢F



















E٦J ٢F E٧J ٢F



















V = I*R

I =

V R

 R=

V I

 K‫א‬  Summary‫א‬  K‫א‬‫א‬‫א‬‫א‬ K١

،‫א‬،‫א‬،‫א‬ Current‫א‬ K٢ KI =

V W R

W،‫א‬‫א‬‫א‬ K٣ V = I*R

‫א‬‫א‬‫א‬ I T ‫א‬‫א‬‫א‬‫א‬ K٤ K‫א‬‫א‬، R T ‫א‬‫א‬‫א‬

‫א‬  ‫א‬‫א‬ K٥ K‫א‬‫א‬‫א‬

- ٢٠ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



 ‫א‬‫א‬



‫א‬‫א‬‫א‬‫א‬ K١ W  K‫א‬ EF

K٧٥٪‫א‬ E F K‫א‬ E F

K٣٥٪‫א‬ E F K‫א‬‫א‬‫א‬‫א‬EF

 K‫א‬‫א‬‫א‬‫א‬ EF 

W‫א‬،‫א‬‫א‬ K٢  V = 5V , R = 1Ω EF V = 15V , R = 10Ω E F F  V = 50V , R = 100Ω E F  V = 30V , R = 15KΩ E  V = 250V , R = 5.6MΩ EF ‫؟‬‫א‬‫א‬‫א‬،١٢V10KΩ  K٣ ،J J J W ‫א‬‫א‬‫א‬ K٤ K١٢V‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬،٢٥V K٥ KJ J J W‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٦   8Ω ‫א‬‫א‬،‫א‬‫א‬‫א‬

W‫א‬

- ٢١ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-





Fuse R

120V

V

100V

   ،‫א‬‫א‬‫א‬Fuse‫א‬   ‫؟‬١٠٠ V‫א‬‫א‬‫א‬



W‫א‬‫א‬R‫א‬I‫א‬‫א‬ K٧  I = 2A ,

 I = 2.5A ,

I = 5A ,

R = 18Ω EF

R = 680Ω EF R = 56Ω EF



‫א‬،٣A 27Ω ‫א‬‫א‬ K٨ ‫؟‬‫א‬K W‫א‬‫א‬I‫א‬،V‫א‬‫א‬ K٩  I = 2A ,

 I = 45A ,

 I = 5A ,

V = 10V EF

V = 90V EF

V = 50V EF



 R = 100Ω ‫א‬،‫א‬‫א‬‫א‬‫א‬ K١٠

‫א‬‫א‬‫א‬،‫א‬Variable Voltage Source

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١٠٠ V‫א‬‫א‬ - ٢٢ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬



 ١-



‫א‬‫א‬KI‫א‬V‫א‬‫א‬K  ‫؟‬‫א‬‫א‬‫א‬‫؟‬ K V = 1V   ‫א‬ I = 5mA ‫א‬‫א‬ K١١ W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  V = 1.5V EF F V = 2 V E F  V = 3V E  V = 4 V E F  V = 10V EF K‫א‬‫א‬،I‫א‬V‫א‬،‫א‬ ، ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ K١٢ K

R = 3.3kΩ

R = 3 .9 k Ω

75V

50V

R = 4 .7 k Ω 100V

- ٢٣ -

   

 ‫א‬‫א‬‫א‬ ã¹]
١ J

 ‫א‬‫א‬

‫א‬‫א‬

٣

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬،‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

- ٢٤ -

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



Introduction ١J ٣

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬ ‫א‬       K‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬   KPower‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Power ‫ א‬٢J ٣

KP،Watt‫א‬‫א‬K ‫א‬‫א‬‫א‬

 W‫א‬‫א‬t‫א‬‫א‬ Power =

P=

Energy time

E١J ٣F

E t

E٢J ٣F

 ‫א‬L‫א‬Z‫א‬

 W  W

 KWatt‫א‬Power‫א‬

 K Watt ⋅ second ⋅‫א‬‫א‬JEnergy‫א‬  Ksecondtime‫א‬

WP

WE

Wt



 Note

WattW،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬،‫א‬Joule‫א‬ Watt =



Joule sec ond

E٣J ٣F

-٢٥-

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 E١J ٣F

 ‫؟‬‫א‬‫א‬،٥ sec‫א‬١٠٠ J‫א‬‫א‬ 

 ‫א‬ Power =

Energy E 100 J = = = 20 Watt t 5 sec time

 W‫א‬

 E٢J ٣F  ‫؟‬‫א‬Kt = ٣٠ sec‫א‬‫א‬‫א‬،P = ١٠٠ W‫א‬‫א‬ Energy ⇒ Energy = Power * time time E = P * t = 100 * 30 = 3000J = 3 kJ

 ‫א‬

Power =

 WNote  KWEEnergy‫א‬‫א‬

 E٣J ٣F

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ٠{٠٤٥ W EF F ٠{٠٠٠٠١٢ W E F ٣٥٠٠ W E F  ٠٠٠ W، ٠٠٠،١٠ E  ‫א‬

‫א‬‫א‬‫א‬KMWkWWmW‫א‬‫א‬

‫א‬‫א‬،mW‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬KKW‫א‬‫א‬‫א‬‫א‬‫א‬

 KMW‫א‬‫א‬‫א‬

mW‫א‬‫א‬‫א‬،‫א‬،P=٠{٠٤٥ W EF -٢٦-

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 W P = 0.045 W = 0.045 * 10 3 * 10 −3 W = 45 * 10 −3 = 45 mW

‫א‬،‫א‬‫א‬،P=٠{٠٠٠٠١٢ W

E F

‫א‬، µW ‫א‬‫א‬‫א‬‫א‬،‫א‬

W

P = 0.000012 W = 0.000012 * 10 6 * 10 −6 W = 12 µW

W‫א‬kW،P=٣٥٠٠ W EF P = 3500 W = 3500 * 10 −3 * 10 3 W = 3.5 kW

WMW‫א‬P=١٠{٠٠٠{٠٠٠ W EF P = 10,000,000 W = 10,000,000 * 10 −6 * 10 6 W = 10 MW

 WNote

W‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J   K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫ א‬‫א‬‫א‬‫א‬J  K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J  E٤J ٣F  W‫א‬‫א‬‫א‬

 K‫א‬١٤٠٠ WEF

 K٢٥٠٠ WEF

 K١٠٠٠{٠٠٠ WEF

 ‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -٢٧-

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬‫א‬ ‫א‬‫א‬

1400 W =

1400 10 3

EF

= 1.4 kW

W = P * t = 1.4 kW * 1h = 1.4 kWh

2500 W =

2500 10 3

EF

= 2.5 kW

W = P * t = 2.5 kW * 2h = 5 kWh

1000000 W =

1000000 10 3

EF

= 1000 kW

W = P * t = 1000 kW * 5h = 5000 kWh

Power in Electric Circuit‫א‬‫א‬‫א‬‫א‬

٣J ٣

 ‫א‬،‫א‬‫א‬Power‫א‬

‫א‬،‫א‬،‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ KOhm’s Law‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬

E٤J ٣F

P = V.I

 W

 KWatt‫א‬،Power‫א‬

WP

 KV،‫א‬

WV

 KA‫א‬

-٢٨-

WI

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 I

+

 R

V

 

 ‫א‬E١J ٣F



‫א‬ V = I.R ‫א‬‫א‬‫א‬  W‫א‬

E٥J ٣F

P = V.I = I.R.I = I 2 .R





‫א‬ I =

V ‫א‬، R

 W‫א‬ V V2 P = V.I = V. = R R

E٦J ٣F

V E , RT = I IT

E٧J ٣F

R=

 E٥J ٣F  W‫א‬‫א‬،10Ω ‫א‬‫א‬ I=٠{٧AEF

 I=١{٤AEF  I=٢{١AEF

-٢٩-

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬

 W‫א‬‫א‬  P = I 2 .R = (0.7)2 *10 = 4.9W

EF

P = I 2 .R = (1.4) 2 *10 = 19.6W

EF

P = I 2 .R = (2.1) 2 *10 = 44.1W

EF

IP‫א‬‫א‬‫א‬،‫א‬‫א‬  WK

E٨J ٣F

P α I2

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ P = 4.9 Watt ← I = 0.7 A EF

 P = 19.6 Watt ← I = 1.4A EF



 KEF‫א‬EF‫א‬EF  E٦J ٣F

،١٥ V10 kΩ ‫א‬‫א‬،E٢J ٣F‫א‬  ‫؟‬12 kΩ ‫א‬‫א‬ 12 kΩ

+

V



I

-



+

10kΩ

١٥V

−  E٦J ٣F‫א‬‫א‬‫א‬E٢J ٣F -٣٠-

  

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬

 W‫א‬‫א‬‫א‬‫א‬ I=

V 15 15 = = = 1.5 mA R 10 * 10 3 10 4

 W12 kΩ ‫א‬‫א‬‫א‬ V = I*R

= 1.5 * 10 −3 * 12 * 10 3 = 12 V

 KV=١٢ V 12 kΩ ‫א‬‫א‬   Summary‫א‬

K Watt =

Joule W،‫א‬‫א‬‫א‬‫• א‬ sec ond K‫א‬ •

‫א‬‫א‬‫א‬‫• א‬ K‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

Kopen circuit‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

‫א‬‫א‬‫א‬‫א‬‫א‬ • K KAmpere. Hourx‫א‬ • K١١x‫א‬ •    -٣١-

 ‫א‬‫א‬ ‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬‫א‬

 ‫؟‬ 350 j s ‫א‬‫א‬‫א‬–١  ‫؟‬ 5 h  7500 j ‫א‬‫א‬–٢  500 ms 1000 j ‫א‬‫א‬‫א‬–٣

 kw ‫א‬‫א‬‫א‬–٤

  3750w EF

 1000w EF

 500 w EF  50000w EF



 Kx‫א‬Ex‫א‬ 5 *106 F‫א‬–٥ ‫א‬ 2A  75V ‫א‬‫א‬‫א‬–٦  ‫؟‬ R L ‫א‬

‫א‬‫א‬ 3A ‫א‬120V –٧  ‫؟‬‫א‬

 ‫؟‬100µA 10kΩ ‫א‬‫א‬‫א‬–٨ 

-٣٢-

 ‫א‬‫א‬‫א‬ ã¹]
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١ J

٤

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 ‫א‬‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬،‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

- ٣٣ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



Introduction ١J ٤

‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K

  ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬    ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K  ‫א‬‫א‬  K‫א‬ Series Connection‫א‬‫א‬‫א‬ ٢J ٤

‫א‬،‫א‬‫א‬‫א‬‫ א‬ ‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ،‫א‬‫א‬K‫א‬   K‫א‬‫א‬‫א‬‫א‬ R١

R١

R١

a

a

R٢

a R٢

R٢

I



R٣

R٣

R٣

b

    

b

R٤

b

I I

 ‫א‬‫א‬‫א‬E١J ٤F

- ٣٤ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



Total Resistance (RT)‫א‬

١J ٢J ٤

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E١J ٤F













R T = R1 + R 2 + R 3 + K + R n

 E١J ٤F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬ R 1 = 56 Ω

R 2 = 100 Ω



I

 R٣ = ٢٧ Ω

VS



 

R 5 = 5.6 Ω R 4 = 10 Ω



 E١J ٤F‫א‬‫א‬‫א‬E٢J ٤F

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R T = 56Ω + 100Ω + 27Ω + 10Ω + 5.6Ω = 198.6Ω

∴ R T = 198.6Ω

 E٢J ٤F

‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬  K 22 Ω  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  E٢J ٤F

Q R T = nR ∴ R T = 8 * 22 = 176 Ω

 K‫א‬ n W - ٣٥ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



Ohm's Law in Series Circuits ‫א‬‫א‬‫א‬ ٣J ٤ ،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  K‫א‬  E٣J ٤F

،12.6 kΩ ‫א‬  ‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬ 3.9 kΩ ‫א‬Voltage Drop‫א‬ R1



R2

Vs = ٢٠ V

R٣ =٣٫٩ kΩ

 + V=?

  

_

  E٣J ٤F‫א‬‫א‬‫א‬E٣J ٤F  ‫א‬ I‫א‬ ،‫א‬ R٢،R١‫א‬ ‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬ I=

VS 20 = = 1.59mA R T 12.6 * 103

 V = I * R 3 = 1.59 *10−3 * 3.9 *103 = 6.19V  ٦{١٩ VR٣‫א‬‫א‬∴  E٤J ٤F KVs،‫א‬‫א‬ ‫א‬‫א‬

 K 5mA Fuse‫א‬ Vs‫א‬

- ٣٦ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 5 mA Fuse + VS

R 1 = 1 kΩ

R 2 = 3 .3 k Ω

I = 1mA

R 3 = 4.7 kΩ

−



 E٤J ٤F‫א‬‫א‬‫א‬E٤J ٤F



 ‫א‬

 W‫א‬‫א‬ V1 = IR 1 = (1mA ) ⋅ (1KΩ ) = 1 * 10 −3 * 10 3 = 1V

(

∴ V1 = 1V

)

V2 = IR 2 = (1mA ) ⋅ 3.3 * 10 3 = 3.3V

(

)

∴ V 2 = 3.3V

V3 = IR 3 = (1mA ) ⋅ 4.7 * 10 3 Ω = 1 * 10 3 * 4.7 * 10 3 = 4.7 V ∴ V3 = 4.7 V

 KRTVS‫א‬ ∴ R T = 1 + 3.3 + 4.7 = 9KΩ

 VS = 1 * 10 −3 * 9 * 10 3 = 9V  WVSV١،V٢ ،V٣   VS = V1 + V2 + V3 = 9V   EKirchhoff’s Voltage LawF‫א‬

‫א‬VS‫א‬EF‫א‬ K‫א‬‫א‬‫א‬  WNote

 K‫א‬‫א‬‫א‬EKVLF - ٣٧ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



٥mA‫א‬‫א‬  W‫א‬ VS = 5mA * 9KΩ VS = 5 * 10 −3 * 9 * 10 3 = 45V

 E٥J ٤F

 ‫؟‬VS‫א‬،1mA ‫א‬‫א‬‫א‬‫א‬‫א‬  − VS +    1 .5 k Ω

1.2 kΩ

I

  

1.2 kΩ



5 .6 k Ω

 E٥J ٤F‫א‬‫א‬‫א‬E٥J ٤F  ‫א‬

RT‫א‬‫א‬،VS‫א‬

R T = 1.2 + 5.6 + 1.2 + 1.5 = 9.5kΩ

∴ R T = 9.5kΩ

 VS‫א‬  VS = IR T = (1mA ) ⋅ (9.5kΩ ) = 1 * 10 −3 * 9.5 * 10 3 ∴ VS = 9.5V

- ٣٨ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



Voltage Sources in Series‫א‬‫א‬‫א‬ ٤J ٤

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

K  ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬K‫א‬  E٦J ٤F

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ E٢،E١‫א‬W‫א‬‫א‬‫א‬  KRT  

+ 30 V − + 20 V

−



E1



R T = 200 Ω



E2





 E٦J ٤F‫א‬‫א‬‫א‬E٦J ٤F  ‫א‬ ‫א‬‫א‬،‫א‬‫א‬ E١،E٢‫א‬  W‫א‬

 E T = E1 + E 2 E T = 30 + 20 = 50V

 W

 ∴I =

ET 50 = = 0.25A R T 200

∴ I = 0.25A - ٣٩ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



‫א‬‫א‬،ESeries–OpposingF‫א‬‫א‬

‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  E٧J ٤F

 ‫؟‬‫א‬‫א‬‫א‬‫א‬ + 25V − + 15V −

 

E1



RT



E2

  

 E٧J ٤F‫א‬‫א‬‫א‬E٧J ٤F  ‫א‬

‫א‬‫א‬‫א‬   E١،E٢‫א‬ ‫א‬–H‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬

 W‫א‬‫א‬‫א‬K‫א‬‫א‬ E = E1 − E 2 E = 25 − 15 = 10 V

- ٤٠ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E٨J ٤F

‫א‬،‫א‬  ‫א‬‫א‬‫א‬‫א‬  ‫؟‬‫א‬‫א‬ − E1 +

1.5V

− E 2 + − E3 + − E 4 +

1.5V

1.5V

1 .5 V

ET

 E٨J ٤F‫א‬‫א‬‫א‬E٨J ٤F  ‫א‬ E T = 4 * 1 .5 = 6 V  Kircchoff's voltage law (KVL) ٥J ٤

?  ‫א‬‫א‬  ‫א‬‫א‬‫א‬

 K?‫א‬EF‫א‬‫א‬‫א‬

 W

Voltage Drops‫א‬‫א‬‫א‬  ?‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬Voltage Drops‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K  ‫א‬‫א‬ ‫א‬   K‫א‬‫א‬‫א‬‫א‬

- ٤١ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-





R٤

R1

R2

R3

− V1 +

− V2 +

− V3 +

− V4 +

     

VS

 ‫א‬‫א‬‫א‬‫א‬‫א‬E٩J ٤F v s = v1 + v 2 + v 3 + v 4

‫א‬Voltage Drops‫א‬ 

 K‫א‬

 v s = v1 + v 2 + v 3 + ..........  E٩J ٤F

 W‫א‬‫א‬‫א‬‫א‬ VS ‫א‬ +

+ 5V -

VS −



+ 10V

 

−

 

 E٩J ٤F‫א‬‫א‬‫א‬E١٠J ٤F  ‫א‬  K v s = v1 + v 2

v s = 5 + 10 = 15v ∴ v s = 15v

- ٤٢ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E١٠J ٤F

‫א‬، I = 200mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

 ‫؟‬ R 4  R 3 ، R 2 ، R1 ‫א‬  

R 3 = 100 Ω R 2 = 47 Ω

 R 1 = 10 Ω

R4

  

E=١٠٠ V



I = 200 mA

 

 E١٠J ٤F‫א‬‫א‬‫א‬E١١J ٤F  ‫א‬ Ohm’s Law‫א‬‫א‬

 KKirchhoff's Voltage Law

 Voltage Drops‫א‬  V1 = IR 1 = 200 * 10 −3 * 10 = 2V  V2 = IR 2 = 200 * 10 −3 * 47 = 9.4V  V3 = IR 3 = 200 * 10 −3 * 100 = 20V  WE R 4 ‫א‬‫א‬F v 4   v s − (v 1 + v 2 + v 3 + v 4 ) = 0  100 − 2 − 9.4 − 20 − v 4 = 0 68.6 − v 4 = 0 ∴ v 4 = 68.6V - ٤٣ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 Kirchhoff's Current Law (KCL)  ٦J ٤  W‫א‬

‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ENodeF?  ?‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬ Node‫א‬ Node

R٢

R١

I3

 

R4



I2



R٣



 ‫א‬‫א‬‫א‬E١٢J ٤F  W  I1 = I2 + I3  W‫א‬KCL‫א‬

 ?‫א‬‫א‬‫א‬‫א‬Node‫א‬‫א‬‫א‬‫א‬?  W‫א‬‫א‬‫א‬‫א‬ I1 − I 2 − I3 = 0

‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KCL ‫א‬‫א‬‫א‬Nods‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KCL  K‫א‬ Voltage Divider ‫א‬ ٧J ٤

،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬



Voltage Dividers‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٤٤ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 

− V1 + R1

+ VS



I



+ R٢

−

V2



_



  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E١٣J ٤F



‫א‬ ‫א‬ R 2 ، R1 ‫א‬‫א‬

 ‫א‬‫א‬ V1 = IR 1 V2 = IR 2

K R1, R 2  V2 ، V1 ‫א‬‫א‬  W R 2 = 100Ω ، R1 = 50Ω ، VS = 10V ‫א‬، R T = 50 + 100 = 150Ω I=

V1 = IR 1 =

10 V 1 = A 150 Ω 15

1 1 * 50 = * 10 V 3 15 ∴ V1 =

V2 = IR 2 =

1 1 * 100 = (20 ) V 15 3

∴ V2 =

- ٤٥ -

1 (10) V 3

2 (10) V 3

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 K‫א‬ V2 ‫א‬ V1 ‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ Voltage Divider Formula‫א‬‫א‬‫א‬

١J ٧J ٤

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ R١ V١ + −

V٢ + −



R٤

R٣

R٢

V٣ + −



V٤ + −



I

  

VS + −



 ‫א‬‫א‬E١٤J ٤F  ،‫א‬ X  VX ‫א‬‫א‬ VX = IR X

  ٤ ، ٣، ٢،١‫א‬ x W    W‫א‬‫א‬‫א‬  I=

VS RT

  VX ‫א‬ I ‫א‬ ⎛V ⎞ VX = ⎜⎜ S ⎟⎟R X ⎝ RT ⎠  W VX ‫א‬ ⎛ RX ⎞ ⎟⎟VS ⎝ RT ⎠

 VX = ⎜⎜

 - ٤٦ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E١١J ٤F

 ‫؟‬‫א‬‫א‬‫א‬ V2 ‫א‬ V1 ‫א‬  +

R 1 = 100Ω

+ VS = 10 V

V1 −

−

+ V2

R 2 = 56 Ω

−

 E١١J ٤F‫א‬‫א‬‫א‬E١٥J ٤F

        ‫א‬

 ‫א‬‫א‬ V2 ، V1  ⎛R ⎞ VX = ⎜⎜ X ⎟⎟VS ⎝ RT ⎠

  R T ‫א‬‫א‬ R T = 100 + 56 = 156Ω ⎛R ⎞ 100 V1 = ⎜⎜ 1 ⎟⎟VS = * 10 = 6.41V R 156 ⎝ T⎠ ∴ V1 = 6.41V

  V2  ⎛R ⎞

56

* 10 = 3.59V  V2 = ⎜⎜ 2 ⎟⎟VS = 156 ⎝ RT ⎠

 ‫א‬  V2 = VS − V1 = 10 − 6.41 = 3.59V

- ٤٧ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E١٢J ٤F

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   C to D (e) B to D (d) B to C (c) A to C (b) A to B (a)  W‫א‬   VCD (e) VBD (d) VBC (c) VAC (b) VAB (a)  A

R١ = ١kΩ

  

VS = ٢٥V

B R٢ = ٨٫٢kΩ



C

 

R٣ = ٣٫٣kΩ



D



 E١٢J ٤F‫א‬‫א‬‫א‬E١٦J ٤F  ‫א‬

 R T ‫א‬‫א‬  R T = R1 + R 2 + R 3  R T = 1 + 8.2 + 3.3 R T = 12.5KΩ

 W‫א‬‫א‬‫א‬ ⎛R ⎞

 VAB = ⎜⎜ 1 ⎟⎟VS ⎝ RT ⎠  VAB =

1 * 25 = 2V 12.5

 ∴ VAB = 2V - ٤٨ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



⎛ R1 + R 2 ⎝ R3

 VAC = ⎜⎜

⎞ ⎟⎟VS ⎠

9 .2 ⎞  VAC = ⎛⎜ ⎟ * 25 = 18.4V ⎝ 12.5 ⎠

∴ VAC = 18.4V   C،B‫א‬‫א‬ ⎛R ⎞ VBC = ⎜⎜ 2 ⎟⎟VS ⎝ RT ⎠ ⎛ 8.2 ⎞ VBC = ⎜ ⎟ * 25 = 16.4V ⎝ 12.5 ⎠ ∴ VBC = 16.4V ⎛ 8.2 + 3.3 ⎞ VBD = ⎜ ⎟ * 25 ⎝ 12.5 ⎠ ⎛ 11.5 ⎞ VBD = ⎜ ⎟ * 25 = 23V ⎝ 12.5 ⎠

∴ VBD = 23V

 VCD ‫א‬  VCD = ⎛⎜

3 .3 ⎞ ⎟ * 25 = 6.6 ⎝ 12.5 ⎠

 ∴ VCD = 6.6V Power in a Series Circuit ‫א‬‫א‬‫א‬‫ א‬٨J ٤

‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   W  PT = P1 + P2 + ........... + Pn  K‫א‬‫א‬‫א‬ PT   W‫א‬‫א‬‫א‬‫א‬ 1) - ٤٩ -

PT = VS I

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



2) PT = I 2 R T VS2 3) PT = RT

  E١٣J ٤F

 W‫א‬‫א‬‫א‬‫א‬‫א‬ R٢ = ١٨ Ω R٣ = ٥٦ Ω VS = ١٥ V R٤ = ٢٢ Ω

 E١٣J ٤F‫א‬‫א‬‫א‬E١٧J ٤F  ‫א‬  K‫א‬‫א‬ R T = 10 + 18 + 56 + 22 = 106 Ω

 W‫א‬E٣F‫א‬‫א‬‫א‬‫א‬ VS2 (15)2  ∴ PT = = = 2.12 W RT 106

∴ PT = 2.12 W

- ٥٠ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E١٤J ٤F

  ،٠{٥ W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫؟‬‫א‬‫א‬‫א‬ R١ = ١kΩ



R٢ = ٢٫٧kΩ

 R٣ = ٩١٠Ω VS = ١٢٠ V R٤ = ٣٫٣kΩ

    

 E١٤J ٤F‫א‬‫א‬‫א‬E١٨J ٤F

 ‫א‬

 ‫א‬‫א‬  R T = R1 + R 2 + R 3 + R 4  R T = 1 + 2.7 + 0.91 + 3.3 = 7.91 kΩ R T = 7.91 kΩ

  ‫א‬‫א‬‫א‬‫א‬‫א‬  I=

VS 120 = = 15.2 mA R T 7.91

 W‫א‬ P1 = I 2 R 1 = (15.2 mA )2 (1 kΩ ) = 231 mW P2 = I 2 R 2 = (15.2 mA )2 (2.7 kΩ ) = 624 mW = 0.62 W P3 = I 2 R 3 = (15.2 mA )2 (910 Ω ) = 210 mW = 0.21 W

 P4 = I 2 R 4 = (15.2 mA )2 (3.3 kΩ ) = 762 mW =

- ٥١ -

762 = 0.762 W 1000

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



‫א‬‫א‬  R 4 ، R 2  ‫א‬‫א‬  W‫א‬‫א‬،15.2mW P2 = 0.62 W > 1 W 2 P4 = 0.762 W > 1 W 2

 K‫א‬١w‫א‬‫א‬‫א‬ Voltage With Respect to Ground ‫א‬ ٩J ٤

E‫א‬F  ‫א‬‫א‬  ‫א‬ 

 K‫א‬ ‫א‬‫א‬‫א‬‫א‬،Reference Point. ‫א‬،١٠٠V‫א‬‫א‬‫א‬ 

 KCircuit Ground‫א‬‫א‬‫א‬١٠٠V‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬Ground‫א‬ ‫א‬‫א‬‫א‬

 KE١٩J ٤F

- ٥٢ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 +

R1

+ V2

a



V1



−

−

+ V2

R2



  

V



−

 

 ‫א‬‫א‬E١٩J ٤F

 Note  a‫א‬‫א‬  E١٥J ٤F

  ،‫א‬‫א‬‫א‬‫א‬‫א‬  K٢٥ VVoltage Dropped ‫א‬‫א‬ +

−

+

+

−

c

a

b

+ 100V

−

− e

+

a

+

+ 100V

−

−

+

b

(a)

−

  c 

+

+

−

d (b)

 E١٥J ٤F‫א‬‫א‬‫א‬ b)،(aE٢٠J ٤F

- ٥٣ -

 

−



e

d



−

 

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 + a

+ 100V

−

C b

−

−

c

e

+ +

− d

(c)

 E١٥J ٤F‫א‬‫א‬‫(א‬c)E٢٠J ٤F  ‫א‬

 W‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬EaF‫א‬‫א‬  Va ‫א‬،a‫א‬‫א‬، Va ‫א‬

 K‫א‬a‫א‬‫א‬a‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬ EaF‫א‬‫א‬ Ve = 0 Vd = +25V

Vc = +50V Vb = +75V Va = +100V

 W‫א‬‫א‬d‫א‬Eb F‫א‬‫א‬  Ve = −25V  Vd = 0V  Vc = +25V  Vb = +50 - ٥٤ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 Va = +75V  W‫א‬‫א‬،c‫א‬،EcF‫א‬‫א‬  Ve = −50V  Vd = −25V  Vc = 0V  Vb = +25V Va = +50V

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،a‫א‬‫א‬‫א‬  K‫א‬

 W‫א‬‫א‬

 Ke ← ،d،c،b‫א‬  ‫א‬a‫א‬‫א‬‫א‬ KJ ،H‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

 W VA EaF‫א‬‫א‬ Va = VS = 100V Vb = 100 − 25 = +75V Vc = 100 − 25 − 25 = +50V

Vd = 100 − 25 − 25 − 25 = +25V

 ‫א‬e‫א‬ Ve = Vs + Vb + Vc + Vd + Ve Ve = 100 − 25 − 25 − 25 − 25 = 0 ∴ Ve = 0

 Note   W‫א‬‫א‬‫א‬‫א‬

- ٥٥ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



‫א‬‫א‬‫א‬‫ א‬‫א‬W  ‫א‬‫ א‬E١ ‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬   KE‫א‬‫א‬F‫א‬‫א‬

‫א‬ ‫א‬‫א‬W ‫א‬‫ א‬E٢  ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  W R1 ‫א‬ Vb = Vs − IR 1

 Kc،b،a‫א‬‫א‬‫א‬‫א‬ Troubleshooting ‫א‬‫א‬ ١٠J ٤

 W‫א‬‫א‬،‫א‬‫א‬‫א‬  KOpen Circuit

‫א‬‫א‬‫א‬‫א‬‫א‬ E١F

KShort Circuit‫א‬‫א‬‫א‬‫א‬‫א‬ E٢F

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،Open Circuit‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K

‫א‬  ‫א‬ ‫א‬‫א‬ K١   V = IR = 0

‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬

Cheek For Burned Resistor‫א‬‫א‬ K٢ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

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‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



0V R1

+ 10V −

0V





 R2

R2





VS = 10V



Short Circuit‫א‬‫א‬E٢١J ٤F

‫א‬‫א‬KShort‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬

 K‫א‬‫א‬‫א‬‫א‬  E١٦J ٤F K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬، VS = 100V   K‫א‬‫א‬‫א‬‫א‬‫א‬E

 ‫؟‬‫א‬‫؟‬‫א‬،‫א‬‫א‬ A, B ‫א‬Short‫א‬E 10Ω



18Ω

c

b

− VS = 100V

33Ω

+

39Ω a

     



 E١٦J ٤F‫א‬‫א‬‫א‬E٢٢J ٤F

- ٥٧ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 ‫א‬

 K R T ‫א‬W   R T = 10 + 18 + 33 + 39 = 100 Ω  I=

100 =1A 100

‫א‬‫א‬‫א‬K A, B ‫א‬ShortW    K‫א‬‫א‬‫א‬ A, B ‫א‬  ‫א‬‫א‬‫א‬  R T = 18 + 10 = 28 Ω 10Ω



18Ω b

C

− VS = 100V



33Ω

I

+

 





  a







39Ω

 E١٦J ٤F‫א‬‫א‬‫א‬E٢٣J ٤F  I=

VS 100 = = 3.57 A RT 28

 W‫א‬

K 3.57 A   1 A ‫א‬‫א‬ ، A, B ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

  A, C ،‫א‬‫א‬‫א‬ ‫א‬ ‫א‬18 Ω ، 33 Ω ، 39 Ω ‫א‬ ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

- ٥٨ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 R T = 10 Ω  I=

VS 100 = = 10 A R T 10

 10 A ‫א‬‫א‬ Summary ‫א‬

K‫א‬‫א‬‫א‬‫א‬‫ א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬

KKVL‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬

Series-Opposition‫א‬‫א‬  ‫א‬ K‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬Voltage Drops‫א‬

‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬Ground‫א‬ K‫א‬Negative Ground‫א‬‫ א‬

‫א‬‫א‬‫א‬‫א‬‫א‬Positive Ground‫א‬‫ א‬ K ‫א‬‫א‬‫א‬‫א‬‫א‬Open circuit‫א‬‫א‬‫א‬‫ א‬  K‫א‬

- ٥٩ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 ‫א‬‫א‬‫א‬ K A, B ‫א‬‫א‬‫א‬‫א‬‫א‬ K١ R١

A

A

 

B



R٢ R١

R٢



R٣

R٣



B

  

A R٢ R١

B R٤

R٣

R٥

    

12V ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ K٢ 120Ω ‫א‬‫א‬

‫א‬ ‫א‬، 5mA ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٣ ‫؟‬‫א‬‫א‬‫א‬ A

+ VS −



R٣

5 mA



A

 

R1

  

A

R2 - ٦٠ -



‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



W‫א‬‫א‬‫א‬ R T ‫א‬‫א‬ K٤



 1000 Ω ، 500 Ω EF

 56 Ω ، 47 Ω EF  10 kΩ ، 2.2 kΩ ،1.5 kΩ EF  2.2 MΩ ،1 kΩ ، 470 kΩ ،1 MΩ EF 

‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٥ R 2 = 10 Ω



R 2 = 10 Ω R1 = 4.7 Ω

R 3 = 12 Ω

R 1 = 25.6 kΩ

  

R4 =1Ω



R 3 = 2.2 kΩ



( b)

(a )



  

R 1 = 1 MΩ R 5 = 10 M Ω R1 = 1 MΩ

  

R 2 = 560 kΩ R 3 = 5.6 MΩ

   

(c)

 

- ٦١ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



‫א‬، 100 mA ‫א‬‫א‬‫א‬‫א‬‫א‬ K٦ ‫؟‬‫א‬‫א‬

R 1 = 45 Ω

−

R 2 = 15 Ω

VS + A

R 3 = 90 Ω

، 25V   R 2 ‫א‬، 25mA  R1 ‫א‬‫ א‬‫א‬‫א‬‫א‬ K٧  ‫؟‬ R 2 

A

−

R1

VS +

R2

V

R3

، R1 = 10Ω ‫א‬، VS = 48V ‫א‬‫א‬‫א‬ K٨ ‫؟‬‫א‬‫א‬‫ ؛‬R 3 = R 4 = 47Ω ، R 2 = 96Ω ، VS = 24V ‫א‬ R 2 = 5.6 kΩ ، R 1 = 4.7 kΩ ‫א‬‫א‬ K٩ ‫؟‬‫א‬ ‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٠  W‫؟‬ VS ، R 3 = 330Ω ، R 2 = 56Ω ، R 1 = 100Ω - ٦٢ -



‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



V5 = 1.124V & R 5 = 47Ω ، R 4 = 220Ω

R1



R2

 

I

VS



R3 R5

  

R4



V

 

، V1 = 4.69 V   R1 ‫א‬‫א‬ VS = 15 V ‫א‬‫א‬‫א‬ K١١ ‫؟‬ R 1 = 1.5 kΩ  R 2   R 1 = 1.5 kΩ, V1 = 4.69 V V

+ VS = 15V

R1

 

R2

  

−

 

 I = 1.43mA ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ K١٢ ، V1 = 2V2 ‫א‬‫א‬، VS = 15V  ‫؟‬ R 3 ، R 2 ، R1 ، V2 = 2V3

‫؟‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٣ - ٦٣ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



، R 2 = 10KΩ ، R 1 = 15KΩ R 4 = 2.2KΩ ، R 3 = 6.8KΩ

 R1

a



R2



VS1 = 24V



R3

VS2 = 12V



R4

 

 VS1 ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ K١٤  ‫؟‬‫א‬‫א‬،a  ‫א‬‫א‬



W 2.16V  R1 ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ K١٥

 WK،E R 3 ‫א‬‫א‬F V3 ‫א‬،E V1 = 2.16V F

R 4 = 220KΩ & R 3 = 560Ω ، R 2 = 1KΩ ، R 1 = 390Ω



VS2 A



R 2 = 1 kΩ

R 1 = 390 Ω

 

I

R 3 = 560 Ω

VS1

R 4 = 220 Ω

    

- ٦٤ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



‫א‬ VS2 ، VS1 = 15V ‫א‬E١٥F‫א‬‫א‬‫א‬ K١٦ KE V1 = 3.77V FW 3.77V  R1 ‫א‬‫א‬



‫א‬‫א‬ R1 ‫א‬‫א‬ VS 2 ‫א‬ K١٧ ‫א‬‫א‬‫א‬ VS2 ‫א‬EE١٥F‫א‬‫א‬F R 2 ‫؟‬‫א‬‫א‬‫א‬ V4 ، V3 ، V2 ، V1 ‫א‬‫א‬،E١٦F

  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K١٨  A, B, C, D ‫א‬‫א‬‫א‬‫א‬‫א‬E‫א‬F  W‫؟‬

 R 1 = 12 kΩ, R 2 = 22 kΩ, R 3 = 47 kΩ & R 4 = 15 kΩ   d c



R4



R3

 

b

+ VS = 48V



R2



a

−

R1

+ V1 −

‫א‬‫א‬‫א‬ 560 Ω ‫א‬‫א‬‫א‬‫ א‬K١٩

    

‫؟‬ R = 27 Ω ‫א‬‫א‬ W‫א‬‫א‬‫א‬ A, B ‫א‬‫א‬ K٢٠  - ٦٥ -

‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-





A

+ 12V −



100 Ω



56 Ω

  

B

   

1kΩ A

+ 8V

2.2kΩ

− 3.3kΩ

B

b

- ٦٦ -

 

 ‫א‬‫א‬‫א‬ ã¹]
١ J  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

٥

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 ‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬،‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬ • K‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

- ٦٧ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



Introduction ١J ٥

،‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬KVoltage Drop‫א‬‫א‬  KVoltage Divider

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬،  ‫א‬‫א‬

‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬،KCL  K‫א‬‫א‬Current Divider‫א‬  Parallel Circuit‫א‬‫א‬‫א‬

‫א‬EF‫א‬‫א‬‫א‬ E‫א‬F‫א‬‫א‬E‫א‬F‫א‬‫א‬

،‫א‬‫א‬‫א‬K‫א‬‫א‬ E١J ٥F‫א‬‫א‬‫א‬K  ‫א‬

 K‫א‬‫א‬‫א‬ A

I1

I

R1

A

I2

I1

I

R1

R2



I2

 

R2



B

B

R1

A

I

I2

I1

A

  

I

I1

R2

 

R1

I2 R2



B

B

 K‫א‬‫א‬‫א‬EJ ١J ٥F - ٦٨ -

 

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-





I1

A

R1

I

A

I2

I1

R2

R1

I

R2 B I2

B

R3

I٢

 K‫א‬‫א‬‫א‬EJ ١J ٥F Voltage Drop in Parallel Circuit‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥

‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

 E١J ٥F

 E٢J ٥F‫א‬‫א‬ 

VS =



25V R1 = 1.8kΩ

R2 = F

1kΩ

 

R3 =

R4 =

2.2kΩ

2.2kΩ

R5 =



3.3kΩ 



 KE١J ٥F‫א‬‫א‬‫א‬E٢J ٥F

 ‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬  W‫א‬‫א‬‫א‬  V1 = V2 = V3 = V4 = V5 = VS = 25V - ٦٩ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 Kirchhoff’s Current Law٣J ٥ ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Node

 K‫א‬‫א‬‫א‬‫א‬  E٢J ٥F ،E٣J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬

 K A ‫א‬‫א‬‫א‬‫א‬‫א‬ 

A

IT

+ VS −

 

I1 = 5mA

I 2 = 12mA

R1

R2

 

IT

 

B

 KE٢J ٥F‫א‬‫א‬‫א‬E٣J ٥F  ‫א‬

‫א‬ R1 ‫א‬‫א‬ 5mA ‫א‬‫א‬ A ‫א‬‫א‬‫א‬

 W A ‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬12mA

I T = I1 + I 2 = 5mA + 12mA = 17 mA ∴ I T = 17mA



- ٧٠ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E٣J ٥F

 KE٤J ٥F‫א‬ R 2 ‫א‬‫א‬‫א‬

 

IT = 100mA



A

I1 = 30mA

+ VS



R1

−

I2 R2





I 3 = 20mA R3



IT



B



 KE٣J ٥F‫א‬‫א‬‫א‬E٤J ٥F  ‫א‬

 I T  A ‫א‬‫א‬‫א‬‫א‬‫א‬ I T = I1 + I 2 + I 3

∴ 100mA = 30mA + I 2 + 20mA ∴ I 2 = 100mA − 50mA = 50mA

 E٤J ٥F

‫א‬ A1 , A 2 ‫א‬‫א‬‫א‬‫א‬

 W‫א‬

5A

y

x



I3



+ VS

R1

−

IT

 

R2

I1 = 1.5A

R3 I 2 = 1A

 KE٤J ٥F‫א‬‫א‬‫א‬E٥J ٥F - ٧١ -

  

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 W 5A  x ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬

5A = 1.5A + I A1

 K A1 ‫א‬‫א‬‫א‬ I A1 W ∴ I A1 = 5 − 1.5 = 3.5A

 K 3.5A ‫א‬‫א‬‫א‬ y ‫א‬‫א‬ ∴3.5A = 1A + I A 2 ∴ I A 2 = 3.5 − 1 = 2.5A

 W‫א‬‫א‬‫א‬∴ I A1 = 3.5A I A 2 = 2 .5 A

 Total Parallel Resistors‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٥  ‫א‬‫א‬ R T ‫א‬‫א‬W

 ‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I1

R1

 

 

I2

R2

 

IT



+ VS − R1 , R 2 ‫א‬‫א‬E٦J ٥F

- ٧٢ -

  

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



‫א‬‫א‬،‫א‬‫א‬ R1, R 2 ‫א‬  ‫א‬‫א‬‫א‬

 W‫א‬ R T E‫א‬‫א‬F

 W‫א‬، E١J ٥F

I T = I1 + I 2

 W‫א‬‫א‬‫א‬‫א‬ VS VS VS = + R T R1 R 2

E٢J ٥F  K VS ‫א‬‫א‬‫א‬

1 1 1 = + R T R1 R 2

E٣J ٥F

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬E٣J ٥F‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬

 W‫א‬‫א‬

1 R + R2 = 1 R T R1 ∗ R 2

E٤J ٥F  W

RT =

R1 ∗ R 2 R1 + R 2

E٥J ٥F

 K‫א‬‫א‬‫א‬ R T  ‫א‬‫א‬ R T W

- ٧٣ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 I1

R1



I2

R2



I3

R3

    

IT

  

+ VS −

  R1, R 2 , R 3 ‫א‬‫א‬E٧J ٥F

 W E٦J ٥F

IT = I1 + I 2 + I3

 W‫א‬

VS VS VS VS = + + R T R1 R 2 R 3

E٧J ٥F  W‫א‬ VS 

1 1 1 1 = + + R T R1 R 2 R 3 RT =

E٨J ٥F  W

R1 ∗ R 2 ∗ R 3 R1R 2 + R1R 3 + R 2 R 3

E٩J ٥F

 ‫א‬‫א‬‫א‬‫א‬ R T ‫א‬‫א‬  K‫א‬

- ٧٤ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



‫א‬ ‫א‬ R T ‫א‬‫א‬‫א‬  RT =

 W‫א‬‫א‬

1

E١٠J ٥F

1 1 1 1 ( ) + ( ) + ( ) +K+ ( ) R1 R2 R3 Rn

 E٥J ٥F

 W‫א‬‫א‬ A, B ‫א‬ R T ‫א‬‫א‬‫א‬



A

R 1 = 100Ω

R 2 = 47Ω



R 3 = 22Ω

  

B



 KE٥J ٥F‫א‬‫א‬‫א‬E٨J ٥F

 ‫א‬

 WE٩J ٥F‫א‬‫א‬‫א‬ RT =

R1 ∗ R 2 ∗ R 3 R1R 2 + R1R 3 + R 2 R 3

  RT =

100 ∗ 47 ∗ 22 = 13Ω 100 ∗ 47 + 100 ∗ 22 + 47 ∗ 22

‫א‬‫א‬‫א‬‫א‬١J ٤J ٥ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 W E١١J ٥F

QR1 = R 2 = R 3 = K = R n = R

- ٧٥ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



∴R T =

1 R n

E١٢J ٥F

R n

E١٣J ٥F

or R T =

 K‫א‬‫א‬‫א‬‫א‬‫א‬ R W ،‫א‬  ‫א‬‫א‬ 

 K‫א‬‫א‬‫א‬  E٦J ٥F

 K R T ‫א‬‫א‬‫א‬‫א‬ 8Ω   ‫א‬  W‫א‬‫א‬

RT =

R 8 = = 2Ω n 4

 Determining an unknown Parallel Resistor‫א‬‫א‬‫א‬٥J ٥ ،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬   ‫א‬‫א‬‫א‬  ‫א‬K‫א‬

‫א‬‫א‬‫א‬ R T ‫א‬‫א‬‫א‬‫א‬  WEE٥J ٥FF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ RT =

R1R 2 R1 + R 2

‫א‬ R X ‫א‬ R A  ‫א‬‫א‬ W‫א‬

- ٧٦ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-

 



RA

 

RX



 

RT

 K‫א‬E٩J ٥F  R X ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W

RT =

R AR X RA + RX

E١٤J ٥F

R T (R A + R X ) = R A R X

E١٥J ٥F

RTR A + RTR X = R AR X

E١٦J ٥F

R T R A = (R A − R T )

E١٧J ٥F

∴R X =

RTRA RA − RT

E١٨J ٥F  E٧J ٥F

‫א‬‫א‬‫א‬ 150Ω ‫א‬‫א‬

 ‫؟‬‫א‬‫א‬‫א‬K 330Ω ‫א‬ 

R A = 330Ω



 RX  KE٧J ٥F‫א‬‫א‬‫א‬E١٠J ٥F - ٧٧ -



‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 ‫א‬

‫א‬ 330Ω ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬ RT =

R AR X RA + RX

150 =

330R X 330 + R X

150(330 + R X ) = 330R X 150 * 330 = 330R X − 150R X ∴R X =

150 * 330 = 275Ω 180

 E٨J ٥F

 KE١١J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬ 10mA

 

+ VS

R 1 = 220Ω

R 2 = 560Ω



R 3 = 1kΩ



−

 

 KE٨J ٥F‫א‬‫א‬‫א‬E١١J ٥F

 ‫א‬

 R T ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

 W

RT =

R1 ∗ R 2 ∗ R 3 R 1R 2 + R 1R 3 + R 2 R 3 - ٧٨ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



RT =

220 ∗ 560 ∗ 1000 = 136Ω 220 ∗ 560 + 220 ∗ 1000 + 560 ∗ 1000

∴ V = IT * R T = 10mA * 136Ω = 1.36V

E٩J ٥F

  ‫א‬،1kΩ ‫א‬ R 3 = 680Ω ‫א‬‫א‬‫א‬

 K IT = 10mA  ‫א‬

 W R T ‫א‬‫א‬‫א‬‫א‬ RT =

R1 ∗ R 2 ∗ R 3 R 1R 2 + R 1R 3 + R 2 R 3

RT =

220 ∗ 560 ∗ 680 = 128Ω 220 ∗ 560 + 220 ∗ 680 + 560 ∗ 680

∴ V = I T * R T = 10mA * 128Ω = 1.28V

 Current Division in Parallel Circuits‫א‬‫א‬‫א‬‫א‬EF٦J ٥ ،‫א‬‫א‬‫א‬‫א‬ R T ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬KBranches‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬ ‫א‬‫א‬Current Divider Law‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ W‫א‬،E١٢J ٥F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

- ٧٩ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



I1

R1

I2

R2



I



+ VS −

 K‫א‬‫א‬‫א‬‫א‬E١٢J ٥F  W I ‫א‬ I1 , I 2 ‫א‬‫א‬‫א‬ V = I*RT

E١٩J ٥F

V = I1 * R 1

(٢٠J ٥F

V = I2 * R 2

E٢١J ٥F

 W،‫א‬‫א‬،E٢٠J ٥F‫א‬E١٩J ٥F‫א‬ I * R T = I1 * R 1

E٢٢J ٥F

RT R1

E٢٣J ٥F

I1 = I

 W،‫א‬‫א‬،E٢١J ٥FE١٩J ٥F‫א‬ I2 = I

RT R2

E٢٤J ٥F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬ Node ‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬ - ٨٠ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



IX = I

RT RX

E٢٥J ٥F  K X = 1,2,3,K, n W  K‫א‬‫א‬‫א‬‫א‬‫א‬ W

RT

 K‫א‬‫א‬‫א‬‫א‬ W

RX

‫א‬‫א‬‫א‬ X ‫א‬ X ‫א‬‫א‬ W

IX

 K‫א‬

- ٨١ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E١٠J ٥F

 KE١٣J ٥F‫א‬Branch‫א‬ I1



R1 = 680Ω

I2

R 2 = 330Ω

I3

R 3 = 220Ω



10A 

 KE١٠J ٥F‫א‬‫א‬‫א‬E١٣J ٥F  ‫א‬ ‫א‬‫א‬‫א‬، 10A ‫א‬‫א‬‫א‬‫א‬

K‫א‬ R T ‫א‬‫א‬

RT =

R1 ∗ R 2 ∗ R 3 R 1R 2 + R 1R 3 + R 2 R 3

RT =

680 ∗ 330 ∗ 220 = 111Ω 680 ∗ 330 + 680 ∗ 220 + 330 ∗ 220

I1 = I T

RT 111 = 10 ∗ = 1.63A 680 R1

I2 = IT

RT 111 = 10 ∗ = 3.36A R2 330

I3 = IT

RT 111 = 10 ∗ = 5.05A R3 220

- ٨٢ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 W I 3 ‫א‬ I1 , I 2  I T = I1 + I 2 + I 3

10 = 1.63 + 3.36 + I 3 I 3 = 10 − (1.63 + 3.36)

∴ I 3 = 5.05A

  ‫א‬‫א‬‫א‬‫א‬ K I1 = 1.63A  R1 = 680Ω ‫א‬‫א‬‫א‬K

‫א‬K I3 = 5.05A  R 3 = 220Ω ‫א‬  K‫א‬

- ٨٣ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



  ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

 W

IT I1

I2

R1

R2

    

 K‫א‬‫א‬‫א‬‫א‬E١٤J ٥F 

WE٥J ٥F‫א‬E٢٣J ٥F‫א‬‫א‬ I1 = I T

RT R1

E٢٣J ٥F  

RT =

R 1R 2 R1 + R 2

E٥J ٥F  WE٢٣J ٥F‫א‬ R T 

I1 = I T

I2 = IT

R1 R1 + R 2 R2 R1 + R 2

E٢٦J ٥F  W‫א‬‫א‬ I 2  E٢٧J ٥F

 I1 , I 2 ‫א‬‫א‬‫א‬‫א‬E٢٧J ٥F،E٢٦J ٥F‫א‬‫א‬‫א‬ ‫א‬ I1 , I 2 , I 3 ‫א‬‫א‬،‫א‬‫א‬ R1, R 2 , R 3   W‫א‬‫א‬‫א‬

- ٨٤ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 I1



R1

 

R2

I2

 

R3

I3

 

IT

 

 



+ VS −

 K‫א‬‫א‬‫א‬‫א‬E١٥J ٥F

I1 = IT

RT R1



 W‫א‬ R1 ‫א‬‫א‬ I1 ‫א‬ E٢٣J ٥F  ‫א‬‫א‬ R T ‫א‬‫א‬

RT =

R1 ∗ R 2 ∗ R 3 R1R 2 + R1R 3 + R 2 R 3

I1 = IT .

R2 ∗ R3 R1R 2 + R1R 3 + R 2 R 3

E٢٨J ٥F  W‫א‬‫א‬ R T  E٢٩J ٥F  W I 2 , I 3 

I2 = IT .

R1 ∗ R 3 R 1R 2 + R 1R 3 + R 2 R 3

E٣٠J ٥F

I3 = IT .

R1 ∗ R 2 R 1R 2 + R 1R 3 + R 2 R 3

E٣١J ٥F - ٨٥ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



Power in Parallel Circuits‫א‬‫א‬‫א‬‫א‬٧J ٥

 WE‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬ PT ‫א‬‫א‬‫א‬‫א‬‫א‬ E٣٢J ٥F

PT = P1 + P2 + P3 + K + Pn

 

IT

I2

I1 PT

R1

P1

R2

P2

I3

R3

In Rn

P3

Pn

    

 K‫א‬‫א‬‫א‬‫א‬E١٦J ٥F PT = V.I =

I T2 .R T

V2 = RT

E٣٣J ٥F  W‫א‬

P1 = I12 .R 1

E٣٤J ٥F

P2 = I 22 .R 2

E٣٥J ٥F

P3 = I 32 .R 3

E٣٧J ٥F

PT = P1 + P2 + P3

E٣٨J ٥F  KWatt‫א‬

- ٨٦ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 E١١J ٥F

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  R 1 = 68 Ω

R 2 = 33 Ω



R 3 = 22Ω

  

 KE١١J ٥F‫א‬‫א‬‫א‬E١٧J ٥F

 ‫א‬  ‫א‬‫א‬ RT =

=

R1 ∗ R 2 ∗ R 3 R 1R 2 + R 1R 3 + R 2 R 3

68 ∗ 33 ∗ 22 = 11.1Ω 68 * 33 + 68 * 22 + 33 * 22

Q PT = I T2 .R T

= (2) 2 * 11.1 = 44.4W ∴ PT = 44.4W

‫א‬K‫א‬‫א‬‫א‬  K‫א‬ VS = I.R T = 2 * 11.1 = 22.2V VS2 (22.2) 2 P1 = = = 7.25W R1 68

- ٨٧ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



VS2 (22.2) 2 P2 = = = 14.9 W R2 33 VS2 (22.2) 2 P3 = = = 22.4W R3 22

Q PT = P1 + P2 + P3 = 7.25 + 14.9 + 22.4

∴ PT = 44.6W

 KE‫א‬F‫א‬‫א‬‫א‬‫א‬‫ א‬‫א‬‫א‬              

- ٨٨ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



 ‫א‬‫א‬



 W‫א‬‫א‬‫א‬E١F  ‫א‬EF‫א‬EF

 EF‫א‬EF 

‫א‬،‫א‬‫א‬ 100Ω ‫א‬1.2kΩ ‫א‬E٢F   R T ‫א‬  1.2kΩ 100Ω EF1.2kΩ EF  90Ω EEF 90Ω 100Ω EF 

 ‫א‬‫א‬،‫א‬‫א‬ 68Ω ، 270Ω  330Ω E٣F  47Ω EF 668Ω EF  22Ω EF 68Ω EF 

،1kΩ ‫א‬‫א‬‫א‬E٤F  ‫א‬‫א‬

 1kΩ EF 8kΩ EF

  500Ω EF1kΩ EF 

 ‫א‬‫א‬‫א‬‫א‬E٥F  EFEF  ‫א‬‫א‬EFEF  

 ‫א‬‫א‬‫א‬‫א‬‫א‬E٦F

 EF‫א‬‫א‬EF  EFEF - ٨٩ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

١-



K 3A ‫א‬، 5A ‫א‬‫א‬‫א‬E٧F  W‫א‬‫א‬‫א‬

 EF 2A EF

 K‫א‬EF 8A EF   ‫א‬ ‫א‬،‫א‬‫א‬ 390 Ω, 560 Ω, 820 Ω ‫א‬‫א‬E٨F  

 560Ω EF 390Ω EF

 K‫א‬EF 820Ω EF 

 ‫א‬‫א‬‫א‬‫א‬‫א‬E٩F  ‫א‬EFEF  EFEF‫א‬EF‫א‬‫א‬EF 

 W‫א‬‫א‬‫א‬‫א‬‫א‬E١٠F  ‫א‬‫א‬‫א‬‫א‬‫א‬EF

 ‫א‬‫א‬‫א‬‫א‬EF

 E‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬EF  K‫א‬EF 

 W‫א‬‫א‬‫א‬،1W ‫א‬‫א‬‫א‬‫א‬E١١F  4W EF1W EF

 16W EF 0.25W EF 

- ٩٠ -

 ‫א‬‫א‬‫א‬ ã¹]
١ J

 ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

٦

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬،‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫• א‬

- ٩١ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



   ١J ٦ ‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬‫א‬–‫א‬‫א‬‫א‬  K‫א‬‫א‬–‫א‬‫א‬‫א‬E١J ٦F‫א‬‫א‬

 ‫א‬‫א‬–‫א‬‫א‬ ٢J ٦  E١J ٦F  KE١J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

R٢



R١



R٣ R٦ R٨

R٥



R٤

 

R٧



R٩



 KE١J ٦F‫א‬‫א‬‫א‬E١J ٦F  ‫א‬ ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ R 1 , R 7 ‫א‬ ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  W‫א‬  R T = R1 + R 2 // R 3 + R 4 // R 5 // R 6 + R 7 + R 8 // R 9  W - ٩٢ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 R T = R1 +

R 2R 3 R 4R 5R 6 R 8R 9 + + R7 + R 2 + R 3 R 4R 5 + R 4R 6 + R 5R 6 R8 + R9

 E٢J ٦F  K‫א‬‫א‬‫א‬‫א‬،E٢J ٦F‫א‬‫א‬‫א‬ 

R1 IT

+ VS −

A

I3 R3

R4

IT

 

I2 R2

 

B



 KE٢J ٦F‫א‬‫א‬‫א‬E٢J ٦F

 ‫א‬

 R1 ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ K R 3 ‫א‬‫א‬، R 2 ،  A ‫א‬

 R1, R 4 ‫א‬‫א‬K R 4 ‫א‬‫א‬ B ‫א‬ ‫א‬، R 2 // R 3   ،‫א‬‫א‬ R 2 , R 3 ‫א‬K‫א‬‫א‬  W R T ‫א‬

 R T = R1 + R 2 // R 3 + R 4  E٣J ٦F

KE٣J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

- ٩٣ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 

R1

 + VS

R2

−

R4

R3

  

R5

 

  KE٣J ٦F‫א‬‫א‬‫א‬E٣J ٦F

 ‫א‬

 KE٤J ٦F‫א‬‫א‬‫א‬‫א‬ 

R1

 + VS

R2

R3

  

−

R4

R5



  

  KE٣J ٦F‫א‬‫א‬‫א‬E٤J ٦F ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬ R T ‫א‬

 R T = R1 + R 2 // R 3 + R 4 // R 5R T1

- ٩٤ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 E٤J ٦F

 KE٥J ٦F‫א‬ A, D ‫א‬‫א‬‫א‬‫א‬‫א‬ R2

R1

R3

A

R6

R4

D

R5

 KE٤J ٦F‫א‬‫א‬‫א‬E٥J ٦F

- ٩٥ -

      

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ‫א‬

‫א‬ R 2 , R 3 ‫א‬‫א‬‫א‬‫א‬ R T1 ‫א‬‫א‬

 W R 4 ‫א‬‫א‬‫א‬  R T1 =

(R 2 + R 3 ) ⋅ R 4 (R 2 + R 3 ) + R 4

  KE٦J ٦F R 5 ‫א‬‫א‬ R T1 ‫א‬‫א‬ 

A



R T1

R1



R6

 

R5

D



 KE٤J ٦F‫א‬‫א‬‫א‬E٦J ٦F  W‫א‬‫א‬ D, A ‫א‬‫א‬‫א‬‫א‬  R T = R1 + R 6 //(R T1 + R 5 )  E٥J ٦F

 K A, B, C ‫א‬‫א‬‫א‬‫א‬،E٧J ٦F‫א‬‫א‬‫א‬ B

  

R1

R2

 

A



R3

C

 KE٥J ٦F‫א‬‫א‬‫א‬E٧J ٦F - ٩٦ -



‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ‫א‬

 ‫א‬‫א‬ R 1 , R 3   A, B ‫א‬‫א‬‫א‬

 W R T ‫א‬‫א‬ R 2 ‫א‬‫א‬  R TAB =

R 2 * (R 1 + R 3 ) R 2 + (R 1 + R 3 )

 W B, C  A, C ‫א‬‫א‬ R TAC =

(R 1 + R 2 ) * R 3 (R 1 + R 2 ) + R 3

 R TBC =

(R 2 + R 3 ) * R 1 (R 2 + R 3 ) + R 1

 Analysis of Series-Parallel Circuits‫א‬‫א‬–‫א‬‫א‬‫א‬ ٣J ٦ ‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ♦  E٦J ٦F

 KE٨J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  R 2 = 47Ω R 3 = 47Ω A

+ VS −

R 1 = 100Ω

R 4 = 68Ω

B

R 6 = 75Ω



R 5 = 39Ω

 KE٦J ٦F‫א‬‫א‬‫א‬E٨J ٦F 

 - ٩٧ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ‫א‬

 ‫א‬‫א‬ R 2 , R 3 ‫א‬  R T2,3 = 47 + 47 = 94Ω

 R 6 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R 4 , R 5  ‫א‬‫א‬  W

 R T4,5, 6 =

68 * 39 + 75 = 99.8Ω 68 + 39

  ‫א‬‫א‬‫א‬‫א‬ 99.8Ω , 94Ω ‫א‬  R TA , B =

99.8 * 94 = 48.41Ω 99.8 + 94

94Ω B

A

+ VS

100Ω

  

99.8Ω



−



 KE٦J ٦F‫א‬‫א‬‫א‬E٩J ٦F ∴ R AB = 48.41Ω

 ∴ R T = 100Ω + 48.41Ω = 148.41Ω  E٧J ٦F

 KE١٠J ٦F R 3 ‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬

- ٩٨ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 IT

+ VS = 22V



R1 = 1kΩ



R 2 = 2 .2 k Ω

I2



I3

R 3 = 3.3kΩ

−

 KE٧J ٦F‫א‬‫א‬‫א‬E١٠J ٦F  ‫א‬

‫א‬‫א‬‫א‬‫א‬  R 3 ‫א‬ R 2 ‫א‬‫א‬  K A ‫א‬‫א‬

 K R T ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R T = R1 + R T = 1kΩ +

R 2R 3 R2 + R3

(2.2kΩ)(3.3kΩ) 2.2kΩ + 3.3kΩ

∴ R T = 1kΩ + 1.32kΩ = 2.32kΩ

∴ R T = 2.32kΩ

 IT =

VS 22V = = 9.48mA R T 2.32kΩ

 ‫א‬‫א‬

- ٩٩ -

I 2 = 9.48mA *

3.3kΩ = 5.69mA 5.5kΩ

I 3 = 9.48mA *

2 .2 k Ω = 3.79mA 5 .5 k Ω

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 E٨J ٦F

  VS = 50V ‫א‬‫א‬‫א‬‫א‬ R 4 ‫א‬‫א‬‫א‬ I2

I1

VS = 50V

 

R2

R1

+



330Ω A

560Ω

I4

I3

−

 

R4

R3

560Ω

330Ω

 KE٨J ٦F‫א‬‫א‬‫א‬E١١J ٦F  ‫א‬

‫א‬‫א‬، 50V ‫א‬‫א‬‫א‬‫א‬

 K R 3 , R 4 ‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬ R1 ‫א‬  W‫א‬‫א‬ R 4 ‫א‬‫א‬ I 4 ‫א‬

 K R 2 , R 3 , R 4 ‫א‬‫א‬‫א‬W

 K R 2 , R 3 , R 4 ‫א‬‫א‬‫א‬ I 2 W

 K‫א‬ I 4 ‫א‬ A ‫א‬ I 2 W R T2,3, 4 = R 2 + R 3 // R 4

= R2 + = 330 +

R 3R 4 R3 + R4

330 * 560 = 538Ω 330 + 560 ∴ R T2,3, 4 = 538Ω

I2 = - ١٠٠ -

50 = 93mA 538

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 W‫א‬‫א‬ ⎛ R3 I 4 = I 2 ⎜⎜ ⎝ R3 + R4

⎞ ⎟⎟ = 34.5mA ⎠

 ∴ I 4 = 34.5mA Voltage Drops in Series-Parallel Circuits‫א‬‫א‬‫א‬‫א‬‫א‬ ٤J ٦

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬ ‫א‬

 K‫א‬‫א‬‫א‬‫א‬  E٩J ٦F

‫א‬،E١٢J ٦F‫א‬‫א‬‫א‬ A ‫א‬‫א‬‫א‬‫א‬

 K R1 ‫א‬‫א‬  

R1 = 150Ω



A

+

R 2 = 560 Ω

R 3 = 560 Ω

VS = 80V −

B

  KE٩J ٦F‫א‬‫א‬‫א‬E١٢J ٦F

   

 ‫א‬

‫א‬،‫א‬‫א‬ R 2 , R 3 ‫א‬‫א‬  K‫א‬‫א‬

 W

 R T2,3 = - ١٠١ -

560 * 560 = 280Ω 560 + 560

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 1 2

 R TAG = (560) = 280Ω  W‫א‬‫א‬‫א‬‫א‬، R1 ‫א‬‫א‬‫א‬ 280Ω ‫א‬ 

R1 = 150Ω



A

 + VS = 80V



280Ω



−



B



 KE٩J ٦F‫א‬‫א‬‫א‬E١٣J ٦F  W R T ‫א‬‫א‬‫א‬  R T = 150 + 280 = 430Ω   VAG ‫א‬‫א‬ ⎛ R AG ⎞ ⎟⎟VS ⎝ RT ⎠

 VAG = ⎜⎜



 K‫א‬‫א‬ R AG   VAG = ⎛⎜

280 ⎞ ⎟ * 80 = 52.1V ⎝ 430 ⎠

  R1 ‫א‬‫א‬  VS = V1 + VAG V1 = VS − VAG

 - ١٠٢ -

= 80 - 52.1 = 27.9V

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ∴ V1 = 27.9V  E١٠J ٦F  KE١٤J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬  

R1 = 1kΩ IT = 1mA + VS



I1 I2

 

R 2 = 2 .2 k Ω

−

I3 R 3 = 3.9kΩ



R 4 = 1.5kΩ I4

 

R 5 = 560Ω

 

 KE١٠J ٦F‫א‬‫א‬‫א‬E١٤J ٦F  ‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ R1 ‫א‬‫א‬K  ‫א‬‫א‬ R1, R 2 ‫א‬ ‫א‬‫א‬  W‫א‬‫א‬ R 2 ‫א‬‫א‬ ⎛ R2 I1 = I T ⎜⎜ ⎝ R1 + R 2

⎞ ⎟⎟ ⎠

2 .2 k Ω ⎞ ⎛ = 1mA⎜ ⎟ = 688µA ⎝ 1kΩ + 2.2kΩ ⎠

 ∴ I1 = 688µA   R1 ‫א‬‫א‬‫א‬  V1 = I1 .R 1 = 688µA * 1kΩ  V1 = 688mV ∴ - ١٠٣ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 W‫א‬ R 3 ‫א‬ I 3 ‫א‬ ⎛

⎞ R4 + R5 ⎟⎟ R + ( R + R ) 4 5 ⎠ ⎝ 3

 I3 = IT ⎜⎜

 W‫א‬ I T   I3 = 346µA  W R 3 , R 4 , R 5 ‫א‬‫א‬‫א‬ V3 = I 3 .R 3 = (346µA)(3.9kΩ)

 ∴ V3 = 1.35V  W، R 4 ‫א‬‫א‬ V4   I 4 = I5 = IT − I3  

= 1mA - 346µA = 1mA - 0.346mA

 ∴ I 4 = 0.654mA  V4 = (0.654mA)(1.5kΩ) = 0.981V  ∴ V4 = 981mV  V5 = I 5 * R 5 = 366mV

- ١٠٤ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 E١١J ٦F

 KE١٥J ٦F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  

R 1 = 3.3kΩ A

+ VS = 8V −



B

 

R 3 = 1kΩ



C

R 2 = 6.2kΩ

R 4 = 1kΩ

R 5 = 680Ω



R 6 = 390Ω



  

D

 KE١١J ٦F‫א‬‫א‬‫א‬E١٥J ٦F

 ‫א‬

،‫א‬ ‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬ E١٥J ٦F‫א‬

 W A, B ‫א‬‫א‬RAB‫א‬‫א‬‫א‬  R AB =

R1R 2 = 2.15kΩ R1 + R 2

 W C, D ‫א‬‫א‬RCD‫א‬‫א‬‫א‬‫א‬  R CD =

R 4 (R 5 + R 6 ) = 517Ω R 4 + R5 + R6

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE١٦J ٦F

- ١٠٥ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 R AB = 2.15kΩ

R 3 = 1kΩ

+ VS = 8V −

R CD = 517Ω

    

 KE١١J ٦F‫א‬‫א‬‫א‬E١٦J ٦F W‫א‬‫א‬‫א‬‫א‬ ⎛R ⎞ VAB = ⎜⎜ AB ⎟⎟VS = 4.69V ⎝ RT ⎠ ⎛R VCD = ⎜⎜ CD ⎝ RT

⎞ ⎟⎟VS = 1.13V ⎠

⎛R ⎞ V3 = ⎜⎜ 3 ⎟⎟VS = 2.18V ⎝ RT ⎠

 W‫א‬‫א‬ ⎛ R AB ⎞ ⎟⎟VS = 4.69V ⎝ RT ⎠

 VAB = V1 = V2 = 4.69V⎜⎜

 K (R 5 + R 6 ) ‫א‬‫א‬ R 4 ‫א‬ VCD ‫א‬ ⎛ R5 V5 = ⎜⎜ ⎝ R5 + R6

⎞ ⎟⎟VCD = 718mV ⎠

⎛ R6 V6 = ⎜⎜ ⎝ R5 + R6

⎞ ⎟⎟VCD = 412mV ⎠

- ١٠٦ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 E١٢J ٦F

 KE١٧J ٦F‫א‬‫א‬‫א‬‫א‬ 

IT

Rc

A



B

Ra VS

C

RL

Rd

Rb

 

D



 KE١٢J ٦F‫א‬‫א‬‫א‬E١٧J ٦F ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬

 W

 K R d // R L ‫א‬‫א‬ R d , R L    R C + R d // R L  R C ‫א‬‫א‬‫א‬ ‫א‬ R b ‫א‬‫א‬‫א‬‫א‬‫א‬–‫א‬‫א‬   

 R b //[R C + (R d // R L )] ‫א‬، R a  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  W‫א‬‫א‬‫א‬

 R T = R a + R b //[R C + (R d // R L )]

- ١٠٧ -



‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 W ‫א‬‫א‬‫א‬ R T ‫א‬‫א‬  

IT



A

Ib

Ra

Ic

Rc

 

B

+ VS

Rb

−

 

Rd Id

C

RL IL

  

D

 KE١٢J ٦F‫א‬‫א‬‫א‬E١٨J ٦F  W‫א‬‫א‬‫א‬‫א‬ Ia = IT

IT = Ib + IC

 IC = Id + IL ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ D‫א‬  W I T ‫א‬  IT = I b + Id + I L  ‫א‬‫א‬‫א‬‫א‬‫ א‬٥J ٦ K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬–‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬

- ١٠٨ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬E١٣J ٦F  E١٣J ٦F  W‫؟‬‫א‬،E١٨J ٦F‫א‬‫א‬‫א‬  V1 = 12V, V2 = 8V, V3 = 8V, V4 = 5V 



R1

 

+ VS −

R2



R3



R4

 

 KE١٢J ٦F‫א‬‫א‬‫א‬E١٩J ٦F

 ‫א‬

 VS ‫א‬‫א‬‫א‬‫א‬‫א‬

 W

VS = V1 + V2 + V4 = 12 + 8 + 5 = 25V

 E١٤J ٦F

 KE٢٠J ٦F‫א‬‫א‬‫א‬‫א‬

R 2 = 100Ω



R 5 = 50Ω

R 3 = 50Ω

R 4 = 100Ω

R1 = 50Ω

R 6 = 100Ω

R 7 = 100Ω

 - ١٠٩ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 KE١٤J ٦F‫א‬‫א‬‫א‬E٢٠J ٦F  ‫א‬ Q R 6 // R 7

 ∴ R 6, 7 =

100 * 100 = 50Ω 100 + 100

 W‫א‬ R 6,7 ‫א‬‫א‬ R 5 R 5 + R 6,7 = 50 + 50 = 100Ω

 R 4 //( R 5 + R 6 // R 7 ) = 100 // 100 = 50Ω  K‫א‬‫א‬ R 3 ‫א‬‫א‬‫א‬‫א‬  R 3 + R 4 //( R 5 + R 6 // R 7 ) = 50 + 50 = 100Ω  W، R 2 ‫א‬‫א‬‫א‬‫א‬‫א‬  R 2 //[R 3 + R 4 //(R 5 + R 6 // R 7 )] =

100 * 100 = 50Ω 100 + 100

  R T ‫א‬ R1 ‫א‬‫א‬‫א‬‫א‬‫א‬  R T = 50 + 50 = 100Ω  E١٥J ٦F  W، VS  V4 = 28.2V ‫א‬W‫א‬‫א‬‫א‬  R 1 = 2.7kΩ, R 2 = 2.2kΩ, R 3 = 5.6kΩ, R 4 = 10kΩ, R 5 = 15kΩ, R 6 = 820Ω 

R1 IT

- ١١٠ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



I1 + VS



R2

−

I3

I5

I4

R3 R6



IT

I2

R4

R5

IT



 KE١٥J ٦F‫א‬‫א‬‫א‬E٢١J ٦F  ‫א‬  W،‫א‬  I T = I3 + I 4 + I 5 ، R 3 , R 4 , R 5 ‫א‬ ‫א‬ V4 = 28.2V  W I 3 , I 4 , I 5 ‫א‬‫א‬ I4 =

28.2 = 2.82mA 10k

I5 =

28.2 = 1.88mA 15k

I3 =

28.2 = 5.04mA 5 .6 k

∴ I T = 5.04mA + 1.88mA + 2.82mA = 9.74mA

 R eq ‫א‬‫א‬ I T 

 W I T  R 3 , R 4 , R 5   IT =

V4 R eq

 W - ١١١ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



R eq =

R 3R 4 R 5 = 2.896kΩ R 3 R 4 ,+ R 3 R 5 + R 4 R 5

 ∴IT =

28.2 2.896 * 10 3

= 9.74mA

 K‫א‬‫א‬   R1 // R 2 ‫א‬‫א‬‫א‬‫א‬ V1 = V2 = I T (R 1 // R 2 )



= IT (

R 1R 2 ) R1 + R 2

 W‫א‬‫א‬  V1 = V2 = 11.8V   R 6 ‫א‬‫א‬ V6 = I T .R 6 = 9.74 * 10 −3 * 0.82 * 10 3

 ∴ V6 = 7.99V   VS ‫א‬ VS = V1 + V4 + V6



= 11.8 + 28.2 + 7.99 = 48V

 ∴ VS = 48V ‫א‬‫א‬ VS E١F  K‫א‬‫א‬

 VS ‫א‬‫א‬‫א‬ VS E٢FKW  W‫א‬  VS = IT * R T Summary‫א‬ - ١١٢ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



‫א‬‫א‬‫א‬E‫א‬–‫א‬F‫א‬‫א‬‫א‬E١F  K‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬E٢F  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٣F  E‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤F ⎛ RX ⎞ ⎟⎟ R ⎝ T⎠

 VX = VS ⎜⎜

  W  ‫א‬‫א‬‫א‬W R X 

 ‫א‬‫א‬‫א‬W VX   ‫א‬W VS 

 K‫א‬‫א‬‫א‬W R T  

‫א‬E  ‫א‬‫א‬F‫א‬E٥F

 K  ‫א‬Common Reference Point

- ١١٣ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ‫א‬

 

 W‫א‬‫א‬‫א‬‫א‬‫א‬J ١

A

R1

R2

R3

R4



R5

B

 

 R 3 , R 4 , R 5 ‫א‬‫א‬ R1 , R 2 EF

 K‫א‬‫א‬ R1, R 2 EF

 ‫א‬‫א‬ R 3 , R 4 , R 5 EF

  R 3 , R 4 , R 5 ‫א‬‫א‬‫א‬‫א‬ R1, R 2 ‫א‬‫א‬EF  EF،EF‫א‬EF 

 W‫א‬‫א‬، R T ‫א‬‫א‬‫א‬‫א‬–٢  R1 + R 2 + R 3 // R 4 // R 5 EF

 R1 // R 2 + R 3 // R 4 // R 5 EF  (R1 + R 2 ) //(R 3 + R 4 + R 5 ) EF

 EF 

‫א‬ A, B ‫א‬‫א‬‫א‬‫א‬‫א‬–٣  W‫א‬‫א‬  R 3 , R 4 , R 5 EF R 5 EF  ‫א‬EF R1, R 2 EF  - ١١٤ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



1kΩ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬–٤ ‫א‬‫א‬، 2.2kΩ ‫א‬‫א‬‫א‬،‫א‬‫א‬

 ،٦V1kΩ ‫א‬‫א‬ 

V1 = 6V

1kΩ

1kΩ 2.2kΩ



   : 2.2kΩ ‫א‬‫א‬‫א‬

 ٣VEF٦VEF

 ١٣{٢VEF

١٢VEF 

 ‫א‬‫א‬‫א‬، 330Ω,470Ω ‫א‬‫א‬‫א‬–٥

100V ‫א‬‫א‬‫א‬K1kΩ 

 W‫א‬‫א‬‫א‬ 

1kΩ 1kΩ

330Ω

1kΩ

1kΩ

470Ω

100V

- ١١٥ -

    

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 W‫א‬‫א‬

 

 470Ω EF 330Ω EF1kΩ EF 

 ‫א‬،E٥F‫א‬‫א‬‫א‬‫א‬J ٦ 

 470Ω EF 330Ω EF1kΩ EF 

‫א‬  ‫א‬‫א‬‫א‬‫א‬،E٥F‫א‬‫א‬‫א‬‫א‬J ٧ ٣١{٣٪ EF

 W1kΩ

٥٠٪EF ٢٥٪EF١٠٠٪EF 

‫א‬F‫א‬٩V‫א‬‫א‬‫א‬J ٨  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، E‫א‬‫א‬  EF

‫א‬EF EFEF 

F10kΩ ‫א‬J ٩  W‫א‬E‫א‬‫א‬  10kΩ +

V2 −

10kΩ

- ١١٦ -

output

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



1MΩ EFK‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬  10kΩ EF

100kΩ EF 20kΩ EF

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J ١٠

‫א‬‫א‬EF EF EFEF 

- ١١٧ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 ‫א‬‫א‬   W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K١ 

R1 = 56Ω

 

+ VS = 1.5V

R 3 = 100Ω

R 2 = 100Ω

−

 

R 4 = 27Ω

  

(a )

 

R1

+ VS = 3V



680Ω

−

R2

R3

680Ω

330Ω

R 3 = 3.3kΩ

R 4 = 10kΩ

−

R 5 = 5.6kΩ



 - ١١٨ -

(c)

  

R 2 = 6 .2 k Ω

R 1 = 1kΩ

180Ω





(b)

+ 5V

R4

      

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 K‫א‬‫א‬‫א‬١‫א‬‫א‬‫א‬‫א‬K٢ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬K٣  ‫א‬‫א‬‫א‬‫א‬‫א‬ 

R 2 = 1kΩ



− 1V

R 1 = 1kΩ



R 4 = 3.3kΩ

R 3 = 2.2kΩ

+

W‫א‬‫א‬‫א‬‫א‬K٤ A



4.7 kΩ

B



10kΩ 5 .6 k Ω

+ 100V

C

E

−

1kΩ

1.8kΩ F

D

1kΩ

 W‫א‬‫א‬ (A, B) ‫א‬‫א‬J ٥ R1 = 1kΩ + 100V −

A

R 4 = 560Ω



R 2 = 330Ω R 3 = 470Ω R 8 = 100Ω - ١١٩ -

 R 5 = 1kΩ

B

R 6 = 1.5kΩ

R 7 = 680Ω

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 W‫א‬‫א‬J ٦ R2

P = 20 W

4A +

R4

R3

40V

R5

1A

−



P = 2W

R1

20V



5V

R6

1V

R8

R7



1A

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J ٧ ‫א‬، R L = 10kΩ ‫א‬KE (A, B) ‫א‬FNo Load‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ 

+ 22V −



R 1 = 10kΩ



A



R 2 = 5 .6 k Ω RL

R 3 = 2 .7 k Ω B



 W‫א‬‫א‬J ٨   R T ‫א‬‫א‬‫א‬EF

 I T ‫א‬‫א‬‫א‬‫א‬EF   910Ω ‫א‬‫א‬EF

 K VA , VB  A, B ‫א‬EF - ١٢٠ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



56Ω

+ 60V



56Ω

 

910Ω

−

 1kΩ

A

560kΩ B

1kΩ



560kΩ

1kΩ 1kΩ

 WLadder Network‫א‬‫א‬‫א‬J ٩  R T ‫א‬‫א‬EF

 VA ،A‫א‬‫א‬EF  VB ،B‫א‬‫א‬ R 1 = 5 .6 k Ω

18V

A

R 3 = 1kΩ

R 2 = 2.2kΩ

B



R 5 = 1kΩ

R 4 = 2 .2 k Ω

 R 6 = 1kΩ

  

‫א‬‫א‬‫א‬‫א‬ A, B ‫א‬‫א‬‫א‬‫א‬J ١٠  W‫א‬

- ١٢١ -

‫א‬‫א‬

‫ א‬١٤٠

‫א‬

‫א‬‫א‬‫א‬

١-



 R 3 = 220Ω

R1 = 100Ω A + −

B

I2

IT

I3

R 2 = 820Ω



R 5 = 100Ω I5

I4



R 4 = 820Ω

R 6 = 680Ω



R 9 = 100Ω

 R 7 = 100Ω

R 8 = 220Ω

IT



‫א‬‫א‬١٠‫א‬‫א‬‫א‬‫א‬‫א‬J ١١  ‫؟‬ VS = 10V ،١٠V A, B ‫א‬‫א‬    ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬J ١٢  W‫א‬‫א‬‫א‬

 R 1 = 10kΩ, R 2 = 20kΩ, R 3 = 60kΩ, R 4 = 15kΩ, R 5 = 5kΩ

R3

+

R2 VA

VC

R4

B R١



R5

A

 

VB

100V −

 C

- ١٢٢ -



 ‫א‬‫א‬‫א‬ ã¹]
١ J

 ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

٧

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 ‫א‬‫א‬‫א‬‫א‬



 W‫א‬‫א‬،‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ •

- ١٢٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



Introduction  ١J ٧

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K  ‫א‬  K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬ KE٢J  F ‫א‬،‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K ‫א‬‫א‬‫א‬‫א‬ ٢J ٧ Voltage Source‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،Current Source Constant Voltage Source ‫א‬‫א‬

١J ٢J ٧

‫א‬‫א‬   ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ R S ‫א‬‫א‬

 KE١J ٧F

+ VS



RS



RL

−

 

  E١J ٧F  R S   ،Ideal Voltage Source ‫א‬‫א‬

 W‫א‬‫א‬ E١J ٧F

R L >> R S - ١٢٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 Constant Current Source 

٢J ٢J ٧

 R S ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٢J ٧F، 

A

iS



RS

A

  

B

 EJ ٢J ٧F 

iS

A

A



RL

RS



  

B

 EJ ٢J ٧F  R S ،Ideal Current Source  ‫א‬‫א‬

 W‫א‬‫א‬

 R S 〉〉 R L

E٢J ٧F

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬ ?Source Conversions " ‫א‬

٣J ٢J ٧

   ‫א‬،‫א‬‫א‬‫א‬

 K‫א‬E٣J ٧F‫א‬ - ١٢٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 A

A

+ VS

iL

RS

RL

−

≡



i L

iS

I



RS

RL

 

B

B



 KE٣J ٧F 

 W IL ‫א‬‫א‬‫א‬ IL =

VS RS + R L

E٣J ٧F

 KW IL ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ⎛ RS ⎞ ⎟⎟iS I L = ⎜⎜ + R R L⎠ ⎝ S

E٤J ٧F  WE٤J ٧FE٣J ٧F‫א‬‫א‬

 VS = R S ⋅ i S

E٥J ٧F

- ١٢٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 E١J ٧F  W‫א‬‫א‬‫א‬‫א‬ (a )R L = 100Ω  (b)R L = 560Ω  (c)R L = 1KΩ A

iL iS 1A

I

RL

RS 10kΩ

   

B

 KE١J ٧F‫א‬‫א‬‫א‬E٤J ٧F

  ‫א‬

 R L = 100Ω 

 IL ،E٣J ٧F ⎛ RS ⎞ ⎟⎟iS I L = ⎜⎜ ⎝ RS + R L ⎠ ⎛ 10kΩ ⎞ IL = ⎜ ⎟ * 1 = 990mA = 0.99A ⎝ 10.1kΩ ⎠

 W، R L = 560Ω  ⎛ 10kΩ ⎞ IL = ⎜ ⎟ *1 = 0.947A ⎝ 10.56kΩ ⎠

 IL  R L = 1KΩ  ⎛ 10kΩ ⎞ IL = ⎜ ⎟ * 1 = 0.909A ⎝ 11kΩ ⎠

 R L  iS ٪١٠ I L ‫א‬ ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬ R S ‫א‬ - ١٢٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 E٢J ٧F  K IL = 750mA ‫א‬ R L ،‫א‬‫א‬‫א‬ 

A

i S = 1A



R S = 10kΩ

I



iL



RL



B

 

 KE٢J ٧F‫א‬‫א‬‫א‬E٥J ٧F  ‫א‬

⎛ RS ⎞ ⎟⎟iS I L = ⎜⎜ R + R L⎠ ⎝ S

 W‫א‬،E٣J ٧F‫א‬‫א‬

 W‫א‬ iS ، R S ‫א‬ 0.75(10 + R L ) = 10 7.5 + 0.75R L = 10 0.75R L = 2.5 RL =

2.5 = 3.33kΩ 0.75

- ١٢٨ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 E٣J ٧F  K‫א‬E٦J ٧F‫א‬‫א‬‫א‬ A

+ VS = 100V

R S = 50Ω

  

−

 B



 KE٣J ٧F‫א‬‫א‬‫א‬E٦J ٧F iS =

 ‫א‬

VS 100 = = 2A R S 50

- ١٢٩ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 W،E٧J ٧F‫א‬‫א‬‫א‬ A

i S = 2A

I

 



R S = 50Ω

 

B

 KE٣J ٧F‫א‬‫א‬‫א‬E٧J ٧F

Superposition Theorem ‫א‬ ٣J ٧

?‫?א‬‫א‬‫א‬‫א‬‫א‬‫א‬

  ‫א‬‫א‬  K 

 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬

‫א‬‫א‬   R S ‫א‬‫א‬،‫א‬‫א‬

♦

 KShort Circuit‫א‬‫א‬

‫א‬‫א‬، R S ‫א‬‫א‬،‫א‬‫א‬ Open-Circuit‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،E٨J ٧F‫א‬‫א‬‫א‬

 K

- ١٣٠ -

♦

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

R١

‫ א‬١٤٠

‫א‬

١-





R2

a



+

+ VS1

VS2

R3

−

 

−

 

b  K‫א‬E٨J ٧F



‫א‬‫א‬‫א‬‫א‬E R 3  ‫א‬Fab‫א‬‫א‬‫א‬‫א‬ ، I1 ‫א‬‫א‬،E٩J ٧F‫א‬ ،‫א‬ab‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I 2

‫א‬ab‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬  I1 + VS1

I2

a

a

R2

R١

R3

+

R١

R2

R3

b

b

 K‫א‬‫א‬‫א‬E٩J ٧F

- ١٣١ -

  +

VS2

  

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 E٤J ٧F  K‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬

 

a

R1 = 100Ω

+ 10V

R 3 = 100Ω R 2 = 100Ω

−

+ 5V −

    

b

 KE٤J ٧F‫א‬‫א‬‫א‬E١٠J ٧F  ‫א‬  K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

 KE١١J ٧F١٠ V‫א‬‫א‬W‫א‬‫א‬‫א‬ a +

R1 = 100Ω

R 3 = 100Ω

10V

R 2 = 100Ω

−

b

 KE٣J ٧F‫א‬‫א‬‫א‬١٠ V‫א‬‫א‬E١١J ٧F

 W‫א‬‫א‬ R 2 ‫א‬

RT =

R2 * R3 + R1 R2 + R3

RT =

100 * 100 + 100 = 150Ω 100 + 100

IT =

VS 10 = = 66.7mA R T 150 - ١٣٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 W‫א‬‫א‬ab‫א‬‫א‬‫א‬ Iab = 66.7 *

100 = 33.3mA 100 + 100

KE١٢J ٧F٥ V‫א‬‫א‬W‫א‬‫א‬‫א‬  

a

R1 = 100Ω

R 3 = 100Ω

R 2 = 100Ω

 + 5V −

  

b



 KE٣J ٧F‫א‬‫א‬‫א‬٥ V‫א‬‫א‬E١٢J ٧F 

 W R T ‫א‬‫א‬‫א‬ab‫א‬‫א‬‫א‬ RT = R3 +

R 1R 2 R + R 21

R T = 100 +

100 * 100 = 150Ω 100 + 100

IT =

VS 5 = = 33.3mA R T 150

 Wab‫א‬‫א‬‫א‬ ⎛ R1 I ab = I T ⎜⎜ ⎝ R1 + R 2

I ab = 33.3 *

⎞ ⎟⎟ ⎠

100 = 16.7 mA 100 + 100

- ١٣٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 W‫א‬‫א‬ ITab = 33.3 + 16.7 = 50mA

 ،‫א‬ ‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 E٥J ٧F

 KE١٣J ٧F‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬ a



R1 = 220Ω

+ 10V

R 2 = 100Ω

−

A

i S = 100mA

b

 KE٥J ٧F‫א‬‫א‬‫א‬E١٣J ٧F

 ‫א‬

 K‫א‬‫א‬‫א‬

 KE١٤J ٧F١٠ V‫א‬‫א‬W‫א‬‫א‬‫א‬ a



R 1 = 220Ω

+ 10V

 R 2 = 100Ω

−

 

b



 KE٥J ٧F‫א‬‫א‬‫א‬‫א‬E١٤J ٧F

 K‫א‬‫א‬‫א‬‫א‬

 W R T ‫א‬‫א‬‫א‬‫א‬ R T = 220 + 100 = 320Ω iT = i ↓R2 =

10 = 31.2mA 320 - ١٣٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 K 31.2mA 10V ‫א‬ R 2 ‫א‬‫א‬‫א‬∴  KE١٥J ٧F١٠٠ mA‫א‬‫א‬W‫א‬‫א‬‫א‬  

a



R1 = 220Ω R 2 = 100Ω

A

i S = 100mA

  

b

 KE٥J ٧F‫א‬‫א‬‫א‬‫א‬E١٥J ٧F



 W‫א‬‫א‬ab‫א‬‫א‬ ⎛ 220 ⎞ i ↓ R = iS ⎜ ⎟ 2 ⎝ 220 + 100 ⎠

‫א‬ i s ،‫א‬ R 2 ‫א‬‫א‬‫א‬ i ↓ R 2   W‫א‬،‫א‬ ⎛ 220 ⎞ i ↓ R 2 = 100⎜ ⎟ = 68.8mA ⎝ 320 ⎠ ∴ i ↓ R 2 = 68.8mA

 K 68.8mA ‫א‬‫א‬‫א‬‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬  W‫א‬‫א‬ R 2 ‫א‬‫א‬‫א‬ i = 31.2 + 68.8 = 100mA

- ١٣٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 Thevinen's Theorem ٤J ٧ ‫א‬ ‫א‬  KThevinen's TheoremEF

 R Th ‫א‬‫א‬ VTh ‫א‬‫א‬  KE١٦J ٧F 

R Th A

VTh



r

I

 

B

 K??‫א‬E١٦J ٧F ‫א‬‫א‬‫א‬ R Th ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I=

VTh R Th + r

 W‫א‬‫א‬‫א‬ r ‫א‬‫א‬ I ‫א‬ E٦J ٧F  W‫א‬

 W‫א‬‫א‬‫א‬‫א‬‫א‬EF‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E١  K VTh ‫א‬ EZF‫א‬‫א‬‫א‬‫א‬ E٢ F R Th ‫א‬‫א‬‫א‬Short Circuit‫א‬‫א‬

KE‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R Th 

- ١٣٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 R Th ‫א‬‫א‬ VTh E‫א‬F E٣ ‫א‬‫א‬KE١٦J ٧F‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬

I=

VTh R Th + r

KComplex Circuit‫א‬‫א‬‫א‬W

‫א‬Output‫א‬‫א‬‫א‬ ‫א‬‫א‬  W‫א‬،‫א‬‫א‬  ‫א‬

‫א‬‫א‬‫א‬‫א‬E‫א‬F‫א‬Open E١ K VTh ‫א‬

‫א‬‫א‬E‫א‬‫א‬F  ‫א‬‫א‬‫א‬‫א‬‫ א‬E٢ K‫א‬‫א‬ R Th 

Series Circuit‫א‬‫א‬E‫א‬F E٣ K‫א‬ R L  R Th ، VTh 

 E٦J ٧F

 K‫א‬a،b‫א‬‫א‬‫א‬‫א‬‫א‬ a

+ 10V

R 1 = 4Ω

R 2 = 8Ω R 3 = 6Ω

−



+ 5V −

b

 KE٦J ٧F‫א‬‫א‬‫א‬E١٧J ٧F

- ١٣٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 ‫א‬ ‫א‬Open‫א‬  ‫א‬‫א‬ab‫א‬‫א‬W  ‫א‬‫א‬

 K VTh b،a‫א‬

a + 10V

R 1 = 4Ω

R 2 = 8Ω

−

I



+ 5V



−





b

 Kab‫א‬E٦J ٧F‫א‬‫א‬‫א‬E١٨J ٧F

 W،‫א‬‫א‬‫א‬‫א‬‫א‬ 10 − 5 = I(4 + 8) ∴I =

10 − 5 5 = A 12 12

 W‫א‬‫א‬ Va  ∴ Va = 10 − I * 4 Va = 10 −

5 * 4 = 8.33V 12

∴ VTh = 8.33V

‫א‬‫א‬‫א‬‫א‬a‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬ ٥V  ‫א‬‫א‬a  W Va ‫א‬

Va = 5 + I * 8 Va = 5 +

8 *8 12

Va = 5 + 3.33 ≈ 8.33V

- ١٣٨ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 K‫א‬‫א‬‫א‬ Va ‫א‬‫א‬  K‫א‬Short R Th W‫א‬‫א‬ R Th = R ab

 KE١٩J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ R 1 = 4Ω

R 2 = 8Ω a b

 K‫א‬‫א‬E٦J ٧F‫א‬‫א‬‫א‬E١٩J ٧F

    

 KE٢٠J ٧F‫א‬‫א‬‫א‬‫א‬ R 1 = 4Ω

R 2 = 8Ω a b

 KE١٩J ٧F‫א‬‫א‬‫א‬E٢٠J ٧F

    

 WRTH‫א‬ ∴ R Th = R ab =

4*8 = 2.66Ω 4+8

- ١٣٩ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 KE٢١J ٧F‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ 

R Th = 2.66Ω



A



VTh = 8.33V

6Ω

I

 

B



 KE٦J ٧FE٢١J ٧F

I ab =

 Wab‫א‬‫א‬

VTh 8.33 = = 0.96A R Th + 6Ω 2.66 + 6

 E٧J ٧F  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬

‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬

 KE٢٢J ٧F، E1 ‫א‬‫א‬W‫א‬‫א‬‫א‬ IT١

+ 10V



a R 1 = 4Ω

R 2 = 8Ω

Iab١

R 3 = 6Ω

−

 

   

b

 KE٧J ٧F‫א‬‫א‬‫א‬١٠ V‫א‬‫א‬E٢٢J ٧F  WIab١‫א‬ - ١٤٠ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

RT = 4 + i T1 =

‫ א‬١٤٠

‫א‬

١-



8*6 = 7.43Ω 8+6

10 = 1.345A 7.43

i ab1 = 1.345 *

8 = 0.77 A 8+6



 KE٢٣J ٧F، E 2 ‫א‬‫א‬W‫א‬‫א‬‫א‬ 

IT٢

a R 1 = 4Ω

R 2 = 8Ω

Iab٢

R 3 = 6Ω

b

 + 5V −

    

 KE٧J ٧F‫א‬‫א‬‫א‬ ٥ V‫א‬‫א‬E٢٣J ٧F  WIab٢‫א‬ RT = 8 + iT =

4*6 = 10.4Ω 4+6

5 = 0.48A 10.4

i ab = 0.48 *

4 = 0.192A 4+6

،‫א‬ab‫א‬‫א‬‫א‬‫א‬‫א‬W ‫א‬‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬ i ab = 0.77 + 0.192 = 0.962A

 K   ‫א‬‫א‬ ‫א‬‫א‬ - ١٤١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 E٨J ٧F  W‫א‬E٢٤J ٧F‫א‬‫א‬‫א‬ R L ‫א‬‫א‬‫א‬  K‫א‬EF

 KEF

a

2mA

I

 

 10kΩ

 



12kΩ



R L = 8kΩ

 

b

 KE٨J ٧F‫א‬‫א‬‫א‬E٢٤J ٧F  ‫א‬ ‫א‬‫א‬12KΩ ، 8KΩ ‫א‬ ‫א‬‫א‬‫א‬‫א‬W   K10KΩ ‫א‬‫א‬

∴i ↓ = 2 * RL

10 10 + 20

1 2 i ↓ = 2 * = mA 3 3 RL

- ١٤٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 K‫א‬W   KEJ ٢٥J ٧F‫א‬‫א‬ VTh  R L ‫א‬W‫א‬‫א‬ 

12kΩ

a

 I=0

2mA

I

VTh

⇐

10kΩ

   

b

 KRLE٨J ٧F‫א‬‫א‬‫א‬EJ ٢٥J ٧F



∴ VTh = 2mA * 10KΩ = 20V

‫א‬‫א‬‫א‬W‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬  KEJ ٢٥J ٧F‫א‬‫א‬‫א‬E F a

12kΩ

I=0 10kΩ

open

 

R Th

⇐

   

b

 K‫א‬E٨J ٧F‫א‬‫א‬‫א‬EJ ٢٥J ٧F



 WRTh ∴ R Th = 10 + 12 = 22KΩ

 KE٢٦J ٧FW‫א‬‫א‬ - ١٤٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 

R Th = 22kΩ



A



VTh = 20V

R L = 8kΩ

I

B



 KE٨J ٧FE٢٦J ٧F

  



 W‫א‬‫א‬‫א‬ ∴I =

I=

VTh R TH + R L

20 20V 2 = = mA 22 + 8 30KΩ 3

 K‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬

١J ٤J ٧

،Bridge Circuit‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬Thevinen's Theorem،‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬،‫א‬

B،A‫א‬‫א‬W  ‫א‬‫א‬،E٢٧J ٧F‫א‬‫א‬

 K R L ‫א‬D،COutput‫א‬ ‫א‬‫א‬D،C‫א‬  ‫א‬‫א‬

KSource‫א‬‫א‬B،A‫א‬‫א‬

- ١٤٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



A



R2

R1



RL

C

VS



D





R 3

R4



B



 K‫א‬‫א‬E٢٧J ٧F  E٩J ٧F  W‫א‬،E٢٨J ٧F‫א‬‫א‬‫א‬  KD،C‫א‬ R L ‫א‬‫א‬EF  A

R 2 = 680Ω

R 3 = 330Ω VS = 24V

C

 K R L ‫א‬‫א‬‫א‬EF

R L = 1kΩ D

R 4 = 560Ω

R 3 = 680Ω



B

 KE٩J ٧F‫א‬‫א‬E٢٨J ٧F

- ١٤٥ -

      

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 ‫א‬  W‫א‬

‫א‬‫א‬‫א‬‫א‬D،C‫א‬ R L ‫א‬W  ‫א‬‫א‬

 W VTh D،C

VTh = VC − VD ⎛ R3 ⎞ ⎛ R4 ⎞ ⎟⎟VS − ⎜⎜ ⎟⎟VS VTh = ⎜⎜ R R R R + + ⎝ 2 3⎠ 4⎠ ⎝ 1

E٧J ٧F

،K ‫א‬‫א‬ R L ‫א‬‫א‬‫א‬‫א‬‫א‬  KE٢٩J ٧F

 W  VC = I1R 3  I1 =

VS R1 + R 3

 VD = I 2 R 4  I2 =

VS R2 + R4

+ 24V −

R 1 = 330Ω C

R 2 = 680Ω

VC

VD

R 4 = 560Ω

  KRL‫א‬E٩J ٧F‫א‬‫א‬E٢٩J ٧F - ١٤٦ -



D

VTh

R 3 = 680Ω



I2

I1

  

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 WVTh ⎛ 680 ⎞ ⎛ 560 ⎞ ∴ VTh = ⎜ ⎟ * 24 − ⎜ ⎟ * 24 ⎝ 330 + 680 ⎠ ⎝ 680 + 560 ⎠ VTh = 16.158 − 10.838 = 5.32V

 R Th ‫א‬ ‫א‬‫א‬W ‫א‬‫א‬  KE٣٠J ٧F‫א‬‫א‬‫א‬‫א‬D،C‫א‬‫א‬ R1 A

R3

C

R Th

B

R2

⇐

R4

D

 KE٩J ٧FRTh‫א‬E٣٠J ٧F

 WRTh

∴ R Th = R Th =

R 1R 3 R 2R 4 + R1 + R 3 R 2 + R 4

E٨J ٧F

330 * 680 680 * 560 + 330 + 680 680 + 560

R Th = 222.178 + 307.096 = 529.27Ω

 KE٣١J ٧FW‫א‬‫א‬

- ١٤٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-





R Th = 529.27Ω



C



VTh = 5.32V



R L = 1kΩ

I

 

D

 KE٩J ٧FE٣١J ٧F

 W،‫א‬CD‫א‬‫א‬ ∴ I CD = I CD =

VTh R Th + R L

5.32 = 3.5mA 529.27 + 1000

 ٣{٥ mACD‫א‬‫א‬‫ ∴א‬  J ‫א‬–‫א‬ ٥J ٧ E Y ← ∆ F‫א‬‫א‬‫א‬‫ א‬١J ٥J ٧ " Conversion From Delta → Star "

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE٣٢J ٧F‫א‬ Y ← ∆ ‫א‬ A

A



≡

R1 R2 B

O

RC



RA

 

R3 C

B

 K Y ↔ ∆ E٣٢J ٧F - ١٤٨ -

RB

C



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 Kc،b،aC،B،A ∆ ‫א‬  K٣،٢،١ Y ‫א‬

" Conversion From (Y←∆)" (Y←∆)‫א‬

،E٣٣J ٧F ∆ ‫א‬‫א‬ Y ‫א‬  K‫א‬  A

R1

RC

O

R2 B

 

RB



RA



R3

 C

 ‫א‬‫א‬‫א‬E٣٣J ٧F ‫א‬= Y W‫א‬‫א‬‫א‬  WK ∆ ‫א‬‫א‬ ∆ ‫א‬ R1 =

R AR C RA + RB + RC

E٩J ٧F

R2 =

R BR C RA + RB + RC

E١٠J ٧F

R3 =

R CR A RA + RB + RC

E١١J ٧F

- ١٤٩ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



E ∆ ← Y F‫א‬‫א‬‫א‬

٢J ٥J ٧

 W‫א‬‫א‬‫א‬ R A = R1 + R 3 +

R 1R 3 R2

E١٢J ٧F

RB = R2 + R3 +

R 2R 3 R1

E١٣J ٧F

R C = R1 + R 2 +

R 1R 2 R3

E١٤J ٧F

‫א‬ Y ‫א‬ ∆ ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  E١٠J ٧F  K‫א‬ Y ‫א‬E٣٤J ٧F‫א‬ ∆ ‫א‬ 

A

 220Ω

560Ω

 100Ω

B

C

 KE١٠J ٧F‫א‬E٣٤J ٧F  ‫א‬ ،E٣٥J ٧F ∆ ‫א‬‫א‬ Y ‫א‬

 K Y ← ∆ ‫א‬

- ١٥٠ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 

A

 

R1

100Ω

R2 B

O

560Ω



220Ω

 

R3



 C



 KE١٠J ٧F‫א‬‫א‬‫א‬E٣٥J ٧F ،E١١J ٧FJ E٩J ٧F‫א‬‫א‬‫א‬‫א‬‫א‬

 W

R1 =

100 * 220 = 25Ω 100 + 220 + 560

R2 =

100 * 560 = 63.6Ω 100 + 220 + 560

R3 =

220 * 560 = 140Ω 100 + 220 + 560

- ١٥١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 KE٣٦J ٧F‫א‬‫א‬ A



R 1 = 25Ω





O

R 2 = 63.5Ω B



R 3 = 140Ω



C

  KE١٠J ٧F‫א‬‫א‬‫א‬E٣٦J ٧F  E١١J ٧F  KE٣٧J ٧F‫א‬‫א‬ ∆ ← Y ‫א‬ 

A



R 1 = 1kΩ

R 2 = 2.2kΩ

 O

B

 R 3 = 5.6kΩ C

 KE١١J ٧F‫א‬E٣٧J ٧F

- ١٥٢ -

 

 

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 ‫א‬ ،E٣٨J ٧F، Y ‫א‬ ∆ ‫א‬

 K ∆ ← Y ‫א‬ 

A

  1kΩ

RB

2.2kΩ B

O

RC



RA

 

5 .6 k Ω C

 KE١٢J ٧F‫א‬‫א‬‫א‬E٣٨J ٧F



‫א‬H Y ‫א‬‫א‬‫א‬= ∆ ‫א‬

 K‫א‬ Y 

 W،E١٤J ٧FJ E١٢J ٧F‫א‬‫א‬ R A = 1 + 5 .6 +

1 * 5 .6 = 9.15KΩ 2.2

R B = 1 + 2.2 +

1 * 2 .2 = 3.59KΩ 5 .6

R C = 2.2 + 5.6 +

2.2 * 5.6 = 20.12KΩ 1

- ١٥٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



K‫א‬‫א‬ ∆ ← Y  Y ← ∆ ‫א‬‫א‬‫א‬

٣J ٥J ٧

 E١٢J ٧F ‫א‬،E٣٩J ٧F‫א‬‫א‬‫א‬ R L ‫א‬‫א‬‫א‬  K∆ → Y 

A

R 1 = 4.7kΩ 18kΩ

C

VS = 120V



R 2 = 3 .9 k Ω



D

R 3 = 2 .2 k Ω

 

R 4 = 2 .7 k Ω

 



B

 KE١٢J ٧F‫א‬‫א‬‫א‬E٣٩J ٧F  ‫א‬ D، C،A‫א‬‫א‬‫א‬ ∆ ‫א‬   ‫א‬‫א‬

‫א‬ Y ‫א‬D،C،B‫א‬‫א‬‫א‬ ∆ ‫א‬ ‫א‬D،C،B‫א‬‫א‬‫א‬ ∆ ‫א‬‫א‬  KE٤٠J ٧F Y ‫א‬‫א‬ C

18kΩ

R 3 = 2 .2 k Ω

C D

≡

R 4 = 2.7kΩ B

R٢

R١ o

R٣ B

 KE١٢J ٧F‫א‬‫א‬‫א‬E٤٠J ٧F - ١٥٤ -

D

 

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 W R 3 ، R 2 ، R1  R1 =

18 * 2.2 = 1.73KΩ 2.2 + 2.7 + 18

R2 =

2.7 * 18 = 2.12KΩ 2.2 + 2.7 + 18

R3 =

2 .2 * 2 .7 = 0.26KΩ 2.2 + 2.7 + 18

 R 3 ، R 2 ، R1 ‫א‬‫א‬‫א‬‫א‬  WE٤١J ٧F 

 

A

R 1 = 4.7 kΩ

R 2 = 3 .9 k Ω



  

VS = 120V

C

D

1.73kΩ

2.12kΩ

o

0.26kΩ B

 K‫א‬‫א‬‫א‬‫א‬‫א‬E٤١J ٧F

     

 WE٤٢J ٧F‫א‬‫א‬‫א‬‫א‬

- ١٥٥ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-





A

+ 120V −



I2

I1 4.7 kΩ

3 .9 k Ω

C

D

1.73kΩ

2.12kΩ

    

0.26kΩ B

  

 KE٤١J ٧F‫א‬E٤٢J ٧F  ‫א‬‫א‬ Υ ‫א‬ ∆ ‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬

 K‫א‬ R T W  K I T ‫א‬‫א‬W

 K‫א‬‫א‬ I 2 ، I1 W  K VC  C ‫א‬‫א‬W‫א‬

 K VD  D ‫א‬‫א‬W VCD = VC − VD

 K D ، C ‫א‬‫א‬‫א‬W

 K R L  VCD ‫א‬‫א‬ CD ‫א‬‫א‬W ∴ ICD =

VCD RL

 W‫א‬‫א‬‫א‬ RT =

(4.7 + 1.73) ⋅ (3.9 + 2.12) + 0.26 ≈ 3.37 KΩ (4.7 + 1.73) + (3.9 + 2.12) - ١٥٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



∴ R T = 3.37 KΩ IT ≈

120 ≈ 35.6mA 3.37

 W‫א‬‫א‬ I1 = I T *

(3.9 + 2.12) (3.9 + 2.12) + (4.7 + 1.73)

∴ I1 = 17.2mA

I 2 = 18.38mA VC ≈ 39.18V VD = 48.32V

 K D ، C ‫א‬‫א‬ ∴ VCD = VC − VD

VCD = 39.18 − 48.32 = −9.14V

 C ‫א‬‫א‬ D ‫א‬‫א‬EJ F‫א‬W  K ICD ‫א‬‫א‬ VD 〉 VC

∴ ICD =

9.14V = 0.507mA 18KΩ

 KE‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٦J ٧ ‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬

- ١٥٧ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



‫א‬ ‫א‬‫א‬Mesh  K‫א‬b،a‫א‬‫א‬،E٤٣J ٧F‫א‬‫א‬‫א‬ a

R١

V١

b

R٢



V٢ 

b

R3

a

 K

d



 c

R5



e

R4



 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٤٣J ٧F



 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KMesh‫א‬‫א‬‫א‬‫א‬

KCL‫א‬ Meshes ‫א‬‫א‬

E١F

E٢F

K‫א‬‫א‬ K‫א‬‫א‬‫א‬KVL‫א‬

E٣F

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

E٤F

Meshes.‫א‬‫א‬‫א‬‫א‬‫א‬

E٥F

K‫א‬‫א‬‫א‬‫א‬‫א‬

- ١٥٨ -

E٦F

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 E١٣J ٧F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 KE٤٤J ٧F‫א‬

I1 b

a

10Ω

I1

20Ω



d

c

10V



I3

I2

20Ω

30Ω

15V

20V 10Ω

I2

 

I3

I4

I5



 

f

 KE١٣J ٧F‫א‬‫א‬‫א‬E٤٤J ٧F



‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬  K،‫א‬‫א‬

‫א‬  ‫א‬ ‫א‬‫א‬‫א‬‫א‬  K I 5 ، I 4 ، I 3 ، I 2 ، I1 ‫א‬‫א‬‫א‬ I 3 ، I 2 ، I1   EbF‫א‬‫א‬‫א‬ I 5 ، I 4 

I 5 = I1 − I 2

(a)

I 4 = I 2 − I3

(b)

‫א‬‫א‬‫א‬ I 3 ، I 2 ، I1 ‫א‬‫א‬ 

 K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  K‫א‬ 

 Mesh E١F‫א‬‫א‬W‫א‬‫א‬ 10 = 10I1 + 20I 5

(c) - ١٥٩ -



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 I1 + I 2 EaF I 5    I 2 ، I1  I 5 KW ∴10 = 10I1 + 20I1 − 20I 2 10 = 30I1 − 20I 2

(d)

 KEdF 

 Mesh E٢F‫א‬‫א‬W‫א‬‫א‬

20 = 30I 2 + 20I5 − 10I 4

(e)

 WEeF I 5 ، I 4 ‫א‬

20 = −30I 2 + 20(I1 − I 2 ) − 10(I 2 − I 3 )

20 = −30I 2 + 20I1 − 20I 2 − 10I 2 + 10I 3

20 = 20I1 − 60I 2 + 10I 3

(f)

 15 = −20I 3 + 10I 4

 Mesh E٣F‫א‬‫א‬W‫א‬ (g)

 WEbF I 4 

15 = −20I 3 + 10(I 2 − I 3 )

15 = −20I 3 + 10I 2 − 10I 3 15 = −30I 3 + 10I 2

(h)

‫א‬ I 3 ، I 2 ، I1 EhF،EfF،EdF‫א‬ 10 = 30I1 − 20I 2 − (0) I 3

 W‫א‬‫א‬‫א‬ (I)

− 20 = −20I1 + 60I 2 − 10I 3

(II)

− 15 = (0) I1 − 10I 2 + 30I 3

(III)

 W(III, II, I)‫א‬‫א‬ 

- ١٦٠ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

⎡ 10 ⎤ ⎡+ 30 ⎢− 20⎥ = ⎢− 20 ⎢ ⎥ ⎢ ⎢⎣− 15 ⎥⎦ ⎢⎣− 0

− 20 + 60 − 10

‫ א‬١٤٠

‫א‬

١-



−0 ⎤ − 10⎥ ⎥ 30 ⎥⎦

⎡I1 ⎤ ⎢I ⎥ ⎢ 2⎥ ⎢⎣I 3 ⎥⎦

(IV)



 WEIVF‫א‬‫א‬

[V] = [R ] ⋅ [I]

E١٥J ٧F



 K‫א‬‫א‬‫א‬‫א‬‫א‬، [I]‫א‬J

MeshE٣F،MeshE٢F،MeshE١F  ‫א‬‫א‬‫א‬W [V ] ‫א‬J

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬W [R ] ‫א‬J ⎡R11 R12 R13 ⎤ [R ] = ⎢⎢R 21 R 22 R 23 ⎥⎥ ⎢⎣R 31 R 32 R 33 ⎥⎦

E١٦J ٨F 

‫א‬‫א‬‫א‬ R 33 ، R 22 ، R11 ‫א‬‫א‬

 W،‫א‬

 KMeshE١F‫א‬‫א‬ R11

 KMeshE٢F‫א‬‫א‬ R 22

 KMeshE٣F‫א‬‫א‬ R 33 

 R12 ‫א‬‫א‬‫א‬‫א‬ E٢F ‫א‬‫א‬‫א‬ R 23 ‫א‬KMeshE٢F،MeshE١F‫א‬‫א‬

 K‫א‬‫א‬‫א‬،‫א‬MeshE٣F‫א‬،Mesh

‫א‬ ‫א‬‫א‬MeshE٣F‫א‬MeshE١F‫א‬

 K‫א‬R١٣ - ١٦١ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



‫א‬‫א‬‫א‬  ‫א‬  K I 3 ، I 2 ، I1  ‫א‬‫א‬‫א‬

 W‫א‬E١ R 11

R 12

 ∆ = R 21 R 22 R 31

R 32

R 13

E١٧J ٧F

R 23 R 33

 K‫א‬∆  W‫א‬‫א‬‫א‬ ∆ = R11{R 22 R 33 − R 32 R 23 } − R12 {R 21R 33 − R 31R 23 } + R13 {R 21R 32 − R 31R 22 }

 K∆‫א‬‫א‬‫א‬  W I1 ‫א‬ V1 R12 R13 1 I1 = V2 R 22 R 23 ∆ V3 R 32 R 33

E١٨J ٧F  W I 2 ‫א‬

R11 1 I2 = R 21 ∆ R 31

V1

R13

V2

R 23

V3

R 33

E١٩J ٧F  W I 3 ‫א‬

R11 1 I3 = R 21 ∆ R 31

R12

V1

R 22

V2

R 32

V3

E٢٠J ٧F

 W‫א‬ I 3 ، I 2 ، I1 ‫א‬ ∆ ‫א‬‫א‬  W ∆ ‫א‬ + 30 − 20 ∆ = − 20 +60 −0 − 10

−0 − 10 + 30 - ١٦٢ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬ ∆ = 30(60 * 30 − (−10) * (−10 )) − (−20) * (− 20 * 30 − 0) + 0(KK) = 39000

+ 10 1 I1 = − 20 ∆ − 15



 W‫א‬‫א‬‫א‬، I1 

− 20 − 0 + 60 − 10 − 10 +30

 W‫א‬ ∴ I1 =

1 {10 * (60 * 30 − 100) − (−20) * (− 20 * 30 − 15 * 10)} = 0.05128A 39000

 W + 30 +10 + 30 + 10 − 0 0 1 1 − 20 − 20 − 10 = ⋅ − 20 − 20 − 10 I2 = ∆ 39000 −0 − 15 + 30 −0 − 15 + 30

 W‫א‬‫א‬‫א‬

I2 =

1 {30 * ((−20) * (30) − (−15) * (−10)) − (10) * ((−20) * (30) − (0))} 39000

I 2 = −0.423A

 K‫א‬‫א‬‫א‬‫א‬‫א‬  W

+ 30 − 20 + 10 1 I3 = − 20 + 60 − 20 ∆ − 0 − 10 − 15

 WI٣‫א‬ ∆ ‫א‬‫א‬‫א‬ I3 =

1 { 30 * ((60) * (−15) − (−10) * (−20)) − (−20) * ((−20) * (−15) 39000 − (−10) * (10)) =

I 3 = −0.641A - ١٦٣ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 K‫א‬‫א‬‫א‬‫א‬‫א‬  W I 5 ، I 4  I 3 ، I 2 ، I1 ‫א‬‫א‬‫א‬‫א‬ I 4 = I 2 − I 3 = 0.218A I 5 = I1 − I 2 = 0.05128 + 0.42300 = 0.47428A

‫א‬‫א‬‫א‬W  K‫א‬‫א‬‫א‬‫א‬‫א‬

 "Summary"‫א‬

 K‫א‬‫א‬‫א‬‫א‬ KCL  E١F

‫א‬‫א‬ KVL  E٢F  K‫א‬

 K E٣F  K‫א‬‫א‬‫א‬‫ א‬E٤F

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٥F

   ‫א‬‫א‬‫א‬‫א‬ ‫א‬ E٦F ،‫א‬‫א‬‫א‬   ‫א‬‫א‬    ‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬E٧F  K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ E٨F K‫א‬‫א‬‫א‬‫א‬ R Th ‫א‬‫א‬ VTh 

 

- ١٦٤ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 ‫א‬‫א‬



 K R S = 50Ω ، VS = 300V E١F   K‫א‬‫א‬‫א‬‫א‬‫א‬E٢F 

2 .2 Ω

100Ω

5kV



12V

   

 K R S = 1.2KΩ ، iS = 600mA ‫א‬‫א‬E٣F 

 K‫א‬‫א‬‫א‬‫א‬E٤F 

0.01A

10mA

2.7 kΩ

I

I



4 .7 k Ω

  

 K‫א‬‫א‬‫א‬ R 5 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥F R1 = 1kΩ

2V



R 3 = 1kΩ

 R 2 = 2 .2 k Ω

R 4 = 1kΩ

3V - ١٦٥ -

 R5

  

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 W‫א‬‫א‬ R 3 ‫א‬‫א‬‫א‬‫א‬‫א‬E٦F 

R 3 = 330Ω R 1 = 680Ω 100mA



R 2 = 220Ω

R 4 = 470Ω

I

 

20V

  

 K R L ‫א‬‫א‬‫א‬‫א‬ E٧F  40V

1kΩ

8.2kΩ



560Ω

 R 5 = 1 .5 k Ω

I

0 .5 A



60V

1kΩ

 

 ‫א‬‫א‬ R L ‫א‬‫א‬‫א‬E٨F A

R 2 = 820Ω

R 1 = 1kΩ

R L = 1kΩ

VS = 12V

C

D

R 3 = 2.2kΩ

R 4 = 1.2kΩ B - ١٦٦ -

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬

‫ א‬١٤٠

‫א‬

١-



 W‫א‬‫א‬‫א‬ AB ‫א‬E٩F   R 1 = 10Ω + 10V −

R 2 = 15kΩ

 

A

R 3 = 12kΩ

B

I = 0.2mA

R4

    

 

- ١٦٧ -

‫א‬‫א‬

 ‫ א‬١٤٠

‫א‬

 ١-



 (References) ‫א‬‫א‬ 

[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, ١١٠٠٥٥, ١٩٩٥. [٣] M. A. PAI, "Introduction to Electric Circuits and Machines", Affiliated east west presses private limited, ١٩٧٥.

- ١٦٨ -

 ‫א‬ 

 ‫ א‬١٤٠

‫א‬

 ١-



 ‫א‬ ‫א‬

 ‫א‬



 



‫א‬‫א‬‫א‬W‫א‬‫א‬

  ٢  ٢  ٢  ٣  ٣  ٤  ٤  ٦  ٧  ٧  ٩  ١٠  ١٢   ١٤  ١٥  ١٥

 ‫א‬‫א‬‫א‬‫א‬  ١J ١

 ‫א‬‫א‬‫א‬٢J ١  ‫א‬‫א‬١J ٢J ١  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ١  ‫א‬‫א‬‫א‬٣J ١  ‫א‬١J ٣J ١  ‫א‬٢J ٣J ١  ‫א‬٣J ٣J ١  ‫א‬٤J ٣J ١  ‫א‬‫א‬٥J ٣J ١  ‫א‬‫א‬٦J ٣J ١  ‫א‬٧J ٣J ١  ‫א‬‫א‬  W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١J ٢  ٢J ٢

 ١٥  ١٦

 ‫א‬EF١J ٢J ٢

 ١٨

 ٣J ٢J ٢

 ‫א‬٢J ٢J ٢

 ‫א‬ 

 ‫ א‬١٤٠

‫א‬

 ١-



 ١٨

 ‫א‬١J ٣J ٢J ٢

 ١٩

 ‫א‬٢J ٣J ٢J ٢  ‫א‬‫א‬

 ٢١ 

 ‫א‬‫א‬W‫א‬‫א‬

 ٢٤

 ‫א‬‫א‬‫א‬‫א‬  ١J ٣

 ٢٥  ٢٥  ٢٨

 ‫א‬٢J ٣  ‫א‬‫א‬‫א‬‫א‬٣J ٣  ‫א‬‫א‬

 ٣٢   ٣٣  ٣٤

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬  ١J ٤

 ٣٤

 ‫א‬‫א‬‫א‬٢J ٤

 ٣٥

 ‫א‬‫א‬١J ٢J ٤

 ٣٦

 ‫א‬‫א‬‫א‬٣J ٤

 ٣٩

 ‫א‬‫א‬‫א‬٤J ٤

 ٤١

 ٤٤  ٤٤



٥J ٤

  ٦J ٤  ‫א‬٧J ٤

 ٤٦

 ‫א‬‫א‬‫א‬١J ٧J ٤

 ٤٩

 ‫א‬‫א‬‫א‬‫א‬٨J ٤

 ٥٢

 ‫א‬٩J ٤

 ٥٦

 ‫א‬‫א‬١٠J ٤

 ٦٠

 ‫א‬‫א‬‫א‬

  ٦٧

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬

 ‫א‬ 

 ‫ א‬١٤٠

‫א‬

 ١-



 ٦٨

 ١J ٥

 ٦٩

 ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥

 ٧٠

 ٣J ٥

 ٧٢

 ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٥

 ٧٥

 ‫א‬‫א‬‫א‬‫א‬١J ٤J ٥

 ٧٦

 ‫א‬‫א‬‫א‬٥J ٥

 ٧٩

 ‫א‬‫א‬‫א‬‫א‬EF٦J ٥

 ٨٦

 ‫א‬‫א‬‫א‬‫א‬٧J ٥

 ٨٩

 ‫א‬‫א‬



 ‫א‬‫א‬‫א‬W‫א‬‫א‬

 ٩١

 ‫א‬‫א‬‫א‬‫א‬   ١J ٦

 ٩٢  ٩٢  ٩٧  ١٠١  ١٠٨

 ‫א‬‫א‬–‫א‬‫א‬٢J ٦  ‫א‬‫א‬–‫א‬‫א‬‫א‬٣J ٦  ‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٦  ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ٦  ‫א‬‫א‬

 ١١٨   ١٢٣  ١٢٤

 ١٢٤  ١٢٤

 ١٢٨

 ‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١J ٧

 ‫א‬‫א‬‫א‬‫א‬٢J ٧ 

‫א‬‫א‬١J ٢J ٧

 ٢J ٢J ٧

 ١٢٨

 ‫א‬٣J ٢J ٧

 ١٣٠

 ‫א‬٣J ٧

 ١٣٦

 ٤J ٧

 ‫א‬ 

 ‫ א‬١٤٠

‫א‬

 ١-



 ١٤٤

 ‫א‬‫א‬١J ٤J ٧

 ١٤٨

 J ‫א‬–‫א‬٥J ٧

 ١٥٠  ١٥٠

 E Y ← ∆ F‫א‬‫א‬‫א‬‫א‬١J ٥J ٧  E ∆ ← Y F‫א‬‫א‬‫א‬٢J ٥J ٧

 ١٥٤

 ∆ ← Y  Y ← ∆ ‫א‬‫א‬‫א‬٣J ٥J ٧

 ١٥٧

‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٦J ٧

 ١٦٥

 ‫א‬‫א‬

 ١٦٨

 K‫א‬‫א‬

 KE‫א‬

 ‫א‬‫א‬

 



      

  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬ GOTEVOT appreciates the financial support provided by BAE SYSTEMS