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Ele140 Ele140 Document Transcript

  •  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬  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  ‫א‬‫א‬‫א‬‫א‬      
  •    ١٤٠ ‫א‬  ١-   ‫א‬  ،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]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ١ J  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ١
  • ‫א‬‫א‬  ‫٠٤١ א‬ ‫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  ‫٠٤١ א‬ ‫א‬‫א‬‫א‬ ‫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  ‫٠٤١ א‬  ١- ‫א‬‫א‬‫א‬ ‫א‬  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 Pico  n  1 *101 Milli Deci  da  1 * 103 Nano  k  1 *102  h  1 *106  M  1 *1012 Deka  T  1 *109 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  ‫٠٤١ א‬ ‫א‬‫א‬‫א‬ ‫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  ‫٠٤١ א‬  ١- ‫א‬‫א‬‫א‬ ‫א‬   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  ‫٠٤١ א‬  ١-  current ( I ) ‫א‬‫א‬‫א‬ ‫א‬ 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  ‫٠٤١ א‬  ١- ‫א‬‫א‬‫א‬ ‫א‬   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  ‫٠٤١ א‬ ‫א‬‫א‬‫א‬ ‫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K5m‫א‬،5mm‫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  ‫٠٤١ א‬  ١- ‫א‬‫א‬‫א‬ ‫א‬  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   K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬  K١ K٢  ‫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  K٣ W‫א‬‫א‬‫א‬‫א‬WLinear Resistors‫א‬‫א‬ K٤ K‫א‬‫א‬‫א‬،VDR  KW‫א‬‫א‬ K  ‫א‬‫א‬‫א‬W‫א‬‫ א‬K   ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬  W -٩-
  •  ‫א‬‫א‬  ‫٠٤١ א‬  ١- ‫א‬‫א‬‫א‬ ‫א‬  ‫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 1 + 2 1 2 V13 3  V23  EF +      ‫א‬‫א‬E٧J ١F  EF 3 -   Conductance‫א‬  ٦J ٣J ١ ‫א‬‫א‬،‫א‬‫א‬‫א‬ ،Ampere per Volt‫א‬SiemensG G=  W‫א‬ 1 R E٥J ١F  KSiemens -١٠-
  •  ‫א‬‫א‬ ‫א‬‫א‬‫א‬ R=  ‫٠٤١ א‬ ‫א‬  ١-   W 1  G E٦J ١F  .Ohm  K‫א‬‫א‬G‫א‬                  -١١-
  •  ‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫٠٤١ א‬ ‫א‬  ١-   ‫א‬‫א‬  :‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K١  29000 kWE  Ω 7000E  0.0003 msE 0.05 AE 0.00009 VE 7000000 VE 0.000000008 sE 9000 kWE W K٢  A15mAE  s0.1 nsE  mA µA 800E  A13 nAE  W‫ א‬K٣ µA 800H15mAE  13 msH0.1 nsE 1A+  µA 800E  7000 µA+13 nAE  WA - B‫ א‬K٤ µA B=800،A=15mAE  B=13 ns A=0.1 msE B= 1000 nA ، µA A=800E  B=7000 µV،A=13mVE -١٢-
  •  ‫א‬‫א‬ ‫א‬‫א‬‫א‬  ‫٠٤١ א‬ ‫א‬  ١-   A ‫ א‬K٥ B µA B=800،A=15mAE W   B=13 ns A=0.1 msE B= 1000 nA ، µA A=800E  B=7000 µV،A=13mVE -١٣-
  •  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ١ J    ٢
  • ‫א‬‫א‬  ‫٠٤١ 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‫א‬‫א‬ • - ١٤ -
  • ‫א‬‫א‬  ‫٠٤١ א‬ ‫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   Slope = R + 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  ‫٠٤١ א‬ ‫א‬   ١-   E١J ٢F ،50V‫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  ‫٠٤١ א‬ ‫א‬   ١-   E٢J ٢F  ، 75µA  ‫א‬،150mV  ‫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  K30V‫א‬‫א‬0.5 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  ‫٠٤١ א‬ ‫א‬   ١-   E٤J ٢F ‫א‬،10mAR1‫א‬‫א‬‫א‬‫א‬‫א‬  ‫؟‬‫א‬‫א‬،25 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  ‫٠٤١ א‬ ‫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  0.1A‫א‬  ‫א‬ E = I T .R T = 0.1 * 500 = 50 V  E٦J ٢F  3mA‫א‬‫א‬ 27KΩ ‫א‬،‫א‬‫א‬  ‫א‬ E = I T .R T = 3 * 10 −3 * 27 * 10 3 = 81 V  E٧J ٢F  0.8mA‫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  ‫٠٤١ א‬ ‫א‬   ١-     V R I  E٥J ٢F   W‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬ E٥J ٢F          I = E٦J ٢F E٧J ٢F V = I*R          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  ‫٠٤١ א‬ ‫א‬   ١-   ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ K١   W  K‫א‬  F E E K75%‫א‬  F K‫א‬  F E E K35%‫א‬  F K‫א‬‫א‬‫א‬‫א‬ F E  K‫א‬‫א‬‫א‬‫א‬ EF   W‫א‬،‫א‬‫א‬ K٢ E  V = 5V , R = 1Ω  F E V = 15V , R = 10Ω  F  V = 50V , R = 100Ω  F E E  V = 30V , R = 15KΩ  F E  V = 250V , R = 5.6MΩ  F ‫؟‬‫א‬‫א‬‫א‬،12V10KΩ  K٣ ،J J J W‫א‬‫א‬‫א‬ K٤  K12V‫א‬‫א‬‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬،25V K٥  KJ J J W‫א‬‫א‬‫א‬ - ٢١ -
  • ‫א‬‫א‬  ‫٠٤١ א‬ ‫א‬   ١-  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٦   8Ω ‫א‬‫א‬،‫א‬‫א‬‫א‬  W‫א‬  Fuse R 120V V 100V    ،‫א‬‫א‬‫א‬Fuse‫א‬   ‫؟‬100 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،3A 27Ω ‫א‬‫א‬ K٨ ‫؟‬‫א‬K W‫א‬‫א‬I‫א‬،V‫א‬‫א‬ K٩  I = 2A ,  I = 45A ,  I = 5A , - ٢٢ - V = 10V EF V = 90V EF V = 50V EF 
  • ‫א‬‫א‬  ‫٠٤١ א‬ ‫א‬   ١-    R = 100Ω ‫א‬،‫א‬‫א‬‫א‬‫א‬ K١٠  ‫א‬‫א‬‫א‬،‫א‬Variable Voltage Source ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K100 V‫א‬‫א‬ ‫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 E  V = 1.5V  F V = 2V  F E E  V = 3V  F E  V = 4V  F  V = 10V  F E K‫א‬‫א‬،I‫א‬V‫א‬،‫א‬ ، ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ K١٢  K R = 3.3kΩ R = 3.9kΩ 75V 50V R = 4.7 kΩ 100V - ٢٣ -    
  •  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ١ J  ‫א‬‫א‬ ‫א‬‫א‬ ٣
  •  ‫א‬‫א‬ ‫א‬‫א‬  ‫٠٤١ 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‫א‬‫א‬‫א‬‫א‬ • - ٢٤ -
  •  ‫٠٤١ א‬ ‫א‬‫א‬ ‫א‬  ١-  ‫א‬‫א‬  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 ‫٢ א‬J 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  KWatt‫א‬Power‫א‬  K Watt ⋅ second ⋅‫א‬‫א‬JEnergy‫א‬  Ksecondtime‫א‬  W  W 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  ‫٠٤١ א‬ ‫א‬  ١-   E١J ٣F  ‫؟‬‫א‬‫א‬،5 sec‫א‬100 J‫א‬‫א‬   ‫א‬ Power = Energy E 100 J = = = 20 Watt t 5 sec time  W‫א‬  E٢J ٣F  ‫؟‬‫א‬Kt = 30 sec‫א‬‫א‬‫א‬،P = 100 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  0.045 W EF  0.000012 W EF  3500 W EF   000 W، 000،10 EF   ‫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=0.045 W EF  -٢٦-
  •  ‫א‬‫א‬ ‫א‬‫א‬  ‫٠٤١ א‬ ‫א‬  ١-   W P = 0.045 W = 0.045 * 10 3 * 10 −3 W = 45 * 10 −3 = 45 mW ‫א‬،‫א‬‫א‬،P=0.000012 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=3500 W EF  P = 3500 W = 3500 * 10 −3 * 10 3 W = 3.5 kW WMW‫א‬P=10,000,000 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1400 WEF  K2500 WEF  K1000,000 WEF  ‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ -٢٧-
  •  ‫٠٤١ א‬ ‫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
  •  ‫٠٤١ א‬ ‫א‬‫א‬ ‫א‬  ١-  ‫א‬‫א‬   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=0.7AEF  I=1.4AEF  I=2.1AEF -٢٩-
  •  ‫٠٤١ א‬ ‫א‬‫א‬ ‫א‬  ١-  ‫א‬‫א‬   ‫א‬  W‫א‬‫א‬  P = I2 .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 = 19.6Watt ← I = 1.4A EF   KEF‫א‬EF‫א‬EF  E٦J ٣F ،15 V10 kΩ ‫א‬‫א‬،E٢J ٣F‫א‬  ‫؟‬12 kΩ ‫א‬‫א‬ 12 kΩ  + V  I -  + 10kΩ 15V −  E٦J ٣F‫א‬‫א‬‫א‬E٢J ٣F -٣٠-   
  •  ‫٠٤١ א‬ ‫א‬‫א‬ ‫א‬  ١-  ‫א‬‫א‬   ‫א‬  W‫א‬‫א‬‫א‬‫א‬ I= V 15 15 = = 4 = 1.5 mA R 10 * 10 3 10  W12 kΩ ‫א‬‫א‬‫א‬ V = I*R = 1.5 * 10 −3 * 12 * 10 3 = 12 V  KV=12 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  ‫٠٤١ א‬ ‫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   3750w EF  kw ‫א‬‫א‬‫א‬–٤   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]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١ J ٤
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 R1 R1 R1 a a R2 a R2 R2 I  R3 R3 R3 b      b R4 b I I  ‫א‬‫א‬‫א‬E١J ٤F - ٣٤ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 R3 = 27 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 ‫٠٤١ א‬ ‫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 = 20 V R3 =3.9 kΩ  + V=? _      E٣J ٤F‫א‬‫א‬‫א‬E٣J ٤F  ‫א‬  I‫א‬،‫א‬ R2،R1‫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  6.19 VR3‫א‬‫א‬∴  E٤J ٤F KVs،‫א‬‫א‬‫א‬‫א‬  K 5mA Fuse‫א‬ Vs‫א‬ - ٣٦ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   5 mA Fuse + VS R 1 = 1 kΩ R 2 = 3.3 kΩ 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 = 4.7V  KRTVS‫א‬ ∴ R T = 1 + 3.3 + 4.7 = 9KΩ  VS = 1 * 10 −3 * 9 * 10 3 = 9V  WVSV1،V2 ،V3   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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-  5mA‫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 kΩ 1.2 kΩ I    1.2 kΩ  5.6 kΩ  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 ‫٠٤١ א‬ ‫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 E2،E1‫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 E1،E2‫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 ‫٠٤١ א‬ ‫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 E1،E2‫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 ‫٠٤١ א‬ ‫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 1.5V 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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   R4 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 + VS + 5V - −  + 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 ‫٠٤١ א‬ ‫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=100 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 ‫٠٤١ א‬ ‫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 R2 R1 I3   R4  I2  R3   ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-    − V1 + R1 + VS  I  + V2 R2 −   _   ‫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 15 3 ∴ V1 = V2 = IR 2 = 1 1 * 100 = (20 ) V 15 3 ∴ V2 = - ٤٥ - 1 (10) V 3 2 (10) V 3
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 R1 V1 + − V2 + −  R4 R3 R2 V3 + −  V4 + −  I    VS + −   ‫א‬‫א‬E١٤J ٤F  ،‫א‬ X  VX ‫א‬‫א‬ VX = IR X   4 ، 3، 2،1‫א‬ x W    W‫א‬‫א‬‫א‬  I= VS RT   VX ‫א‬ I ‫א‬ V  VX =  S R X R   T  W VX ‫א‬  RX  V RT  S    VX =    - ٤٦ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   E١١J ٤F  ‫؟‬‫א‬‫א‬‫א‬ V2 ‫א‬ V1 ‫א‬  + R 1 = 100Ω + V1 − VS = 10 V − + R 2 = 56 Ω V2 −  E١١J ٤F‫א‬‫א‬‫א‬E١٥J ٤F         ‫א‬  ‫א‬‫א‬ V2 ، V1  R  VX =  X VS R   T   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  V2 =  2 VS = * 10 = 3.59V R  156  T  ‫א‬  V2 = VS − V1 = 10 − 6.41 = 3.59V - ٤٧ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 R1 = 1kΩ    VS = 25V B R2 = 8.2kΩ  C   R3 = 3.3kΩ  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  R1  RT  VAB =    VAB =  VS   1 * 25 = 2V 12.5  ∴ VAB = 2V - ٤٨ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 R   T  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‫٨ א‬J 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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-  2) PT = I 2 R T 2 VS 3) PT = RT   E١٣J ٤F  W‫א‬‫א‬‫א‬‫א‬‫א‬ R2 = 18 Ω R3 = 56 Ω VS = 15 V R4 = 22 Ω  E١٣J ٤F‫א‬‫א‬‫א‬E١٧J ٤F  ‫א‬  K‫א‬‫א‬ R T = 10 + 18 + 56 + 22 = 106 Ω  W‫א‬E3F‫א‬‫א‬‫א‬‫א‬ 2 VS (15)2  ∴ PT = = = 2.12 W RT 106 ∴ PT = 2.12 W - ٥٠ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   E١٤J ٤F ،0.5 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫؟‬‫א‬‫א‬‫א‬ R1 = 1kΩ  R2 = 2.7kΩ  R3 = 910Ω VS = 120 V R4 = 3.3kΩ  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 ‫٠٤١ א‬ ‫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1w‫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،100V‫א‬‫א‬‫א‬  KCircuit Ground‫א‬‫א‬‫א‬100V‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ،‫א‬Ground‫א‬‫א‬‫א‬‫א‬  KE١٩J ٤F - ٥٢ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   + R1 + V2 a  V1  − −   + R2 V2   V  −    ‫א‬‫א‬E١٩J ٤F  Note  a‫א‬‫א‬  E١٥J ٤F ،‫א‬‫א‬‫א‬‫א‬‫א‬   K25 VVoltage Dropped ‫א‬‫א‬ + − + + − c a b + + 100V a + − + b   − − e + −   − − (a) (b)  E١٥J ٤F‫א‬‫א‬‫א‬ b)،(aE٢٠J ٤F - ٥٣ - +  − d e d  c  + 100V −   
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   + a + − C c b + 100V − − 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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 - ٥٦ -
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   ‫א‬‫א‬‫א‬ K A, B ‫א‬‫א‬‫א‬‫א‬‫א‬ K١ R1 A A B    R2 R1 R2  R3 R3  B    A R2 R1 B R4 R3 R5      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  R3 5 mA  A   − R1    A R2 - ٦٠ - 
  • ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 3 = 12 Ω    R4 =1Ω  R 3 = 2.2 kΩ  ( b) (a )   R 2 = 10 Ω R1 = 4.7 Ω R 1 = 25.6 kΩ     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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 R1 +   R2 VS = 15V    −   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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 VS2 ‫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 +  R2 VS = 48V  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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   A  100 Ω +  56 Ω 12V  −   B     1kΩ A + 2.2kΩ 8V − 3.3kΩ B b - ٦٦ -  
  •  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ١ J  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٥
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   I1 A R1 I A I2 I1 R2 R1 I R2 B I2 B R3 I2  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 = R2 = 1.8kΩ 1kΩ F R3 = 2.2kΩ   R4 = 2.2kΩ  KE١J ٥F‫א‬‫א‬‫א‬E٢J ٥F R5 =  3.3kΩ    ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬   W‫א‬‫א‬‫א‬  V1 = V2 = V3 = V4 = V5 = VS = 25V - ٦٩ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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    I1 = 5mA + VS − I 2 = 12mA R1 IT 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 = 17mA ∴ I T = 17mA  - ٧٠ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 + VS R1 − IT y x    I3  R2 I1 = 1.5A R3 I 2 = 1A  KE٤J ٥F‫א‬‫א‬‫א‬E٥J ٥F - ٧١ -   
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 = 2.5A  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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-   I1 R1  I2 R2     R3 I3   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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 = RTR A 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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-  I1 I2  R1 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 ‫٠٤١ א‬ ‫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  K‫א‬‫א‬‫א‬‫א‬ W ‫א‬‫א‬‫א‬ X ‫א‬ X ‫א‬‫א‬ W  K‫א‬ - ٨١ - RT RX IX
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 220 R3 - ٨٢ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬    W IT I1 R1  I2 R2      K‫א‬‫א‬‫א‬‫א‬E١٤J ٥F  I1 = I T RT = RT R1 WE٥J ٥F‫א‬E٢٣J ٥F‫א‬‫א‬ E٢٣J ٥F   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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 2 I T .R T V2 = RT       K‫א‬‫א‬‫א‬‫א‬E١٦J ٥F PT = V.I =  E٣٣J ٥F  W‫א‬ 2 P1 = I1 .R 1 E٣٤J ٥F P2 = I 2 .R 2 2 E٣٥J ٥F 2 P3 = I 3 .R 3 E٣٧J ٥F PT = P1 + P2 + P3 E٣٨J ٥F  KWatt‫א‬ - ٨٦ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 2 Q PT = I T .R T = (2) 2 * 11.1 = 44.4W ∴ PT = 44.4 W ‫א‬K‫א‬‫א‬‫א‬   K‫א‬ VS = I.R T = 2 * 11.1 = 22.2V 2 VS (22.2) 2 P1 = = = 7.25W R1 68 - ٨٧ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ١-  2 VS (22.2) 2 P2 = = = 14.9 W R2 33 2 VS (22.2) 2 P3 = = = 22.4 W R3 22 Q PT = P1 + P2 + P3 = 7.25 + 14.9 + 22.4 ∴ PT = 44.6 W  KE‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬               - ٨٨ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ١ J  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ٦
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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  R2  R1  R3 R6 R8 R5  R4   R7  R9   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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-   IT + VS = 22V  R1 = 1kΩ  R 2 = 2.2kΩ 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 I 2 = 9.48mA * I 3 = 9.48mA * - ٩٩ - 3.3kΩ = 5.69mA 5.5kΩ 2.2kΩ = 3.79mA 5.5kΩ
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-   W‫א‬‫א‬  R3 I4 = I2  R + R 4  3   = 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 + VS = 80V R 2 = 560 Ω − R 3 = 560 Ω 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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 = 2.2kΩ − 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  R + R  1 2      2.2kΩ  = 1mA  = 688µA  1kΩ + 2.2kΩ   ∴ I1 = 688µA   R1 ‫א‬‫א‬‫א‬  V1 = I1 .R 1 = 688µA * 1kΩ  V1 = 688mV ∴ - ١٠٣ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-   W‫א‬ R 3 ‫א‬ I 3 ‫א‬   R 4 + R5    R 3 + (R 4 + R 5 )   I3 = I T    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 ‫٠٤١ א‬ ‫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 5 = 680Ω R 6 = 390Ω R 4 = 1kΩ   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 R4 + R5 + R6 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE١٦J ٦F - ١٠٥ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-   R AB = 2.15kΩ + VS = 8V R 3 = 1kΩ − R CD = 517Ω       KE١١J ٦F‫א‬‫א‬‫א‬E١٦J ٦F W‫א‬‫א‬‫א‬‫א‬ R  VAB =  AB VS = 4.69V  R   T  R VCD =  CD  R  T  VS = 1.13V   R  V3 =  3 VS = 2.18V R   T  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 =  R + R 6  5  VCD = 718mV    R6 V6 =  R + R 6  5  VCD = 412mV   - ١٠٦ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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  I T = I b + Id + I L  ‫א‬‫א‬‫א‬‫א‬‫٥ א‬J 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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 = I 3 + I 4 + I5  ، 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 5.6k ∴ 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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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   RT     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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-   ‫א‬    W‫א‬‫א‬‫א‬‫א‬‫א‬J ١ R1 A 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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-  1kΩ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬–٤   ‫א‬‫א‬، 2.2kΩ ‫א‬‫א‬‫א‬،‫א‬‫א‬   ،6V1kΩ ‫א‬‫א‬  V1 = 6V 1kΩ 1kΩ 2.2kΩ     : 2.2kΩ ‫א‬‫א‬‫א‬  3VEF6VEF  13.2VEF 12V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 ‫٠٤١ א‬ ‫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  31.3% EF  W1kΩ 50%EF 25%EF100%EF  ‫א‬F‫א‬9V‫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 ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫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 = 6.2kΩ R 1 = 1kΩ 180Ω   (b) + 5V − R4       
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 + A  W‫א‬‫א‬‫א‬‫א‬K٤  4.7 kΩ B  10kΩ 5.6kΩ + 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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-   W‫א‬‫א‬J ٦ R2 P = 20 W 4A + 40V − R4 R3  P = 2W R1 20V  R5 1A 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 = 5.6kΩ RL R 3 = 2.7 kΩ 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 ‫٠٤١ א‬ ‫א‬ ‫א‬‫א‬‫א‬ ١-  56Ω + 60V −  56Ω   910Ω  1kΩ A 1kΩ 560kΩ B 1kΩ  560kΩ 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 R1 = 5.6kΩ 18V A R 3 = 1kΩ R 2 = 2.2kΩ B  R 5 = 1kΩ R 4 = 2.2kΩ  R 6 = 1kΩ    ‫א‬‫א‬‫א‬‫א‬ A, B ‫א‬‫א‬‫א‬‫א‬ J ١٠  W‫א‬ - ١٢١ -
  • ‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ،10V 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 R1 VC R4 B VB  R5 A   + 100V −  C - ١٢٢ - 
  •  ‫א‬‫א‬‫א‬ ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹] ‫א‬‫א‬‫א‬‫א‬ ١ J  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ٧
  •  ‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫٠٤١ א‬ ‫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 ‫٠٤١ א‬ ‫א‬‫א‬‫א‬ ‫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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   A A + VS iL RS RL − ≡   iL 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  IL =   R + R iS  L  S E٤J ٧F  WE٤J ٧FE٣J ٧F‫א‬‫א‬  VS = R S ⋅ i S E٥J ٧F - ١٢٦ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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  IL =   R + R iS  L  S  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 IL ‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬‫א‬‫א‬‫א‬ R S ‫א‬ - ١٢٧ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   E٢J ٧F  K I L = 750mA ‫א‬ R L ،‫א‬‫א‬‫א‬  A  iL i S = 1A R S = 10kΩ I  RL B      KE٢J ٧F‫א‬‫א‬‫א‬E٥J ٧F  ‫א‬  RS  IL =   R + R iS  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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   E٣J ٧F  K‫א‬E٦J ٧F‫א‬‫א‬‫א‬ A + VS = 100V R S = 50Ω   −  B  KE٣J ٧F‫א‬‫א‬‫א‬E٦J ٧F iS =  VS 100 = = 2A R S 50 - ١٢٩ -   ‫א‬
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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   ♦ ‫א‬‫א‬، R S ‫א‬‫א‬،‫א‬‫א‬ ♦  KShort Circuit‫א‬‫א‬ Open-Circuit‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬،E٨J ٧F‫א‬‫א‬‫א‬  K - ١٣٠ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ R1 ‫א‬   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 R1 R3 + R1 R2 R3 b b  K‫א‬‫א‬‫א‬E٩J ٧F - ١٣١ -   +  VS2   
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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10 V‫א‬‫א‬W‫א‬‫א‬‫א‬ a + 10V − R1 = 100Ω R 3 = 100Ω R 2 = 100Ω b  KE٣J ٧F‫א‬‫א‬‫א‬10 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   W‫א‬‫א‬ab‫א‬‫א‬‫א‬ Iab = 66.7 * 100 = 33.3mA 100 + 100 KE١٢J ٧F5 V‫א‬‫א‬W‫א‬‫א‬‫א‬   a R1 = 100Ω R 3 = 100Ω R 2 = 100Ω  + 5V −    b   KE٣J ٧F‫א‬‫א‬‫א‬5 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  R + R  1 2 I ab = 33.3 *     100 = 16.7 mA 100 + 100 - ١٣٣ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 + 10V −  R1 = 220Ω R 2 = 100Ω A i S = 100mA b  KE٥J ٧F‫א‬‫א‬‫א‬E١٣J ٧F  ‫א‬  K‫א‬‫א‬‫א‬  KE١٤J ٧F10 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   K 31.2mA 10V ‫א‬ R 2 ‫א‬‫א‬‫א‬∴ KE١٥J ٧F100 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   ‫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 5V ‫א‬‫א‬a    W Va ‫א‬ Va = 5 + I * 8 Va = 5 + 8 *8 12 Va = 5 + 3.33 ≈ 8.33V - ١٣٨ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 IT1 + 10V −  a R 1 = 4Ω R 2 = 8Ω Iab1 R 3 = 6Ω       b  KE٧J ٧F‫א‬‫א‬‫א‬10 V‫א‬‫א‬E٢٢J ٧F  WIab1‫א‬ - ١٤٠ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ RT = 4 + i T1 = ‫א‬  8*6 = 7.43Ω 8+6 10 = 1.345A 7.43 i ab1 = 1.345 * 8 = 0.77A 8+6   KE٢٣J ٧F، E 2 ‫א‬‫א‬W‫א‬‫א‬‫א‬  IT2 a R 1 = 4Ω R 2 = 8Ω Iab2 R 3 = 6Ω b  + 5V −       KE٧J ٧F‫א‬‫א‬‫א‬ 5 V‫א‬‫א‬E٢٣J ٧F  WIab2‫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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   K‫א‬W   KEJ ٢٥J ٧F‫א‬‫א‬ VTh  R L ‫א‬W‫א‬‫א‬  12kΩ a  I=0 2mA ⇐ 10kΩ I VTh     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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬    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 2 20 20V = = 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬  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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   ‫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 −  VTh =   R + R VS  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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 R2 B ⇐ 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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  3.5 mACD‫א‬‫א‬‫ ∴א‬  J ‫א‬–‫א‬ ٥J ٧ E Y ← ∆ F‫א‬‫א‬‫א‬‫١ א‬J 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   Kc،b،aC،B،A ∆ ‫א‬  K3،2،1 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬  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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬    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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   ‫א‬ ،E٣٨J ٧F، Y ‫א‬ ∆ ‫א‬  K ∆ ← Y ‫א‬  A   1kΩ RB 2.2kΩ B O RC  RA   5.6kΩ 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬  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 = 3.9kΩ  D R 3 = 2.2kΩ   R 4 = 2.7kΩ    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 = 2.2kΩ C D ≡ R 4 = 2.7kΩ B R2 R1 o R3 B  KE١٢J ٧F‫א‬‫א‬‫א‬E٤٠J ٧F - ١٥٤ - D  
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 = 3.9kΩ     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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   A + 120V −  I2 I1 4.7 kΩ 3.9kΩ 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬  ∴ R T = 3.37KΩ 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬Mesh   K‫א‬b،a‫א‬‫א‬،E٤٣J ٧F‫א‬‫א‬‫א‬ a R1 V1 b R2  V2  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 E١F KCL‫א‬ Meshes ‫א‬‫א‬ E٢F K‫א‬‫א‬‫א‬KVL‫א‬ E٣F K‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ E٤F K‫א‬‫א‬‫א‬‫א‬‫א‬ E٦F Meshes.‫א‬‫א‬‫א‬‫א‬‫א‬ - ١٥٨ - E٥F
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   E١٣J ٧F ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE٤٤J ٧F‫א‬ I1 I2 b a 10Ω 10V I1 d c 20Ω 15V 20V 10Ω I4 I5  20Ω 30Ω I2  I3 I3     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) I4 = I2 − I3 (b) ‫א‬‫א‬‫א‬ I 3 ، I 2 ، I1 ‫א‬‫א‬   K‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   K‫א‬   Mesh E1F‫א‬‫א‬W‫א‬‫א‬ 10 = 10I1 + 20I 5 (c) - ١٥٩ - 
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   I1 + I2 EaF I 5    I 2 ، I1  I 5 KW ∴10 = 10I1 + 20I1 − 20I 2 10 = 30I1 − 20I 2 (d)  KEdF   Mesh E2F‫א‬‫א‬W‫א‬‫א‬ 20 = 30I2 + 20I5 − 10I4 (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 E3F‫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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬  10  + 30 − 20 = − 20    − 15  − 0    − 20 + 60 − 10 ‫א‬  −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E3F،MeshE2F،MeshE1F‫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E1F‫א‬‫א‬ R11  KMeshE2F‫א‬‫א‬ R 22  KMeshE3F‫א‬‫א‬ R 33   R12 ‫א‬‫א‬‫א‬‫א‬ E2F‫א‬‫א‬‫א‬ R 23 ‫א‬KMeshE2F،MeshE1F‫א‬‫א‬  K‫א‬‫א‬‫א‬،‫א‬MeshE3F‫א‬،Mesh ‫א‬‫א‬‫א‬MeshE3F‫א‬MeshE1F‫א‬   K‫א‬R13 - ١٦١ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬   K I 3 ، I 2 ، I1  ‫א‬‫א‬‫א‬  W‫א‬E١ R 11 R 12 R 13  ∆ = R 21 R 22 R 23 R 31 R 32 E١٧J ٧F 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 R 21 I3 = ∆ 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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬  ،‫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 0 + 30 + 10 − 0 + 30 +10 1 1 I2 = − 20 − 20 − 10 = ⋅ − 20 − 20 − 10 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I3‫א‬ ∆ ‫א‬‫א‬‫א‬ I3 = 1 { 30 * ((60) * (−15) − (−10) * (−20)) − (−20) * ((−20) * (−15) 39000 − (−10) * (10)) = I 3 = −0.641A - ١٦٣ -
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   ‫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 kΩ     K‫א‬‫א‬‫א‬ R 5 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E٥F R1 = 1kΩ 2V  R 3 = 1kΩ  R 2 = 2.2kΩ R 4 = 1kΩ 3V - ١٦٥ -  R5   
  •  ‫א‬‫א‬ ‫٠٤١ א‬ ١- ‫א‬‫א‬‫א‬ ‫א‬   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 = 1.5kΩ 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 ‫٠٤١ א‬ ‫א‬‫א‬‫א‬ ‫א‬ ١-   W‫א‬‫א‬‫א‬ AB ‫א‬E٩F   R 1 = 10Ω R 2 = 15kΩ + 10V −   A R 3 = 12kΩ B I = 0.2mA R4        - ١٦٧ -
  •  ‫٠٤١ א‬ ‫א‬  ١- ‫א‬‫א‬   (References) ‫א‬‫א‬  [1] Thomas L. Floyed, Electrical Engineering Fundamentals, Prentice, Inc, sixth edition, 2000. [2] B. L. Theraja, A. K. Theraja, " Electrical Technology", published by Ninja Construction development Co. Ltd. Ram Nagar, New Delhi, 110055, 1995. [3] M. A. PAI, "Introduction to Electric Circuits and Machines", Affiliated east west presses private limited, 1975. - ١٦٨ -
  •   ‫٠٤١ א‬ ‫א‬  ١-  ‫א‬   ‫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  ١٥  ١٦  ١٨  ‫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  ‫א‬EF١J ٢J ٢  ‫א‬٢J ٢J ٢  ٣J ٢J ٢
  •   ‫٠٤١ א‬ ‫א‬  ١-  ‫א‬   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  ٣٦  ‫א‬‫א‬‫א‬٣J ٤  ٣٥  ٣٩  ٤١  ٤٤  ٤٤  ‫א‬‫א‬١J ٢J ٤  ‫א‬‫א‬‫א‬٤J ٤  ٥J ٤   ٦J ٤  ‫א‬٧J ٤  ٤٦  ‫א‬‫א‬‫א‬١J ٧J ٤  ٥٢  ‫א‬٩J ٤  ٦٠  ‫א‬‫א‬‫א‬  ٤٩  ٥٦   ٦٧  ‫א‬‫א‬‫א‬‫א‬٨J ٤  ‫א‬‫א‬١٠J ٤  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬
  •   ‫٠٤١ א‬ ‫א‬  ١-  ‫א‬   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  ‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬  ١J ٧  ١٢٤  ‫א‬‫א‬‫א‬‫א‬٢J ٧  ١٢٨  ٢J ٢J ٧  ١٢٤  ‫א‬‫א‬١J ٢J ٧  ١٢٨  ‫א‬٣J ٢J ٧  ١٣٦  ٤J ٧  ١٣٠  ‫א‬٣J ٧
  •   ‫٠٤١ א‬ ‫א‬  ١-  ‫א‬   ١٤٤  ‫א‬‫א‬١J ٤J ٧  ١٥٠  E Y ← ∆ F‫א‬‫א‬‫א‬‫א‬١J 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  ١٤٨  ١٥٠  ١٦٨  J ‫א‬–‫א‬٥J ٧  E ∆ ← Y F‫א‬‫א‬‫א‬٢J ٥J ٧  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