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1نظرى المحولات MOTEUR DC +TRANSFO MONO وآلات التيار المستمر

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 ‫א‬‫א‬‫א‬
ã¹]<gè…‚jÖ]æ<ËÖ]<Üé×Ãj×Ö<íÚ^ÃÖ]<퉉ö¹]
‫א‬‫א‬‫א‬‫א‬
‫א‬
‫א‬‫א‬‫א‬
١٤٢
 ‫א‬
 ١٤٢
 
‫א‬
 ‫א‬‫א‬‫א‬
 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
W‫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

‫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
 K‫א‬‫א‬‫א‬‫א‬‫א‬

   W    ‫א‬ ‫א‬  ‫א‬    ‫א‬
 K‫א‬

 ‫א‬‫א‬‫א‬‫א‬






 
 ١٤٢
 
 ‫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K‫א‬‫א‬‫א‬
‫א‬    ‫א‬   K ‫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   K  
 ،‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬   ‫א‬ ‫א‬ K‫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‫א‬‫א‬‫א‬ K‫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   K‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬ 
 K‫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
 K‫א‬
 
 ١٤٢
 ‫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
‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬   ‫א‬       ‫א‬ K   ‫א‬ 
 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   ‫א‬     ،‫א‬  ‫א‬ ‫א‬ ‫א‬ 
‫א‬ ‫א‬ ‫א‬      ‫א‬  K‫א‬  ‫א‬
 K‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬‫• א‬
K‫א‬‫א‬‫א‬‫א‬‫• א‬
K‫א‬‫א‬‫א‬‫א‬‫• א‬
K‫א‬‫א‬‫א‬‫• א‬
K‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬
K‫א‬‫א‬‫א‬‫• א‬
K‫א‬‫א‬‫א‬‫א‬‫• א‬
 ‫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

١
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
.‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

 W‫א‬‫א‬W‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬ K١
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٢
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٣

 ٪٨٥‫א‬‫א‬W‫א‬‫א‬‫א‬

.٤ W‫א‬‫א‬

K W‫א‬‫א‬


.‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

-١-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬‫א‬
  ١J ١
‫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    (permanent magnet) ‫א‬‫א‬ ‫א‬
(Smarum   ‫ א‬ (Niodenum Boron Iron)    ،(ferrait)
F‫א‬‫א‬K‫א‬‫א‬‫א‬،cobalt)
‫א‬ ‫א‬ ‫א‬      ،‫א‬    E‫א‬‫א‬
‫א‬‫א‬ ،‫א‬،‫א‬
K‫א‬،‫א‬ ‫א‬
‫א‬K‫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     
K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

‫א‬‫א‬‫ א‬٢J ١
  ‫א‬ ‫א‬  ‫ א‬ E‫א‬F‫א‬  ،‫א‬ ‫א‬ 
 K‫א‬‫א‬K‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬ W‫א‬‫ א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬‫א‬
‫א‬K‫א‬‫א‬ 
 K‫א‬‫א‬
-٢-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫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  :(Permeability) µ‫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
 (Magnetic permeability)  ‫א‬ ‫א‬    µ   
K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬،(Magnetization curve)‫א‬
   ‫א‬  ،‫א‬ ‫א‬   ‫א‬ ‫א‬ ‫א‬  ‫א‬
‫א‬   ‫א‬ ‫א‬   K‫א‬    ،‫א‬  ‫א‬ ‫א‬
‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬
 W
١ ١
µ = µo µr
 ‫א‬‫א‬ (Absolute permeability)‫א‬‫א‬ µo
 W‫א‬‫א‬
µo=٤πx١٠ ٧ H/m
   ‫א‬   (Relative permeability) ‫א‬ ‫א‬   µr 
 
‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬ ‫א‬    : Ф ‫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K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

-٣-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬ :B‫א‬‫א‬J
 WEFL‫א‬
B=
Φ
A
wb / m 2
١-٢
K  :H‫א‬‫א‬J
 W‫א‬‫א‬‫א‬‫א‬‫א‬
H=
B
µ
h/m
١-٣
‫א‬‫א‬ :(Magneto-motive-force m.m.f) ‫א‬‫א‬‫א‬‫א‬‫א‬ N 
 K‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬   
(ampere.turn) K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
m.m.f=N.I
AT
 W
١-٤
‫א‬‫א‬ :(Magnetic reluctance) Rmag ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
Rmag =
m.m. f N .I
=
Φ
Φ
W‫א‬
AT / wb
١-٥
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
 µ ‫א‬  A   L ‫א‬  ‫א‬   ‫א‬ ،‫א‬
 W‫א‬
Rmag =
L
µA

١-٦
K   E F ‫א‬  ‫א‬   ‫א‬ ‫א‬
،‫א‬‫א‬‫א‬
  ‫א‬   K   ‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬
١J ١K‫א‬‫א‬‫א‬،
 K٢LBI‫א‬L

-٤-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬‫א‬  F‫א‬‫א‬‫א‬‫א‬


F=BLI

 W‫א‬‫א‬‫א‬
١-٧
‫א‬‫א‬،‫א‬‫א‬‫א‬  
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

 ١J ١

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١
‫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K‫א‬
‫א‬‫א‬    ،٦J ١ ‫א‬   E‫א‬ F ‫א‬ ‫א‬   
‫א‬‫א‬‫א‬‫א‬K
‫א‬   ٢J ١  K ‫א‬ ‫א‬‫א‬   ‫א‬  ‫א‬
K A,F‫א‬‫א‬ ABCDEF‫א‬ 
K‫א‬‫א‬ AB, BC, CD, DE, EF‫א‬‫א‬
 ΦEFKINCD‫א‬
-٥-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
  ٦J ١ ‫א‬ ‫א‬ K  ‫א‬‫א‬ ‫א‬  ‫א‬ ‫א‬  
 W‫א‬‫א‬‫א‬‫א‬

RmagAB =
LAB
µ AB AAB

RmagBC =
Rmag − gap =
LBC
µ BC ABC
RmagCD =
LCD
µ CD ACD
RmagDE =
LDE
µ DE ADE
Lgap
µ o Agap
RmagEF =
LEF
µEF AEF

 WRmag-t‫א‬‫א‬‫א‬
Rmag−t =
L
L
L
LAB
L
L
+ BC + CD + DE + EF + gap
µ AB AAB µ BC ABC µCD ACD µ DE ADE µ EF AEF µo Agap

١ ٨
N.IEF‫א‬‫א‬‫א‬‫א‬Ф‫א‬‫א‬‫א‬
 W‫א‬‫א‬٥J ١،Rmag-t‫א‬‫א‬‫א‬
Φ =
N.I
L
L
L
LAB
L
L
+ BC + CD + DE + EF + gap
µ AB AAB µ BC ABC µCD ACD µ DE ADE µ EF AEF µo Agap
١ ٩
J ١ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ٣
‫א‬  ،‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬  ،‫א‬
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬١J ١

 ‫א‬‫א‬٢J ١

-٦-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬

 ٢J ١‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١


 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١J ١
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 m.m.f KK
L
‫א‬‫א‬
 Rmag =
µA
m.m. f
 Φ=
‫א‬‫א‬
Rmag
Φ
B = ‫א‬
A
 e.m.f KKK
ρL
‫א‬‫א‬
 R=
A
E
 I = ‫א‬‫א‬
R
I
 J = ‫א‬
A
 K‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬J
 K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬ J
 K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J
 K‫א‬‫א‬‫א‬‫א‬


-٧-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬‫א‬ ٤J ١
 ‫א‬K‫א‬‫א‬‫א‬ ٤J ١
    K‫א‬ ‫א‬‫א‬  ‫א‬‫א‬  ‫א‬     ‫א‬ 
 g،‫א‬  p‫א‬‫א‬K‫א‬‫א‬
K‫א‬  ac،‫א‬‫א‬  y ،‫א‬  t،‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬٢J ١،
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ١
‫א‬‫א‬‫א‬




‫א‬
m.m.f
L‫א‬
H‫א‬
A‫א‬
B‫א‬
Fg
٢ Lg
Hg
Ag
٢ Lt
Ht
Ft
Fac
Fp
 Fy
Lac
٢ Lp
 Ly
Φ‫א‬
‫א‬‫א‬
Bg
Φm
 ‫א‬‫א‬‫א‬
At
Bt
Φm
 ‫א‬
Hac
Hp
Aac
Ap
Bac
Bp
 Hy
 Ay
 By
 ‫א‬
Φac=Φm/٢
 ‫א‬
Φm
 ‫א‬‫א‬
Φy= Φm/٢
‫א‬‫א‬‫א‬ ٥J ١‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬ ،‫א‬‫א‬‫א‬
m.m. f = Ftotal = Φ m
2Lg
2L p Φ m L y
2Lt Φ m Lac
+ Φm
+
+ Φm
+
µ o Ag
µ t At 2 µ ac Aac
µ p Ap 2 µ y Ay
-٨-

١-١٠
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬‫א‬٤J ١
   ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  ١٠J ١ ‫א‬
 W١٠J ١‫א‬٢J ١‫א‬B‫א‬‫א‬
Ftotal =
2 B g Lg
µo
+
2 Bt Lt
µt
+
Bac Lac
µ ac
+
2B p L p
µp
+
By Ly
µy
١ ١١
 ١١J ١‫א‬٣J ١‫א‬
F
= 2 H g L g + 2 H t Lt + H ac Lac + 2 H p L p + H y L y
١ ١٢
total
F
= Fg + Ft + Fac + F p + F y
total
١ ١٣
‫א‬‫א‬ ‫א‬  ‫א‬   ‫א‬ ‫א‬‫א‬ ‫א‬    ١٣J ١ ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬ ٥J ١
W‫א‬‫א‬‫א‬
‫א‬‫א‬  
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
K‫א‬ ‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬



-٩-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬١J ٥J
١
 L، ٥J ١
 E‫א‬‫א‬‫א‬،L B
 W‫א‬


١ ١٤
E=BLV sin(θ)
volt
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬θ
‫א‬     K‫א‬ ‫א‬‫א‬ ‫א‬   ‫א‬  ‫א‬  ‫א‬
‫א‬    ،‫ א‬‫א‬   K‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬  E٦J ١ F
،‫א‬ ‫א‬   ‫א‬ ‫א‬ ‫א‬      ‫א‬ ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬
 E‫א‬‫א‬‫א‬٥J ١
 ‫א‬٦J ١

-١٠-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥J
١
،‫א‬
W‫א‬‫א‬‫א‬(Faraday)‫א‬
E = N(
dΦ
)
dt
١-١٥
    ‫א‬ ‫א‬  ‫א‬   ‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬ 
‫א‬ ،‫א‬ ‫א‬ ‫א‬   ‫א‬  K‫א‬ ‫א‬ ‫א‬ ‫א‬  
 ‫א‬،E٧J ١F‫א‬،‫א‬ 
‫א‬‫א‬‫א‬K(self induced )‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬ ‫א‬‫א‬ ‫א‬          ،‫א‬ 
. E٨J
١F(mutual induced)‫א‬
 ‫א‬٧J ١
‫א‬٨J ١
،٣٠x٢٠‫א‬١J ١
٢٢٥‫א‬K٥
،‫א‬‫א‬W‫א‬،٠{٠٠٨‫א‬‫א‬‫א‬‫א‬K٢٤
 K‫א‬‫א‬،‫א‬‫א‬

-١١-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
، X,Y ‫א‬ ،‫א‬‫א‬‫א‬ ٩J ١ ‫א‬
W‫א‬L ‫א‬‫א‬‫א‬
L=٢*((x-٥)+(y-٥))=٢*(٢٠-٥+٣٠-٥)=٨٠ cm=٠٫٨m
N=٢٥ turns R=٢Ω V=٢٤V B=٠٫٠٠٨ tesla
A=(٥*١٠-٢)٢=٢٥*١٠-٤ m٢
V 24
i= =
= 12 A
R 2
Ni 25 *12
H=
=
= 375 A / m
0.8
L
Φ = BA = 0.008 * 25 *10 − 4 = 0.00002 wb
٩J ١
-١٢-
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
K٢٣ ٥٠‫א‬‫א‬ ٢J ١
J ١ W‫א‬ K١٥٠٠  ‫א‬ ‫א‬   ‫א‬ K ٢ ‫א‬    ٦٠٠ 
‫א‬J ٣،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J ٢،‫א‬‫א‬
 K‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬،‫א‬‫א‬ d ‫א‬
-٢
Lav=πd=π*٥٠*١٠ =١٫٥٧ m
µr=١٥٠٠
µo=٤π*١٠-٧
N=٦٠٠
I=٢ A
A= ٣*١٠-٤ m٢
Lav
1.57
=
= 2.78 *10 6 At / wb
١- Rmag =
µ r µ o A 1500(4π *10 − 7 )(3 *10 − 4 )
٢- mmf=NI =٦٠٠*٢=١٢٠٠ At
H=
1200
mmf
=
= 763.33 At / m
L
0.0157
av
1200
mmf
=
= 4.32 *10 − 4 wb
6
R
2.78 *10
mag
Φ 4.32 *10 − 4
B= =
= 1.44 tesla
A
3 *10 − 4
٣- Φ =
-١٣-
W‫א‬Lav
 ‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬

 ‫א‬ ‫א‬   ‫א‬ ‫א‬  ‫א‬ ‫א‬  J ١
 K
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J ٢
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J ٣
‫؟‬‫א‬‫א‬‫א‬ J ٤
K‫א‬ J ٥
K‫א‬‫א‬‫א‬‫א‬ J ٦
K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬J ٧
٦ ‫א‬          ‫א‬   J ٨
‫א‬‫א‬KL ١٢‫א‬‫א‬ ،
‫א‬‫א‬ ‫א‬ ‫א‬ K  ٠{٠٠٠١٥ ‫א‬    K,٥ ‫א‬
K‫א‬‫א‬،‫א‬‫א‬‫א‬
    ، ٢٠     ‫א‬   J ٩
١٥‫א‬K٥x٣
‫א‬‫א‬‫א‬K١٢ ١{٤
‫א‬ ،‫א‬ ‫א‬  ، ‫א‬  ‫א‬ W‫א‬ ، ٠{٠٠٦ ‫א‬ 
K‫א‬
‫א‬‫א‬٠{٠٠٠٢‫א‬‫א‬ J ١٠
‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬ K٢٥ ‫א‬    ١٠٠ ‫א‬
K٥٠٠‫א‬‫א‬‫א‬،‫א‬‫א‬
-١٤-
 ‫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
٢
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
  ‫א‬ ‫א‬‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬    W‫א‬‫א‬
 K‫א‬‫א‬‫א‬

 W‫א‬‫א‬W‫א‬‫א‬
K‫א‬‫א‬ K١
K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٢
K‫א‬‫א‬‫א‬‫א‬ K٣
K‫א‬‫א‬‫א‬‫א‬ K٤
K‫א‬‫א‬‫א‬ K٥
K‫א‬‫א‬‫א‬‫א‬‫א‬ K٦

 ٪٨٥‫א‬‫א‬W‫א‬‫א‬‫א‬

 K٦W‫א‬‫א‬

 KEFW‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬





-١٥-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬

DC Generators ‫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K‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
  ‫א‬‫א‬    K‫א‬     ‫א‬ ‫א‬  ‫א‬ 
 K‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬  ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬‫א‬ ‫א‬     ‫א‬
‫א‬K‫א‬ ‫א‬  ‫א‬  ‫א‬  ‫א‬
K‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬١J ٢
 ‫א‬‫א‬‫א‬١J ١J ٢
‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬
    ،  ،     ‫א‬  
‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬K
J ‫א‬‫א‬EF
‫א‬‫א‬‫א‬‫א‬
  ‫א‬   ‫א‬ ‫א‬     ‫א‬  J  
  ،K‫א‬
 (S)‫א‬ (N) (abcd)‫א‬
،‫א‬‫א‬‫א‬‫א‬١J ٢
‫א‬‫א‬،‫א‬‫א‬‫א‬
-١٦-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬،‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 e=BLv
٢ ١
‫א‬ ‫א‬‫א‬ v(m/sec)، ‫א‬ L(m)،‫א‬‫א‬ B(wb/m٢)
‫א‬  K(volt)   ‫א‬   (e) ‫א‬ ‫א‬‫א‬ ‫א‬ K‫א‬  
    ‫א‬    (cd)  ‫א‬  ‫א‬  (ab) 
 K١J ٢‫א‬
 EF


 EFEF
 ‫א‬‫א‬١J ٢
‫א‬   ‫א‬     ١J ٢    (abcd) ‫א‬  
‫א‬  o٩٠‫א‬‫א‬‫א‬،E o٩٠‫א‬‫א‬F
‫א‬  o٩٠‫א‬‫א‬K‫א‬
  ،‫א‬  ‫א‬ ٠٢٧٠ ‫א‬‫א‬   ‫א‬   ‫א‬  ‫א‬
،١J ٢(sinewave)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
-١٧-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
   (DC) ‫א‬     ‫א‬    E F ‫א‬ ‫א‬
‫א‬   ‫א‬  ‫א‬   K‫א‬‫א‬   ‫א‬ ‫א‬ 
K٢J ٢ A, BE ‫א‬F
(abcd)‫א‬‫א‬،٢J ٢A‫א‬‫א‬‫א‬
 ،B‫א‬‫א‬‫א‬٢J ٢ ، ١٨٠
 ١٨٠‫א‬ ‫א‬، ١٨٠ ‫א‬‫א‬ ٢J ٢
‫א‬ ‫א‬‫א‬‫א‬ ٣٦٠
‫א‬‫א‬‫א‬K١J ٢ 
‫א‬‫א‬‫א‬KEF
 K‫א‬‫א‬ ‫א‬‫א‬K‫א‬

c
d
b
a

EF
E
F

 EF
‫א‬‫א‬‫א‬٢J ٢
-١٨-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬٢J ١J ٢
‫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
 W‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬٣J ٢

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬W(Yoke)‫א‬‫• א‬
‫א‬‫א‬‫א‬،‫א‬
K‫א‬‫א‬٤J ٢K،‫א‬

‫א‬‫א‬‫א‬W(Main poles)‫א‬‫א‬
‫א‬‫א‬  (Pole face or shoe)‫א‬‫א‬‫א‬
W  (Field coils)‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬  ‫א‬‫א‬  ، (series field coil)‫א‬ (shunt field coil)‫א‬
K‫א‬ ‫א‬  ‫א‬ ‫א‬   K ‫א‬
،‫א‬‫א‬‫א‬ ‫א‬
 K‫א‬E٥J ٢F
-١٩-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬


 ٣J ٢
 ‫א‬‫א‬W (Commutating poles)‫א‬
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‫א‬‫א‬‫א‬،E‫א‬٢F‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
 K‫א‬‫א‬


 ‫א‬‫א‬٤J ٢

-٢٠-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬


 ‫א‬٥J ٢
 W‫א‬E‫א‬F‫א‬‫א‬‫א‬
‫א‬‫א‬W(Armature core)‫א‬
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   K‫א‬‫א‬ ‫א‬‫א‬   ،‫א‬    ‫א‬  
،‫א‬‫א‬K‫א‬‫א‬
K٦J ٢

‫א‬‫א‬‫א‬W(Armature windings)‫א‬
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‫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‫א‬‫א‬W (Commutator )E‫א‬F‫א‬
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‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬   ‫א‬   KE‫א‬F    ‫א‬   
K‫א‬‫א‬‫א‬،‫א‬
‫א‬   ‫א‬ ‫א‬   W(Brushes holder) ‫א‬ ‫א‬ 
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‫א‬  ‫א‬ ‫א‬     ‫א‬ ‫א‬   ‫א‬ ‫א‬
-٢١-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
K‫א‬‫א‬‫א‬E‫א‬F‫א‬
 K

 WArmature winding‫א‬٣J ١J ٢
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬


 E‫א‬F‫א‬‫א‬‫א‬٦J ٢
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ ‫א‬
J ‫א‬   ‫א‬   ‫א‬    K‫א‬ ‫א‬ ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬  J ‫א‬‫א‬
 ‫א‬ ‫א‬   ،‫א‬      ‫א‬ ‫א‬  
     ‫א‬ ‫א‬   ، (commutator segments) ‫א‬ ‫א‬
 W‫א‬‫א‬
     ‫א‬  ‫א‬‫א‬  W(Lap winding)‫א‬‫א‬J
 ‫א‬،٧J ٢

٣‫א‬‫א‬ ٢ ‫א‬ ٢ ‫א‬‫א‬ ١‫א‬E ١{٢{٣F
‫א‬K‫א‬‫א‬‫א‬
-٢٢-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬ 
‫א‬٧J ٢K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬
 W(Wave winding) ‫א‬‫א‬J
  ،‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬   
،‫א‬‫א‬‫א‬ ‫א‬‫א‬
 K٨J ٢(commutator pitch)‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬


 EFEF
 ‫א‬‫א‬‫א‬‫א‬٧J ٢


 ‫א‬‫א‬‫א‬‫א‬٨J ٢



-٢٣-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢
‫א‬ ‫א‬‫א‬
     K  ‫א‬ ‫א‬     
‫א‬v (m/sec)‫א‬ B (tesla) L (m)
e (volt)‫א‬‫א‬‫א‬E٩J ٢F‫א‬
 W‫א‬
 e=BLv
volt
٢ ٢
 W‫א‬‫א‬r meter‫א‬
  v = ωr = 2πn r
٢ ٣
60
 E‫א‬F‫א‬‫א‬‫א‬ (rad/sec) ω،L‫א‬‫א‬(rpm) n
 ‫א‬‫א‬‫א‬‫א‬‫א‬
 B=
φ
A
=
φ
2πrl / 2 p
٢ ٤
 ٢J ٢ ‫א‬  ٤J ٢‫א‬ ٣J ٢  ،‫א‬  ‫א‬  A 
 W‫א‬‫א‬‫א‬‫א‬‫א‬
 e = φ 2 p l 2πn r
2πrl 60
 e = φ 2 pn
60
٢ ٥
 ٥J ٢‫א‬
٢ ٦
 ‫א‬‫א‬‫א‬‫א‬‫א‬ ٢a‫א‬‫א‬‫א‬ Za ‫א‬‫א‬‫א‬
 Ea =
2p
n
φZ a 
2a
60
 W‫א‬‫א‬‫א‬
٢ ٧





-٢٤-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
،٢٥٠‫א‬‫א‬٦١J ٢
‫א‬ ‫א‬‫א‬ ‫א‬  ، ٤   ‫א‬  ‫א‬ KL ١٢٠٠ 
 K‫א‬
٢p=٦
٢a=٢[wave winding]
Za=٢٥٠
n=١٢٠٠ rpm
Φ=٤ megalines/pole
Φ=٤*١٠٦ *١٠ ٨=٠{٠٤ wb/pole
2p
n
Ea =
φZ a
2a
60
1200
6
E a = * 0.04 * 250 *
= 600 volt
2
60
‫א‬
‫א‬، ٩٦٠‫א‬‫א‬ ٨  ٢J ٢
‫א‬  ، ٢٢٠ ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬ KL ٦٠٠  
 K‫א‬
٢p=٨
٢a=٢p[lap winding]
Za=٩٦٠
n=٦٠٠ rpm
2p
n
φZ a
2a
60
8
600
220 = * φ * 960 *
8
60
Φ=٢٢٠*٦٠/(٦٠٠*٩٦٠)=٠٫٠٢٣ wb/pole
Ea=٢٢٠ V
‫א‬
Ea =
 ‫א‬‫א‬‫א‬٩J ٢



-٢٥-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 (Armature Reaction) ‫א‬٣J ٢
‫א‬    ‫א‬    ،‫א‬ ‫א‬   ‫א‬ ‫א‬ 
‫א‬‫א‬،‫א‬،‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬
(Lenz Law) ‫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 K‫א‬ ‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬ ،‫א‬K
 ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬   ١٠J ٢   K‫א‬
 (M.M.Ff)  ‫א‬     KE‫א‬    F ‫א‬  
‫א‬‫א‬F ‫א‬‫א‬ ، ‫א‬
‫א‬   (G.M.A) ‫א‬ ‫א‬  ‫א‬ ‫א‬     KE‫א‬ 
 K(M.N.A)‫א‬

 ‫א‬    ‫א‬‫א‬‫א‬‫א‬١٠J ٢ 
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
 ‫א‬K‫א‬ x ،‫א‬ ‫א‬‫א‬‫א‬
‫א‬  ‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬ ‫א‬   ،‫א‬  ‫א‬ ‫א‬
 ‫א‬         ‫א‬      ‫א‬
K‫א‬‫א‬ ‫א‬ (M.M.Fa)‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
  ‫א‬‫א‬‫א‬ ‫א‬‫א‬
-٢٦-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
،‫א‬‫א‬،‫א‬‫א‬
θ ‫א‬   (M.M.Ft)  ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬   K ١٠J ٢
(M.N.A) ‫א‬ ‫א‬   ،  (M.M.Ff)‫א‬ ‫א‬  
‫א‬ ١٠J ٢K(G.M.A)‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K١٠J ٢‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬ ١٠J ٢K (ab)‫א‬
‫א‬ ‫א‬‫א‬  (bc)‫א‬،‫א‬‫א‬
‫א‬K١٠J ٢‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬،‫א‬ ،‫א‬‫א‬
،‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬ ‫א‬ 
 (Demagnetizing effect)‫א‬‫א‬‫א‬‫א‬ 
‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬J
 K‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J
 K‫א‬‫א‬
-٢٧-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬


 EFEFEF


 ‫א‬‫א‬‫א‬١٠J ٢
‫א‬K‫א‬ ‫א‬‫א‬‫א‬
‫א‬ ‫א‬
‫א‬K‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬١٢J ٢،‫א‬‫א‬‫א‬ ١١J ٢
‫א‬K (Fa) ‫א‬ (Fc)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬
،‫א‬‫א‬،‫א‬E‫א‬F
١٣J ٢‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬
-٢٨-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬



 ‫א‬‫א‬١١J ٢



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٢J ٢

-٢٩-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬

 ‫א‬١٣J ٢
 (Methods of Excitation)‫א‬‫א‬E‫א‬F‫א‬٤J ٢
‫א‬‫א‬ ‫א‬   ‫א‬  EF    ‫א‬ ‫א‬ ‫א‬ 
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 KW‫א‬‫א‬
‫א‬ (Separately excited) EF‫א‬‫א‬ J
KE‫א‬F
  ، ‫א‬  ‫א‬    (Self excited) ‫א‬  ‫א‬ ‫א‬ J
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 (Separately excited generators)‫א‬‫א‬‫א‬‫א‬‫א‬١J ٤J ٢
‫א‬   ،‫א‬ ‫א‬ ‫א‬  ‫א‬‫א‬  ١٤J ٢  
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬
 ‫א‬‫א‬،‫א‬‫א‬‫א‬
K
-٣٠-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬


 ‫א‬‫א‬١٤J ٢
 W‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬(Kirechhoff’s Law)
 Ea = VL + I a Ra
٢ ٨
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Ea،E‫א‬F‫א‬‫א‬‫א‬VL
 W‫א‬‫א‬

2p
φZ a N / 60 
٢ ٩
2a
 K‫א‬‫א‬IL،‫א‬Ra،‫א‬Ia
Ea =
Ia = IL
٢ ١٠
-٣١-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
   L ١٢٠٠    ،‫א‬      ٣J ٢ 
١٠٠٠ ‫א‬‫א‬‫א‬‫א‬‫א‬K ١٢٥ ٢٠٠‫א‬
 K٠{٠٤‫א‬K‫א‬،L
n١=١٢٠٠ rpm
IL١=٢٠٠ A
Ea α n
as If is constant
Ea١=VL١+IL١Ra
VL١=١٢٥ V
n٢=١٠٠٠ rpm
Ra=٠{٠٤ Ω
‫א‬
= ١٢٥H٢٠٠*٠{٠٤=١٣٣ V
Ea1 n1
=
E a 2 n2
133 1200
=
Ea 2 1000
1000 *133
Ea 2 =
= 110.8 V
1200
Ea٢=VL٢+IL٢Ra=IL٢RL+ IL٢Ra
V 125
RL = L =
= 0.625Ω
I L 200
١١٠{٨=IL٢[٠{٦٢٥H٠{٠٤]=IL٢[٠{٦٦٥]
110.8
I L2 =
= 166.62 Amp.
0.665
 (Self excited generators)‫א‬‫א‬‫א‬‫א‬٢J ٤J ٢
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬(series excitation)‫א‬ J
‫א‬‫א‬‫א‬(shunt excitation)‫א‬ J
‫א‬‫א‬‫א‬(compound excitation) J
 (series excited generator)‫א‬‫א‬‫א‬١J ٢J ٤J ٢
K١٥J ٢‫א‬‫א‬‫א‬‫א‬
-٣٢-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬


 ‫א‬‫א‬‫א‬١٥J ٢
:‫א‬‫א‬
 Ea = VL + I a (Ra + R f )
٢ ١١
Ia = IL = I f
٢ ١٢
 ١٢٥‫א‬ ١٥‫א‬‫א‬ ٤، ‫א‬ ٤J ٢
‫א‬‫א‬K,٢٤‫א‬,١٥‫א‬KL١١٥٠‫א‬
K ١٢٥‫א‬L ١٢٠٠‫א‬‫א‬
 K٪٣٠‫א‬‫א‬‫א‬
Pout=١٥Kw
Φ٢= ١٫٣Φ١
VL١=١٢٥ V
n١=١١٥٠ rpm
Rf=٠{١٥Ω
Ra=٠{٢٤Ω n٢=١٢٠٠rpm
Pout 15 * 103
=
= 120 Amp.
I L1 =
V L1
125
Ea١=VL١+IL١Rf+IaRa=VL١+IL١[Rf+Ra]
as IL=Ia
Ea١=١٢٥+١٢٠[٠٫١٥+٠٫٢٤]=١٧١٫٨ V
Ea1 φ1 n1
=
E a 2 φ 2 n2
φnE
1.3φ1 * 1200 * 171.8
= 233.05 V
E a 2 = 2 2 a1 =
φ1n1
φ1 * 1150
Ea٢=VL٢+IL٢Rf+IaRa=VL٢+IL٢[Rf+Ra]
VL٢=Ea٢-IL٢[Rf+Ra]=٢٣٣٫٠٥-١٢٥[٠٫١٥+٠٫٢٤]=١٨٤٫٣ volt
-٣٣-
‫א‬
IL٢=١٢٥ A
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 (Shunt excited generators)‫א‬‫א‬‫א‬‫א‬٢J ٢J ٤J ٢
K١٦J ٢‫א‬‫א‬‫א‬‫א‬
 ‫א‬ ‫א‬      ‫א‬ ‫א‬    ‫א‬ 
‫א‬‫א‬     ،‫א‬    ‫א‬     ،‫א‬ ‫א‬
 K‫א‬‫א‬

 :‫א‬‫א‬
Ea = VL + I a Ra
٢ ١٣
 V f = VL = I f R f
٢ ١٤
 Ia = IL + I f
٢ ١٥
‫א‬‫א‬،‫א‬٪٥ ٪١‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬

‫א‬‫א‬‫א‬١٦J ٢
 ‫א‬ ،  ٢٤٠ ‫א‬   ٣٥٠     ‫א‬  ٥J ٢ 
 K‫א‬‫א‬‫א‬‫א‬‫א‬K ٥٥  ٠ ,٠٢‫א‬‫א‬‫א‬
If =
Vf
Rf
=
IL=٣٥٠ A
VL=٢٤٠ V
VL 240
=
= 4.36
Rf
55
Amp
Ra=٠{٠٢Ω
Ia=IL+If=٣٥٠H٤{٣٦=٣٥٤{٣٦ Amp
-٣٤-
Rf=٥٥Ω
‫א‬
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
Ea=VL+IaRa=٢٤٠H٣٥٤{٣٦*٠{٠٢=٢٤٧{١ V
 ، ٥٠٠ ‫א‬   ‫א‬   ‫א‬‫א‬    ٦J ٢ 
‫א‬ ٦٠ ٢٠٠،٩٥‫א‬ ٠{٠١‫א‬
 K٠, ٠٢‫א‬‫א‬‫א‬‫א‬‫א‬K١٢٠
٢p=٢a [lap winding]
Za=٥٠٠
Ra=٠{٠١Ω
Rf=٩٥Ω
Pout=٢٠٠*٦٠=١٢٠٠٠W
‫א‬
VL=١٢٠
V
Φ=٠{٠٢ wb/pole
Pout=VL*IL
P
200 * 60
= 100 A
I L = out =
VL
120
V
120
If = f =
= 1.26 A
Rf
95
Ia=IL+If=١٠٠H١{٢٦=١٠١{٢٦ A
Ea=VL+IaRa=١٢٠H١٠١{٢٦*٠{٠١=١٢١{٠١ V
2p
φZ a n / 60
Ea =
2a
2p
121.01 =
* 0.02 * 500 * n / 60
2p
n=١٢١{٠١*٦٠/(٠{٠٢*٥٠٠)=٧٢٦ rpm
 (Compound excited generators)‫א‬‫א‬‫א‬٣J ٢J ٤J ٢
‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬
(cumulative compound )‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬
 K(differential compound)‫א‬‫א‬
‫א‬   ‫א‬ ‫א‬    ‫א‬‫א‬   ،‫א‬ ‫א‬ 
‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(short-shunt)‫א‬‫א‬‫א‬
‫א‬ ‫א‬ ،(long-shunt) ‫א‬ ‫א‬‫א‬  ‫א‬   E‫א‬‫א‬  
-٣٥-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
،١٧J ٢‫א‬‫א‬،١٧J ٢‫א‬
Ksh‫א‬‫א‬se‫א‬‫א‬
W‫א‬‫א‬‫א‬
٢ ١٦
 Ea = VL + I a Ra + I L Rse
I a = I L + I sh
٢ ١٧
 I se = I L
٢ ١٨

 Ea = VL + I a ( Ra + Rse )
:‫א‬‫א‬‫א‬
٢ ١٩
I a = I L + I sh
٢ ٢٠
I se = I a
٢ ٢١


 EFEF
 EFEF ‫א‬‫א‬١٧J ٢
  ‫א‬‫א‬  K‫א‬  ‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬  
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
(demagnetize the machine)‫א‬‫א‬‫א‬
K‫א‬‫א‬ 
‫א‬ ‫א‬ K  ٢٣٠    ٦٠        ٧J ٢ 
 ٠{٠١‫א‬‫א‬، ٠{٠٤‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
 K١٢٥‫א‬‫א‬
VL=٢٣٠ V IL=٦٠ A
Ra=٠{٠٤ Ω
Rse=٠{٠١Ω
-٣٦-
Rsh=١٢٥Ω
‫א‬
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
Vsh VL 230
=
=
= 1.84 A
Rsh Rsh 125
Ia=IL+Ish=٦٠H١{٨٤=٦١{٨٤ A
I sh =
Ea=VL+Ia(Ra+Rse)=٢٣٠H٦١{٨٤*(٠{٠٤H٠{٠١)=٢٣٣{٠٩٢ Volt
-٣٧-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 (Characteristic Curves of DC Generators) ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ٢
  ‫א‬  J ‫א‬ ‫א‬  ‫א‬ ‫א‬    
  ‫א‬ J ‫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
      Ea ‫א‬ ‫א‬‫א‬ ‫א‬   ٢a,٢P  ،‫א‬  ‫א‬
 KN‫א‬‫א‬،Φ‫א‬‫א‬
 Ea = kφ N
‫א‬ ‫א‬‫א‬ ‫א‬    ،‫א‬  ‫א‬‫א‬   ‫א‬ 
 KVL‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬
No-load characteristic, Eo=f(If), N=constant ‫א‬‫א‬ J
‫א‬‫א‬  (o.c.c)‫א‬‫א‬‫א‬ ‫א‬
 K‫א‬(If) ‫א‬(Eo)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
Load characteristic, VL=f(If), Ia and N=constant ‫א‬‫א‬ J
‫א‬ (If)‫א‬  (VL) ‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬
External characteristic, VL=f(IL), If and N=constant ‫א‬‫א‬‫א‬ J
K‫א‬‫א‬(IL)‫א‬(VL)‫א‬‫א‬‫א‬‫א‬
Internal characteristic, Ea=f(Ia), If and N=constant ‫א‬‫א‬‫א‬‫א‬ J
‫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
K‫א‬‫א‬‫א‬‫א‬‫א‬
-٣٨-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬١J ٥J ٢
 No-load characteristic‫א‬‫א‬ J
،‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬Ea‫א‬‫א‬‫א‬‫א‬
 Ea = kφ
 (If) ‫א‬‫א‬‫א‬،‫א‬
 Ea = k ′I f
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬Eo‫א‬
     ‫א‬‫א‬    ‫א‬ ‫א‬  ،١٨J ٢ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،
  ‫א‬‫א‬     ‫א‬ ‫א‬     ،‫א‬  
‫א‬،If ‫א‬ Eo‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
،‫א‬    ‫א‬ ‫א‬  (b) ‫א‬ ،(a)  ‫א‬   ١٨J ٢
 K‫א‬‫א‬‫א‬‫א‬

 EFEF
‫א‬‫א‬EF‫א‬EF‫א‬‫א‬١٨J ٢
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 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 Load characteristic‫א‬‫א‬J
      ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬  
‫א‬،(armature reaction)‫א‬ (Eo)‫א‬
‫א‬   ‫א‬  ‫א‬ ‫א‬ (Ea) ‫א‬ ‫א‬‫א‬ ‫א‬    (VL) ‫א‬
   ‫א‬   ‫א‬   E‫א‬F ‫א‬     ‫א‬ ،(IaRa)
‫א‬FVL، VL‫א‬‫א‬(RL)‫א‬
 ‫א‬  ‫א‬ ‫א‬  ،‫א‬    E ‫א‬F ‫א‬  E
J ٢،‫א‬‫א‬‫א‬١٩J ٢K‫א‬‫א‬
I‫א‬‫א‬ III،١٩J ٢‫א‬ K‫א‬١٩
‫א‬، III‫א‬(IaRa)AB ‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬ CB‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ II
‫א‬(VL)‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬ (CD)‫א‬‫א‬  (Eo)‫א‬
 K‫א‬

 EFEF
 ‫א‬‫א‬EF‫א‬EF‫א‬‫א‬١٩J ٢
 (External characteristic)‫א‬‫א‬‫א‬J
‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬ ٢٠J ٢
،‫א‬‫א‬‫א‬Ea(II)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
-٤٠-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬‫א‬ Eo‫א‬ (I)‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
  ،(III)  ‫א‬     ‫א‬ ‫א‬‫א‬    ‫א‬
 K‫א‬‫א‬(IL)‫א‬(VL)‫א‬‫א‬‫א‬‫א‬
 (Internal characteristic)‫א‬‫א‬‫א‬‫א‬J
‫א‬‫א‬،Ea=f(Ia)‫א‬‫א‬‫א‬‫א‬ ٢٠J ٢ II‫א‬
‫א‬(IL) ‫א‬‫א‬(Ia)‫א‬‫א‬(Ea)‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬،‫א‬‫א‬
 ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬ Ea  ،‫א‬ ‫א‬‫א‬   AB ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬
  ε ‫א‬    ،٢٠J ٢  ، ‫א‬ ‫א‬‫א‬  
 %ε =

E o − VL
∗ 100
VL
 W‫א‬‫א‬
٢ ٢٢
 ‫א‬‫א‬‫א‬٢٠J ٢
 ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥J ٢
‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ،E‫א‬F‫א‬
‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬
-٤١-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
    ،‫א‬      ‫א‬  ‫א‬    K ‫؟‬‫א‬‫א‬
،‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬ ،‫א‬ ‫א‬
  ‫א‬ (Magnetization curve)  ‫א‬  ٢١J ٢ ‫א‬  ،‫א‬ 
‫א‬(Eo)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،(If)‫א‬‫א‬
‫א‬K‫א‬‫א‬‫א‬‫א‬
 (Er)‫א‬‫א‬‫א‬‫א‬ ،‫א‬
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
 ،(Rf)‫א‬ (Lf)‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ 
 K(Residual magnetism) Er‫א‬‫א‬‫א‬‫א‬‫א‬



 ‫א‬‫א‬‫א‬‫א‬٢١J ٢
 ‫א‬‫א‬‫א‬‫א‬‫א‬١J ٢J ٥J ٢
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬    ‫א‬ ‫א‬   ‫א‬ ‫א‬‫א‬ ٢٢J ٢  
‫א‬‫א‬‫א‬K(RL)‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬،(Ia)‫א‬‫א‬‫א‬
-٤٢-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬K(VL)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬I‫א‬،‫א‬‫א‬‫א‬‫א‬ ٢٢J ٢
I ‫א‬  ‫א‬  ‫א‬ ‫א‬   ‫א‬ ‫א‬‫א‬   III 
،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬KA.C‫א‬
‫א‬‫א‬‫א‬،‫א‬
‫א‬‫א‬‫א‬ ‫א‬ OPK IL‫א‬‫א‬
 K٢٢J ٢
EIIIF‫א‬‫א‬‫א‬ IaRa‫א‬‫א‬‫א‬
‫א‬‫א‬ Ea‫א‬‫א‬‫א‬ ‫א‬EIIF‫א‬‫א‬‫א‬‫א‬
‫א‬ II‫א‬‫א‬‫א‬‫א‬،I‫א‬‫א‬‫א‬‫א‬،E‫א‬ ‫א‬F
 K‫א‬‫א‬

 EFEF
‫א‬‫א‬J ‫א‬‫א‬‫א‬J ‫א‬‫א‬‫א‬٢٢J ٢
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 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٢J ٥J ٢
  ‫א‬   ‫א‬‫א‬  ‫א‬‫א‬  ٢٣J ٢   I ‫א‬ 
‫א‬K‫א‬‫א‬‫א‬ III‫א‬،‫א‬‫א‬‫א‬‫א‬ II‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
KEo‫א‬‫א‬‫א‬‫א‬‫א‬ IV ‫א‬K‫א‬‫א‬
 W‫א‬‫א‬‫א‬
E − AA
 %ε = o
∗100
٢ ٢٣
AA

 EFEF
 ‫א‬‫א‬J ‫א‬‫א‬‫א‬J ‫א‬‫א‬‫א‬٢٣J ٢
 ‫א‬‫א‬‫א‬‫א‬٣J ٢J ٥J ٢
 (long-shunt )‫א‬‫א‬‫א‬،‫א‬‫א‬
،‫א‬ K(short-shunt)‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬،‫א‬
   E  ‫א‬  ‫א‬F ‫א‬  ‫א‬ ‫א‬‫א‬  
 K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
 ‫א‬ ‫א‬ ‫א‬     ‫א‬‫א‬   W‫א‬ J
 ‫א‬ ‫א‬       ‫א‬   ‫א‬  ،‫א‬‫א‬
‫א‬‫א‬ VL‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K٢٤J ٢
-٤٤-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬  WJ
    ،‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬
 K‫א‬VL‫א‬‫א‬‫א‬،‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ WJ
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬
 K٢٤J ٢‫א‬‫א‬،‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬٢٤J ٢
Energy Losses and Efficiency of DC Generators‫א‬‫א‬‫א‬‫א‬‫א‬٦J ٢
،‫א‬  ‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬،‫א‬
،‫א‬ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬،EF،‫א‬‫א‬ ‫א‬
K‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬
F          ،‫א‬ ‫א‬‫א‬   ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬KE‫א‬
 Magnetic losses (Iron losses)E‫א‬F‫א‬‫א‬‫א‬J
 Electrical losses (Cupper losses)E‫א‬F‫א‬‫א‬‫א‬J
 Mechanical losses (Friction losses)E‫א‬FJ

-٤٥-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 E‫א‬F‫א‬‫א‬‫א‬١J ٦J ٢
 W‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ :Hysteresis loss‫א‬‫א‬J
 W‫א‬‫א‬‫א‬‫א‬
 Wh = B1g.6 f
٢ ٢٤
 ‫א‬‫א‬‫א‬WEddy current loss E‫א‬F‫א‬‫א‬‫א‬‫א‬J
 We = B g2 f
٢ ٢٥
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
 K‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬ ٢J ٦J ٢
‫א‬‫א‬‫א‬‫א‬‫א‬
W‫א‬‫א‬،‫א‬‫א‬
 W‫א‬‫א‬ J
٢
 Armature cupper loss=I aRa
 ‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬
 For shunt machine=I٢shRsh(or VIsh)
J
 K‫א‬‫א‬
 For series machine=I٢seRse
 W‫א‬‫א‬J
 Loss due to brush contact resistance=IaVB
 K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬VB
 ‫א‬‫א‬٣J ٦J ٢
‫א‬،(bearing)‫א‬‫א‬‫א‬،‫א‬
 ‫א‬‫א‬  ‫א‬ ‫א‬  K‫א‬ ‫א‬  ‫א‬‫א‬   ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬
-٤٦-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬

 ‫א‬‫א‬٤J ٦J ٢
‫א‬  ‫א‬    ‫א‬ ‫א‬   ‫א‬    
‫א‬‫א‬   ‫א‬‫א‬‫א‬ (Prime mover)
،٢٥J ٢ Input power‫א‬
K H.P=٧٤٦ Watt.W‫א‬‫א‬‫א‬‫א‬، H.P‫א‬‫א‬‫א‬
 ‫א‬ Pi ‫א‬‫א‬ Pmech‫א‬‫א‬‫א‬
WE‫א‬F‫א‬PgPg
Pg=Ea Ia
 Pg=Pin-(Pmech+Pi)
٢ ٢٦
‫א‬‫א‬‫א‬ Pg‫א‬ ‫א‬‫א‬
J ٢K PL‫א‬ Pout‫א‬ ‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬٢٦
B
A
‫א‬
Pin

C
‫א‬ ‫א‬ ‫א‬ ‫א‬
Pcu
Pi&Pmech
Pout
Pg
 ‫א‬‫א‬‫א‬‫א‬‫א‬٢٥J ٢

-٤٧-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
i/p
‫א‬‫א‬
o/p
VLIL
‫א‬‫א‬
‫א‬‫א‬
IaEa
‫א‬‫א‬
I2seRse
I2shRsh
I2aR
∆VIa
Pmech+Pi

 ‫א‬‫א‬٢٦J ٢
 ‫א‬‫א‬‫א‬
-٤٨-
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
 Efficiency‫א‬‫א‬٥J ٦J ٢
 ‫א‬    ،‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬  
 W
 W‫א‬‫א‬J
 ηm =
Ea I a
B
=
A HP * 746
٢ ٢٧
 W‫א‬‫א‬J
ηe =
 η =
C VL I L
=
B Ea I a
٢ ٢٨
VL I L
o/ p
C
= η mη e = =
i/ p
A HP * 746
 W‫א‬‫א‬J
٢ ٢٩
 ‫א‬‫א‬‫א‬
Pout
Pout + losses
P − losses
η = in
Pin
η =
٢ ٣٠
٢ ٣١
٤٥    L ١٠٠٠  ،     ٨J ٢ 
 ٠{٠٢‫א‬‫א‬  ٠{٠٥‫א‬‫א‬،K ٢٤٠‫א‬
‫א‬ ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  K ٦٥  ‫א‬‫א‬ 
 K‫א‬٣٥٠٠

n=١٠٠٠ rpm
Pout=٤٥ Kw
VL=٢٤٠ V
Pi+Pmech=٣٥٠٠ W
Pout 45 * 103
IL =
=
= 187.5 A
VL
240
V
V
240
I sh = sh = L =
= 3.7 A
Rsh Rsh
65
Ia=IL+Ish=١٨٧{٥H٣{٧=١٩١{٢ A
-٤٩-
Ra=٠{٠٥Ω
Rse=٠{٠٢Ω
 ‫א‬
Rsh=٦٥Ω
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
Pcu=I٢aRa+ I٢aRse+ I٢shRsh= I٢a (Ra+Rse)+ I٢shRsh
=(١٩١{٢)٢*(٠{٠٥H٠{٠٢) + (٣{٧)٢*٦٥=٣٤٤٨{٨٧ W
Losses=Pcu+Pi+Pmech
=٣٤٤٨{٨٧H٣٥٠٠=٦٩٤٨{٨٧ W
Pout
45 * 103
=
= 0.866 = 86.6%
 η=
Pout + Losses 45 * 103 + 6948.87
 ١٢٠٠، ٨ ٩J ٢
٠٦‫א‬K٠{٠٢٢‫א‬‫א‬٦٠‫א‬،L٦٠٠
 ‫א‬ ‫א‬  K ٢٥٠ ‫א‬‫א‬    ٠{٠٤ ‫א‬‫א‬   ، ,
 K‫א‬٤٥٠٠‫א‬‫א‬‫א‬‫א‬
٢p=٨
٢a=٢ [wave winding]
Za=١٢٠٠
n=٦٠٠ rpm
Ra=٠{٠٦Ω Rse=٠{٠٤Ω Rsh=٢٥٠Ω Pi+Pmech=٣٥٠٠W
2p
Ea =
φZ a n / 60
2a
8
Ea = * 0.022 * 1200 * 600 / 60 = 1056 V
2
Ea=Va+IaRa
Va=Ea-IaRa=١٠٥٦ ٦٠*٠{٠٦=١٠٥٢{٤ V
V
1052.4
I sh = a =
= 4.21 A
Rsh
250
IL=Ia-If=٦٠ ٤{٢١=٥٥{٧٩ A
VL=Va-ILRse=١٠٥٢{٤ ٥٥{٧٩*٠{٠٤=١٠٥٠{١٦ V
Pout=VLIL=١٠٥٠{١٦*٥٥{٧٩=٥٨٥٨٩ W
Pcu=I٢aRa+ I٢LRse+ I٢shRsh
=(٦٠)٢*٠{٠٦H(٥٥{٧٩)٢*٠{٠٤H(٤{٢١)٢*٢٥٠=٤٧٧١{٥ W
losses=Pcu+Pi+Pmech=٤٧٧١{٥H٣٥٠٠=٨٢٧١{٥ W
Pout
58589
η=
=
= 0.876 = 87.6%
Pout + Losses 58589 + 8271.5
-٥٠-
Ia=٦٠ A
‫א‬
Φ=٠{٠٢٢ wb
 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬J ١
K‫א‬‫א‬‫ א‬J ٢
K‫א‬‫א‬‫؟‬‫א‬‫א‬‫א‬‫א‬ J ٣
‫؟‬‫א‬‫؟‬‫א‬‫א‬‫א‬ J ٤
K‫א‬‫א‬‫א‬ J ٥
‫א‬J ‫א‬J ‫א‬ J ٦
K‫א‬
‫؟‬‫א‬‫א‬‫؟‬‫א‬‫א‬ J ٧
‫؟‬‫א‬‫א‬ J ٨
K‫א‬J ‫א‬J ‫א‬‫א‬‫ א‬J ٩
K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬J ١٠
K‫א‬‫א‬‫א‬‫א‬‫א‬ J ١١
‫א‬ ٢٣٠‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ J ١٢
١٢٠٠ ‫א‬‫א‬‫א‬‫א‬‫א‬ J WK ١{٢٥L ١٠٠٠
‫א‬٢١٠‫א‬‫א‬‫א‬‫א‬‫א‬J K‫א‬١{١‫א‬L
K٢٠٥‫א‬L١٢٠٠‫א‬J K١{٢
، ١٢٠ ‫א‬      ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  ‫א‬ J ١٣
‫א‬٪١١٠ ‫א‬‫א‬‫א‬٪٩٥ ‫א‬‫א‬‫א‬‫א‬‫א‬
K١٢٠
‫א‬   ، ٢٥٠  ‫א‬K ٣٠  ‫א‬     J ١٤
‫א‬‫א‬K ٢٦٥‫א‬‫א‬‫א‬‫א‬‫א‬K ,١٢٥
K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬١٠٥‫א‬
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 ‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 ‫א‬
، ٩٦٠ ٨‫א‬ J ١٥
 K,٢٥ ‫א‬   ‫א‬  ٢٨٠    ٦{٥   L٥٠٠
‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬J   ‫א‬ J  W  ١٧٥ ‫א‬  
K‫א‬‫א‬J 
  ١٠٠ ، K,٨  ‫א‬  ‫א‬  ، ٤ ‫א‬    J ١٦
‫א‬‫א‬‫א‬،‫א‬ ٣٠٠،‫א‬
‫א‬   L ١٠٠٠ ‫א‬‫א‬   ١٢ ‫א‬  ، ٠{٠٣ 
K
٥٠٠‫א‬‫א‬K ٢٥ ‫א‬ ٤ J ١٧
   ٠{٠٤ ‫א‬‫א‬    ٠{٠٣ ‫א‬   ‫א‬ ،
  ‫א‬ ‫א‬ J  ‫א‬ ‫א‬‫א‬ ‫א‬J  W  ٢٠٠ ‫א‬‫א‬
K٠{٠٢‫א‬‫א‬L١٢٠٠‫א‬‫א‬
،‫א‬   ‫א‬  ٨٠ ‫א‬     ٢٥٠    J ١٨
‫א‬ ،‫א‬  ١٠٠ ، ٠{٠٣ ، K٠{٠٥ ‫א‬‫א‬  ‫א‬‫א‬ 
K‫א‬‫א‬‫א‬‫א‬
٣٠‫א‬L١٥٠٠‫א‬ J ١٩
١٨٠٠  ‫א‬ ‫א‬ ‫א‬‫א‬  ‫א‬   ، ١٥٠ ‫א‬  ‫א‬
‫א‬‫א‬ ٦٠ ‫א‬‫א‬‫؟‬ ٦٠ ‫א‬‫א‬L
K‫א‬K,١٥،, ١‫א‬‫א‬٪٥٠
٢٥٠‫א‬K٢٥L١٠٠٠ J ٢٠
 ١١٠، ٠{٠٦، ٠{٠٥‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬J ‫א‬‫א‬‫א‬J W٪٨٨‫א‬‫א‬‫א‬،‫א‬
K‫א‬‫א‬
‫א‬ ٤٥ L ١٠٠٠ J ٢١
 ٠{٠٢ ‫א‬‫א‬   ٠{٠٥ ‫א‬    ‫א‬ ، ٢٤٠  
‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬ ‫א‬ ‫א‬  ٦٥  ‫א‬‫א‬ 
‫א‬٣٥٠٠‫א‬
-٥٢-
 ‫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
٣
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
.‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬

 W‫א‬‫א‬ W‫א‬‫א‬
K‫א‬‫א‬ K١
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٢
K‫א‬‫א‬‫א‬ K٣
K‫א‬‫א‬‫א‬‫א‬ K٤
‫א‬‫א‬‫א‬‫א‬‫א‬ K٥
K‫א‬‫א‬‫א‬ K٦
‫א‬‫א‬‫א‬‫א‬ K٧

 ٪٨٥‫א‬‫א‬ ‫ أن‬W‫א‬‫א‬‫א‬

.٦W‫א‬‫א‬

.(F W‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

K‫א‬



-٥٢-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
‫א‬

DC Motors ‫א‬‫א‬
‫א‬  K‫א‬ ‫א‬   ‫א‬ ‫א‬ ‫א‬ ‫א‬ 
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬٪٦٠‫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 K‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
 K‫א‬
 ‫א‬‫א‬١J ٣
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
KE‫א‬‫א‬F‫א‬‫א‬‫א‬
    ‫א‬      ‫א‬  ‫א‬   
   ‫א‬ ‫א‬  ،‫א‬      E‫א‬F ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬
 ١J ٣K‫א‬
I B XX’‫א‬
‫א‬‫א‬F،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬L‫א‬‫א‬K‫א‬‫א‬‫א‬cd, ab‫א‬
 W
٣ ١
F=BIL
T ‫א‬    ،‫א‬    cd, ab ‫א‬   ‫א‬ ‫א‬
K‫א‬‫א‬‫א‬‫א‬
-٥٣-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

 ‫א‬‫א‬١J ٣
‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٣ Back e.m.f (Eb)
‫א‬‫א‬‫א‬‫א‬
:‫א‬‫א‬‫א‬‫א‬(Back e.m.f)‫א‬‫א‬‫א‬‫א‬
Eb =
n
2P
φZ a
2a
60
٣ ٢
‫א‬‫א‬، ٢J ٣‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬ ‫א‬    ‫א‬  ،‫א‬    ‫א‬   ،‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫ א‬ ٢J ٣
‫א‬‫א‬‫א‬‫א‬ KE٢J ٣F‫א‬
‫א‬      ‫א‬   K      ‫א‬
‫א‬،‫א‬ ‫א‬‫א‬
K‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬
 K‫א‬‫א‬
 ‫א‬‫א‬H‫א‬Z‫א‬‫א‬‫א‬‫א‬W‫א‬
E a = V L + I a Ra
٣ ٣
 ‫א‬‫א‬J ‫א‬ZE‫א‬F‫א‬‫א‬‫א‬‫א‬W‫א‬
Ea = VL − I a Ra
٣ ٤
-٥٤-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬

‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ KE٤J ٣F،E٣J ٣F‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬
‫א‬‫א‬‫א‬ ‫א‬  ‫א‬   
،E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
Ia =
 W٤J ٣‫א‬‫א‬
VL − Eb
٣ ٥
Ra
‫א‬،٢J ٣‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K‫א‬‫א‬ Eb n‫א‬‫א‬
Eb‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬٢J ٣
starting) ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 WEb=٠٥J ٣‫א‬(current
 
I a ( st ) =
VL
Ra
٣ ٦
E‫א‬FRaEFVL‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬
-٥٥-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬

K‫א‬ ،‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
 ٣J ٣‫א‬ Rst‫א‬ ‫א‬
 W‫א‬‫א‬
I a ( st ) =
VL
Ra + Rst
٣ ٧
K‫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٣J ٣
Developed Torque ‫א‬‫א‬‫א‬٣J ٣
ra L‫א‬ ٤J ٣
 F‫א‬ Ic‫א‬KB n
F = BLI
 W‫א‬‫א‬‫א‬
٣ ٨
c
 W‫א‬‫א‬E‫א‬F‫א‬‫א‬
-٥٦-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

T = Fr
c
a
= BLI r
ca
B 2πr L
a I
=
c 
2π
٣ ٩
٢πraL‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٣
 W‫א‬‫א‬‫א‬‫א‬
 Φ = B(2πra L)
٣ ١٠
 W‫א‬‫א‬‫א‬٩J ٣‫א‬B
I
Tc = Φ c
2π
٣-١١
Za‫א‬‫א‬ Ia‫א‬‫א‬‫א‬ ٢p‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬٢a‫א‬‫א‬‫א‬
T = Tc Z a 2 p
I
= Φ c Za 2 p
2π
٣ ١٢
 W‫א‬‫א‬‫א‬‫א‬‫א‬Ic‫א‬‫א‬‫א‬
I
Ic = a
2a
٣ ١٣
‫א‬‫א‬‫א‬ ‫א‬‫א‬ ١٢J ٣‫א‬ ١٣J ٣‫א‬
T=
W‫א‬
2p Φ
Z I
2a 2π a a
٣ ١٤
 W‫א‬‫א‬
T = KΦ I a
٣ ١٥
2 p Za
2a 2π =‫א‬K
KIa،Ф  ‫א‬ ‫א‬‫א‬‫א‬١٥J ٣‫א‬
 WEb‫א‬‫א‬‫א‬٢J ٣‫א‬‫א‬
-٥٧-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬

E Ia
T= b
2πn
60
٣ ١٦
 W‫א‬‫א‬‫א‬‫א‬
T=
P
ω 
 ٣ ١٧
‫א‬‫א‬‫א‬ ωE‫א‬ x‫א‬F EbIa =‫א‬ P
ω=
 W‫א‬‫א‬
2πn
60
٣ ١٨
 K‫א‬‫א‬‫א‬‫א‬١٦J ٣‫א‬
٤-٣ ‫ﺷﻜﻞ‬
Types of DC motors ‫א‬‫א‬٤J ٣
 F ‫א‬        ‫א‬ ‫א‬  
 WE‫א‬‫א‬
 E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬J
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J
    ‫א‬ ،‫א‬‫א‬    ‫א‬ ‫א‬ ‫א‬ ‫א‬  ‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 DC shunt motor ‫א‬‫א‬١J ٤J ٣
-٥٨-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

  RshE‫א‬F ‫א‬    ‫א‬‫א‬   ٥J ٣  
  Ra ‫א‬   K‫א‬   ‫א‬   ‫א‬  ‫א‬‫א‬ 
‫א‬‫א‬‫א‬‫א‬K Rst‫א‬‫א‬
K

 ‫א‬‫א‬٥J ٣
 W٥J ٣‫א‬‫א‬‫א‬‫א‬
Eb = Vin − I a Ra
 I in = I a + I sh
 ٣ ١٩
 W‫א‬‫א‬‫א‬‫א‬
Eb = K nφ
٣ ٢٠
b
 W‫א‬٢٠J ٣‫א‬١٩J ٣‫א‬
n=

Eb
V − I a Ra
= in
KΦ
KΦ
b
٣ ٢١
b
 ‫א‬‫א‬ •
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 n=f(Ia)
‫א‬‫א‬J
 T=f(Ia)‫א‬‫א‬J
-٥٩-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬


n=f(T) ‫א‬‫א‬J
‫א‬‫א‬E‫א‬F‫א‬‫א‬‫א‬٢١J ٣‫א‬
‫א‬‫א‬KI٦J ٣‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬، ١٥J ٣‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬E‫א‬F‫א‬
KII٦J ٣‫א‬

‫א‬ ٢١J ٣‫א‬ ١٥J ٣‫א‬‫א‬
 W‫א‬
n=
Vin
Ra
−T
KΦ
K 2Φ 2
b
٣ ٢٢
b
     K‫א‬‫א‬  ‫א‬  ‫א‬ ‫א‬   ٢٢J ٣ ‫א‬
n=
‫א‬
Vin
KΦ
b
‫א‬ (T=٠)‫א‬K‫א‬‫א‬‫א‬
 ‫א‬  ‫א‬ ‫א‬  ، ٢٢J ٣ ‫א‬  ‫א‬   (no load speed )
K‫א‬‫א‬‫א‬‫א‬  ٧J ٣K‫א‬‫א‬
 K‫א‬
-٦٠-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

 ‫א‬‫א‬‫א‬٦J ٣








‫א‬‫א‬‫א‬‫א‬‫א‬٧J ٣
 :‫א‬‫א‬‫א‬‫• א‬
 ‫א‬  ‫א‬ ‫א‬‫א‬‫א‬
    ،‫א‬  ‫א‬   ،‫א‬ ‫א‬    ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K‫א‬‫א‬،‫א‬
 K‫א‬‫א‬‫א‬‫א‬
‫א‬L ٧٥٠ ٢٤٠‫א‬ ١J ٣
 KK‫א‬‫א‬٠{٠٥‫א‬‫א‬،٣٠
Vin=٢٤٠ V
n=٧٥٠ rpm
Ia=٣٠ A
-٦١-
Ra=٠{٠٥Ω
‫א‬
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

Eb=Vin-IaRa
=٢٤٠ ٣٠*٠{٠٥=٢٣٨{٥ volt
T=EbIa/ω
ω=٢πn/٦٠ rad/sec
 T=٢٣٨{٥*٣٠/(٢*π*٧٥٠L٦٠)=٩١{١ N.m





٩٦٠‫א‬، ٥٠٠‫א‬ ٢J ٣
٣   ‫א‬ ‫א‬   ٥٢   ‫א‬  K  
‫א‬K‫א‬ ٢٠٠ ٠{٠٤‫א‬‫א‬‫א‬K
 K‫א‬‫א‬
٢p=٤ Vin=٥٠٠ V
Za=٩٦٠
Iin=٥٢ A
Φ=٣megalines
Ra=٠{٠٤ Ω ‫א‬
Rsh=٢٠٠ Ω
Ish=Vin/Rsh=٥٠٠L٢٠٠=٢{٥ A
Ia=Iin-Ish=٥٢ ٢{٥=٤٩{٥ A
Eb=Vin-IaRa
=٥٠٠- ٤٩{٥*٠{٠٤=٤٩٨{٠٢ V
2P
n
φZ a
2a
60
n
4
498.03 = * (3 *10 6 *10 −8 ) * 960 *
2
60
Eb =
n=٥١٢{٧٧ rpm
ω=٢πn/٦٠ ω=٢π*٥١٢{٧٧L٦٠=٥٤{٣٣ rad/sec
T=EbIa/ω
T=٤٩٨{٠٣*٤٩{٥L٥٤{٣٣=٤٥٣{٧٥ N.m
 DC series motor‫א‬٢J ٤J ٣
‫א‬  ‫א‬ ‫א‬    ،‫א‬‫א‬    ٨J ٣  
 W‫א‬‫א‬،‫א‬
-٦٢-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬

٣ ٢٣
Eb=Vin-Ia(Ra+Rse)
٣ ٢٤
Ia=Iin=Ise
 :Ia‫א‬،Ise‫א‬Φ‫א‬‫א‬‫א‬
٣ ٢٥
Φ=CIse=CIa
 W‫א‬‫א‬‫א‬‫א‬١٥J ٣‫א‬
٣ ٢٦
T=K´Ia٢
 K‫א‬‫א‬‫א‬،‫א‬‫א‬
Eb = K b nΦ = K ′ nI a
b
٣{٢٧
 W‫א‬٢٣J ٣‫א‬٢٦J ٣‫א‬
n=
Eb
V − I a ( Ra + Rse )
= in
K ′Ia
K ′I a
b
b
٣ ٢٨

 ‫א‬‫א‬٨J ٣

 ‫א‬‫א‬ •
‫א‬‫א‬  ،‫א‬‫ א‬ ٢٦J ٣‫א‬
‫א‬K ٩J ٣ (parabola)  ‫א‬
    ،   ‫א‬‫א‬  ‫א‬  ‫א‬  ‫א‬  ٢٨J ٣
   (hyperabola) ‫א‬       ‫א‬  E‫א‬F ‫א‬
 K٩J ٣‫א‬‫א‬‫א‬
-٦٣-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬

‫א‬ ٢٨J ٣‫א‬ ٢٥J ٣‫א‬‫א‬
n=
 W‫א‬
R +R
Vin
− T a 2 2 se
αI a
α Ia
٣ ٢٩
 W‫א‬‫א‬٢٩J ٣‫א‬٢٦J ٣‫א‬

n=
Vin Ra + Rse
−
α
αT
٣ ٣٠
K١٠J ٣‫א‬‫א‬‫א‬‫א‬‫א‬ ٣٠J ٣‫א‬
 (T=٠) ‫א‬ ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ 
‫א‬‫א‬‫א‬‫א‬
 K‫א‬


‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٩J ٣
-٦٤-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬١٠J ٣
 ‫א‬‫א‬‫א‬‫• א‬
E‫א‬F‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬E‫א‬F‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K‫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
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
٥٠‫א‬ ٢٢٠‫א‬‫א‬٣J ٣
‫א‬K,١‫א‬,١٥ ‫א‬،L١٠٠٠‫א‬
‫א‬ ‫א‬‫א‬ ٦٠‫א‬‫א‬‫א‬٪٨٠ ‫א‬‫א‬
Vin= ٢٢٠ V
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
Ia١=٥٠A n١=١٠٠٠rpm Ra=٠{١٥ Ω Rse=٠{١Ω
Ia٢=٦٠A
Eb١=Vin-Ia١ (Ra+Rse)
=٢٢٠ ٥٠(٠{١٥H٠{١)=٢٠٧{٥ V
Eb٢=Vin-Ia٢ (Ra+Rse)
=٢٢٠-٦٠(٠٫١٥+٠٫١)=٢٠٥ V
-٦٥-
n٢=٠{٨n١ ‫א‬
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 ‫א‬‫א‬‫א‬

T١=Eb١Ia١/ω١
=٢٠٧٫٥*٥٠/(٢π*١٠٠٠/٦٠)=٩٩٫٠٧ N.m
T٢=Eb٢Ia٢/ω٢
=٢٠٥*٦٠/(٢π*٠٫٨*١٠٠٠/٦٠)=١٤٦٫٨٢ N.m
-٦٦-
 
‫א‬
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
‫א‬

 ٢٢٠        ‫א‬‫א‬      ٤J ٣ 
٦٣٠ ‫א‬      K‫א‬ ‫א‬   ٥٢ ‫א‬  
,١ ,٢‫א‬‫א‬‫א‬، ٠{٠١٨‫א‬‫א‬
٪٦٠ ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬K
 K‫א‬‫א‬‫א‬،‫א‬‫א‬
٢p=٤ Vin=٢٢٠V Ia=٥٢A Za=٦٣٠
Φ=٠٫٠١٨ wb
Eb١=Vin-Ia١(Ra+Rse)
=٢٢٠-٥٢(٠٫٢+٠٫١)=٢٠٤٫٤V
n
2p
E b1 =
φZ a 1
2a
60
n
4
204.4 = * 0.018 * 630 * 1
2
60
n١=٥٤١ rpm
T١=Eb١Ia١/ω١ =٢٠٤٫٤*٥٢/(٢π*٥٤١/٦٠)=١٨٧٫٦١ N.m
TαIa٢
I2
I2
T2
= 0.6 = a22 = a 2 2
T1
I a1 (52)
I a 2 = 0.6 * (52) 2 = 40.3 A
Eb٢=Vin-Ia٢(Ra+Rse)
=٢٢٠-٤٠٫٣(٠٫٢+٠٫١)=٢٠٨ V
Eb 2 n2 Φ 2 n2 I a 2
=
=
Eb1 n1Φ 1 n1 I a1
208 n2 * 40.3
=
204.4 541 * 52
208 * 541 * 52
n2 =
204.4 * 40.3
n٢=٧١٠ rpm
-٦٧-
Ra=٠٫٢Ω
Rse=٠٫١Ω
‫א‬
T٢=٠٫٦T١
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬

 DC compound motor‫א‬‫א‬٣J ٤J ٣
‫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 
K‫א‬١١J ٣،
J J ‫א‬‫א‬١١J ٣
 W‫א‬‫א‬
Eb = Vin − I a Ra − I in Rse
Vsh = I sh R sh = Vin − I in Rse
I in = I se = I a + I sh
V − I a Ra − I in Rse
n = in
KΦ
٣-٣١
٣-٣٢
٣-٣٣
٣-٣٤
Eb = Vin − I a ( Ra + Rse )
Vsh = I sh R sh = Vin
I in = I a + I sh
V − I a ( Ra + Rse )
n = in
KΦ
-٦٨-
:‫א‬‫א‬
٣-٣٥
٣-٣٦
٣-٣٧
٣-٣٨
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
‫א‬

‫א‬    Φ  ‫א‬  ١٦J ٣ ‫א‬ ‫א‬‫א‬  ‫א‬‫א‬  
‫א‬ ‫א‬  K ‫א‬‫א‬  ‫א‬‫א‬      ‫א‬ ‫א‬
      ،E ‫א‬ ‫א‬F‫א‬‫א‬     ‫א‬ ‫א‬
 W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
 :(Comulative compound motor)‫א‬J
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Φ‫א‬
 K‫א‬‫א‬‫א‬١٢J ٣،‫א‬‫א‬
: (Level compound motor)J
‫א‬،‫א‬‫א‬ Φ ‫א‬‫א‬‫א‬
 K١٢J ٣،‫א‬‫א‬
 W(Differential compound motor)J
‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ 
‫א‬ ‫א‬‫א‬‫א‬‫א‬ ΦK‫א‬
 K١٢J ٣‫א‬
 ‫א‬‫א‬‫א‬١٢J ٣
:‫א‬‫א‬‫א‬‫א‬
•
‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬    ‫א‬ ‫א‬ ‫א‬  K‫א‬   ‫א‬    
‫א‬‫א‬‫א‬‫א‬‫א‬،(Rolling mills )
-٦٩-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

 ‫א‬   ‫א‬   ،‫א‬     ،‫א‬  ‫א‬


K‫א‬‫א‬‫א‬
Speed control and reversal ‫א‬‫א‬٥J ٣
 ، E ٣٤J ٣، ٢٩J ٣، ٢١J ٣F ‫א‬،‫א‬ ‫א‬  ‫א‬   
‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬
‫א‬ ‫א‬‫א‬     K‫א‬ ‫א‬   ‫א‬ ‫א‬   
 K‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬‫א‬١J ٥J ٣
 ‫א‬‫א‬WJ
،‫א‬‫א‬‫א‬‫א‬‫א‬
 S١, S٢, S٣ ‫א‬‫א‬K١٣J ٢
‫א‬ ١٣J ٣K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬١٣J ٣K‫א‬‫א‬ ،‫א‬
K S١, S٢, S٣‫א‬S‫א‬‫א‬
‫א‬‫א‬‫א‬ ‫א‬
 K‫א‬
‫א‬‫א‬‫א‬‫א‬١٣J ٣
-٧٠-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬

 ‫א‬‫א‬‫א‬WJ
،‫א‬ ‫א‬  ‫א‬ ‫א‬   ‫א‬     ‫א‬ 
،١٤J ٣     ? ?  ‫א‬‫א‬‫א‬ ‫א‬
‫א‬‫א‬‫א‬،GM‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬،M’
‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬K‫א‬
(flux control)‫א‬‫א‬WJ
   ،‫א‬‫א‬‫א‬ ‫א‬  ‫א‬  
‫א‬‫א‬‫א‬‫א‬،‫א‬
‫א‬‫א‬‫א‬‫א‬  ‫א‬
 K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬٢J ٥J ٣
 W‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬W
‫א‬  ‫א‬   ‫א‬‫א‬       ٢٩J ٣ ‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
.‫א‬‫א‬
??‫א‬‫א‬‫א‬١٤J ٣
-٧١-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 ‫א‬‫א‬‫א‬
 
‫א‬

W‫א‬‫א‬‫א‬W
I-‫א‬‫א‬‫א‬ Φ‫א‬‫א‬‫א‬
 ‫א‬‫א‬،‫א‬‫א‬ Iin‫א‬K‫א‬ in
‫א‬،‫א‬‫א‬‫א‬
 ‫א‬‫א‬١٥J ٣K‫א‬،‫א‬
 W‫א‬W
‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬‫א‬‫א‬K١٥J ٣‫א‬
 K‫א‬
‫א‬‫א‬‫א‬١٥J ٣
 ‫א‬‫א‬‫א‬٣J ٥J ٣
‫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K‫א‬
K‫א‬،‫א‬‫א‬١٦J ٣

-٧٢-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 ‫א‬‫א‬‫א‬
 
‫א‬


‫א‬‫א‬١٦J ٣
Starting Methods‫א‬٦J ٣
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬ 
Ia =
Ia =
 W‫א‬‫א‬
Vin − Eb
Ra
٣ ٣٩
 W‫א‬‫א‬
Vin − Eb
Ra + Rse
٣ ٤٠
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬KE‫א‬F‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬٤٠J ٣،٣٩J ٣،٣J ٣
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
 W‫א‬‫א‬
 I starting =
Vin
Ra
٣ ٤١
 W‫א‬‫א‬
I starting =
Vin
Ra + Rse
٣ ٤٢
-٧٣-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 ‫א‬‫א‬‫א‬
 
‫א‬

,١‫א‬٢٠٠‫א‬‫א‬،٤٢J ٣،٤١J ٣
‫א‬‫א‬٢٠٠٠‫א‬‫א‬E١F
‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬(starter)
‫א‬EF‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬
 ‫א‬‫א‬١J ٦J ٣
‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
K‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬(A)‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬١٧J ٣
‫א‬‫א‬‫א‬‫א‬(B)‫א‬‫א‬‫א‬Rst‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
on‫א‬٣٢١‫א‬(A)‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
(S)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
(on)‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
K(off)‫א‬
-٧٤-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
‫א‬

١٧J ٣
 ‫א‬‫א‬٢J ٦J ٣
EF ٢٠ ‫א‬‫א‬‫א‬‫א‬ 
‫א‬‫א‬‫א‬‫א‬ (overload)‫א‬
١٨J ٣‫א‬K‫א‬‫א‬(s)‫א‬‫א‬(circuit breaker)
،off‫א‬ A‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬E‫א‬‫א‬‫א‬S‫א‬
‫א‬،‫א‬‫א‬‫א‬ C‫א‬ B‫א‬‫א‬ A
     K‫א‬    ‫א‬  ‫א‬‫א‬   ‫א‬ ‫א‬ 
A‫א‬‫א‬C‫א‬D‫א‬C‫א‬
A‫א‬‫א‬Rst‫א‬‫א‬KC‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬on‫א‬
C‫א‬‫א‬‫א‬‫א‬‫א‬ S‫א‬‫א‬
on‫א‬ A‫א‬‫א‬ D‫א‬‫א‬‫א‬ 
K‫א‬ A‫א‬ (spring)‫א‬ off‫א‬
-٧٥-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
‫א‬

‫א‬   ‫א‬    ،F        E 
‫א‬،E‫א‬ F‫א‬
‫א‬‫א‬ C‫א‬
 K‫א‬‫א‬‫א‬A‫א‬‫א‬D‫א‬
١٨J ٣
 Losses and Efficiency ‫א‬‫א‬‫א‬٧J ٣
 W‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬
 Mechanical loss‫א‬‫א‬J
 Copper loss‫א‬‫א‬J
Iron loss‫א‬‫א‬J
،‫א‬‫א‬ ‫א‬‫א‬‫א‬
KE‫א‬‫א‬F‫א‬‫א‬K‫א‬‫א‬
-٧٦-
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

 ‫א‬‫א‬١J ٧J ٣
 ‫א‬    ‫א‬ ‫א‬   ‫א‬    
 ‫א‬ ‫א‬‫א‬
(W).‫א‬  ‫א‬‫א‬‫א‬ ١٩J ٣  Input power‫א‬
،Pg ‫א‬ ‫א‬‫א‬‫א‬
W‫א‬Pg
Pg=Ea Ia
 Pg=Pin-Pcu
٣-٤٣
 Pmech    ‫א‬    Pg ‫א‬  ‫א‬ ‫א‬ 
      ‫א‬ ‫א‬  ‫א‬ ‫א‬   Pin  
 K‫א‬‫א‬‫א‬‫א‬٢٠J ٣KPout‫א‬
 W‫• א‬
 W‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

η =
 ‫א‬‫ א‬J
o / p HP * 746
=
i/ p
Vin I in
٣ ٤٤
 ‫א‬‫א‬‫א‬
η =
Pout
Pout + losses
η =
Pin − losses
Pin
‫א‬
Pin
٣ ٤٥
٣ ٤٦
‫א‬ ‫א‬ ‫א‬‫א‬
Pi&Pmech
Pcu
Pout
Pg
 ‫א‬‫א‬‫א‬‫א‬‫א‬١٩J ٣
-٧٧-
HP
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬


‫א‬‫א‬‫א‬
o/p
HP
‫א‬‫א‬
i/p
IaEa
‫א‬‫א‬‫א‬‫א‬
∆VI
2
I2aRa
I
Pmech+Pi
I2seRse
shR sh
 ‫א‬‫א‬‫א‬‫א‬٢٠J ٣
‫א‬‫א‬١٥٠‫א‬‫א‬ ٥J ٣
٪٩١‫א‬K٥٥٠،L٩٦٠
 W‫א‬KK,١‫א‬٢٧٥‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬J
K,٢‫א‬‫א‬‫א‬٪٦٠‫א‬‫א‬‫א‬J
 K‫א‬‫א‬‫א‬
HP=١٥٠ n=٩٦٠rpm Vin=٥٥٠V η=٩١٪
Rsh=٢٧٥Ω
Ra=٠٫١Ω
Pout
Pin
150 * 746
0.91 =
Pin
150 * 746
Pin =
= 122967 W
0.91
Pin = Vin I in
122967 = 550 * I in
I in = 122967 / 550 = 223.6
V
V
550
I sh = sh = in =
=2 A
Rsh Rsh 275
I a = I in − I sh = 223.6 − 2 = 221.6 A
Pcu = I a2 Ra + I sh2 Rsh = (221.6) 2 * 0.1 + (2) 2 * 275 = 6011 W
η=
-٧٨-
A
‫א‬
 ‫א‬‫א‬
 ١٤٢
‫א‬‫א‬
 
 ‫א‬‫א‬‫א‬
‫א‬

Plosses = Pin − Pout = 122967 − 150 * 746 = 11067 W
Plosses = Pmech + Pi + Pcu
- Pmech + Pi = Plosses − Pcu = 11067 − 6011 = 5056 W
Eb = Vin − I a Ra = 550 − 221.6 * 0.1 = 527.84 V
EI
EI
527.84 * 221.6 * 60
= 1163.5 N .m
-T = b a = b a =
2πn
ω
2 * π * 960
60
TαΦ Ia
 Φ،‫א‬
TαI a
T1 I a1
=
= 0 .6
T
Ia
I a1 = 0.6 * I a = 0.6 * 221.6 = 132.96 A
Eb1 = Vin − I a1 ( Ra + Rad ) = 550 − 132.96 * (0.1 + 0.2) = 510.1 V
T1 =
E b1 I a 1
ω1
=
E b1 I a1
2π n1
60
510.1 * 132.96 * 60
2 * π * n1
510.1 * 132.96 * 60
- n1 =
= 928 rpm
2 * π * 0.6 * 1163.5
0.6 *1163.5 =
-٧٩-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
‫א‬

 ‫א‬‫א‬

 K‫א‬‫א‬‫ א‬J ١
K‫א‬‫א‬‫؟‬‫א‬‫א‬‫א‬ J ٢
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬J ٣
K‫א‬‫א‬‫א‬‫ א‬J ٤
K‫؟‬‫א‬‫א‬ J ٥
‫א‬ ‫א‬‫א‬   ،‫א‬ ‫א‬     ‫ א‬J ٦
K‫א‬‫א‬
‫؟‬‫א‬‫א‬‫א‬‫א‬ J ٧
‫א‬‫א‬‫א‬،‫א‬‫א‬ J ٨
‫؟‬‫א‬
‫؟‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫ א‬J ٩
   ٥٤٠  ‫א‬   ٢٢٠J  ٤ ‫א‬   J ١٠
١‫א‬‫א‬،‫א‬K ٦ ٣٢‫א‬،‫א‬
‫–א‬ ٠{٠٣‫א‬‫א‬ ,٩‫א‬
K‫א‬‫–א‬
K٥٠‫א‬L٥٠٠ ٢٢٠‫א‬ J ١١
K,٢‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
٧٨٤‫א‬ ٤ J  ٢٥٠‫א‬ J ١٢
‫א‬ ,٢٥، ,٥‫א‬‫א‬‫א‬‫א‬K
‫א‬‫א‬‫א‬، ٢٥‫א‬
K‫א‬٤٠‫א‬
‫א‬ ، ١٠٠ ‫א‬   L ٨٥٠    ٢٤٠ ‫א‬  J ١٣
‫א‬ ‫א‬، ,١، ,١٥‫א‬‫א‬‫א‬
-٨٠-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 ‫א‬‫א‬‫א‬
 
‫א‬

 ‫א‬ ‫א‬  ‫א‬  ، ٣٠ ‫א‬    ‫א‬  
K‫א‬‫א‬
 ٥٥‫א‬‫א‬‫א‬ ٥٠٠‫א‬ J ١٤
‫א‬K ٢٤٥‫א‬K,٨‫א‬‫א‬، ٢١
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬٨٢٠‫א‬٤‫א‬ J ١٥
L ١٢٠٠‫א‬، ٢‫א‬
 ‫א‬ K ١٢٠ ‫א‬   ‫א‬ ‫א‬  ،  ٦  ‫א‬ ‫א‬ 
، ١٢٠، ٠{٠٥، ,١٥‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬  ‫א‬   –  ‫א‬ ‫א‬  ‫א‬ J  W
K‫א‬
-٨١-
 ‫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
٤
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬ W‫א‬‫א‬
K‫א‬‫א‬‫א‬ K١
K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٢
K‫א‬‫א‬‫א‬ K٣
K‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K٤
K‫א‬‫א‬‫א‬ K٥
K‫א‬‫א‬‫א‬‫א‬ K٦
K‫א‬‫א‬‫א‬‫ א‬K٧
K‫א‬‫א‬‫א‬‫א‬ K٨
K‫א‬‫א‬‫א‬‫א‬‫א‬ K٩

 ٪٨٥‫א‬‫א‬W‫א‬‫א‬‫א‬

K٨ W‫א‬‫א‬

KEF W‫א‬‫א‬


.‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬


-٨١-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 Single Phase Transformers ‫א‬‫א‬‫א‬
E‫א‬F‫א‬ ‫א‬‫א‬
‫א‬‫א‬‫א‬ ‫א‬ ‫א‬ ‫א‬‫א‬
‫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‫א‬  ‫א‬ K‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
 ‫א‬    ‫א‬ ‫א‬‫א‬    K ‫א‬  
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬
‫א‬١J
‫א‬‫א‬‫ א‬‫א‬
٤
‫א‬(core) 
‫א‬K‫א‬‫א‬‫א‬،E١J ٤F‫א‬
، (Magnetic flux)‫א‬‫א‬‫א‬
‫א‬   ‫א‬    ‫א‬    ‫א‬ ‫א‬  ‫א‬ ‫א‬
  ‫א‬ ‫א‬ ‫א‬ ،   ‫א‬ ‫א‬   ‫א‬  K‫א‬ 
‫א‬ ‫א‬  ،N١     (primary winding) ‫א‬‫א‬ ‫א‬    ‫א‬
  KN٢   (secondary winding) ‫א‬ ‫א‬    ‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬ ‫א‬   ‫א‬ ‫א‬  ‫א‬  K‫א‬ ‫א‬  ‫א‬ ‫א‬
 ‫א؟‬ ،‫א‬‫א‬
-٨٢-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 ‫א‬‫א‬١J ١J ٤
 W‫א‬
‫א‬‫א‬‫א‬‫א‬ (Power transformers)‫א‬-
 K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬ (Electronic transformers) ‫א‬  K       ‫א‬ ‫א‬   ‫א‬ ‫א‬ 
K‫א‬‫א‬
‫א‬ ‫א‬      (Instrument transformers) ‫א‬  K‫א‬‫א‬،‫א‬‫א‬‫א‬
 W‫א‬‫א‬
 ‫א‬J
 E‫א‬F‫א‬J
 J
 J
 W‫א‬‫א‬
 ‫א‬J
 ‫א‬J
‫א‬،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
 K‫א‬‫א‬‫א‬
١J ٤
-٨٣-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 ‫א‬٢J ١J ٤
  (windings) ‫א‬ ،(core)‫א‬ ‫א‬ W‫א‬ ‫א‬‫א‬  ‫א‬ 
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 (legs)‫א‬‫א‬‫א‬W(core)‫א‬‫א‬J
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬ (yoke)‫א‬‫א‬
K,٣٥‫א‬‫א‬ ،E‫א‬‫א‬‫א‬F‫א‬ ‫א‬
‫א‬ ,K٣,K٢‫א‬‫א‬‫א‬KK,٥
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬،
       ،   ‫א‬  K‫א‬ ‫א‬‫א‬ ‫א‬
K‫א‬  ‫א‬       ،‫א‬   ‫א‬  
 K٢J ٤
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  ‫א‬   K‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬‫א‬     
 K‫א‬‫א‬‫א‬
 (Leg) ٢J ٤
:‫א‬
(Core type) ‫א‬‫א‬‫א‬J 
‫א‬     ١J ٤    ‫א‬ ‫א‬  ‫א‬ ‫א‬ 
‫א‬L‫א‬،‫א‬‫א‬
   ،EF   ‫א‬  ‫א‬   ،٣J ٤    ‫א‬
‫א‬EF‫א‬،EF‫א‬‫א‬
‫א‬   ‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬  K ‫א‬    ‫א‬
K‫א‬،‫א‬‫א‬،
-٨٤-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 core type‫א‬‫א‬‫א‬٣J ٤
Shell typeE‫א‬‫א‬F‫א‬‫א‬‫א‬J 
‫א‬،٤J ٤IE‫א‬‫א‬‫א‬
،EFIE
‫א‬‫א‬EF E I
‫א‬ ‫א‬ ‫א‬    ‫א‬   ‫א‬ ‫א‬‫א‬  ،
‫א‬‫א‬‫א‬K‫א‬‫א‬ 
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
shell type‫א‬‫א‬٤J ٤
-٨٥-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
‫א‬‫א‬ ‫א‬  ،‫א‬  ‫א‬     W(windings) ‫א‬J
‫א‬ ‫א‬‫א‬،(disc windings)‫א‬‫א‬،(cylindrical windings)
 K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
‫א‬٢J ٤
 ‫א‬   ،   ‫א‬     ‫א‬ 
K(Sandwich) ‫א‬
‫א‬‫א‬‫א‬١J ٢J ٤
‫א‬ ‫א‬ ‫א‬ ‫א‬   ‫א‬     ‫א‬ ‫א‬ 
 ‫א‬    ،‫א‬    ٥J ٤   Kcore) (type
،‫א‬‫א‬‫ א‬‫א‬
‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬
K,١‫א‬K,٥‫א‬
 K‫א‬
‫א‬‫א‬ ‫א‬‫א‬  ‫א‬‫א‬
‫א‬‫א‬EF‫א‬‫א‬‫א‬ ،‫א‬‫א‬
EF‫א‬K‫א‬‫א‬،‫א‬
 K‫א‬‫א‬
 ‫א‬‫א‬٥J ٤




-٨٦-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 ‫א‬‫א‬‫א‬٢J ٢J
٤
 ، ‫א‬ ‫א‬   ‫א‬    ‫א‬ ،‫א‬  
   ، ‫א‬ ‫א‬     ‫א‬ ‫א‬     
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬ ‫א‬      ‫א‬    ،‫א‬  ‫א‬
 K٦J ٤،‫א‬
 ‫א‬‫א‬٦J ٤

‫א‬     ،‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬  
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

Ideal Transformer‫א‬‫א‬‫א‬٣J ٤
‫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K‫א‬
‫א‬‫א‬‫א‬ ‫א‬ ،٧J ٤   ‫א‬      
‫א‬ ‫א‬   ‫א‬    EF   ،   
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬ ‫א‬ ،v١  ‫א‬‫א‬     K‫א‬ ‫א‬     
 W‫א‬‫א‬‫א‬ e١،Ф‫א‬
-٨٧-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
v1 = e1 = N1
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
dΦ
dt
٤ ١
‫א‬ ‫א‬  ‫א‬ ‫א‬     ،‫א‬‫א‬ ‫א‬   N١ 
v 2 = e2 = N 2
 W
dΦ
dt
٤ ٢
‫א‬١J ٤‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ e٢،‫א‬ N٢ 
 W‫א‬‫א‬٢J ٤
v1 e1 N 1
= =
v 2 e2 N 2
٤-٣
 ‫א‬   N١>N٢  ‫א‬ ، ‫א‬   
N1
 
N2
‫א‬‫א‬‫א‬ K‫א‬‫א‬ N٢>N١‫א‬،
،‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬
 W‫א‬‫א‬‫א‬‫א‬
٤ ٤
v1i1 = v2 i2
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٤J ٤‫א‬٣J ٤‫א‬

i1 N 2
=
i2 N 1
٤ ٥
 ‫א‬‫א‬٧J ٤



 
-٨٨-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
١J ٤‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬  ٧J ٤‫א‬‫א‬‫א‬ K٥J ٤
 ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K‫א‬‫א‬‫א‬
 ‫א‬  ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬    ‫א‬  ‫א‬
Kv٢‫א‬‫א‬v١‫א‬‫א‬K‫א‬
 W‫א‬،٥J ٤‫א‬٣J ٤‫א‬‫א‬‫א‬‫א‬
2
V1 ⎛ N 1 ⎞ V2
⎟
=⎜
I 1 ⎜⎝ N 2 ⎟⎠ I 2
٤ ٦
 WZ٢(load impedance)‫א‬
V2
= Z2
I2
٤ ٧
 ٦J ٤‫א‬٧J ٤‫א‬
2
V1 ⎛ N 1 ⎞
⎟ Z2
=⎜
I 1 ⎜⎝ N 2 ⎟⎠
٤ ٨
 Z٢’‫א‬‫א‬‫א‬‫א‬Z٢‫א‬٨J ٤‫א‬
2
⎛N ⎞
Z 2′ = ⎜⎜ 1 ⎟⎟ Z 2
⎝ N2 ⎠
٤ ٩
Z٢‫א‬ Z’٢‫א‬،‫א‬‫א‬‫א‬‫א‬ ٨J ٤


 K‫א‬K‫א‬‫א‬‫א‬



 ‫א‬‫א‬‫א‬‫א‬٨J ٤


-٨٩-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬٤J ٤
 K‫א‬‫א‬‫א‬‫א‬‫א‬
Φ(t ) = Φ m sin ωt
٤ ١٠
 W‫א‬‫א‬١J ٤‫א‬‫א‬
 e1 (t ) = N 1Φ mω cosωt ٤-١١
 W‫א‬‫א‬١١J ٤‫א‬ ‫א‬f،ω=٢πf 
o
 e1 (t ) = 2πN 1Φ m f sin(ωt + 90 )
٤ ١٢
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
o
 e1 (t ) = 2 E1 sin(ωt + 90 )
٤ ١٣
 We١‫א‬‫א‬‫א‬‫א‬‫א‬E١
2π
N 1Φ m f
2


E1 = 4.44 N 1Φ m f
٤ ١٤
E1 =
‫א‬  ،‫א‬ ‫א‬  ‫א‬ ‫א‬ ‫א‬  ‫א‬  ‫א‬ ‫א‬ 
 W
 E2 = 4.44 N 2 Φ m f
٤ ١٥
‫א‬‫א‬‫א‬‫א‬  ١٥J ٤‫א‬ ١٤J ٤‫א‬
 E١‫א‬١٣J ٤‫א‬١٠J ٤‫א‬K‫א‬
‫א‬،‫א‬‫א‬‫א‬ Ko٩٠‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬





-٩٠-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬


‫א‬‫א‬‫א‬،L ٥٠ ‫א‬ ١J ٤
‫א‬‫א‬‫א‬‫א‬‫א‬ ٢٠‫א‬
‫א‬ ‫א‬‫א‬ ‫א‬    ‫א‬ ‫א‬  ‫א‬ – ٢L١٠٠٠٠ ‫א‬
 K٣٠٠٠L٢٢٠‫א‬
B=١٠٠٠٠lines/cm٢
A=٢٠x٢٠=٤٠٠cm٢

E١=٣٠٠٠ V
Φ=BA=١٠٠٠٠*٤٠٠*١٠ ٨=٠{٠٤ wb
E٢=٢٢٠V
‫א‬
E=٤{٤٤fΦN
E١=٤{٤٤fΦN١
N١=٣٠٠٠/(٤{٤٤*٥٠*٠{٠٤)=٣٣٨ turns
E٢=٤{٤٤fΦN٢
N٢=٢٢٠/(٤{٤٤*٥٠*٠{٠٤)=٢٥ turns


 ٤٠‫א‬ ٥٠٠‫א‬‫א‬ ٢٥‫א‬ ٢J ٤
‫א‬‫א‬–‫א‬‫א‬‫א‬J ‫א‬، ٣٠٠٠ ‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬J ‫א‬‫א‬‫א‬‫א‬‫א‬J ‫א‬‫א‬

KVA=٢٥ N١=٥٠٠ N٢=٤٠
V1 N 1 500
=
=
= 12.5
V2 N 2
40
3000
V2 =
= 240V
12.5
KVA 25 *10 3
=
= 8.33 A
I1 =
V1
3000
KVA N 2
500
=
I1 =
I2 =
* 8.33 = 104.13 A
V2
N1
40
E1 = 4.44 fφN 1
-٩١-
V١=٣٠٠٠V
‫א‬
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
φ=
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
3000
= 0.027 wb
4.44 * 50 * 500


٦٠٤٤٠L١١٠،٥‫א‬  ٣J ٤
‫א‬K‫א‬‫א‬K,٨٤٠‫א‬ 
 ‫א‬‫א‬‫א‬–‫א‬J ‫א‬‫א‬J W‫א‬،


 KVA=٥
‫א‬
V١/V٢=٤٤٠/١١٠
f=٦٠ Hz
I٢=٤٠ A
P.F=٠{٨ lead
 W‫א‬‫א‬‫א‬
V2 = 110∠0 volt 
I 2 = 40∠ cos −1 0.8 A
I 2 = 40∠36.87 o A
-The transformer ratio is
V1 N 1 440
=
=
=4
V2 N 2 110
Thus
V١=٤٤٠ V
N2
1
I 2 = (40∠36.87 o ) = 10∠36.87 o A
N1
4
- The load impedance is
V
110∠0
= 2.75∠ − 36.87 o Ω
Z2 = 2 =
o
I 2 40∠36.87
- The impedance of the load referred to the primary side is
2
⎛ N1 ⎞
⎟⎟ Z 2 = (4) 2 (2.75∠ − 36.87 o = 44∠ − 36.87 o Ω
Z 2′ = ⎜⎜
⎝ N2 ⎠
V
440
= 44∠ − 36.87 o Ω
or Z 2′ = 1 =
o
I 1 10∠36.87
I1 =
-٩٢-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 ‫א‬‫א‬‫א‬٥J ٤
‫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،R١‫א‬‫א‬‫א‬K‫א‬‫א‬
 KR٢‫א‬
‫א‬   ‫א‬   ،    ‫א‬ ‫א‬   ‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
X١‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬KX١=٢πfL١ ‫א‬‫א‬ (Leakage reactance)
‫א‬ ‫א‬ ‫א‬ ،‫א‬ ‫א‬         ‫א‬ ‫א‬
X٢ ‫א‬      ‫א‬    ‫א‬ ‫א‬  
    ،‫א‬ ‫א‬ ‫א‬ ٩J ٤    K‫א‬  (X٢=٢πfL٢)
‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬K‫א‬‫א‬
K‫א‬‫א‬‫א‬
-٩٣-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 ‫א‬‫א‬٩J ٤


‫א‬‫א‬‫א‬ Xo K‫א‬‫א‬‫א‬ ١٠J ٤
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ Ro،
‫א‬   ،    ‫א‬   Io  Ia ‫א‬ ‫א‬ ‫א‬ 
 ‫א‬ E١٠J ٤ F‫א‬ ‫א‬‫א‬   K ‫א‬  Im ‫א‬
 ١١J ٤K‫א‬‫א‬‫א‬ ١١J ٤‫א‬‫א‬
( )‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬١٠J ٤
N1
V2
N2
N
I 2′ = 2 I 2
N1
V2′ =
-٩٤-
٤-١٦
٤-١٧
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
⎛N ⎞
R2′ = R2 ⎜⎜ 1 ⎟⎟
⎝ N2 ⎠
2
٤-١٨
⎛N ⎞
X 2′ = X 2 ⎜⎜ 1 ⎟⎟
⎝ N2 ⎠
2
٤-١٩
 ‫א‬‫א‬‫א‬‫א‬‫א‬١١J ٤
‫א‬‫א‬‫א‬ ‫א‬١١J ٤‫א‬‫א‬‫א‬‫א‬
،E ‫א‬F
 ‫א‬‫א‬E ‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬
  E
 ‫א‬F 
 ‫א‬‫א‬ K ‫א‬‫א‬،١٢J ٤
K١٣J ٤‫ א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٢J ٤
-٩٥-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٣J ٤
١٣J ٤،١٢J ٤Xeq١‫א‬‫א‬Req١‫א‬‫א‬
W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
٤ ٢٠
Req1 = R1 + R2′
٤ ٢١
X eq1 = X 1 + X 2′
 W‫א‬‫א‬‫א‬‫א‬
2

⎛N ⎞
Z L′ = Z L ⎜⎜ 1 ⎟⎟ ٤
⎝ N2 ⎠
٢٢


‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W
N2
V1 ٤ ٢٣
N1
N
I 1′ = 1 I 1
٤-٢٤
N2
V1′ =
⎛N ⎞
R1′ = R1 ⎜⎜ 2 ⎟⎟
⎝ N1 ⎠
2
٤-٢٥
⎛N ⎞
X 1′ = X 1 ⎜⎜ 2 ⎟⎟
⎝ N1 ⎠
2
٤-٢٦
‫א‬‫א‬،١٤J ٤‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬ Xeq٢‫א‬‫א‬Req٢
-٩٦-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
Req 2 = R1′ + R2
٤ ٢٧
′
 X eq 2 = X 1 + X 2
٤ ٢٨

 ‫א‬‫א‬‫א‬‫א‬١٤J ٤







‫א‬‫א‬‫א‬٤٠٠L٢٠٠٠١٠٠‫א‬٤J ٤
R١=٠{٠١ Ω
X١=٠{٠٣ Ω
R٢=٠{٢٥ Ω X٢=٠{٧٥ Ω
R٠=٥٠٠ Ω W
 Xo=١٥٠ Ω
‫א‬KK,٨٢٠٠٠‫א‬٩٠
 KEF١٢J ٤‫א‬‫א‬‫א‬‫א‬‫א‬
 W،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
2
 R١=٠{٠١٥ Ω
X١=٠{٠٣٥ Ω
2
2
⎛N ⎞
⎛ 400 ⎞
R2′ = R2 ⎜⎜ 1 ⎟⎟ = 0.25⎜
⎟ = 0.01Ω
2000
N
⎝
⎠
⎝ 2⎠
2
⎛N ⎞
⎛ 400 ⎞
X 2′ = X 2 ⎜⎜ 1 ⎟⎟ = 0.75⎜
⎟ = 0.03Ω
⎝ 2000 ⎠
⎝ N2 ⎠
-٩٧-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
Req=R١+R’٢=٠{٠١٥H٠{٠١=٠{٠٢٥Ω
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
Xeq=X١+X’٢=٠{٠٣٥H٠{٠٣=٠{٠٦٥ Ω
Zo=Ro//JXo=٥٠٠//J١٥٠
The voltage V٢=٢٠٠٠ V; thus
V2′ =
N1
⎛ 400 ⎞
V2 = 2000⎜
⎟ = 400V
N2
⎝ 2000 ⎠
The current I٢=KVA*١٠٣/V٢=٩٠*١٠٣/٢٠٠٠=٤٥ A
I 2′ =
N2
⎛ 2000 ⎞
I2 = ⎜
⎟45 = 225 A
N1
⎝ 400 ⎠
The power factor=٠{٨ lagging
I 2′ = 225∠ − 36.87 o
V١=V’٢+I’٢(Req+JXeq)
= 400∠0 + 225∠ − 36.87 o (0.025 + J 0.065)
= 400∠0 + 225∠ − 36.87 o * 0.07∠68.96 o
= 400∠0 + 15.75∠32.1o
V1 = 400 + 13.34 + J 8.37 = 413.34 + J 8.37 = 413.42∠1.16V
500 * J 150 75000∠90 o
Zo =
=
= 143.7∠73.3 o Ω
o
500 + J 150 522∠16.7
V
413.42∠1.16
Io = 1 =
= 2.88∠ − 72.14 A
Zo
143.7∠73.3
I 1 = I 2′ + I o = 225∠ − 36.87 o + 2.88∠ − 73.3o
= 180 − J 135 + 0.83 − J 2.76 = 180.83 − J 137.83 = 227.37∠ − 37.31o A
١٣J ٤‫א‬‫א‬EF١٢J ٤‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬
 Transformer operation ‫א‬٦J ٤
 No load operation‫א‬‫א‬١J ٦J ٤
‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬ Io‫א‬ ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
 ‫א‬   ‫א‬      ‫א‬     
‫א‬ Ia‫א‬،Im, Ia  Io‫א‬K
-٩٨-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 V١ ‫א‬    ‫א‬ K‫א‬ ‫א‬‫א‬  ‫א‬  Im  ،‫א‬
 
 V1 = E m sin ωt
٤ ٢٩
‫א‬o٩٠‫א‬Im‫א‬‫א‬‫א‬
 W‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬
 Φ = Φ m cos ωt ٤ ٣٠
o٩٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬Ia
 KIo‫א‬‫א‬‫א‬KIm‫א‬

r r r
I o = I m + I a ٤
٣١
‫א‬،‫א‬‫א‬١٥J ٤

I a = I o cos φ o
I m = I o sin φ o
 W‫א‬Im،Ia‫א‬
٤ ٣٢
 K‫א‬‫א‬‫א‬Io‫א‬‫א‬‫א‬φo
‫א‬X١R١‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
r r r r
 V1 = E1 + I o Z 1 ٤
٣٢
 K Z 1 = R12 + X 12 
E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬
 W‫א‬‫א‬
 Po = V1 I o cos φ o ٤ ٣٤
 W‫א‬‫א‬Ro‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 Ro =
V1
V1
=
 ٤
I a I o cos φ o
٣٥
 W‫א‬‫א‬Xo‫א‬
-٩٩-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 Xo =
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
V1
V1
=
 ٤
I m I o sin φ o
٣٦
‫א‬‫א‬‫א‬‫א‬Io‫א‬
 K‫א‬‫א‬‫א‬


 ‫א‬١٥J ٤
-١٠٠-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 Load operation‫א‬‫א‬٢J ٦J ٤
I٢ ‫א‬‫א‬‫א‬‫א‬EFZL‫א‬
‫א‬‫א‬‫א‬‫א‬
 ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬I٢
‫א‬K١٧J ٤‫א‬I’٢‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬Io‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
r
r
r
 I 1 = I 2′ + I a ٤ ٣٧
 W‫א‬I٢‫א‬
I2 =
V2
ZL
٤-٣٨
‫א‬‫א‬،١٧J ٤‫א‬I’٢
K١٦J ٤
 ‫א‬‫א‬١٦J ٤


-١٠١-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 Transformer regulation‫א‬٣J ٦J ٤
‫א‬K‫א‬،‫א‬‫א‬‫א‬‫א‬
W‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
Percentage Voltage Re gulation ( PVR ) =
V2 ( noload ) − V2 ( rated )
V2 ( rated )
٤ ٣٩
x100
V’١‫א‬‫א‬‫א‬‫א‬ V٢‫א‬‫א‬‫א‬‫א‬
    ‫א‬  ‫א‬ ‫א‬  ،E١٤J ٤  ‫א‬F‫א‬  
W‫א‬V’١‫א‬‫א‬
 Percentage Voltage Re gulation( PVR) =
V1′ − V2
x100
V2
٤ ٤٠
 W‫א‬V’١
V1′ = V2 + I 2 ( Req 2 + JX eq 2 ) ٤
٤١
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
⎧⎪ I 2 ( Req 2 cos φ 2 + X eq 2 sin φ 2 ) 1 ⎛ I 2 ( X eq 2 cos φ 2 − Req 2 sin φ 2 ) ⎞ 2 ⎫⎪
⎟⎟ ⎬100
 ( PVR) = ⎨
+ ⎜⎜
2⎝
V2
V2
⎪⎩
⎠ ⎪⎭
٤ ٤٢
E١٣J ٤F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬
 Percentage Voltage Re gulation( PVR) =
V1 − V2′
x100 ٤
V2′
٤٣
 W‫א‬V١
 V1 = V2′ + I 2′ ( Req1 + JX eq1 ) ٤ ٤٤
W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
⎧ I R cos φ1 I 1 X eq1 sin φ1 ⎫
( PVR ) = ⎨ 1 eq1
+
⎬100
V
V
⎩
⎭
1
1
٤ ٤٥
‫א‬F٤٥J ٤‫א‬٤٢J ٤‫א‬‫א‬
 KE‫א‬‫א‬‫א‬‫א‬‫א‬


-١٠٢-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 Equivalent circuit parameters ‫א‬‫א‬‫א‬٧J ٤
،٥J ٤‫א‬‫א‬‫א‬‫א‬
،R٢‫א‬‫א‬،X١‫א‬‫א‬‫א‬،R١‫א‬‫א‬‫א‬
KXo‫א‬Ro‫א‬‫א‬‫א‬‫א‬،X٢‫א‬‫א‬
X١=X’٢R١=R’٢‫א‬K‫א‬N١/N٢ ‫א‬
 W‫א‬‫א‬
 R1 =
ρl1
A1
ρl
R2 = 2
A2

l٢ ,A٢ ،‫א‬‫א‬‫א‬l١ ,A١ ،‫א‬‫א‬ρ
 W‫א‬‫א‬K‫א‬‫א‬
R1 l1 A2
=
R2 l 2 A1

 W‫א‬،‫א‬‫א‬

l1 N1
=
l2 N 2
 W‫א‬‫א‬‫א‬‫א‬

A2 I 2 N1
= =
A1 I 1 N 2
 W‫א‬‫א‬‫א‬

⎛N ⎞
R1 = R2 ⎜⎜ 1 ⎟⎟
⎝ N2 ⎠
2
 W‫א‬
 R1 = R2′
،٢٠J ٤‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
 W٢١J ٤‫א‬
 Req = 2 R1 = 2 R2′
٤ ٤٦
 X eq = 2 X 1 = 2 X 2′
٤ ٤٧

-١٠٣-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 ،‫א‬ ‫א‬‫א‬           ‫א‬ ‫א‬
 K‫א‬‫א‬KReq,Xeq, Ro,Xo
 
No load test ‫א‬‫א‬١J ٧J ٤
‫א‬‫א‬(open circuit test)‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬
J ٤،‫א‬‫א‬‫א‬
‫א‬‫א‬،Po‫א‬‫א‬‫א‬‫א‬Io‫א‬K١٧
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
:Ro,Xo
 Po = I oVo cos φ o
 cos φ o =
Po
I oVo
 I a = I o cos φ o
 I m = I o sin φ o
V1
Ia
V
Rm = 1
Im
 Ro =

 ‫א‬١٧J ٤




-١٠٤-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 Short circuit test‫א‬‫א‬٢J ٧J ٤
،١٨J ٤‫א‬‫א‬‫א‬‫א‬
Vsc‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬KI٢‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬   ،Isc ‫א‬   ‫א‬‫א‬  ،Psc ‫א‬   ‫א‬
:‫א‬‫א‬‫א‬ Req,
Xeq‫א‬‫א‬‫א‬،Vsc
Psc = I Req
V
Z sc = sc = Req2 + X eq2
I sc
2
sc
٤-٤٨
٤-٤٩
‫א‬KXeq٤٩J ٤‫א‬،Req٤٨J ٤‫א‬
 ‫א‬ R١,X١,R’٢,X’٢       ٤٧J ٤ ،٤٦J ٤ ‫א‬ 
 K‫א‬R٢,X٢‫א‬
 ‫א‬١٨J ٤







-١٠٥-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
‫א‬ K ٢٣٠٠L٢٣٠    ٥٠٠  ‫א‬      ٥J ٤ 
،٩{٤‫א‬‫א‬٢٢٥٠‫א‬،‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬ ٨٢٢٠‫א‬‫א‬‫א‬K ٢٣٠٠‫א‬
 K‫א‬‫א‬‫א‬‫א‬K ٩٤{٥‫א‬‫א‬
Open circuit test: Vo=٢٣٠٠V Io=٩{٤A Po=٢٢٥٠W
Short circuit test: Vsc=٩٤{٥V Isc=Irated
Psc=٨٢٢٠W
Po = I oVo cos φ o
P
2250
cos φ o = o =
= 0.1156
I oVo 9.4 * 2300
φ o = cos −1 (0.1156) = 83.36 o
Vo
V
2300
Ro = 1 =
=
= 2116Ω
I a I o cos φ o 9.4 * 0.1156
Vo
V1
2300
=
=
= 246.33Ω
I m I o sin φ o 9.4 * 0.9933
500 *10 3
I sc = I f .l =
= 217.39 A
2300
P
8220
Req = sc2 =
= 0.1739Ω
I sc (217.39) 2
V
Z sc = sc = ( Req2 + X eq2 )
I sc
Rm =
2
⎛ 94.5 ⎞
2
2
⎟ = (0.1739) + X eq
⎜
⎝ 217.39 ⎠
As a result, we get Xeq=٠{٣٩٨٤Ω
0.1739
= 0.08695Ω
2
2
X eq 0.3984
=
= 0.1992Ω
X 1 = X 2′ =
2
2
2
⎛ N1 ⎞
⎟⎟
R2′ = R2 ⎜⎜
⎝ N2 ⎠
R1 = R2′ =
Req
=
2
2
⎛N ⎞
⎛ 230 ⎞
R2 = R2′ ⎜⎜ 2 ⎟⎟ = 0.08695 * ⎜
⎟ = .0008695Ω
⎝ 2300 ⎠
⎝ N1 ⎠
-١٠٦-
‫א‬
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
⎛N ⎞
X 2′ = X 2 ⎜⎜ 1 ⎟⎟
⎝ N2 ⎠
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
2
2
2
⎛N ⎞
⎛ 230 ⎞
X 2 = X 2′ ⎜⎜ 2 ⎟⎟ = 0.1992 * ⎜
⎟ = .001992Ω
N
2300
⎝
⎠
⎝ 1⎠
Losses and Efficiency ‫א‬‫א‬‫א‬٨J ٤
 ‫א‬‫א‬‫א‬١J ٨J ٤
، Cupper loss‫א‬ Iron loss‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬ ‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬K‫א‬
  ‫א‬   ‫א‬  ‫א‬  Po ‫א‬   ‫א‬ ‫א‬ 
  ‫א‬ ‫א‬   ‫א‬ ،    ‫א‬    ،‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬
Piron=Po
٤ ٥٠
‫א‬ ‫א‬   ‫א‬   K‫א‬   ‫א‬ ‫א‬   
‫א‬‫א‬‫א‬‫א‬،‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
K‫א‬E٪٥٣F‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
Pcu=Psc
٤ ٥١
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 Pcu ( sc ) = I sc2 Req 
٤ ٥٢
 Pcu ( f .l ) = I 2f .l Req ٤ ٥٣
 Pcu ( f .l )
⎛I
= Pcu ( sc ) ⎜⎜ f .l
⎝ I sc
2
⎞
⎟ ٤
⎟
⎠
-١٠٧-
٥٤
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬
Pcu ( x ) = x 2 Pcu ( f .l ) ٤
٥٥
 ‫א‬٢J ٨J ٤
‫א‬‫א‬‫א‬‫א‬output power‫א‬‫א‬
 W‫א‬‫א‬‫א‬،‫א‬‫א‬
η=
η=
P2
x100
P2 + Piron + Pcu
٤
P2
x100
P1
٥٦
٤ ٥٧
 W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬P١،‫א‬P٢
 P2 = V2 I 2 cosφ 2 ٤ ٥٨
 KPower factor‫א‬cosφ٢
‫א‬‫א‬‫א‬٥٦J ٤‫א‬٥٨J ٤‫א‬P٢
η=

 WE‫א‬‫א‬‫א‬F‫א‬‫א‬
V2 I 2 cos φ 2
V2 I 2 cos φ 2 + Piron + I 2 Req
2
100
٤ ٥٩
‫א‬‫א‬٢٥٠٠‫א‬‫א‬،٥٠٠‫א‬٦J ٤
 ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬٧٥٠٠‫א‬‫א‬‫א‬
 K,٨
KVA=٥٠٠
Piron =٢٥٠٠W
Pcu(f.l.)=٧٥٠٠ W
cosφ=٠{٨
‫א‬
P٢=٥٠٠*١٠٣*٠{٨=٤٠٠٠٠٠ W
η=
P2
400000
x100 =
x100 = 97.56%
400000 + 7500 + 2500
P2 + Piron + Pcu
At half load
-١٠٨-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
P٢(١L٢)=١L٢*٥٠٠*١٠٣*٠{٨=٢٠٠٠٠٠W
Pcu(x)=x٢Pcu(f.l)
Pcu(١L٢)=١L٤*٧٥٠٠=١٨٧٥W
η=
P2 (1 / 2 )
P2 (1 / 2 ) + Piron + Pcu (1 / 2 )
x100 =
200000
x100 = 97.86%
200000 + 1875 + 2500
٥J ٤‫א‬‫א‬‫א‬‫א‬٧J ٤
 K,٨
 W‫א‬
V٢=٢٣٠ V Pi=٢٢٥٠ W
I٢=٥٠٠*١٠٣/٢٣٠=٢١٧٤A
Req٢=٠٫٠٠١٧٣Ω
Xeq٢=٠٫٠٠٣٩٨Ω
Thus, substituting in Equation ٢-٤٢, we get
⎧ 2174(0.00173(0.8) + 0.00398(0.6)) 1 ⎛ 2174(0.00398(0.8) − 0.00173(0.6)) ⎞ 2 ⎫
+ ⎜
( PVR) = ⎨
⎟ ⎬100
230
2
230
⎝
⎠ ⎭
⎩
= 3.64%
Also, substituting in Equation ٤-٥٩, we get
η=
230 * 2174 * 0.8
2
230 * 2174 * 0.8 + 2250 + 2174 * 0.00173
* 100 = 97.46%
 Auto-transformer ‫א‬‫א‬‫א‬٩J ٤
‫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 K١٩J ٤‫א‬
 K‫א‬K٢٠J ٤
-١٠٩-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
‫א‬ BC‫א‬ (N١)‫א‬‫א‬‫א‬ ١٩J ٤ AB‫א‬
 K‫א‬‫א‬‫א‬(N٢)‫א‬
 WK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

V1 N 1 I L
=
= ٥
V2 N 2 I 1
٦٠
 W‫א‬‫א‬‫א‬
 I 2 = I L − I 1 ٤ ٦١
 C‫א‬K‫א‬‫א‬‫א‬ ‫א‬
‫א‬      ‫א‬‫א‬     ‫א‬    ‫א‬ 
K“Variac”  ‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬ ‫א‬  K٢٠J ٤  ‫א‬‫א‬ ‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ ٢{٥ W١
‫א‬  ‫א‬ ‫א‬    ‫א‬  ‫א‬ ‫א‬   ‫א‬  
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬


 ‫א‬١٩J ٤
 ‫א‬‫א‬٢٠J ٤
-١١٠-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 ‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬ J ١
‫א‬‫א‬‫א‬‫א‬‫ א‬J ٢
 ‫א‬‫א‬‫א‬‫ א‬J ٣
K‫א‬‫א‬‫ א‬J ٤
K‫؟‬‫א‬ J ٥
‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬J ٦
‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬ J ٧
‫א‬‫؟‬‫א‬‫א‬‫א‬‫א‬ J ٨
‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J ٩
‫؟‬‫א‬‫א‬ J ١٠
‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬ J ١١
K‫א‬‫א‬‫ א‬J ١٢
‫؟‬‫א‬‫א‬‫א‬‫א‬ J ١٣
K‫א‬‫א‬‫א‬‫א‬‫א‬ J ١٤
‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬ J ١٥
 ‫א‬ ‫א‬  ‫א‬ ، ٦٠  ‫א‬    ‫א‬   J ١٦
‫א‬    ‫א‬ ‫א‬   ٢٥X٢٠  ‫א‬  
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، ٢L ٠{٠٠٠١‫א‬
K٣٠٠٠L٢٢٠‫א‬‫א‬
‫א‬ o٣٠‫א‬ ١٠‫א‬K١W٤‫א‬‫א‬ J ١٧
J ،‫א‬‫א‬K١٢٠،‫א‬
 ‫א‬ – ‫א‬‫א‬ ‫א‬ – ‫א‬ ‫א‬  ‫א‬‫א‬ ‫א‬ 
K‫א‬


-١١١-
 ‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬‫א‬
 K٤٠٠L٢٠٠٠ ‫א‬   ، ‫א‬   ٥٠  ‫א‬   J ١٨
 K K,٨    ٢٠٠٠      ٤٠  
K‫א‬‫א‬–‫א‬J W‫א‬
  ٦٠٠٠L٦٦٠ ‫א‬   ،   ٢٠٠ ‫א‬   J ١٩
R١=١{٥٦Ω
R٢=٠{٠١٦Ω
X١=٤{٦٧Ω
X٢=٠{٠٤٨Ω W‫א‬‫א‬‫א‬
‫א‬‫א‬K,٢٦٣ ,٩٦‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬
،٢٣٠٠L٢٣٠‫א‬،٥٠٠‫א‬J ٢٠
‫א‬‫א‬J ١W‫א‬‫א‬‫א‬‫א‬‫א‬
Vo=٢٣٠V
Io=٩٤A
Po=٢٢٥٠W
‫א‬‫א‬J ٢
Vsc=١٠٠V  Isc=٢٢٨A   Psc=٩{٢KW
 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
٣٣٠٠L٢٠٠ ‫א‬     ٢٥  ‫א‬   ‫א‬ J ٢١
 W‫א‬‫א‬
Vo=٣٣٠٠V
Io=٠{٨A
Po=٣٠٠W
Vo=١٠٠V
Io=٧{٥A
Po=٥٨٠W
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
  K‫א‬   ‫א‬  ، ,٨   ‫א‬ ‫א‬ 
 K‫א‬

-١١٢-
 ‫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
٥
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
،‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬ W‫א‬‫א‬
K‫א‬‫א‬‫א‬ K١
K‫א‬ K٢
K‫א‬‫א‬ K٣
.‫א‬‫א‬‫א‬ .٤

 ٪٨٥‫א‬‫א‬W‫א‬‫א‬‫א‬

. ٤ W‫א‬‫א‬

KEF W‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬




-١١٢-
.‫א‬
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
Three Phase Transformers‫א‬‫א‬
 ‫א‬‫א‬١J ٥
 ‫א‬ ‫א‬   K       ‫א‬ ‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬K‫א‬ 
 three phase) ‫א‬‫א‬‫א‬‫א‬ ‫א‬
  ‫א‬‫א‬‫א‬ (transformer
K٥٠٠،١J ٥K‫א‬‫א‬
‫א‬‫א‬، ‫א‬‫א‬‫א‬K‫א‬‫א‬ ‫א‬
 KE‫א‬F‫א‬‫א‬‫א‬‫א‬،‫א‬
 ‫א‬‫א‬‫א‬١J ٥

-١١٣-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬

Core type W‫א‬‫א‬١J ١J ٥
    ‫א‬‫א‬    ،‫א‬    ٢J ٥  
،‫א‬‫א‬‫א‬‫א‬ V-U‫א‬‫א‬،‫א‬
‫א‬K‫א‬‫א‬‫א‬ v-u‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
.‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 EF
 ‫א‬‫א‬٢J ٥








-١١٤-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 Shell type WE‫א‬F‫א‬‫א‬٢J ١J ٥
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ ٣J ٥
 K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬
 ‫א‬‫א‬٣J ٥
‫א‬٢J ٥
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
 W‫א‬
Star-Star


Y-Y
‫א‬J ‫א‬‫א‬ J
Delta-Delta
∆-∆
‫א‬–‫א‬‫א‬J
Star-Delta
Y-∆
‫א‬–‫א‬‫א‬J
Delta-Star
∆-Y
‫א‬–‫א‬‫א‬J
 Y-YJ ١J ٢J ٥
Y‫א‬‫א‬،J ‫א‬٤J ٥
‫א‬،‫א‬‫א‬‫א‬KY‫א‬
‫א‬،‫א‬(Third-harmonic)‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬


-١١٥-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 Y-Y٤J ٥

 ∆-∆J ٢J ٢J ٥
  ،   ‫א‬ ‫א‬‫א‬     ،‫א‬  ‫א‬ ‫א‬ 
‫א‬‫א‬  ‫א‬  ‫א‬ ‫א‬ ‫א‬      K٥J ٥   
‫א‬،‫א‬‫א‬‫א‬K‫א‬
 K‫א‬
‫א‬  ‫א‬ ‫א‬ ‫א‬‫א‬      ،‫א‬  ‫א‬ ‫א‬ 
 K‫א‬،‫א‬

 ∆-∆٥J ٥

-١١٦-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 Y-∆J ٣J ٢J ٥
‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬،٦J ٥
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬K
 K‫א‬‫א‬‫א‬
 Y-∆٦J ٥
 ∆- Y  J ٤J ٢J ٥
 ‫א‬‫א‬‫א‬‫א‬
 ٧J ٥K‫א‬K‫א‬‫א‬‫א‬
 K‫א‬‫א‬
 ∆- Y٧J ٥

-١١٧-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬‫א‬٣J ٥
  ‫א‬  ‫א‬   ‫א‬   ‫א‬ ‫א‬ ‫א‬ 
‫א‬‫א‬ ‫א‬‫א‬K K‫א‬
  ‫א‬ ‫א‬    ‫א‬ ‫א‬   K  
 ‫א‬‫א‬‫א‬K‫א‬ ‫א‬
 K‫א‬
‫א‬‫א‬‫א‬ ‫א‬
‫א‬‫א‬        ‫א‬‫א‬  ‫א‬    ،‫א‬  
‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
 K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،(KVA) ‫א‬
(container) ،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬K
،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K
K‫א‬ K‫א‬‫א‬ ‫א‬‫א‬
 ‫א‬     ‫א‬ ‫א‬     ‫א‬‫א‬  
 ‫א‬ (radiators)‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K‫א‬ ‫א‬ ‫א‬
‫א‬‫א‬ (forced cooling)‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬   ٨J ٥   K‫א‬  ‫א‬   ‫א‬   ‫א‬  
 K‫א‬‫א‬‫א‬‫א‬،
-١١٨-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 ١٠٠٠٨J ٥
 ‫א‬‫א‬‫א‬٤J ٥
،‫א‬‫א‬‫א‬‫א‬
،‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
 K‫א‬‫א‬

 W‫א‬‫א‬‫א‬EFJ
‫א‬‫א‬K‫א‬‫א‬ 
  ،K          K‫א‬  ‫א‬ ،‫א‬
 ‫א‬‫א‬ ،‫א‬      K‫א‬‫א‬  ‫א‬    
‫א‬  ‫א‬‫א‬         K‫א‬  ،‫א‬
 ،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬K
-١١٩-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
‫א‬K‫א‬،‫א‬‫א‬‫א‬
 K‫א‬‫א‬‫א‬
‫א‬K‫א‬‫א‬ J ١
‫א‬،‫א‬‫א‬‫א‬
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
    ‫א‬ K‫א‬ ‫א‬  (circulating current)  ‫א‬
 K‫א‬
 K‫א‬،‫א‬‫א‬ J ٢
،،‫א‬‫א‬‫א‬K‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬IZ‫א‬‫א‬‫א‬K‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬ J ٣
،‫א‬‫א‬‫א‬ ،‫א‬‫א‬
‫א‬K‫א‬ ‫א‬
‫א‬‫א‬ ‫א‬‫א‬ ‫א‬
K‫؟‬K‫א‬K‫א‬
،‫א‬    ،(phase sequence)‫א‬ ‫א‬ ‫א‬ ‫א‬  J ٤
‫א‬،‫א‬‫א‬‫א‬  
K
  ،  ‫א‬‫א‬  ‫א‬     ٩J ٥  
 K‫א‬‫א‬‫א‬
‫א‬‫א‬٩J ٥
-١٢٠-
 ‫א‬‫א‬
‫א‬‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬‫א‬

 ‫؟‬‫א‬‫א‬‫א‬‫א‬ J ١
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫ א‬J ٢
K‫א‬
K‫א‬‫א‬‫א‬ J ٣
K‫א‬‫א‬‫ א‬J ٤
‫؟‬‫א‬‫א‬ J ٥
 ‫؟‬‫א‬‫א‬‫א‬ J ٦
-١٢١-
 ‫א‬‫א‬
 ١٤٢
 ‫א‬‫א‬‫א‬
 
‫א‬
 ‫א‬‫א‬‫א‬‫א‬
 K١٩٨٨،L،?‫א‬‫א‬‫א‬‫?א‬‫א‬‫א‬ J ١
K١٩٨٨،L،‫א‬‫א‬‫א‬‫ א‬J ٢
‫א‬ ‫א‬ J   ،SI ‫א‬  ‫א‬ ‫ א‬J ٣
K١٩٨١‫א‬‫א‬J ‫א‬‫א‬‫א‬‫א‬
K‫א‬‫א‬LL،‫א‬‫א‬‫א‬‫ א‬J ٤
 W‫א‬‫א‬‫א‬
٥٦٧٨٩-

Electrical Technology, Edward Hughes , ISBN:٠-٠٧-٠٢١٣٤-٥
Electrical Machines, G. R. Slemon and A. Straughan, Eddison-Weslley ١٩٨٠.
Electric Machinery, M. S. Sarma, West Publishing Company, ١٩٩٤.
Electrical Machines and Transformers –Principles and Applications, P. F. Ryff, D.
Platnick and J. A. Karnas, Printice Hall.
Principles of Electricity, B. J. Theraga, and B. K. Theraga.

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 ‫א‬
 ١٤٢
 
 ‫א‬‫א‬‫א‬
 ‫א‬
 ‫א‬
 
 







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
‫א‬‫א‬‫ א‬K١
 









 ١J ١
 ٥
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



‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣J ١

 ‫א‬‫א‬‫א‬٤J ١
 ٢



 ٨

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 ١٠
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 ٩
 ١١
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
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

 ‫א‬‫א‬‫א‬٢J ١
 ‫א‬‫א‬‫א‬‫א‬‫א‬٥J ١

‫א‬‫א‬‫א‬‫א‬‫א‬١J ٥J ١
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢J ٥J ١





 ١٦





‫א‬‫א‬١J ٢
 ١٩





‫א‬‫א‬٢J ١J ٢

 ‫א‬٣J ١J ٢
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
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١٦
 ١٦
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‫א‬‫א‬‫א‬ K٢
‫א‬‫א‬‫א‬١J ١J ٢
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 ٢٢
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 ٢٦
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 ٣٠
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‫א‬‫א‬‫א‬١J ٢J ٤J ٢
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
 ٣٤
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
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‫א‬‫א‬‫א‬٢J ٢J ٤J ٢
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 ١٤٢
 
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 ‫א‬E‫א‬F‫א‬‫א‬
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