كتاب بالعربي( دوائر وقياسات كهربائية -2 )

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June 2020
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 ‫א‬‫א‬‫א‬ ã¹]
‫א‬ ٢–‫א‬

١٣٢

‫א‬

١٣٢

 ‫א‬

 ٢ –‫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  ?  ? ٢J   ‫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















١٣٢

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬  ، ‫א‬‫א‬٢-‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬ K‫א‬

K‫א‬‫א‬‫א‬‫• א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬ • K‫א‬‫א‬ •

K‫א‬‫א‬‫א‬‫א‬‫א‬‫• א‬

K‫א‬‫א‬‫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‫א‬،‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬ K  ‫א‬‫א‬‫א‬

 K‫א‬،‫א‬W

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬‫א‬



١٣٢

 ‫א‬

 ٢ –‫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

 K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  W،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬ F ‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬‫א‬،E‫א‬J   ‫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K ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W،‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K  ‫א‬،‫א‬E‫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 ã¹]
٢–‫א‬

 ‫א‬

‫א‬

١

‫א‬‫א‬ ‫א‬

١٣٢  ٢ –‫א‬

 ‫א‬  ‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ 

 W‫א‬‫א‬‫א‬W‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ o K‫א‬‫א‬‫א‬‫א‬‫א‬

o

 K‫א‬‫א‬‫א‬‫א‬

o

  ٪٨٠‫א‬‫א‬W‫א‬‫א‬‫א‬  ‫א‬‫א‬،‫א‬‫א‬W  ‫א‬‫א‬ K

-١-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ KESSouthF‫א‬ENNorthF‫א‬ K  ‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬FF‫א‬ 

، E١-

 F=

µ P1 P2 4π r 2

١ ١

 

‫א‬‫א‬، ‫א‬‫א‬µ • ‫؛‬‫א‬‫א‬

KEA.mF-  ‫א‬‫א‬‫א‬ P٢ P١ • ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬ 

µ ‫א‬‫א‬،١m١A/m  4π

K

K‫א‬‫א‬r •  ‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬،E‫א‬‫א‬ -٢-

‫א‬‫א‬

١٣٢

‫א‬

 ٢ –‫א‬

 ‫א‬  ‫א‬

‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬ ١ ١‫א‬K‫א‬ K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬١-٢‫א‬K ‫א‬‫א‬‫א‬، ،‫א‬‫א‬

‫א‬١ ٣‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬

 K‫א‬

 ‫א‬‫א‬ W١ ١ ‫א‬

 ‫א‬W١-٢‫א‬

-٣-

 

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬W١-٣‫א‬



 ‫א‬‫א‬ ‫א‬‫א‬ AΦ‫א‬‫א‬

K(WbWeberF‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬،(TTeslaF‫א‬‫א‬‫א‬B‫א‬

 ،‫א‬‫א‬‫א‬  B=

Φ A

١ ٢

،Ф=٢×١٠ ٥Wb،١-٤‫א‬‫ א‬A  ‫א‬ ‫א‬‫א‬‫א‬W١ ١  K‫א‬‫א‬‫א‬ ٢

Φ

A=٠٫٥m ١-٤ ‫א‬

Φ 2 × 10 − 5 = 4 × 10 − 5 T  B= = A 0.5

     W‫א‬

‫א‬E١ ٥‫א‬FA٢ A١‫א‬‫א‬‫א‬‫א‬‫א‬W١ ٢  KA١‫א‬‫א‬،B=١٠ ٥T‫א‬‫א‬‫א‬ -٤-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

  

٢



A١=٠٫٦m B

A٢=٠٫٦m



٢

 

١-٥ ‫א‬ -٥

Ф = B A١ = ٠{٦ × ١٠ Wb





 W‫א‬ 

WA١‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬A٢‫א‬‫א‬  ‫א‬ K‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬µ‫א‬‫א‬‫א‬‫א‬

 µ٠‫א‬‫א‬KEH/mHenry/mF



µ 0 = 4 π × 10 −7 H / m

‫א‬‫א‬µ٠‫א‬‫א‬Kµ٠‫א‬‫א‬‫א‬  ،µr‫א‬  µr =

µ µ0

١ ٣

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  W

‫א‬‫א‬µrEFerromagnetic‫א‬F‫א‬‫א‬‫• א‬ ‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬ KE‫א‬‫א‬‫א‬µrF‫א‬‫א‬‫א‬‫א‬

µrEParamagnetic‫א‬‫א‬F‫א‬‫א‬‫• א‬ ‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫א‬ -٥-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

µrEDiamagnetic‫א‬F‫א‬‫א‬‫• א‬

‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬‫א‬

K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬  ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

KEmagnetic domainsF‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬١ ٦‫א‬

‫א‬‫א‬K  ،‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ 

S

N N

S

N



S

N

N

S

S

‫א‬ :١-٦ ‫א‬ ‫א‬‫א‬‫א‬  ‫א‬‫א‬

 K‫א‬‫א‬‫א‬،١-٧‫א‬  

N

S

  :١-٧ ‫א‬

 

‫א‬،،‫א‬‫א‬‫א‬  K١-٨‫א‬‫א‬‫א‬ -٦-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 W١-٨ ‫א‬



،‫א‬‫א‬‫א‬‫א‬ K ‫א‬  ‫א‬‫א‬،‫א‬‫א‬

K ‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬H‫א‬‫א‬  ،‫א‬‫א‬  H=

B µ

١ ٤

‫א‬‫א‬‫א‬، EА/mF‫א‬

‫א‬،‫א‬‫א‬K   ‫א‬‫א‬‫א‬‫א‬ KE‫א‬F‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬

-٧-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬K ‫א‬‫א‬٢٠A/mW١ ٣    W‫א‬‫א‬‫א‬‫א‬‫א‬  E‫א‬‫א‬‫א‬‫א‬Fµ٠ J 

E‫א‬W‫א‬F١٫٠٠٠٠٢٢µ٠ J  EF٠٫٩٩µ٠ J 

 KEW‫א‬F٥٠٠٠µ٠ J 

 ‫א‬

 W B = µ H ١ ٤‫א‬  B = µ٠ H = ٤π × ١٠

٧

 × ٢٠ = ٢{٥١×  J  ٥

١٠ B = ١٫٠٠٠٠٢٢ µ٠ H = ١٫٠٠٠٠٢٢ × ٤π × ١٠

٧

× ٢٠ = ٢{٥١٣× ١٠

٥

T T J 

B = ٠٫٩٩ µ٠ H = ٠٫٩٩ × ٤π × ١٠

٧

× ٢٠ = ٢{٤٨ × ١٠

٥

T J 

B = ٥٠٠٠ µ٠ H = ٥٠٠٠ × ٤π × ١٠

٧

× ٢٠ = ١٢٥٦٦× ١٠

٥

T J 

 K‫א‬‫א‬

-٨-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫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‫א‬

 ‫א‬‫א‬،‫א‬‫א‬

 K‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬،

 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

،‫א‬‫א‬‫א‬‫א‬‫א‬K١-٩‫א‬  K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  ‫א‬I‫א‬‫א‬‫א‬‫א‬  B=

µI 2π r

١ ٥

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬r

 K١-١٠‫א‬،‫א‬

 ‫א‬‫א‬‫א‬‫א‬١ ٤‫א‬  H=

I 2π r

١ ٦

-٩-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬،‫א‬А/m‫א‬‫א‬  K‫א‬‫א‬‫א‬ 

I H

r

‫א‬‫א‬‫א‬W١-١٠‫א‬

‫א‬‫א‬ W١-٩‫א‬



  

‫א‬‫א‬K ‫א‬‫א‬ ١٥A W١ ٤  K‫א‬٤cm‫א‬‫א‬‫א‬

 W‫א‬

 µ = µ 0 = 4π × 10 − 7 H / m ‫א‬‫א‬١-٦١-٥‫א‬ 

µ I 4π × 10 − 7 ×15 B= = = 7.5×10 − 5 T 2 π r 2 π × 4 ×10 − 2

H=

I 15 = = 59.7 A / m 2 π r 2 π × 4 ×10 − 2

   ‫א‬ I   ‫א‬F‫א‬‫א‬ ‫א‬،١-١١‫א‬‫א‬‫א‬‫א‬ B

‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬W  ‫א‬K‫א‬  F = I B l sin θ

 ١ -١٠-

٧

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬ θ‫א‬l ‫א‬‫א‬‫א‬K θ = 90o ‫א‬‫א‬IBl‫א‬  K‫א‬ θ = 0o 

  ‫א‬ W١-١١‫א‬



‫א‬‫א‬‫א‬‫א‬K  ١٠cmW١ ٥

‫א‬‫א‬‫؟‬‫א‬‫א‬،٠{٠٤N‫א‬‫א‬‫א‬،٢A  K٣٠o‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬

 ١ ٧‫א‬ B=

F I l sin θ

=

0.04 2 ×10 × 10 − 2 × sin(90 o )

= 0 .2 T

 ‫א‬θ = ٣٠o‫א‬‫א‬

B=

0.04

2 ×10 × 10 − 2 × sin(30 o )

= 0 .4 T

 ‫א‬  ‫א‬  dI٢ I١‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬

،١‫א‬‫א‬‫א‬B٢‫א‬‫א‬٢  E١-٧‫א‬F‫א‬١‫א‬ F21 = I1 B 2 -١١-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ١-٥‫א‬ .l = ١m ،θ = ٩٠o B٢ I١  ‫א‬‫א‬  B2 =

µ I2 2π d

 ‫א‬  F21 =

µ I1 I 2 2π d

١ ٨

F٢١ ‫א‬،F١٢،٢‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬  KE١-١٢‫א‬F‫א‬‫א‬‫א‬،‫א‬‫א‬

I٢

I١

F١٢

F٢١

F٢١ F١٢ d

d



I٢

I١

 ‫ א‬W١ ١٢ ‫א‬ ، ‫א‬‫א‬ ‫א‬‫א‬

‫א‬‫א‬

K  ٢×١٠ ٧N١m‫א‬‫א‬١A

 K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬W١ ٦

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K٢٠×١٠ ٧N/m٣٠cm  .٢A‫א‬‫א‬‫א‬‫א‬

-١٢-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 W‫א‬ I2 = =

 ١ ٨‫א‬

2 π d F21 µ 0 I1 2π × 30 ×10 − 2 × 20 ×10 − 7 4π × 10 − 7 × 2

= 1 .5 A

 ‫א‬ N‫א‬ K ‫א‬‫א‬‫א‬‫א‬،‫א‬

‫א‬K١-١٣‫א‬  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K  ‫א‬

‫א‬W١-١٤‫א‬‫א‬‫א‬‫א‬ ‫א‬K  ‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬  



‫א‬‫ א‬W١ ١٣ ‫א‬

  

-١٣-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

      

‫א‬ W١ ١٤ ‫א‬

  ‫א‬‫א‬‫א‬

‫א‬I‫א‬E‫א‬‫א‬‫א‬FNΦ‫א‬‫א‬

 L‫א‬‫א‬ Φ‫א‬‫א‬‫א‬  L=

NΦ I

١ ٩

 KEHHenryF‫א‬  ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ I١‫א‬  ‫א‬K‫א‬‫א‬‫א‬  M 21 =

N 2 Φ 21 I1

١ ١٠

 K‫א‬‫א‬‫א‬ N٢،‫א‬‫א‬‫א‬I١‫א‬‫ א‬‫א‬‫א‬Φ٢١،١ ١٠‫א‬  K‫א‬‫א‬  KM١٢ = M٢١‫א‬KM١٢‫א‬‫א‬ F،N‫א‬‫א‬W١ ٧ ‫א‬K   ‫א‬‫א‬‫א‬‫א‬I،B=µNI/l،lµE

‫א‬‫א‬‫א‬‫א‬Kd‫א‬‫א‬ -١٤-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬‫א‬‫א‬Kd=٥mmE  Fµr=١٠٠٠،l=١٠cm،N=١٠٠  ‫؟‬  W‫א‬  Ф‫א‬‫א‬١ ٢‫א‬ Φ = BA =

µ NI A l

 ‫א‬١ ٩‫א‬.A=πd٢/٤‫א‬ L=

µ N2 A µ0 µr N2 π d2 = l 4l

=

4 π ×10 − 7 ×1000 × (100) 2 π (5 × 10 − 3 ) 2 4 ×10 ×10

−2

= 2.5× 10 − 3 H = 2.5 mH

 ،µr‫א‬‫א‬‫א‬

L = 2.5×10 − 3 / µ r = 2.5× 10 − 3 / 1000 = 2.5× 10 − 6 H = 2.5 µH

‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

 ‫א‬‫א‬ ١ ‫א‬‫א‬‫א‬

‫א‬‫א‬K‫א‬‫א‬EKKKF‫א‬،١٥ ‫א‬Φ‫א‬‫א‬K  ‫א‬‫א‬

 EFaradayF‫א‬‫א‬e ‫א‬‫א‬‫א‬KKK‫א‬،t

dΦ ١ ١١ dt KKK ‫א‬  ‫א‬ELenzF‫א‬‫א‬K‫א‬N

 e=− N

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

‫א‬  ‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬ -١٥-

‫א‬‫א‬

١٣٢

‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬W١ ١٥‫א‬ ‫א‬

  

‫א‬،‫א‬‫א‬i ‫א‬

‫א‬‫א‬‫א‬E ‫א‬‫א‬‫א‬‫א‬‫א‬F  ١ ١١١ ٩‫א‬K‫א‬  e= − L

di dt

١ ١٢

-١٦-

‫א‬‫א‬ ‫א‬

١٣٢  ٢ –‫א‬

 ‫א‬  ‫א‬

  ‫א‬‫א‬‫א‬K ‫א‬‫א‬٢A W١ ١  .‫א‬ ٨cm‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K١٠cm٤AW١ ٢ ‫א‬‫א‬K٠٫٠٦T‫א‬‫א‬  ‫ ؟‬٤٠°‫א‬‫א‬‫א‬‫א‬

K٠٫٤٠T٨A٠٫٥٠mW ١ ٣  ‫ ؟‬١٥°‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K٨cm‫א‬‫א‬‫א‬٤A٢A‫א‬‫א‬W١ ٤  ‫؟‬‫א‬K‫א‬‫א‬‫א‬ ٥٠٠٠‫א‬،٨cm،٢٠٠‫א‬‫א‬‫א‬‫א‬W١ ٥

 K٣mm

‫א‬١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬W١ ٦

 K‫א‬٢Wb

-١٧-

 ‫א‬‫א‬‫א‬ ã¹]
٢–   ‫א‬

 ‫א‬‫א‬‫א‬

‫א‬ ‫א‬‫א‬

٢

-١-

‫א‬‫א‬ ‫א‬‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬

o

K‫א‬‫א‬‫א‬‫א‬‫א‬

o

K‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬

o o



 ٪٩٠‫א‬‫א‬W‫א‬‫א‬‫א‬ ،‫א‬،‫א‬ W  ‫א‬‫א‬ K‫א‬‫א‬،‫א‬‫א‬،‫א‬

- ١٨ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

K‫א‬‫א‬‫א‬K‫א‬

 ‫א‬‫א‬‫א‬ ،t‫א‬‫א‬   ‫א‬‫א‬E ‫א‬F‫א‬ ‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬، E ‫א‬F‫א‬‫א‬

‫א‬٢ ١‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W،‫א‬



 ‫א‬‫א‬‫ א‬W٢ ١ 

  ‫א‬

‫א‬‫א‬F‫א‬E‫א‬F‫א‬‫א‬‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬KE 

 K‫א‬‫א‬

 EΤF‫א‬EfF‫א‬

EHzHertzF‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬f‫א‬

KT‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬  ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  T=

1 f

٢ ١ - ١٩ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬W٢ ١  ٥٠ Hz J  ٦٠ Hz J 

 W‫א‬  T= 1 f

 T= =

1 1 = = 0.02 s = 20 ms f 50



J 

1 = 0.01667 s = 16.67 ms 60



J 

‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  KE٦٠ Hz  ‫א‬‫א‬

v ‫ﺒ‬،E F‫א‬tE‫א‬F‫א‬ 

. EImFVmEF‫א‬‫א‬‫א‬KEiF

W٢ ٢ ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬Fω‫א‬‫א‬ A‫א‬

‫א‬‫א‬‫א‬‫א‬A‫א‬Aa‫א‬ (rad/s

α‫א‬‫א‬،‫א‬‫א‬OA‫א‬‫א‬K ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬OA‫א‬ ٢ ٢

 α =ω t +θv

 KEt = ٠F‫א‬‫א‬‫א‬θv

،‫א‬٢π‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ ٢ ٣

 ω =2πf

 

- ٢٠ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬



 ‫א‬

 ٢ –‫א‬

 ‫א‬

v( t ) = Vm sin α = Vm sin (ω t + θ v )

٢ ٤

= Vm sin (2 π f t + θ v )

 ٢ ٣‫א‬α‫א‬‫א‬E‫א‬F‫א‬ 



 ‫א‬‫א‬ W٢ ٢ 



‫א‬‫א‬‫ א‬: ٢ ٣ 

K



 ٦٠ Hz‫א‬‫א‬‫א‬‫א‬W٢ ٢

 W‫א‬



ω = 2 π f = 2 π × 60 = 377 rad / s

 ‫א‬‫א‬W٢ ٣ π 6

 v( t ) =100 sin(377 t + ) V 

- ٢١ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 W‫א‬ ‫א‬‫ א‬J 

‫א‬‫א‬‫א‬‫א‬ J  t = ٠{٠٢٥ s ‫א‬‫א‬‫א‬ J 

t = ٠{٠٢٥ s ‫א‬‫א‬‫ א‬J 

 W‫א‬ Vm = ١٠٠ V θv =

J 

π rad = 30o 6

 J 

α = 377 × 0.025 +

π 9.95×180 = 9.95 rad = deg = 570o 6 π

v = 100 × sin 570o = − 50 V

 J  

 J 

 ‫א‬‫א‬  ‫א‬a(t)‫א‬T٠‫א‬‫א‬‫א‬‫א‬ 

Aav =

1 T0

T0

∫ a(t ) dt

 ٢ -٥

0

‫א‬‫א‬‫א‬‫א‬‫א‬a(t)‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬ K ‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W٢ ١‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ٤ T  J  T/٢  J 

 W‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ J  ‫א‬‫א‬‫א‬ K٢ ٥‫א‬T/٢T٠ J  - ٢٢ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

Vav =

1 T /2

T /2

∫ v(t ) dt = 0

 ‫א‬

 ٢ –‫א‬

1 T /2

T /2

∫V

m

sin( ω t + θ v ) dt =

0

2

π

 ‫א‬

Vm = 0.636Vm

 ‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬ R‫א‬‫א‬‫א‬‫א‬‫א‬

 K

‫א‬(T F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬



T

1  Pac = ∫ R i( t ) 2 dt T 0

  Idc‫א‬‫א‬ 2  Pdc = R I dc

   Pac = Pdc   T

1  I dc = i( t ) 2 dt ∫ T

٢ -٦

0

‫א‬‫א‬‫א‬‫א‬. IrmsIEIdc‫א‬F‫א‬  K٢ ٦‫א‬‫א‬ERoot Mean SquareF‫א‬  ‫א‬‫א‬‫א‬

T

1  Vdc = v( t ) 2 dt ∫ T

٢ -٧

0

 ،٢ ٤‫א‬  V = Vdc =

Vm = 0.707 Vm 2

٢ -٨

  - ٢٣ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 I=

 ‫א‬

 ٢ –‫א‬

 ‫א‬

Im = 0.707 I m 2

٢ ٩

W٢ ٤ ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ R K ‫א‬‫א‬،V/RI‫א‬‫א‬،١ ‫א‬

‫א‬٢ ‫א‬K ‫א‬‫א‬ ‫א‬١‫א‬

   ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬  K٢-٩‫א‬I/٠{٧٠٧‫א‬‫א‬‫א‬K‫א‬‫א‬ R

٢

١  







 ‫א‬‫א‬W٢ ٤  ،Vdc = ٢٢٠V‫א‬‫א‬،R = ٥٠Ω‫א‬٢ ٤‫א‬W٢ ٥  K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬  Idc‫א‬‫א‬  I dc =

Vdc 220 = = 4 .4 A R 50

 ،‫א‬‫א‬‫א‬‫א‬‫א‬I‫א‬‫א‬‫א‬  I = I dc = 4.4 A ٢-٩‫א‬‫א‬‫א‬‫א‬

 I m = 2 I = 2 × 4.4 = 6.2 A

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 P = R I 2 = 50 × 4.4 2 = 968 W - ٢٤ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫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  K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬R‫א‬‫א‬

 ‫א‬‫א‬‫א‬،E٢ ٥a‫א‬F‫א‬  v( t ) = Vm sin (ω t + θ v )  ‫א‬‫א‬ i( t ) =

v( t ) Vm sin (ω t + θ v ) = = I m sin (ω t + θ v ) R R

  

 Im =

Vm R

 ‫א‬‫א‬‫א‬  I=

V R

٢ ١٠

٢ ٥b‫א‬‫א‬،‫א‬‫א‬‫א‬  K‫א‬θv=٠  ‫א‬‫א‬‫א‬‫א‬‫א‬

L‫א‬‫א‬i(t)‫א‬‫א‬‫א‬‫א‬

KK ‫א‬K١ ١٢e(t)‫א‬‫א‬‫א‬‫א‬‫א‬E٢ ٦a‫א‬F - ٢٥ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬v(t)‫א‬  ‫א‬‫א‬  v( t ) = − e(t) = L

di( t ) dt

٢ ١١

(a)

(b)

 

‫א‬‫ א‬W٢ ٥ 

  ‫א‬  i( t ) = I m sin (ω t + θ i )  ‫א‬‫א‬‫א‬، 

v( t ) = ω L I m cos (ω t + θ i )



= ω L I m sin (ω t + θ i + 90° ) = Vm sin (ω t + θ i + 90° )

 ‫א‬‫א‬‫א‬‫א‬ ٢ ١٢

 Vm = ω L I m

 ‫א‬ ٢ ١٣

 XL = ωL

 K‫א‬‫א‬‫א‬،‫א‬  ‫א‬‫א‬ ٢ ١٤

 V = ωL I = XL I - ٢٦ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

٢-٦b‫א‬‫א‬،٩٠°‫ﺒ‬‫א‬‫א‬  K‫א‬θi=٠ W‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬K‫א‬‫א‬

‫א‬،E  F‫א‬‫א‬K  K‫א‬



(a)

(b)



‫א‬‫א‬W٢ ٦



 ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬C‫א‬١- ‫א‬‫א‬‫א‬

‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬

 E٢ ٧a‫א‬F‫א‬‫א‬‫א‬،

 i( t ) = C

dv( t ) dt

٢ ١٥

 ‫א‬‫א‬ 

 v( t ) = Vm sin (ω t + θ v )

 ‫א‬‫א‬ 

i( t ) = ω C Vm cos (ω t + θ ) = ω C Vm sin (ω t + θ + 90° ) = I m sin (ω t + θ + 90° )

 ‫א‬‫א‬‫א‬‫א‬ - ٢٧ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 Vm =

1 Im ωC

 ‫א‬

٢ ١٦

 ‫א‬  XC =

1 ωC

٢ ١٧

 K‫א‬‫א‬،‫א‬  ‫א‬‫א‬  V=

1 I = XC I ωC

٢ ١٨

٢ ٧b‫א‬‫א‬،٩٠°‫ﺒ‬‫א‬‫א‬

 K‫א‬θv=٠ 



(a)

(b) 

‫א‬‫א‬W٢ ٧



 ‫א‬‫א‬‫א‬  EPhasorF‫א‬

 ‫א‬‫א‬‫א‬E‫א‬F

E٢ ٢  ‫א‬FK ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬E ‫א‬F‫א‬ ،‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬،‫א‬ - ٢٨ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

٢ ٨‫א‬K ‫א‬‫א‬‫א‬‫א‬Kt=٠‫א‬ ‫א‬‫א‬iv،ImVmiv ‫א‬‫א‬‫א‬

 K‫א‬‫א‬ θiθv

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ F‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

 KVmVv‫א‬KE 2 ‫א‬



 ‫א‬‫א‬‫א‬W٢ ٨  

‫א‬‫א‬‫א‬‫א‬،E‫א‬F‫א‬ ‫א‬،‫א‬E ‫א‬F‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ v( t ) = Vm sin (ω t + θ v ) = V 2 sin (ω t + θ v )

 ‫א‬‫א‬  ٢ ١٩

 V = V ∠θ v

‫א‬‫א‬F‫א‬‫א‬‫א‬θvE ‫א‬‫א‬F‫א‬‫א‬V K ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬KE‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ ٢-٢٠

 V = V cos θ v + j V sin θ v

 K j = − 1   KEPhasor diagramF‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ - ٢٩ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 K v( t ) =144.4 sin (377 t + 30o ) V ‫א‬‫א‬‫א‬W٢ ٦

 ‫א‬

 V=

Vm 141.4 = =100 V ‫א‬‫א‬ 2 2

 V =100 ∠30o V ‫א‬‫א‬

 ‫א‬‫א‬ ‫א‬I‫א‬‫א‬V‫א‬‫א‬  ‫א‬،Z‫א‬‫א‬  ٢-٢١ V=ZI

K ‫א‬Z‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫• א‬

 ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ 

 V = V ∠θ v

 ‫א‬‫א‬ 

 I = I∠θ v

 ‫א‬‫א‬‫א‬‫א‬  ZR =

V∠θ v V o = ∠0 = R ∠0o = R I ∠θ v I

 ٢ ٢٢

‫א‬‫א‬‫א‬K٢ ١١‫א‬‫א‬  K‫א‬‫א‬٢-٩‫א‬K‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬W٢ ٩ - ٣٠ -



‫א‬‫א‬ ‫א‬‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫• א‬ ‫א‬،٩٠°‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬، θ i = θ v − 90o ZL =

V∠θ v V = ∠90o = X L ∠90o = jX L I ∠(θ v − 90) I

٢ ٢٣

‫א‬j‫א‬‫א‬ ‫א‬‫א‬‫א‬،٢ ١٤‫א‬‫א‬ ‫א‬K  ‫א‬‫א‬K٩٠°‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬٢ ١٠

 ‫א‬‫א‬W٢ ١٠

  ‫א‬‫• א‬

‫א‬،٩٠°‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬، θ i = θ v + 90o ZC =

V∠θ v V = ∠ − 90o = X C ∠ − 90o = − jX C I ∠(θ v + 90) I

٢ ٢٤

‫א‬-j‫א‬‫א‬‫א‬‫א‬،٢ ١٨‫א‬‫א‬

K   ‫א‬‫א‬K ٩٠o‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬٢ ١١‫א‬

  ‫א‬‫ א‬W ٢ ١١  - ٣١ -



‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬‫א‬ K ‫א‬‫א‬‫א‬٢ ١٢‫א‬  KZT ‫א‬





‫א‬‫א‬‫א‬ : ٢ ١٢‫א‬



   V = V١ + V٢ +

…



+ VN

 ‫א‬  Vx = Zx I

,



V = ZT I

 ،x = ١, ٢, …, N

 ZT = Z١ + Z٢ +

…

 ٢ ٢٥

+ ZN

 ZT‫א‬‫א‬ ٢ ٢٦

 ZT = RT + j XT = ZT ∠θ

‫א‬F،‫א‬‫א‬RT‫א‬‫א‬  W‫א‬‫א‬XT‫א‬‫א‬KE‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W o ‫א‬،  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬W o K‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W o  XT‫א‬RT‫א‬ZT‫א‬‫א‬  ٢-٢٧

 Z T = R T2 + X T2

 - ٣٢ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 XTRTθ‫א‬‫א‬‫א‬‫א‬‫א‬ ⎛X ⎞  θ = tan −1 ⎜⎜ T ⎟⎟ ⎝ RT ⎠

٢ ٢٨

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K  ‫א‬

،EImpedance Diagram)‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬

XL‫א‬‫א‬،‫א‬‫א‬R‫א‬٢ ١٣‫א‬

 K‫א‬jXC‫א‬‫א‬‫א‬j



‫א‬W٢ ١٣



،L=٨mH،R=٧Ω،٢ ١٤‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ٧ ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬K v =100 2 sin (377 t ) V

 K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬VLVR‫א‬



XL = ω L = ٣٧٧ × ٨ × ١٠

٣

٢ ١٤

 W‫א‬ ‫א‬‫א‬

=٣Ω

 ZT = R + jXL W‫א‬‫א‬ o

 = ٧ + j٣ Ω = ٧{٦ ∠ ٢٣{٢ Ω

 K‫א‬٢ ١٥a‫א‬ o

V = ١٠٠ ∠٠ VW‫א‬‫א‬ - ٣٣ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 I = V / ZT= ١٠٠ ∠٠o/ ٧{٦ ∠ ٢٣{٢oW‫א‬ o

 o o VR = R I = × ١٣{٢ ∠ ٢٣{٢ = ٩٢{٤ ∠ ٢٣{٢ V ‫א‬‫א‬ ٧  = ١٣{٢ ∠

٢٣{٢ A

VL = jXL I = ٣∠٩٠o× ١٣{٢ ∠

o

o

٢٣{٢ = ٣٩{٦ ∠ ٦٦{٨ V ‫א‬‫א‬

K‫א‬‫א‬٢ ١٥b‫א‬



٢ ١٥



‫א‬‫א‬٩٠o٠‫א‬‫א‬‫א‬‫א‬  KE-F

‫א‬،‫א‬٢ ١٦‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ٨ ،E  ‫א‬FVCE  ‫א‬FVRV‫א‬‫א‬‫א‬

 K v = 200 2 sin (377 t ) V ،C=٣٣٢µF،R=٥Ω



٢ ١٦

  W‫א‬

-

XL = ١ / (ω C) = ١/ (٣٧٧ × ٣٣٢ × ١٠ ٦) = ٨ Ω



‫א‬‫א‬

ZT = R – jXC W‫א‬‫א‬ - ٣٤ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 = ٥ – j٨ Ω = ٩{٤ ∠

 ‫א‬

 ٢ –‫א‬

 ‫א‬

o

٥٨ Ω

 K‫א‬٢ ١٧a‫א‬ o

V = ٢٠٠ ∠٠ VW‫א‬‫א‬

 I = V / ZT= ٢٠٠ ∠٠o/ ٩{٤ ∠

o

٥٨ W‫א‬

 = ٢١{٣ ∠ ٥٨o A VR = R I = ٥× ٢١{٣ ∠ ٥٨o= ١٠٦{٥ ∠ ٥٨o V ‫א‬‫א‬ o

o

٣٢ V ‫א‬‫א‬

VC = - jXL I = ٨ ∠ × ٢١{٣ ∠ ٥٨ = ١٧٠{٤ ∠

٩٠o  K‫א‬‫א‬٢ ١٧b‫א‬ 

‫א‬‫א‬٩٠o٠‫א‬‫א‬‫א‬‫א‬  KE-F





٢ ١٧

I‫א‬ZT‫א‬‫א‬‫א‬٢ ١٨‫א‬‫א‬‫א‬‫א‬ ‫א‬W٢ ٩

 K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

- ٣٥ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬



 ٢ –‫א‬

٢ ١٨

- ٣٦ -

 ‫א‬  ‫א‬



‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 W‫א‬  ZT = ZR + ZL + ZC = ٥ + j٧ – j٤ o



= ٥ + j٣ Ω= ٥{٨ ∠ ٣١ Ω

 I

=

VR

V =

/

ZT

=

١٠٠

∠٠

R

I

=

٥

×

o

o

o

/

∠٣١

٥{٨

١٧{٢

∠ ٣١

o

o

o

=

=

١٧{٢ ٨٦

∠ ٣١

o

∠ ٣١

A o

V

 VL = jXL I = ٧∠٩٠ × ١٧{٢ ∠ ٣١ = ١٢٠{٤ ∠٥٩ V o

o

o

 VC =- jXC I = ٤∠ ٩٠ × ١٧{٢ ∠ ٣١ = ٦٨{٨ ∠ ١٢١ V

 VR + VL + V C = (٧٣{٦ – j٤٤{٣) + (٦١{٩ + j١٠٣{٢) + (- ٣٥{٥ – j٥٩) = ١٠٠ V = V  K‫א‬‫א‬٢ ١٩b‫א‬،‫א‬٢ ١٩a‫א‬



٢ ١٩



‫א‬٣١o‫א‬V‫א‬‫א‬I‫א‬‫א‬،‫א‬   ‫א‬‫א‬ ،‫א‬‫א‬‫א‬VR‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬VC‫א‬،٩٠o‫א‬‫א‬‫א‬VL‫א‬

 K٩٠o‫א‬‫א‬

- ٣٧ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  Vx =

Zx V ZT

٢ ٢٩

‫א‬‫א‬ZT‫؛‬Zx‫א‬‫א‬ Vx   K‫א‬‫א‬V‫؛‬‫א‬

،٢ ٢٠‫א‬‫א‬‫א‬‫א‬‫א‬V١VC،VL،VR‫א‬‫א‬W٢ ١٠  K‫א‬



٢-٢٠ o

 W‫א‬

ZT = R + j XL – j XC = ٦ + j٧ – j١٥ = ٦ – j٨ Ω = ١٠ ∠ ٥٣{١ Ω

  VR =

R V 6∠0o ×100∠0o = = 60∠53.1o V  o ZT 10∠ − 53.1

j X L V 7∠90o ×100∠0o = = 70∠143.1o V   VL = o ZT 10∠ − 53.1 - j X C V 15∠ − 90o ×100∠0o =  VC = = 150∠ − 36.9o V  o ZT 10∠ − 53.1



V1 =

(jX L - j X C ) V (7∠90o −15∠ − 90o ) 100∠0o 8∠ − 90o × 100∠0o = = o ZT  ∠ − 10 53.1 10∠ − 53.1o

= 80∠ − 36.9o V

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬٢-٢١‫א‬  KZT ‫א‬K‫א‬‫א‬

 

- ٣٨ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ٢ –‫א‬

 ‫א‬  ‫א‬

 IT = I١ + I٢ + . . . + IN

 ‫א‬  Ix = V / Zx , IT = V / ZT



 ،x = ١, ٢, …, N 

1 1 1 1 = + + ... + Z T Z1 Z 2 ZN

٢ ٣٠





‫א‬‫א‬‫א‬W٢ ٢١‫א‬

‫א‬،Y = ١/Z،Z ‫א‬Y ‫א‬‫א‬‫א‬  ٢ ٣٠‫א‬

 ٢ ٣١

 YT = Y ١ + Y ٢ + . . . + Y N

 ‫א‬E S F Siemens‫א‬  ٢ ٣٢

 YT = GT + j BT

XT‫א‬‫א‬،E  ‫א‬F‫א‬‫א‬GT‫א‬‫א‬  KEFEF‫א‬

،‫א‬‫א‬ ‫א‬‫א‬،٢-٢٢‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ١١  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 - ٣٩ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ٢ –‫א‬

٢ ٢٢‫א‬ 1 R

 ‫א‬  ‫א‬

  W‫א‬

1 1 1 = + = 0.2 − j0.5 S = 0.54 ∠ − 68.2o S  jX L 5 j2 1 1 = =1.9 ∠68.2o Ω   ZT = o YT 0.54 ∠ − 68.2

 YT = +

 K‫א‬٢-٢٣a‫א‬

 IT =

V = YT V = 0.54 ∠ − 68.2o × 30 ∠0o =16.2∠ − 68.2o A  ZT

V 30 ∠0o = 6∠0o A   IR = = R 5

 IL =

V 30 ∠0o = 15 ∠ − 90o A  = o jX L 2 ∠90

 ‫א‬‫א‬‫א‬‫א‬‫א‬٢ ٢٣b‫א‬

 ٢ ٢٣‫א‬



 -‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ١٢

 K٢-٢٤‫א‬



٢ ٢٤‫א‬ - ٤٠ -



‫א‬‫א‬ ‫א‬‫א‬‫א‬

١٣٢  ٢ –‫א‬

 ‫א‬  ‫א‬

 W‫א‬

1 1 1 1 = + = 0.3 + j0.4 S = 0.5 ∠53.1o S  R − jX C 3.33 − j2.5 1 1  ZT = = = 2 ∠ − 53.1o Ω  YT 0.5 ∠53.1o

 YT = +

 K‫א‬٢-٢٥a‫א‬

 IT =

V = YT V = 0.5 ∠53.1o × 20 ∠30o =10∠83.1o A  ZT

20 ∠30o V = 6∠30o A   IR = = R 3.33 V 20 ∠30o = 8 ∠120o A  =  IC = o − jX C 2.5 ∠ − 90

 K‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬٢ ٢٥b‫א‬

 ٢ ٢٥‫א‬



‫א‬‫א‬YT‫א‬‫א‬‫א‬٢-٢٦‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ١٣  K‫א‬‫א‬‫א‬‫א‬،ITICILIR‫א‬‫א‬IT



٢ ٢٦‫א‬

  W‫א‬

- ٤١ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬



YT = YR + YL + YC =

 ‫א‬

 ٢ –‫א‬

 ‫א‬

1 1 1 1 1 1 + + = + + R jX L − jX C 4 j5 − j3.33 

= 0.25 + j 0.1 S = 0.27 ∠21.8o S o

 ZT = ١ / YT = ٣{٧ ∠ ٢١{٨ Ω o

o

o

 IT = YT V = ٠{٢٧ ∠٢١{٨ × ٥٠ ∠٥٣{١ = ١٣{٥ ∠٧٤{٩ A o

o

 IR = V / R = ٥٠ ∠٥٣{١ / ٤ = ١٢{٥ ∠٥٣{١ A  o

o

o

 IL = V / jXL = ٥٠ ∠٥٣{١ / ٥ ∠٩٠ = ١٠ ∠ ٣٦{٩ A o

o

o

 IC = V / -jXC = ٥٠ ∠٥٣{١ / ٣{٣٣ ∠-٩٠ = ١٥ ∠١٤٣{١ A

 IR + IL + I C = (٧{٥ + j ١٠) + (٨ – j ٦) + (-١٢ + j ٩) = ٣{٥ + j ١٣ A = IT  K‫א‬‫א‬٢-٢٧b‫א‬،‫א‬٢-٢٧a‫א‬



 ٢ ٢٧‫א‬  K – ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  ‫א‬  ‫א‬‫א‬‫א‬ Z٢Z١‫א‬‫א‬  I1 =

Z2 IT Z I , I2 = 1 T Z1 + Z 2 Z1 + Z 2

٢ ٣٣

 K‫א‬‫א‬‫א‬‫א‬IT - ٤٢ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ٢ –‫א‬

 ‫א‬  ‫א‬

 K‫א‬،٢ ٢٨‫א‬‫א‬‫א‬W٢ ١٤



٢ ٢٨‫א‬

  W‫א‬



− jXC IT 3∠ − 90o ×10∠30o 30 ∠ − 60o I RL = = = = 6.71∠3.4o A  o (R + jX L ) − jX C 2 + j7 − j3 4.47 ∠63.4



(R + jX L ) I T (2 + j7) 10∠30o 7.28∠74.1o × 30 ∠ − 60o IC = = = = 48.86 ∠ − 49.3o A  o o (R + jX L ) − jX C 4.47 ∠63.4 4.47 ∠63.4

 ‫א‬–‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬،

 K‫א‬‫א‬‫א‬

 W‫א‬،٢ ٢٩‫א‬‫א‬‫א‬‫א‬W٢ ١٥ ‫؛‬ZT‫א‬‫ א‬J  ‫؛‬IT‫א‬‫ א‬J  ‫؛‬IL‫א‬‫א‬ J  ‫؛‬VR‫א‬‫ א‬J  KVC‫א‬‫ א‬J 

 ٢ ٢٩‫א‬ - ٤٣ -



‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 W‫א‬  ،٢ ٣٠‫א‬‫א‬‫א‬‫א‬‫א‬ J   Z1 = R = 2 Ω 



















( j X L ) (− j X C ) (6 ∠90o ) (4 ∠ − 90o ) = = − j12 Ω = 12 ∠ − 90o Ω   Z2 = ( j X L ) + (− j X C ) j6 − j 4

 Z T = Z1 + Z 2 = 2 − j12 Ω =12.17 ∠ − 80.5o Ω









-‫א‬





٢-٣٠‫א‬   







J 

V 100 ∠ 0o IT = = = 8.22 ∠ 80.5o A o Z T 12.17 ∠ − 80.5

W‫א‬‫א‬‫א‬ J  IL =

(- j X C ) I T (4 ∠ − 90o ) (8.22∠80.5o ) = = 16.44 ∠ 99.5o A  o (- j X C ) + ( j X L ) 2 ∠ 90

VR = R I T = 2 × 8.22 ∠ 80.5o = 16.44 ∠80.5o V 





VC = Z 2 I T =12 × ∠ − 90o × 8.22 ∠ 80.5o = 98.64 ∠ − 9.5o V 









J 





J  

 W‫א‬،٢-٣١‫א‬‫א‬‫א‬‫א‬WW٢ ١٦ K‫א‬ VC‫א‬‫ א‬J 

KIT‫א‬‫ א‬J 

- ٤٤ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬





٢-٣١‫א‬

 W‫א‬

،٢ ٣٢‫א‬‫א‬‫א‬ VC‫א‬ J  

  Z1 = R1 = 8 Ω 









 Z 3 = − j X C = − j5 Ω 







٢-٣٢‫א‬  

 









R 2 (R 3 + j X L ) 8 (6 + j5) 62.48 ∠39.8o = = = 4.2 ∠20.1o Ω = 3.94 + j1.44 Ω   Z2 = o R 2 + (R 3 + j X L ) 8 + (6 + j5) 14.87 ∠19.7

 VC =   IT =



       ‫א‬‫א‬

(5 ∠ − 90o ) (50 ∠0o ) 250 ∠ − 90o = = 20.06 ∠ − 73.4o V  o Z1 + Z 2 + Z 3 (8) + (3.94 + j1.44) + (− j5) 12.46 ∠ − 16.6 Z3 V





=





 











VC 20.06 ∠ − 73.4o = = 4.01∠16.6o A  o − jXC 5 ∠ − 90









 J  



 W‫א‬،٢-٣٣‫א‬‫א‬‫א‬‫א‬W٣ ١٧ ‫؛‬ZT‫א‬‫ א‬J  ‫؛‬IT‫א‬‫ א‬J  ‫؛‬I١‫א‬-‫א‬‫א‬‫ א‬J   KI٢‫א‬-‫א‬‫א‬‫ א‬J  - ٤٥ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬



 ‫א‬



٢-٣٣‫א‬

 W‫א‬

 W،٢ ٣٤b ٢ ٣٤a‫א‬‫א‬‫א‬ 



















٢-٣٤‫א‬   

















Z1 = 2 + j3 Ω = 3.61∠56.3o Ω

 Z 2 = 9 − j 7 Ω = 11.4 ∠ − 37.9o Ω 







Z 3 = 6 + j5 Ω = 7.81∠39.8o Ω



Z T1 =

Z 2 Z3 (11.4 ∠ − 37.9o ) (7.81∠39.8o ) 80.94 ∠1.9o = = (9 − j 7) + (6 + j5) Z 2 + Z3 15.13 ∠ − 7.6o 

= 5.35 ∠9.5o Ω = 5.28 + j 0.88 Ω

 Z T = Z1 + Z T1 = 2 + j3 + 5.28 + j 0.88 = 7.28 + j3.88 Ω = 8.25 ∠28.1o Ω  IT =

V 100 ∠ 0o = = 12.12 ∠ − 28.1o A  o Z T 8.25 ∠ 28.1









J 

  J 

I١‫א‬‫א‬ J 

I1 =

Z 3 I T (7.8 ∠ 39.8o ) (12.12∠ − 28.1o ) 94.536∠11.7 o = = = 6.25 ∠19.3o A  o Z 2 + Z3 (9 − j 7) + (6 + j5) 15.13∠ − 7.6

 

I٢‫א‬ J  - ٤٦ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ٢ –‫א‬

 I 2 = I T − I1 = (10.69 − j5.71) − (5.9 + j 2.07) = 9.14 ∠ − 58.4o A 

 ‫א‬  ‫א‬







 ‫א‬‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

E‫א‬F ‫א‬‫א‬‫א‬‫א‬  ‫א‬

EdiodesF‫א‬‫א‬‫א‬K ‫א‬‫א‬

‫א‬ ‫א‬،‫א‬‫א‬‫א‬E‫א‬F‫א‬ KEcathodeF‫א‬E ‫א‬‫א‬F‫א‬‫א‬،EanodeF‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬٢ ٣٥‫א‬



W٢ ٣٥‫א‬  K‫א‬   EF،‫א‬‫א‬ ٢ ٣٦‫א‬ ‫א‬‫א‬‫א‬ KRLD v٠‫א‬i٠‫א‬‫א‬‫א‬‫א‬،  Kvs‫א‬‫א‬،٢ ٣٧‫א‬

 ‫א‬‫א‬W٢ ٣٦‫א‬

 

‫א‬،‫א‬‫א‬‫א‬ ٢ ٥‫א‬E‫א‬‫א‬F - ٤٧ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬



V0 =

1 T

 ٢ –‫א‬

T 2

∫V

m

sin ωt dt =

0

 ‫א‬

Vm

π

 ‫א‬

٢-٣٤

= 0.318Vm

 ‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬Vm  I 0 = 0.318

Vm = 0.318 I m RL

٢-٣٥



 ‫א‬‫א‬‫א‬‫א‬W٢ ٣٧‫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٢ ٣٨‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬a‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬Kb‫א‬‫א‬‫א‬ - ٤٨ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬،‫א‬،‫א‬ ‫א‬‫א‬٢ ٣٩‫א‬K  ‫א‬

 K‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬ T

2V 1 V0 = ∫ Vm sin ωt dt = m = 0.636Vm T π

٢-٣٦

0

 I 0 = 0.636

Vm = 0.636 I m RL

٢-٣٧

 ‫א‬‫א‬‫א‬‫א‬W٢ ٣٨‫א‬

   

- ٤٩ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ٢ –‫א‬



 ‫א‬  ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ٣٩‫א‬

- ٥٠ -

 

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬  Z = Z ∠θ  v(t) = Vm sin ω t = V 2 sin ω t

 ‫א‬

 i ( t ) = I m sin ( ω t − θ) = I 2 sin ( ω t − θ)  ‫א‬‫א‬‫א‬‫א‬t‫א‬K‫א‬‫א‬ ٢ ٣٨

 p(t) = v(t) i(t)

 ‫א‬‫א‬K  ‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬،‫א‬

 K‫א‬′‫א‬′،

 ‫א‬‫א‬ p( t ) = V I cos θ − V I cos θ cos 2ωt + V I sin θ sin 2ωt

٢ ٣٩

‫א‬،‫א‬‫א‬W‫א‬  ‫א‬‫א‬

 KE‫א‬F‫א‬

 t٢t١ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ t2

 W = ∫ p( t ) dt

٢-٤٠

t1

 KEJJouleF‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬  ‫א‬‫א‬‫א‬ T

1  P = ∫ p( t ) dt = V I cos θ T

٢-٤١

0

- ٥١ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬F‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  KEWWattF‫א‬‫א‬،E‫א‬

‫א‬θ=٠‫א‬‫א‬‫א‬‫א‬‫א‬ R

 ‫א‬‫א‬ ٢-٤٢

 p R (t) = V I − V I cos 2ωt

 ‫א‬.٢-٤٠ ‫א‬  ‫א‬  P = V I =R I 2 = V 2 / R

٢-٤٣

‫א‬‫א‬‫א‬‫א‬‫א‬ KE‫א‬F‫א‬f٢f

 ‫א‬‫א‬‫א‬‫א‬K‫א‬

T

WR =∫ p R ( t ) dt = V I T = R I 2 T = (V 2 / R ) T

٢-٤٤

0





‫א‬‫א‬W٢-٤٠‫א‬



‫א‬‫א‬θ=٩٠o‫א‬‫א‬EF‫א‬EF

‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬

 K‫א‬

- ٥٢ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬ZS‫א‬‫א‬  ،EVAF‫א‬،‫א‬‫א‬

٢

٢

 ٢-٤٥

 S=VI=ZI =V /Z

‫א‬ ‫א‬‫א‬‫א‬‫א‬

 K‫א‬E‫א‬F

 ‫א‬‫א‬‫א‬‫א‬٢-٤٥ ٢-٤١ ‫א‬  ٢-٤٦

 P = S cosθ

 ‫א‬  cos θ =

P S

٢ ٤٧

‫א‬K ‫א‬‫א‬‫א‬‫א‬،‫א‬ F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬، θ=٠

‫א‬‫א‬‫א‬ cosθ=٠KE‫א‬  K‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  K‫א‬،‫א‬‫א‬‫א‬‫א‬

 ‫א‬‫א‬

 ‫א‬‫א‬‫א‬، ٢ ٣٩‫א‬٩٠o‫ﺒ‬θ‫א‬‫א‬EF ٢ ٤٨

 p L ( t ) = V I sin 2ωt

،‫א‬‫א‬‫א‬  K‫א‬

‫א‬K  ‫א‬‫א‬‫א‬‫א‬pL‫א‬٢-٤١‫א‬ ،‫א‬‫א‬E pLF‫א‬VI‫א‬‫א‬

‫א‬K  ‫א‬‫א‬‫א‬ - ٥٣ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬  K‫א‬ 



‫א‬‫א‬‫א‬‫א‬W٢-٤١‫א‬



‫א‬‫א‬،٢ ٣٩‫א‬ ٩٠°‫ﺒ‬θ‫א‬‫א‬EF  ‫א‬



٢ ٤٩

p C ( t ) = − V I sin 2ωt

،‫א‬‫א‬‫א‬  K‫א‬

K‫א‬‫א‬‫א‬‫א‬pC‫א‬٢-٤٢‫א‬

،‫א‬‫א‬ E pCF‫א‬VI‫א‬‫א‬‫א‬

‫א‬K  ‫א‬‫א‬  ‫א‬  K‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬



 ‫א‬‫א‬‫א‬‫א‬W٢-٤٢‫א‬ - ٥٤ -



‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 Z = Z∠θ Q‫א‬‫א‬‫א‬‫א‬  Q = V I sin θ

 ٢-٥٠

‫א‬‫א‬‫א‬EVARvolt-ampere reactiveF-‫א‬  KEFEF‫א‬‫א‬  QL‫א‬‫א‬،XL ٢

٢

 ٢-٥١

 QL = V I = XL I = V / XL

 K‫א‬‫א‬″″‫א‬‫א‬،  QC‫א‬‫א‬،XC  ٢

٢

 ٢-٥٢

 QC = -V I = -XC I = -V / XC

 K‫א‬‫א‬″″‫א‬‫א‬‫א‬،  ‫א‬ K ‫א‬‫א‬‫א‬‫א‬ ‫א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬،‫א‬‫א‬

 K٢-٥٠٢ ٤٥٢-٤١‫א‬

‫א‬K  -  -  ‫א‬٢-٤٣b٢-٤٣a‫א‬ QLQ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K ‫א‬‫א‬QC‫א‬‫א‬QL،QC

‫א‬‫א‬‫א‬،-  ‫א‬Q

 K‫א‬QCQL‫א‬K-

 

  (b)-،(a)-‫א‬W٢-٤٣‫א‬ - ٥٥ -

 

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬  S2 = P 2 + Q 2

٢-٥٣

  K‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬

‫؛‬‫א‬‫א‬‫א‬PT‫א‬‫א‬‫א‬ •

‫؛‬‫א‬‫א‬‫א‬QT‫א‬‫א‬‫א‬ • ‫א‬‫א‬K ST = PT2 + Q T2 ST‫א‬‫א‬‫א‬ • K‫א‬،‫א‬‫א‬‫א‬‫א‬

 cos θ T = PT S W‫א‬‫א‬ • T

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ١٨  K‫א‬‫א‬K‫א‬‫א‬،٢-٤٤‫א‬‫א‬





٢-٤٤‫א‬

  W‫א‬

 PT = P١ + P٢ + P٣ = ٢٠٠ + ١٠٠ + ٣٠٠ = ٦٠٠ WW‫א‬‫א‬‫א‬  QT = Q١ + Q٢ + Q٣ = ٠ + ٨٠ - ٢٥٠ =

W‫א‬‫א‬‫א‬

١٧٠ VAR

 K-‫א‬‫א‬   ST = PT2 + Q T2 = (600) 2 + (−170) 2 = 624 VA W‫א‬‫א‬‫א‬  cos θ T =

PT 600 = = 0.96  ST 624



 - ٥٦ -





 W‫א‬‫א‬

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 K‫א‬٢-٤٥‫א‬KθT = ١٥{٩o ‫א‬‫א‬‫א‬‫א‬‫א‬ 



٢-٤٥‫א‬ 

 K-W٣‫א‬،-W٢،‫א‬،W١‫א‬W‫א‬  W٢ ١٩

‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬‫א‬

J 

.٢-٤٦‫א‬‫א‬

K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬J 





٢-٤٦‫א‬

  W‫א‬ J  W١‫א‬

 I1 =

V 50 ∠0o 50 ∠0o =10 ∠ − 36.9o A  = = o Z1 4 + j3 5 ∠36.9

 P1 = R1 I12 = 4 ×10 2 = 400 W 



 Q1 = X L1 I12 = 3×10 2 = 300 VAR 

 S1 = V I1 = 50 ×10 = 500 VA 













































- ٥٧ -













‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 cos θ1 =

 ‫א‬

 ٢ –‫א‬

P1 400 = = 0.8  S1 500









 ‫א‬









  

W٢‫א‬ 50 ∠0o V 50 ∠0o = = 5.3 ∠58o A   I2 = = Z 2 5 − j8 9.43 ∠ − 58o













 



 Q 2 = − X C2 I 22 = − 8 × 5.32 = − 225 VAR 

















 S 2 = V I 2 = 50 × 5.3 = 265 VA 

 P2 = R 2 I 22 = 5× 5.32 =141 W 

 cos θ 2 =

P2 140.5 = = 0.53  S2 265























 







  W٣‫א‬

 I3 =

V 50 ∠0o 50 ∠0o = = =12.5 ∠ − 90o A  o Z 3 j10 − j 6 4 ∠90

 P3 = 0 W 



















 





















 





 Q3 = (X L3 − X C3 ) I32 = (10 − 6) 12.5 2 = 625 VAR 





 S3 = V I3 = 50×12.5 = 625 VA 











 

 cos θ 3 =

P3 = 0  S3





 J 

PT = P١ + P٢ + P٣ = ٤٠٠ + ١٤١ = ٥٤١ W  QT = Q١ + Q٢ + Q٣ = ٣٠٠ – ٢٢٥ + ٦٢٥ = ٧٠٠ VAR 2 = (541) 2 + (700) 2 = 885 VA    ST = PT2 + Q T P 541 = 0.61     cos θ T = T = ST 885













 













 

- ٥٨ -

‫א‬‫א‬ ‫א‬‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬KE ‫א‬F‫א‬   ‫א‬‫א‬‫א‬‫א‬ ،E‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬K‫א‬E‫א‬F

‫א‬K ‫א‬‫א‬‫א‬‫א‬ ‫א‬ E F‫א‬‫א‬E  ‫א‬‫א‬F‫א‬‫א‬EF

‫א‬K١٢٠°‫א‬‫א‬‫א‬‫א‬‫א‬ ١٢٠°‫ﺑـ‬‫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K١٢٠° ‫א‬،‫א‬‫א‬‫א‬‫א‬

 ‫א‬١٢٠°‫א‬

v AA' = V 2 sin ωt

 v BB' = V 2 sin (ωt − 120o )

٢-٥٤

v CC' = V 2 sin (ωt − 240o )

‫א‬‫א‬V،EC'C B' B‫א‬F‫א‬‫א‬A'A ٢ ٤٨‫א‬،‫א‬٢ ٤٧‫א‬K ‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬  VAA' = V ∠0o ٢ ٥٥

 VBB' = V ∠ − 120o VCC' = V ∠ − 240o = V ∠120o - ٥٩ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬ 





‫א‬‫א‬ W٢-٤٧ ‫א‬





‫א‬‫א‬‫א‬‫ א‬W٢-٤٨ ‫א‬



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬W  ‫א‬ ‫א‬‫א‬‫א‬  ‫א‬K ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬

‫א‬  ‫א‬‫א‬‫א‬‫א‬ ،‫א‬C'B'A'‫א‬

BA‫א‬‫א‬،E٢ ٤٩‫א‬FN‫א‬‫א‬‫א‬‫א‬ - ٦٠ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬‫א‬‫א‬K  ‫א‬C ٢-‫א‬‫א‬vAA'‫א‬‫א‬A‫א‬vAN‫א‬F ‫א‬‫א‬

KEB‫א‬A‫א‬vAB‫א‬F‫א‬‫א‬،E٥٤ ‫א‬‫א‬،‫א‬EAA'‫א‬‫א‬IA'AF‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬K‫א‬EA‫א‬‫א‬‫א‬‫א‬IAF‫א‬  K‫א‬‫א‬‫א‬‫א‬،٢ ٤٩‫א‬

  ‫א‬‫א‬‫א‬ W٢-٤٩ ‫א‬

 

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬  VAB‫א‬٢-٥٥‫א‬ VAB = VAN − VBN



= V ∠0o − V ∠ − 120o

٢ ٥٦

= V 3 ∠30o

‫א‬‫א‬ 3   ‫א‬VL‫א‬‫א‬‫א‬  ،‫א‬ ٢ ٥٧

 VL = V 3

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬٢-٥٠‫א‬

‫א‬‫א‬ K ‫א‬‫א‬

 K‫א‬

- ٦١ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫ א‬W٢-٥٠ ‫א‬

 

‫א‬ CA'BC'A‫א‬  ‫א‬،٢-٥١‫א‬ ‫א‬K‫א‬،CBA‫א‬‫א‬‫א‬،B'  ‫א‬‫א‬‫א‬‫א‬،‫א‬

 K‫א‬  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ I AB = I ∠0o  ٢ ٥٨

 I BC = I ∠ − 120o



I CA = I ∠ − 240o = I ∠120o

 ‫א‬K‫א‬‫א‬‫א‬ I  I B = I AB − I BC



= I ∠0o − I ∠ − 120o

٢ ٥٩

= I 3 ∠30o

 ،‫א‬‫א‬‫א‬ 3 IL‫א‬‫א‬‫א‬ ٢-٦٠

 IL = I 3

- ٦٢ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢-٥٢‫א‬ ‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬





 ‫א‬‫א‬‫א‬ W٢-٥١ ‫א‬



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬W٢-٥٢ ‫א‬

  ‫א‬

‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬

‫א‬  ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬  ،١٢٠°‫ﺑـ‬‫א‬ ٢-٦١

 I N = IA + IB + IC = 0 - ٦٣ -

‫א‬‫א‬ ‫א‬‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K 

 K‫א‬

‫א‬‫א‬W٢ ٢٠

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K٢ ٥٣‫א‬

 K





٢-٥٣ ‫א‬

  W‫א‬

 VL = 3 V = 3 ×127 = 220 V 









W‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬

Van E AN 127 ∠ 0o 127 ∠ 0o I an = = = = = 25.4 ∠ − 53.1o A Z Z 3 + j4 5 ∠ 53.1o

 I bn =

Vbn E BN 127 ∠ − 120o = = = 25.4 ∠ − 173.1o A o Z Z 5 ∠ 53.1



Vcn E CN 127 ∠120o I cn = = = = 25.4 ∠ 66.9o A o Z Z 5 ∠ 53.1

 W‫א‬‫א‬‫א‬‫א‬‫א‬

- ٦٤ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

I Aa = I an = 25.4 ∠ − 53.1o A

 I Bb = I bn = 25.4 ∠ − 173.1o A 

















I Cc = I cn = 25.4 ∠ 66.9o A

 W‫א‬‫א‬ I N = I Aa + I Bb + I Cc

 = 25.4 ∠ − 53.1o + 25.4 ∠ − 173.1o + 25.4 ∠ 66.9o = (15.25 − j 20.31) + (−25.22 − j3.05 ) + (9.97 + j 23.36) = 0









 K‫א‬‫א‬ ‫א‬‫א‬‫א‬W٢ ٢١

 K‫א‬‫א‬‫א‬‫א‬‫א‬K٢ ٥٤





٢-٥٤ ‫א‬

  W‫א‬











V V − VBN V I ab = ab = AB = AN Z Z Z

 

=









220 ∠ 0o − 220 ∠ − 120o 380 ∠ 30o = = 38 ∠ − 23.1o A  o 6 + j8 10 ∠ 53.1

- ٦٥ -



W‫א‬‫א‬





‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

V V V − VCN I bc = bc = BC = BN Z Z Z



220 ∠ − 12 0o − 220 ∠120o 380 ∠ − 90o = = = 38 ∠ − 143.1o A  6 + j8 10 ∠ 53.1o









V V V − VAN I ca = ca = CA = CN Z Z Z



=

220 ∠12 0o − 220 ∠ 0o 380 ∠150o = = 38 ∠ 96.9o A  o 6 + j8 10 ∠ 53.1

 I L = 3 I = 3 × 38 = 65.8 A 













W‫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،E ‫א‬‫א‬‫א‬‫א‬F

‫א‬‫א‬‫א‬‫א‬K  ‫א‬  K‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬‫א‬

 W‫א‬‫א‬‫א‬‫א‬

 P = V I cos θ  ‫א‬‫א‬‫א‬KV‫א‬I‫א‬‫א‬‫א‬θ PT = ٣ P

 E‫א‬‫א‬F‫א‬ ٢-٦٢

 PT = 3 VL I L cos θ

 ‫א‬‫א‬‫א‬‫א‬ ٢-٦٣

 Q T = 3 VL I L sin θ

 ‫א‬‫א‬‫א‬ ٢-٦٤

 ST = 3 VL I L - ٦٦ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

٢  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٢ ٢٢

 KZ = ٦ - j ٨Ω‫א‬،٥٥

 ٢-٥٥ ‫א‬

  W‫א‬

 Z = 6 − j8 Ω =10 ∠ − 53.1o Ω  VL 380 = = 38 A  Z 10



































 I L = 3 I = 3 × 38 = 65.8 A 















 I=

PT = 3 VL I L cos θ = 3 × 380 × 65.8× cos(−53.1o ) = 26 kW

o  Q T = 3 VL I L sin θ = 3 × 380 × 65.8× sin( −53.1 ) = − 34.6 kVAR 

PT = 3 VL I L = 3 × 380 × 65.8 = 43.3 kVA





         

- ٦٧ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

   K٣٠ ms١٠٠‫ א‬٢ ١  ‫؟‬٦٠ Hz‫א‬‫א‬٦‫א‬‫א‬٢ ٢  W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢ ٣ o

o

 ٨{٤ sin ١٠٠٠٠ t‫؛‬١٠٠ cos (٧٥٤ t + ٤٥ )، ٣٠ sin ٩٤٢ t ‫؛‬٥٠ sin (٣١٤ t + ٣٠ )

 K‫א‬‫א‬‫א‬،‫א‬٢ ٣‫א‬‫א‬٢ ٤ ‫א‬،i(t)=٦sin(٣٧٧tH٣٠o)A‫א‬‫א‬‫א‬٢ ٥

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،v(t)=٢٢٠sin(٣٧٧t+٦٠o)V  K‫א‬‫א‬‫א‬

 Kv(t)=٣٨٠cos(٣٧٧t+٦٠o)V‫א‬،i(t)=١٠sin(٣٧٧t)A‫א‬‫א‬٢ ٥‫א‬٢-٦ ‫א‬‫א‬‫א‬،‫א‬٢ ٤٠‫א‬‫א‬‫א‬‫א‬‫א‬‫ א‬٢ ٧  K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬



٢-٤٠‫א‬



 K‫א‬،٢-٤١‫א‬‫א‬‫א‬‫א‬V٢V١‫א‬‫א‬ ٢-٨



٢-٤١‫א‬ - ٦٨ -



‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

 ‫א‬

‫א‬‫א‬‫א‬،‫א‬٢-٤٢‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٢-٩  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ٢-٤٢‫א‬



٢ ٤٣‫א‬‫ א‬b a‫א‬‫א‬‫א‬‫א‬ ٢-١٠

 K‫א‬



٢-٤٣‫א‬



‫؛‬VL‫א‬I١‫א‬‫א‬،٢-٤٤‫א‬‫א‬‫א‬‫א‬ ٢-١١

 ٢-٤٤‫א‬

 

‫א‬‫א‬‫א‬،٢ ٤٥‫א‬‫א‬‫א‬ ‫א‬ ٢-١٢  K‫א‬‫א‬

- ٦٩ -

‫א‬‫א‬

١٣٢

‫א‬‫א‬‫א‬

 ٢ –‫א‬



٢-٤٥‫א‬

 ‫א‬  ‫א‬

 

 K٢ ٤٦‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٢ ١٢‫א‬ ٢-١٣

 ٢-٤٦‫א‬

 

٢ ٤٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٢-١٤  K‫א‬‫א‬‫א‬‫א‬،  K٢-٤٤‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٢-١٥ ‫א‬‫א‬،٢ ٤٧‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ٢-١٦  K‫א‬‫א‬‫א‬‫א‬

 ٢-٤٧‫א‬

- ٧٠ -

 

 ‫א‬‫א‬‫א‬ ã¹]
٢–  ‫א‬

 ‫א‬‫א‬



٣

‫א‬‫א‬

‫א‬‫א‬ ‫א‬‫א‬

١٣٢  ٢ –‫א‬

 ‫א‬ ‫א‬

 K‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬ 

 W‫א‬‫א‬  W‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬ o

K‫א‬‫א‬‫א‬

o

K‫א‬

o

 K‫א‬‫א‬‫א‬‫א‬

o

  ٪٨٠‫א‬‫א‬W‫א‬‫א‬‫א‬ 

،‫א‬،‫א‬W  ‫א‬‫א‬  K‫א‬‫א‬،‫א‬

-٦٩-

‫א‬‫א‬ ‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ١-‫א‬



‫א‬‫א‬

‫א‬‫א‬‫א‬KEd'Arsonval meterF ‫א‬‫א‬‫א‬E  ٦٠Hz٥٠HzF‫א‬‫א‬، ‫א‬

 KE‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬،

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬E F‫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F‫א‬‫א‬‫א‬‫א‬‫א‬  KE‫א‬‫א‬‫א‬

‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬

٠{٦٣٦-Im ٠{٣١٨-Im،‫א‬ ‫א‬‫א‬‫א‬  KE٢ ٣٧٢ ٣٥‫א‬F‫א‬‫א‬‫א‬Im،‫א‬‫א‬‫א‬ EF‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬ ٣ ١- ‫א‬

‫א‬‫א‬‫א‬‫א‬Rm‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬  K‫א‬‫א‬‫א‬،EShunt ResistorFRsh

-٧٠-

‫א‬‫א‬ ‫א‬‫א‬

١٣٢  ٢ –‫א‬

 ‫א‬ ‫א‬

 ‫א‬‫א‬‫א‬‫א‬W٣-١‫א‬

 

 EF‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣-٢- ‫א‬ ‫א‬‫א‬Rs‫א‬‫א‬‫א‬Rm‫א‬‫א‬‫א‬‫א‬K‫א‬  K‫א‬Rs،‫א‬‫א‬Rm‫א‬ 

 

 ‫א‬‫א‬‫א‬‫א‬W٣ ٢‫א‬

 

V=١٠V vs‫א‬‫א‬‫א‬Rs‫א‬‫א‬W٣ ١

‫א‬‫א‬IfsIfs=١mARm=٣٠٠Ω،٣ ٢‫א‬‫א‬ ‫א‬K  ‫א‬‫א‬Efull scale deviationF‫א‬‫א‬‫א‬‫א‬

 ‫؟‬‫א‬‫א‬  W‫א‬

 W‫א‬‫א‬‫א‬‫ א‬E‫א‬‫א‬FVav‫א‬‫א‬  Vav = (Rm + Rs) Ifs 



-٧١-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

Vav = ٠{٦٣٦ Vm = ١{١V



‫א‬





1.1 V − R m ‫א‬‫א‬ I fs 1.1×10  = − 3 − 300 = 9.7 kΩ  10 Vav = Rm Ifs= ١{١ V ⇒ V = Rm Ifs/ ١{١ = ٠{٢٧ V‫א‬‫א‬

 Rm =



 ‫א‬ ،،‫א‬ ‫א‬  ‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬  K‫א‬‫א‬‫א‬٣ ٣-‫א‬K‫א‬‫א‬‫א‬‫א‬

 Wθ‫א‬‫א‬‫א‬‫א‬

،B‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬i‫א‬‫א‬   ،‫א‬‫א‬‫א‬‫א‬T ٣ ١

 T=kiB

i'‫א‬،‫א‬‫א‬‫א‬‫א‬i'‫א‬B‫א‬K  k  ‫א‬Ki‫א‬

 T = k k1 i 2 = k ' i 2

 ٣ -٢

‫א‬‫א‬T‫א‬‫א‬KiB‫א‬k١  E٢ ٥‫א‬‫א‬F‫א‬‫א‬‫א‬K  Tav = k ' I 2

 ٣ -٣

 .i‫א‬‫א‬I

 ،θ‫א‬‫א‬‫א‬Tr‫א‬‫א‬  ٣ -٤

 Tr = k" θ

 K‫א‬k"  -٧٢-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬



‫א‬

 W٣ ٣ ‫א‬



 ،TrTav‫א‬‫א‬‫א‬  θ=

k' 2 I = k 2 I2 k"

٣ -٥

‫א‬K  ‫א‬‫א‬‫א‬‫א‬k٢‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬

 KE‫א‬F‫א‬‫א‬‫א‬،‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬E‫א‬‫א‬F‫א‬‫א‬  ‫א‬‫א‬‫א‬

٠{١A‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

BA‫א‬‫א‬‫א‬‫א‬C‫א‬‫א‬،‫א‬٠{٥A

‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬،٣-٤- ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬،٣-٥- ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ 

-٧٣-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

 ‫א‬ 

‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ W٣ ٤ ‫א‬

 ‫א‬ 

 

‫א‬ 

‫א‬‫א‬‫א‬‫א‬ W٣ ٥ ‫א‬



 ‫א‬‫א‬‫א‬

‫א‬‫א‬EF،‫א‬‫א‬‫א‬

 K‫א‬٣-٦-‫א‬K‫א‬‫א‬ 



‫א‬



 ‫א‬‫א‬ W٣ ٦ ‫א‬



 ‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬ K  ‫א‬‫א‬ ‫א‬‫א‬‫א‬ ‫א‬ K ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ -٧٤-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

،‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬K K ‫א‬‫א‬ ‫א‬،٣-٧-‫א‬K‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬E٢F‫؛‬‫א‬E١FW  ، E٣F‫؛‬‫א‬‫א‬

 KE٥F‫א‬‫א‬E٤F‫א‬  





‫א‬‫א‬ W٣ ٧ ‫א‬

  ‫א‬‫א‬

‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬،‫א‬ K‫א‬‫א‬ K ‫א‬‫א‬‫א‬

W‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬٣ ٨- ‫א‬ ،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬ -٧٥-

‫א‬‫א‬ ‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

‫א‬

، ،‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬



‫א‬‫א‬ W٣ ٨ ‫א‬  

‫א‬‫א‬،  ‫א‬،  ‫א‬W ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫؛‬‫א‬‫א‬W ‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،٠{٥  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

-٧٦-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

 ‫א‬‫א‬‫א‬ ‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬

 K‫א‬،‫א‬E‫א‬F  ‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬،E F‫א‬‫א‬ ‫א‬‫א‬‫א‬K  ‫א‬‫א‬‫א‬

‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬ ‫א‬٣ ٩‫א‬،‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬ ،‫א‬‫א‬‫א‬K ‫א‬

K   ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  K٣ ١٠‫א‬

‫א‬



‫א‬

‫א‬



‫א‬ W٣ ٩ ‫א‬ -٧٧-



‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬





‫א‬‫א‬‫א‬‫א‬ W٣ ١٠‫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‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ ،‫א‬‫א‬E ‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ε =100

 ε‫א‬

k Is − I p

٣ ٦

Ip

KIs‫א‬‫א‬k‫א‬‫א‬Ip‫א‬‫א‬‫א‬‫א‬

‫א‬  ‫א‬‫א‬

 K‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 K-‫א‬‫א‬،‫א‬‫א‬

،٦٠٠A‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣ ٢ 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،٥A‫א‬

 K‫א‬

-٧٨-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

 W‫א‬ 

k=

 W‫א‬‫א‬‫א‬‫א‬

I p 600 Ns = = = 120 Np Is 5





















 KNs = ١٢٠‫א‬،Np = ١‫א‬‫א‬  ‫א‬ ،‫א‬‫א‬‫א‬‫א‬

‫א‬٣ ١١‫א‬K  ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K ‫א‬ ‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 

 ‫א‬

‫א‬



‫א‬ 

‫א‬‫א‬ W٣ ١١ ‫א‬



K ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ε =100

 ‫א‬‫א‬

k Vs − Vp

٣ ٧

Vp

 K‫א‬‫א‬‫א‬ Vs ،‫א‬‫א‬‫א‬‫א‬Vp،‫א‬‫א‬k ‫א‬،٢٠٠V‫א‬١١kV‫א‬W٣ ٣  K Ns = ١٠٠‫א‬‫א‬Np‫א‬‫א‬‫א‬

 W‫א‬

k=

Np Ns

=

Vp 11000 = = 55 ⇒ N p = 55 N s = 55×100 = 5500  Vs 200 -٧٩-



W‫א‬

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

 ‫א‬‫א‬  ‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  W‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ K‫א‬‫א‬‫א‬‫• א‬ K‫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 ‫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‫א‬‫א‬٣ ١٢‫א‬

‫א‬‫א‬R‫א‬‫א‬E‫א‬‫א‬FM‫א‬ ‫א‬F‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬KE‫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 T

T

0

0

1 1 Tav = k ∫ v( t ) i( t ) dt = ∫ V 2 sin (ωt ) I 2 sin (ωt − θ) dt T T = k V I cos θ = k P -٨٠-

 ٣

٨

‫א‬‫א‬ ‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

‫א‬

 Kk‫א‬‫א‬θ‫א‬‫א‬‫א‬IV ‫א‬‫א‬،‫א‬‫א‬P‫א‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬  

  ‫א‬ ‫א‬‫א‬W٣ ١٢‫א‬



‫א‬،π-θθ‫א‬‫א‬‫א‬‫א‬‫א‬  K‫א‬‫א‬‫א‬

K ‫א‬‫א‬‫א‬ ‫א‬،‫א‬‫א‬،‫א‬  K  ‫א‬‫א‬‫א‬ ،  ‫א‬‫א‬‫א‬٣ ١٣‫א‬ ‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬  ‫א‬K ‫א‬‫א‬ ‫א‬‫א‬EEddy currentsF‫א‬‫א‬K‫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‫א‬ -٨١-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

K‫א‬،‫א‬‫א‬ •

K‫א‬،‫א‬‫א‬ •

٩٠o‫א‬‫א‬‫א‬،‫א‬ •  K‫א‬‫א‬  ‫א‬  ‫א‬‫א‬

‫א‬

 

‫א‬ 

‫א‬‫א‬‫ א‬W٣ ١٣ ‫א‬



‫א‬‫א‬‫א‬‫א‬،‫א‬W‫א‬‫א‬  K‫א‬‫א‬،‫א‬  K‫א‬‫א‬،‫א‬‫א‬‫א‬W‫א‬  ‫א‬  W‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬E‫א‬CCF‫א‬،٣ ١٤‫א‬‫א‬‫א‬‫א‬

‫א‬K ‫א‬‫א‬E‫א‬PCF‫א‬،‫א‬  K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬PC‫א‬،٣ ١٥‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬CC‫א‬‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬ 

-٨٢-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

‫א‬‫א‬ ‫א‬

‫א‬ 

  ‫א‬‫א‬‫א‬‫ א‬W٣ ١٤ ‫א‬    ‫א‬‫א‬ ‫א‬

‫א‬ 

  ‫א‬‫א‬‫א‬‫ א‬W٣ ١٥ ‫א‬  ‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬

E ‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬K ‫א‬

 K‫א‬E‫א‬‫א‬F‫א‬‫א‬

 K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  ،V=٢٢٠V‫א‬‫א‬‫א‬W٣ ٤

‫א‬‫א‬‫א‬‫א‬،cosθ=٠{٨ ،I=٣A  KRi=٣Ω‫א‬،Rv=٢٠٠٠Ω‫א‬،‫א‬

-٨٣-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

 W‫א‬ P = V I cosθ = ٢٢٠×٣×٠{٨ = ٥٢٨ W W ‫א‬‫א‬‫א‬‫א‬

 W‫א‬‫א‬

٢

٢

Pi = Ri I = ٣×٣ = ٢٧ W





 W‫א‬‫א‬‫א‬  

 PT = P + Pi = ٥٢٨ + ٢٧ = ٥٥٥ W  Pv = V٢/ Rv = ٢٢٠٢/٢٠٠٠ = ٢٤{٢ W









 W‫א‬‫א‬‫א‬





 PT = P + Pv = ٥٢٨ + ٢٤{٢ = ٥٥٢{٢ W 







W‫א‬‫א‬‫א‬

 W‫א‬‫א‬

W‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬   ‫א‬‫א‬٣ ١٦‫א‬‫א‬‫א‬‫א‬،

‫א‬‫א‬‫א‬K ‫א‬‫א‬

‫א‬،c‫א‬‫א‬‫א‬W٢‫א‬‫א‬a‫א‬‫א‬‫א‬W١  KVcbVac‫א‬ 

 

 



∆ Y

 ‫א‬‫א‬ W٣ ١٦ ‫א‬ 

 KW٢ W١‫א‬‫א‬‫א‬P‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 W‫א‬

-٨٤-

‫א‬‫א‬ ‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

‫א‬

WE--‫א‬F٠{٥‫א‬‫א‬ • KW١=W٢‫א‬‫א‬KP=W١+W٢

‫א‬E--‫א‬F٠{٥‫א‬‫א‬ • ‫א‬ ،‫א‬‫א‬‫א‬‫א‬EW٢F KP=W١-W٢K‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬E--‫א‬F٠{٥‫א‬‫א‬ • K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣ ٥ ‫א‬K٢kW‫א‬‫א‬، ٦kW‫א‬‫א‬

 K‫א‬‫א‬  W‫א‬

 W‫א‬‫א‬K‫א‬‫א‬‫א‬٠{٥‫א‬  P = W١ – W٢ = ٦ – ٢ = ٤ kW

 ‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬‫א‬‫א‬K 

EPC٢ PC١F،٣ ١٧‫א‬  PC٢ PC١‫א‬KECC٢ CC١F ‫א‬‫א‬‫א‬‫א‬K ‫א‬‫א‬،‫א‬

،‫א‬‫א‬، ‫א‬‫א‬ PC١‫א‬‫א‬‫א‬RK ‫א‬  KPC٢‫א‬‫א‬‫א‬L  W‫א‬

‫א‬‫א‬KCC٢ CC١‫א‬‫א‬‫א‬Фi • K‫א‬ -٨٥-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

‫א‬‫א‬‫א‬‫א‬،PC١‫א‬Фv١ • K‫א‬‫א‬‫א‬‫א‬‫א‬KR‫א‬‫א‬ ‫ﺒ‬‫א‬‫א‬‫א‬‫א‬،PC٢‫א‬Фv٢ • K٩٠o‫ﺒ‬‫א‬‫א‬‫א‬‫א‬‫א‬KL‫א‬٩٠o -





- 

‫א‬

‫א‬

   W٣ ١٧ ‫א‬  ‫א‬‫א‬  ‫א‬‫א‬E ‫א‬‫א‬F‫א‬‫א‬ ‫א‬‫א‬‫א‬،Фv١ Фi‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬ F‫א‬‫א‬‫א‬‫א‬،Фv٢Фi‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬KEF‫א‬E

 K‫א‬‫א‬‫א‬‫א‬،٩٠o٠o‫א‬‫א‬

،‫א‬‫א‬‫א‬‫א‬‫א‬ o

 K١٢٠ ‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬  ‫א‬‫א‬‫א‬–‫א‬ ‫א‬،‫א‬‫א‬‫א‬‫א‬ K ‫א‬‫א‬،‫א‬‫א‬‫א‬ -٨٦-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

‫א‬‫א‬١kWhEkWhF-  ‫א‬‫א‬ ‫א‬‫א‬، ‫א‬‫א‬‫א‬‫א‬K ‫א‬١kW  K‫א‬‫א‬‫א‬‫א‬‫א‬

W‫א‬‫א‬‫א‬‫א‬‫א‬، ٣ ١٨‫א‬

‫א‬‫א‬E١F ‫א‬‫א‬E٢FKE‫א‬ ‫א‬‫א‬‫א‬‫א‬‫א‬E٣FKU‫א‬ ‫א‬‫א‬‫א‬E٤FK ‫א‬‫א‬‫א‬‫א‬‫א‬

K E٦FK ‫א‬‫א‬E٥F‫؛‬‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬E٧F

  ‫א‬‫א‬‫א‬‫א‬‫א‬ W٣ ١٨ ‫א‬

 

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬K ‫א‬،  ‫א‬‫א‬E ‫א‬‫א‬F -‫א‬‫א‬‫א‬،‫א‬  K‫א‬

-٨٧-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ٢ –‫א‬

 ‫א‬ ‫א‬

‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬

  ‫א‬٩٠o‫א‬،٩٠o‫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

 K‫א‬‫א‬‫א‬،‫א‬‫א‬ ‫א‬،-  ‫א‬ ٦٠٠‫א‬‫א‬،٣٠A،٢٢٠V‫א‬W٣ ٦  K‫א‬‫א‬K ٣٠٣٠٠٠W‫א‬‫א‬‫א‬

 W‫א‬

 ٣ kW =‫א‬‫א‬

 ٠{٥ = ‫א‬  W = ٣ × ٠{٥ = ١{٥ kWhW-‫א‬‫א‬‫א‬  K٩٠٠=١{٥×٦٠٠=-‫א‬‫א‬×‫א‬‫א‬=‫א‬               -٨٨-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ٢ –‫א‬

 ‫א‬ ‫א‬

 

 ‫א‬‫א‬  ‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ ‫א‬‫א‬‫א‬  K  ‫א‬ ‫א‬،‫א‬ ‫א‬E ‫א‬١F‫א‬‫א‬٣ ١٩‫א‬‫א‬ ‫א‬‫א‬‫א‬K‫א‬

K ‫א‬‫א‬E٣FE٢F

،‫א‬‫א‬‫א‬K‫א‬ ‫א‬‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬K  ‫א‬‫א‬‫א‬‫א‬

 K‫א‬‫א‬



‫א‬ ‫א‬ W٣ ١٩ ‫א‬ -٨٩-



‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

 ‫א‬‫א‬–‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬ ‫א‬١- ‫א‬K  ‫א‬،‫א‬

‫א‬،‫א‬‫א‬‫א‬ ‫א‬  K‫א‬ Zx‫א‬٣-٢٠ ‫א‬K ‫א‬‫א‬‫א‬‫א‬‫א‬

‫א‬‫א‬،

 KEacF‫א‬





  W٣ ٢٠ ‫א‬



Z٢Z١‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬  ،Z٣Zx‫א‬  Z١ I ١ = Z٢ I ٢

٣ -٩

 Z٣ I٣ = Zx Ix

 ٣-١٠

 ‫א‬

-٩٠-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

I1 = I 3



I2 =Ix

 ٣-١٠‫א‬‫א‬‫א‬  Z 3 I1 = Z x I 2 

Z3 Z x = Z1 Z 2

 ‫א‬٣-٩‫א‬‫א‬   ٣-١١

 Z x Z1 = Z 2 Z 3

‫א‬‫א‬ ،‫א‬‫א‬  K‫א‬  

،‫א‬٣-٢١‫א‬

 ،٣-٢٠‫א‬K‫א‬‫א‬ Z1 =

R1 1+ jωR1C1

 Z2 = R 2 Z3 = R 3

Z x = R x + jωL x

 E‫א‬‫א‬F٣ ١١‫א‬ 

R1 (R x + jωL x ) = R 2 R 3 1+ jωR1C1 R R R x + jωL x = 2 3 + jωR 2 R 3C1 R1

 ‫א‬ 

Rx =

R2 R3 R1

٣-١٢

Lx = R2 R3C1

 -٩١-

‫א‬‫א‬

١٣٢

‫א‬‫א‬

 ‫א‬

 ٢ –‫א‬

‫א‬

  W٣ ٢١ ‫א‬



 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣ ٧  W‫א‬‫א‬‫א‬ C١ = ٠{٠١ µF , R١ = ٤٧٠ kΩ ,

R٢ = ١٠٠ kΩ

,

R٣ = ٥ k Ω .

 W‫א‬ R 2 R 3 (100 ×103 ) (5×103 ) Rx = = =1.06 kΩ R1  (470 ×103 )

L x = R 2 R 3C1 = (100 ×103 ) (5×103 ) (0.01×10 − 6 ) = 5 H

          -٩٢-

‫א‬‫א‬ ‫א‬‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

‫א‬

   ‫؟‬‫א‬‫א‬‫א‬‫א‬ W٣ ١ V=٢٠V vs‫א‬‫א‬‫א‬Rs‫א‬‫א‬W٣-٢  ‫א‬‫א‬IfsIfs=١mA Rm=٣٠٠Ω،‫א‬‫א‬‫א‬  K‫א‬‫א‬Efull scale deviationF‫א‬‫א‬‫א‬‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣-٣  ‫؟‬‫א‬‫א‬‫א‬‫א‬  ‫؟‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣-٤ ‫א‬‫א‬‫א‬  ،V=١٢٧V‫א‬‫א‬‫א‬ W٣-٥ ‫א‬‫א‬‫א‬‫א‬،cosθ=٠{٨٥،I=٦A ،Rv=١٥٠٠Ω‫א‬،٣ ١٤‫א‬‫א‬‫א‬  KRi=٢Ω‫א‬ ،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣-٦  K‫א‬‫א‬‫א‬‫א‬‫א‬K٤kW‫א‬‫א‬

‫א‬،٣-٢١‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W٣-٧  W‫א‬‫א‬‫א‬  C١ = ٠{٠٢ µF , R١ = ٥٠٠ kΩ , R٢ = ٥٠ kΩ

,

R٣ = ٦ kΩ.



-٩٣-

‫א‬‫א‬

١٣٢  ٢ –‫א‬

 ‫א‬ ‫א‬

 ‫א‬‫א‬ L‫א‬LW  ،‫א‬،‫א‬‫א‬،‫א‬‫א‬ ‫א‬‫א‬،

‫א‬،،،‫א‬‫א‬‫א‬  Introductory Circuit Analysis, Boylestad, Charles E. Merrill Publishing Company

‫א‬L ،‫א‬L ،‫א‬L،‫א‬ ‫א‬‫ א‬ ‫א‬‫א‬‫א‬،‫א‬‫א‬،

‫א‬‫א‬،L،‫א‬‫א‬‫א‬ 

- ٩٥ -

‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

‫א‬

 ‫א‬  ١  ٢

 ‫א‬W‫א‬‫א‬  ‫א‬‫א‬W‫א‬‫א‬

 ٢

 ‫א‬‫א‬

 ٥

 ‫א‬

 ٢

 ٤

 ‫א‬‫א‬

 ‫א‬‫א‬

 ٧

 ‫א‬‫א‬

 ٩

 ‫א‬W‫א‬‫א‬

 ٩

 ‫א‬‫א‬ 

 ١١

 ‫א‬

 ١٥

 ‫א‬‫א‬

 ١٨  ١٩

 ‫א‬‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬W‫א‬‫א‬

 ١٩

 ‫א‬‫א‬‫א‬

 ٢٢

 ‫א‬‫א‬‫א‬‫א‬‫א‬

 ١٠  ١٣  ١٧

 ٢٢

 ‫א‬  ‫א‬

 

 ‫א‬‫א‬ 

 ٢٥

 ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

 ٢٥

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ٢٨

 EPhasorF‫א‬

 ٣٠

 ‫א‬‫א‬

 ٢٨

 ٣٢

 ‫א‬‫א‬‫א‬

 ‫א‬‫א‬‫א‬

‫א‬

١٣٢

 ‫א‬

 ٢ –‫א‬

‫א‬

 ٣٧

 ‫א‬

 ٣٧

 ‫א‬‫א‬‫א‬

 ٤١

 ‫א‬

 ٤٢

 ‫א‬–‫א‬‫א‬

 ٤٥

 ‫א‬‫א‬‫א‬‫א‬

 ٤٦

 

 ٤٧

 ‫א‬‫א‬‫א‬

 ٤٩

 ‫א‬‫א‬‫א‬W‫א‬‫א‬

 ٤٩

 ‫א‬‫א‬

 ٥٠

 ‫א‬‫א‬‫א‬

 ٥١

 ‫א‬‫א‬

 ٥٧

 ‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬‫א‬

 ٥٨

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ٦٤

‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ٦٩  ٧٠

 ‫א‬‫א‬W‫א‬‫א‬  ‫א‬‫א‬‫א‬‫א‬W‫א‬‫א‬

 ٧٢

 ‫א‬

 ٥٣

 ٥٧

 ٦٦

 ٧٠

 ‫א‬

 ‫א‬‫א‬‫א‬‫א‬

 

 ‫א‬‫א‬‫א‬

 ٧٤

 ‫א‬‫א‬

 ٧٥

 ‫א‬‫א‬

 ٧٧

 ‫א‬

 ٧٤  ٧٧  ٧٩

 ‫א‬‫א‬  ‫א‬

 ‫א‬

‫א‬

١٣٢  ٢ –‫א‬

 ‫א‬ ‫א‬

 ٨٠

 ‫א‬‫א‬‫א‬W‫א‬‫א‬

 ٨٠

 ‫א‬‫א‬‫א‬‫א‬

 ٨١

 ‫א‬‫א‬‫א‬

 ٨٤

 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬

 ٨٥

 ‫א‬

 ٨٠  ٨٢

 ‫א‬‫א‬‫א‬  ‫א‬

 ٨٦

 ‫א‬‫א‬‫א‬–‫א‬

 ٨٩

 ‫א‬‫א‬W‫א‬‫א‬

 ٩٠

 ‫א‬‫א‬–‫א‬

 ٩٣

 

 ٨٩  ٩١  ٩٥ 

 ‫א‬

 

 ‫א‬‫א‬

 ‫א‬

      

 

    ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬  ‫א‬E‫א‬F‫א‬‫א‬ GOTEVOT appreciates the financial support provided by BAE SYSTEMS

كتاب بالعربي( دوائر وقياسات كهربائية -2 )

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