Analise de Circuitos

July 17, 2019 | Author: Oziel Ferreira Silva | Category: Rede Elétrica, Equações, Circuitos em Série e em Paralelos, Resistência Elétrica e Condutividade, Resistor

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�� E�� L� L�� K�� . C�� , � �� . P�� , �� . �� 01: D 01: D �� . C�� 1 = 0,4Ω R2 = 1Ω, R3 = 0,2Ω; E 1 = 1�, E2 = 2�, 3 = 3�.

�� 1: ��

I�� I�� L�� K�� M�� M��. P�� 1 + �2 = �3 (L�� N��). A�� L�� M�� 1 � �2, �� , ��, �� .�.�. E1 � E2, ��:

��

R2�3 + E1 + R2�3 + R2�2 � E2 = 0 S�� , �� 2 + 2� 3 = 1. P�� 1 � � 2, �� , �� .�.�. E 2 � E3, ��: � R3�1 + E3 � R1�1 � R1�1 + R2�2 � E2 = 0 S�� , �� 1 � �2 = 1. P��,�� :

�  +� +�  −2�� � � � − �  � 

L�� N��

E�� . C��, �� , �� (�� C��). I�� Δ. Q�� Δ �� . O �� : Δ =

10 11 −12  � 5 1 −1 0

N� �� 1, ��, 1, 0 (�� 1) � 1. O �� , �� 2, � �� 3. A�� Δ � �� . P�� (� 1), �� , �� , �� , �� (�� ). D�� 1: Δ1 =

 11 −12  � 4  −1 0

O� �� (� 2) � �� (�3) �� , �� , � �� , � �� .

��

D�� 2: Δ2 =

101  −120  � −1 10 11  � 3 1 −1 

D�� 3: Δ3 =

C�� (� ��) �� : �� = Δ� / Δ; �� = 1, 2, 3, ... P��, � �� 1 �� : �1 = Δ1 / Δ = (4/5) A A �� 2 ��: �2 = Δ2 / Δ = (�1/5) A E � �� 3 � �� : �3 = Δ3 / Δ = (3/5) A O�� , �� (��) ��. A �� . �� 2: ��

��

I�� , �1 � �3, �� . O�� , ��, �� (�� ). �� (�� ) � �� 1 � �� 3 , �� R2. L�� , �� . O �� , �� L�� K��. �� : �� / �� : �� R2�3 + E1 + R2�3

+ −  

� E2 = 0 T�� R2.

S�� , ��: 3�3 � �1 = 1. �� : �� / �� : �� E2

+ −  

+ R1�1 + R1�1 � E3 + R3�1 = 0 T� �� R2.

S�� , ��: 2�1 � �3 = 1. R�� 1 = (4/5) A �3 = (3/5) A

32�� � � � �� 11

, �� :

C�� , � �� . J� �� , �� , �� , �� E 2, ��:



N� �� , �� 2 �� . N� �� 1, �� , � �� .

��





C�� , �� , �� , �� (1/5) A. � �� , �� M�� M��, �� (� 2) �� (1/5) A, �� (4 5) A � (3/5) A = (1/5) A .



�� M��, �� K��, �� , � �� . �� 02: D�� .

��: P�� K��, �� , �� , �� . N� ��, �� M��, �� , �� . D�� , �� . U�� M�� M�� , �� (�� ) :

��



    

O �� A � B, � � �� 2 Ω. E�� ( � �� 2 ( ). J� � �� A � C, �� 4Ω, � �� 1 ( � �� 3 ( ). E�� (�.�.�.��) �� . H� �� , � � �� B � C, �� 10 � � �� 2 . E�� 2 ( ) � � 3 ( ), �� . � �� , �� , �� , �� . A�� . �� (�� ): 2�1 � 40 + 2� 1 � 2�2 + 4�1 � 4�3 = 0 8�1 � 2�2 � 4�3 = 40 �� (�� ): 2�2 � 2�3 � 10 + 2� 2 � 2�1 + 12 = 0 4�2 � 2�1 � 2�3 = �2 �� (�� ): 7�3 + 4�3 � 4�1 + 10 +2� 3 � 2�2 = 0 13�3 � 2�2 � 4�1 = �10

R�� 1 = 7 A �2 = 4 A �3 = 2 A

8� 4� �� 2�2� � � 2�4� �� −240 13� � 2� � 4�  � −10

��:

P��, �� :

��, � ��

��

A�� , �� . M�� , � �� . �� :

A� �� , �� (�1) � �� (�2). T�� , � �� . �� : 10�1 � 25 + 15� 1 + 15�2 = 0 O �� 15K �� . A��, �� , �� , �� . A�� , �� 15K �� 15�1 + 15�2, �� 1 ( ) � �2 ( ) �� 15K.

,

 

�� : 15�2 + 15�1 + 4�2 � 0 = 0





A� ��, �� 1 = 0,7 �A � � 2 = 0,5 �A. P��, � �� 15K �� 0,7 �A ( ) + 0,5 �A ( ) = 1,2 �A N�� : 10K = 10000 Ω, �� A (10 �3 A), �� 10K �� 10�1, �� 4K � 4� 2 � � 15K � 15.(� 1 +

�2) �� .

�� O T�� T�� . A�� , �� G�� R�� T�� :

��

�� (��): � �� , �� , � �� , �� . �� (��): � �� , �� , �� , �� . ��

N�� , �� , �� , �� , �� R1 � R2 �� , ��:

�1.�2 � � �1+�2 ��

P�� G�� E�� T��, �� , �� . C�� , �� ET�.

��

2−�1 � � ��1+�2

A�� , ��:

A �� , �A � �B, ��: UAB = ET� = E2 � R2.�

2−�1 � � �2�1+�2−�2� �1+�2

P��, �� ET� ��, ��:

N�� , �� E�� T��, � �� R3 �� . P�� , � �� , �� . E�� M�� T��.

�� 03: D �� R3. D��: E1 = 15�, E2 = 10�, R1 = 150Ω, R2 = 1 00Ω � R3 = 1�Ω.

��: O �� M�� T��. U�� ET� � RT� �� M��, � � �� R�� 03, ��: 

�� ...

2−�1 � � �2�1+�2−�2� �1+�2 0 1 0−15 � � 10150+100−10 150+10 � � 12 � ��



�� ...

�1.�2 � � �1+�2 150.100 � � 150+100 � � 60 Ω

P��, �� :

12 � ,   � � 60+1000

C�� RT� = 60 Ω � E T� = 12 �. P�� R3 = 1000 Ω, ��, � �� R3 ��:

C�� R3: U = R3 . �� = 1000 . 11,32 . 10 �3 = 11,32 � �� 04: ( TA 2005) U� �� 2 Ω �� . P�� , �� . O �� RG = 5 �Ω � ��, �� , �� 0,1 �A. D�� .

��

��:

S�� 24 � � 12 � �� 4 Ω � 2 Ω �� T�� ET� � RT�, ��: �� : 4.2 / (4 + 2) = 8/6 = 4/3 �� : 2� + 12 � 24 + 4� = 0 � = 2A P��, ET� = 12 + 2� = 16� L�� 12 Ω �� , ��:

� � 4316+12 � 1,2 � �� :

C�� , �� 12 Ω �� 1,2 A. P�� A��, �� :

��

O �� R, ��: RG.�G = R.(1,2 � � G)

≤

S��, RG = 5000 Ω � � G 0,1 �A , ��:

� � 5.11,02� + � ≤ 0,1. 10  ⟹ � ≤ 01,,12.1−0,0 1..51.010 ⇒ � ≤ 0,42

Ω

P��, � �� R � 0,42 Ω.

�� O T�� M�� (�� T�� ) �� . C�� .

�� (� ��):

1 1 1 �1.  +�2.  +�3.   �1 �2 �3 � � �11 + �21 + �31 ��

�� 05. N� �� , �� AB?

��:

1 1 1 20.  +60.   60 30 � � 601 + 301 + 301 � 8 � P�� M��, ��:

O �� 30 Ω, �� , �� 48 �, ��: 48 = 30.� � = 1,6 A .

⇒

T�� , T�� M��, � �� . ☺

��

D��? E�� : ��31@��.��

��

Analise de Circuitos

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