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288 ⏐⏐⏐ METHODS OF ANALYSIS AND SELECTED TOPICS (dc)
EXAMPLE 8.24 Find the voltage across the 3-� resistor of Fig. 8.55
by nodal analysis.
4 A
+
8 V
–
2 �
V 1
2 �
6 � 10 �
+
4 � V3� 3 � 1 V
–
FIG. 8.55
Example 8.24.
Solution: Converting sources and choosing nodes (Fig. 8.56), we
have
resulting in
and
6 �
4 � V3� 3 �
FIG. 8.56
Defining the nodes for the network of Fig. 8.55.
+
–
V 2
Reference
10 �
� � � �V 1 1 1 1
� � � 1 � � � �V2��4 A
2 � 4 � 6 � 6 �
� � � �V 1 1 1 1
� � � 2 � � � �V1��0.1 A
10 � 3 � 6 � 6 �
11 1
�V1 � �V2 � 4
12 6
1 3
��V1 � �V2 ��0.1
6 5
11V 1 � 2V 2 ��48
�5V 1 � 18V 2 ��3
⎫
⎪
⎬
⎪
⎪
⎭
–
+
0.1 A
� 11 48�
��5 �3� �33 � 240 207
V 2 � V 3� � ––––––––– � –––––––––– � –––– � 1.101 V
� 11 �2� 198 � 10 188
��5 18�
As demonstrated for mesh analysis, nodal analysis can also be a very
useful technique for solving networks with only one source.
N A