boylistad

292 ⏐⏐⏐ METHODS OF ANALYSIS AND SELECTED TOPICS (dc)
R 1
R 3
R 5
R 2
R 4
R1 Rs 3 � 4 �
R5 R2 E 20 V
R 3
FIG. 8.64
Standard bridge configuration.
R 1
R 3
R2 R5 (a) (b)
(c)
5 �
2 �
R 4
2 �
1 �
Rs 3 � R R 2 �
1
2 4 �
R5
I2 E 20 V
R 3
I 1
5 �
2 � R 4
I 3
1 �
FIG. 8.65
Assigning the mesh currents to the network of
Fig. 8.64.
I R s
20 3 A
V 1
V2 3 �
R 1
R 3
(0 V)
4 �
R5
5 �
2 �
R 2
R 4
2 �
1 �
FIG. 8.66
Defining the nodal voltages for the network of
Fig. 8.64.
V 3
R 4
FIG. 8.63
Various formats for a bridge network.
Mesh analysis (Fig. 8.65) yields
(3 ��4 ��2 �)I1 � (4 �)I2 � (2 �)I3 � 20 V
(4 ��5 ��2 �)I2 � (4 �)I1 � (5 �)I3 � 0
(2 ��5 ��1 �)I3 � (2 �)I1 � (5 �)I2 � 0
and 009I 1 � 4I 2 � 2I 3 � 20
�4I 1 � 11I 2 � 5I 3 � 0
�2I 1 � 5I 2 � 8I 3 � 0
with the result that
I1 � 4 A
I2 � 2.667 A
I3 � 2.667 A
The net current through the 5-� resistor is
I5� � I2 � I3 � 2.667 A � 2.667 A � 0 A
Nodal analysis (Fig. 8.66) yields
and
� � � �V 1 1 1 1 1 20
� � � 1 � � � �V2�� � �V3��A 3 � 4 � 2 � 4 � 2 � 3
� � � �V 1 1 1 1 1
� � � 2 � � � �V1�� � �V3�0 4 � 2 � 5 � 4 � 5 �
� � � �V 1 1 1 1 1
� � � 3 � � � �V1�� � �V2�0 5 � 2 � 1 � 2 � 5 �
� � � �V 1 1 1 1 1 20
� � � 1 � � � �V2�� � �V3��A 3 � 4 � 2 � 4 � 2 � 3
1
�
4 �
� � � V 1 � � � � � V 2 � � � V 3 � 0
1
�
2 �
det[[20/3,�1/4,�1/2][0,(1/4�1/2�1/5),�1/5][0,�1/5,(1/5�1/2�1/1)]] ENTER 10.5
CALC. 8.4
1
�
4 �
1
�
5 �
1
�
2 �
1
�
5 �
1
�
5 �
R 1
1
�
2 �
R 2
R 4
R 3
1
�
5 �
1
�
1 �
� � � V 1 � � � V 2 � � � � � V 3 � 0
Note the symmetry of the solution.
With the TI-86 calculator, the top part of the determinant is determined
by the following (take note of the calculations within parentheses):
R 5
N A