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264 ⏐⏐⏐ METHODS OF ANALYSIS AND SELECTED TOPICS (dc)
Step 4: Applying Kirchhoff’s current law at node a (in a two-node network,
the law is applied at only one node),
I1 � I2 � I3 Step 5: There are three equations and three unknowns (units removed
for clarity):
2 � 2I1 � 4I3 � 0 Rewritten: 2I1 � 0 � 4I3 � 2
4I3 � 1I2 � 6 � 0 0 � I2 � 4I3 � 6
I1 � I2 � I3 I1 � I2 � I3 � 0
Using third-order determinants (Appendix C), we have
I 1 �
D �
I 2 �
I 3 �
2 0 4
6 1 4
0 1 �1
2 0 4
0 1 4
1 1 �1
2 2 4
0 6 4
1 0 �1
D
2 0
0 1
1 1
D
2
6
0
� �1 A
� 2 A
� 1 A
A negative sign in front of a
branch current indicates only
that the actual current is
in the direction opposite to
that assumed.
Mathcad Solution: Once you understand the procedure for entering
the parameters, you can use Mathcad to solve determinants such as
FIG. 8.23
Using Mathcad to verify the numerical calculations of Example 8.9.
N A