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340 ⏐⏐⏐ NETWORK THEOREMS
R 2
R 2
4 �
I N = 3 A
4 �
R 1
5 �
I
10 A
R N = 2 �
FIG. 9.64
Substituting the Norton equivalent circuit for
the network external to the resistor R L of
Fig. 9.60.
FIG. 9.66
Example 9.12.
R 1
5 �
a
R L
b
R N
9 �
FIG. 9.68
Determining R N for the network of Fig. 9.67.
a
R L
b
a
b
Step 5: See Fig. 9.64. This circuit is the same as the first one considered
in the development of Thévenin’s theorem. A simple conversion
indicates that the Thévenin circuits are, in fact, the same (Fig. 9.65).
EXAMPLE 9.12 Find the Norton equivalent circuit for the network
external to the 9-� resistor in Fig. 9.66.
Solution:
Steps 1 and 2: See Fig. 9.67.
R 2
I N
4 �
3 A
R 1
5 �
I
10 A
a
R N = 2 �
b
a
I N
b
R Th = R N = 2 �
FIG. 9.69
Determining I N for the network of Fig. 9.67.
R 2
4 �
I
b a
I N
R1 10 A
Th
E Th = I N R N = (3 A)(2 �) = 6 V
FIG. 9.65
Converting the Norton equivalent circuit of Fig. 9.64 to a Thévenin
equivalent circuit.
R 2
4 �
R 1
5 �
I
10 A
FIG. 9.67
Identifying the terminals of particular interest for the network of Fig. 9.66.
Step 3: See Fig. 9.68, and
RN � R1 � R2 � 5 ��4 ��9 �
Step 4: As shown in Fig. 9.69, the Norton current is the same as the
current through the 4-� resistor. Applying the current divider rule,
R1I (5 �)(10 A) 50 A
IN � ��� ���5.556 A
5 ��4 � 9
� R1 � R 2
a
b
a
b
5 �