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EXAMPLE 8.7 Reduce the network of Fig. 8.13 to a single current
source, and calculate the current through RL. Solution: In this example, the voltage source will first be converted
to a current source as shown in Fig. 8.14. Combining current sources,
I1 4 A R1 8 �
I1 = E1 =
R1 32 V
= 4 A
8 �
I2 6 A R2 24 � RL 14 �
FIG. 8.14
Network of Fig. 8.13 following the conversion of the voltage source to a current
source.
Is � I1 � I2 � 4 A � 6 A � 10 A
and Rs � R1 � R2 � 8 � � 24 ��6 �
Applying the current divider rule to the resulting network of Fig. 8.15,
R
IL � �
sIs (6 �)(10 A) 60 A
� ��� ���3 A
Rs � 6 ��14 � 20
R L
EXAMPLE 8.8 Determine the current I2 in the network of Fig. 8.16.
Solution: Although it might appear that the network cannot be
solved using methods introduced thus far, one source conversion as
shown in Fig. 8.17 will result in a simple series circuit:
Es � I1R1 � (4 A)(3 �) � 12 V
and Rs � R1 � 3 �
Es � E2 12 V � 5 V 17 V
and I2 ����� ���3.4 A
Rs � R2 3 ��2 � 5 �
8.5 CURRENT SOURCES IN SERIES
The current through any branch of a network can be only single-valued.
For the situation indicated at point a in Fig. 8.18, we find by application
of Kirchhoff’s current law that the current leaving that point is greater
than that entering—an impossible situation. Therefore,
current sources of different current ratings are not connected in
series,
just as voltage sources of different voltage ratings are not connected in
parallel.
8.6 BRANCH-CURRENT ANALYSIS
We will now consider the first in a series of methods for solving networks
with two or more sources. Once the branch-current method is
I L
R 1
E 1
BRANCH-CURRENT ANALYSIS ⏐⏐⏐ 261
8 �
32 V
I2 6 A R2 24 � RL 14 �
I s
FIG. 8.13
Example 8.7.
Is 10 A Rs 6 � RL 14 �
FIG. 8.15
Network of Fig. 8.14 reduced to its simplest
form.
I1 4 A R1 3 � R2 2 �
E s
R s
3 �
–
12 V
+
a
b
FIG. 8.16
Example 8.8.
a
b
+
E 2
5 V
+ –
E2 5 V
–
R 2
I L
2 �
FIG. 8.17
Network of Fig. 8.16 following the conversion
of the current source to a voltage source.
No!
a
6 A 7 A
FIG. 8.18
Invalid situation.
I 2
I 2
I L