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324 ⏐⏐⏐ NETWORK THEOREMS
+
E1– 54 V R 2 12 �
R 1
24 �
R 1
24 �
R 2
54-V battery replaced
by short circuit
12 �
R 3
4 �
I″ 3
E 2
EXAMPLE 9.2 Using superposition, determine the current through
the 4-� resistor of Fig. 9.6. Note that this is a two-source network of
the type considered in Chapter 8.
FIG. 9.6
Example 9.2.
Solution: Considering the effects of a 54-V source (Fig. 9.7):
RT � R1 � R2 �� R3 � 24 ��12 � �� 4 ��24 ��3 ��27 �
E1 54 V
I �����2 A
RT 27 �
I� 3
+
48 V
–
48-V battery
replaced by short
circuit
R 1
E 1
24 �
R T
FIG. 9.8
The effect of E 2 on the current I 3.
+
–
I
R 1
24 �
+
E1 –
54 V R2 12 �
4 �
54 V
8 �
R 1
24 �
R 2
R 2
R 3
12 �
12 �
E 2
I 3
I″ 3
RT R 3
4 �
E 2
+
48 V
–
R3 = 4 �
3 �
FIG. 9.7
The effect of E1 on the current I3. Using the current divider rule,
R2I (12 �)(2 A) 24 A
I′ 3 ����� ���1.5 A
R2 � R3 12 ��4 � 16
Considering the effects of the 48-V source (Fig. 9.8):
RT � R3 � R1 �� R2 � 4 ��24 � �� 12 ��4 ��8 ��12 �
E2 48 V
I″ 3 �����4 A
RT 12 �
R 3
I� 3
4 �
+
48 V
–
Th