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372 ⏐⏐⏐ NETWORK THEOREMS
R1 200 � E2 + R3 20 V
–
+
RL 200 �
–
E3 –
10 V
E1 400 V
+
R2 100 �
I 1
10 mA
FIG. 9.142
Problem 28.
8 mA
R2 R1 2 k�
4.7 �
I3 E
E 1
I 2
FIG. 9.144
Problem 30.
2.5 k� a
60 V
R 1
4 �
20 V
FIG. 9.145
Problem 31.
R 2
b
a
15 k�
12 �
b
R L
6.8 k�
8 k�
R 3
8 �
FIG. 9.147
Problem 33.
E 2
10 k�
4 mA
7 k�
40 V
R 3
8.2 k�
Th
28. Repeat Problem 26 for the network of Fig. 9.142.
29. Using the dual of Millman’s theorem, find the current
through and voltage across the resistor RL of Fig. 9.143.
I 1 = 4 A
R 1
4.7 � 3.3 � RL 2.7 �
FIG. 9.143
Problem 29.
I 2 = 1.6 A
*30. Repeat Problem 29 for the network of Fig. 9.144.
SECTION 9.7 Substitution Theorem
31. Using the substitution theorem, draw three equivalent
branches for the branch a-b of the network of Fig. 9.145.
32. Repeat Problem 31 for the network of Fig. 9.146.
I
4 mA
R 1
a
FIG. 9.146
Problem 32.
*33. Repeat Problem 31 for the network of Fig. 9.147. Be
careful!
R 2
0.51 k�
R 2
E b
10 V
2 k� 1.5 k�