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21. For each network of Fig. 9.130, find the value of R for
maximum power to R, and determine the maximum
power to R for each network.
22. a. For the network of Fig. 9.136, determine the value of
R for maximum power to R.
b. Determine the maximum power to R.
1
c. Plot a curve of power to R versus R for R equal to �
4,
1 3 1 1 3
�, �, 1, 1 �, 1 �, 1 �
2 4 4 2 4,
and 2 times the value obtained in
part (a).
*23. Find the resistance R1 of Fig. 9.137 such that the resistor
R4 will receive maximum power. Think!
*24. a. For the network of Fig. 9.138, determine the value of
R2 for maximum power to R4. b. Is there a general statement that can be made about
situations such as those presented here and in Problem
23?
*25. For the network of Fig. 9.139, determine the level of R
that will ensure maximum power to the 100-� resistor.
E
R 1
25 �
25 �
100 V R2 R4 FIG. 9.138
Problem 24.
SECTION 9.6 Millman’s Theorem
26. Using Millman’s theorem, find the current through and
voltage across the resistor RL of Fig. 9.140.
27. Repeat Problem 26 for the network of Fig. 9.141.
R 3
E
R 1
4 �
24 V
I
PROBLEMS ⏐⏐⏐ 371
4 �
5 A R
R 2
FIG. 9.136
Problems 22 and 43.
R 1
50 �
100 V R2 50 � R4 50 �
12 V
FIG. 9.137
Problem 23.
R
FIG. 9.139
Problem 25.
R1 10 � R2 6 �
E1 –
5 V
+
R2 8.2 k�
+
+
RL 3 �
+
E1 40 V
–
E2 42 V
–
R1 2.2 k� E2 –
20 V
FIG. 9.140
Problem 26.
FIG. 9.141
Problem 27.
R 3
500 � Pot.
R L
R L
100 �
5.6 k�