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Th
(8.54 V) 72.93
and Pmax � � ��W 2.88
� 25.32 W
2
E
��
4(0.72 �)
2 Th
�
4R
If the load resistance is adjustable but the magnitude of the load
reactance cannot be set equal to the magnitude of the Thévenin reactance,
then the maximum power that can be delivered to the load
will occur when the load reactance is made as close to the Thévenin
reactance as possible and the load resistance is set to the following
value:
RL � �R� 2 �Th �� (�X� �Th �� X� lo� ad�) 2 �
MAXIMUM POWER TRANSFER THEOREM ⏐⏐⏐ 821
(18.21)
where each reactance carries a positive sign if inductive and a negative
sign if capacitive.
The power delivered will be determined by
P � E 2 Th/4R av
(18.22)
where Rav � � (18.23)
RTh � RL �
2
The derivation of the above equations is given in Appendix G of the
text. The following example demonstrates the use of the above.
EXAMPLE 18.21 For the network of Fig. 18.88:
E Th = 20 V ∠0°
+
–
R Th
X Th
4 � 7 �
FIG. 18.88
Example 18.21.
R L
X C = 4 �
a. Determine the value of RL for maximum power to the load if the
load reactance is fixed at 4 �.
b. Find the power delivered to the load under the conditions of part (a).
c. Find the maximum power to the load if the load reactance is made
adjustable to any value, and compare the result to part (b) above.
Solutions:
a. Eq. (18.21): RL � �R� 2 Th � �� (�X� Th � �� X� lo� ad�) 2 �
� �(4� ��) 2 � �� (�7� �� �� 4� ��) 2 �