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Th
Note, in particular, that P L is, in fact, a maximum when R L � R Th �
9 �. The power curve increases more rapidly toward its maximum value
than it decreases after the maximum point, clearly revealing that a small
change in load resistance for levels of R L below R Th will have a more
dramatic effect on the power delivered than similar changes in R L above
the R Th level.
If we plot V L and I L versus the same resistance scale (Fig. 9.81), we
find that both change nonlinearly, with the terminal voltage increasing
with an increase in load resistance as the current decreases. Note again
that the most dramatic changes in V L and I L occur for levels of R L less
than R Th. As pointed out on the plot, when R L � R Th, V L � E Th/2 and
I L � I max/2, with I max � E Th/R Th.
50
40
30
20
10
V L (V) I L (A)
8
7
6
5
4
3
2
1
I max = E Th /R L = 6.67 A
I L
E Th /2
I max /2
V L
R L = R Th = 9 �
FIG. 9.81
V L and I L versus R L for the network of Fig. 9.79.
MAXIMUM POWER TRANSFER THEOREM ⏐⏐⏐ 345
0 0 5 9 10 15 20 25 30 RL (�)
The dc operating efficiency of a system is defined by the ratio of the
power delivered to the load to the power supplied by the source; that is,
h% � � PL
� � 100%
P
For the situation defined by Fig. 9.77,
I
h% � �100% � �100%
2 PL LRL � �2 Ps
I LRT s
(9.5)