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822 ⏐⏐⏐ NETWORK THEOREMS (ac)
� �1�6� �� 9� � �2�5�
RL � 5 �
b. Eq. (18.23): Rav � �
� 4.5 �
Eq. (18.22): P �
� � W
� 22.22 W
c. For ZL � 4 ��j 7 �,
(20 V)
Pmax � �
� 25 W
exceeding the result of part (b) by 2.78 W.
2
E
�
4(4 �)
2 (20 V) 400
�
18
Th
�
4RTh
2
E
�
4(4.5 �)
2 RTh � RL 4 ��5 �
� ��
2
2
Th
�
4Rav
18.6 SUBSTITUTION, RECIPROCITY,
AND MILLMAN’S THEOREMS
Th
As indicated in the introduction to this chapter, the substitution and
reciprocity theorems and Millman’s theorem will not be considered
here in detail. A careful review of Chapter 9 will enable you to apply
these theorems to sinusoidal ac networks with little difficulty. A number
of problems in the use of these theorems appear in the problems section
at the end of the chapter.
18.7 APPLICATIONS
Soldering Gun
Soldering and welding are two operations that are best performed by
the application of heat that is unaffected by the thermal characteristics
of the materials involved. In other words, the heat applied should not be
sensitive to the changing parameters of the welding materials, the metals
involved, or the welding conditions. The arc (a heavy current) established
in the welding process should remain fixed in magnitude to
ensure an even weld. This is best accomplished by ensuring a fixed current
through the system even though the load characteristics may
change—that is, by ensuring a constant current supply of sufficient
amperage to establish the required arc for the welding equipment or even
heating of the soldering iron tip. A further requirement for the soldering
process is that the heat developed be sufficient to raise the solder to its
melting point of about 800°F.
The soldering gun of Fig. 18.89(a) employs a unique approach to
establishing a fixed current through the soldering tip. The soldering tip
is actually part of a secondary winding of a transformer (Chapter 21)
having only one turn as its secondary as shown in Fig. 18.89(b).
Because of the heavy currents that will be established in this single-turn
secondary, it is quite large in size to ensure that it can handle the current
and to minimize its resistance level. The primary of the transformer