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414 ⏐⏐⏐ CAPACITORS
C be
(a)
E C
P N P
B Cce (b)
(c)
C bc
Conductors
FIG. 10.71
Examples of stray capacitance.
where V is the steady-state voltage across the capacitor. In terms of Q
and C,
2 1 Q
WC � �C �
2 �C� Q
or WC � �� (J) (10.36)
2C
EXAMPLE 10.19 For the network of Fig. 10.69, determine the energy
stored by each capacitor.
Solution:
For C1, WC � � 1 2
�CV
2
� � 1
2 �(2 � 10�6 F)(16 V) 2 � (1 � 10 �6 )(256)
� 256 mJ
For C2, WC � � 1 2
�CV
2
� � 1
2 �(3 � 10�6 F)(56 V) 2 � (1.5 � 10 �6 )(3136)
� 4704 mJ
Due to the squared term, note the difference in energy stored
because of a higher voltage.
10.15 STRAY CAPACITANCES
In addition to the capacitors discussed so far in this chapter, there are
stray capacitances that exist not through design but simply because
two conducting surfaces are relatively close to each other. Two conducting
wires in the same network will have a capacitive effect between
them, as shown in Fig. 10.71(a). In electronic circuits, capacitance levels
exist between conducting surfaces of the transistor, as shown in Fig.
10.71(b). As mentioned earlier, in Chapter 12 we will discuss another
element called the inductor, which will have capacitive effects between
the windings [Fig. 10.71(c)]. Stray capacitances can often lead to serious
errors in system design if they are not considered carefully.
10.16 APPLICATIONS
This Applications section for capacitors includes both a description of
the operation of one of the less expensive, throwaway cameras that have
become so popular today and a discussion of the use of capacitors in the
line conditioners (surge protectors) that have found their way into most
homes and throughout the business world. Additional examples of the
use of capacitors will appear throughout the chapter to follow.
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