Biomedical Engineering Reference
In-Depth Information
9.9 CAPACITORS
A capacitor is a device that stores energy in an electric field by charge separation when
appropriately polarized by a voltage. Simple capacitors consist of parallel plates of con-
ducting material that are separated by a gap filled with a dielectric material. Dielectric
materials—that is, air, mica, or Teflon—contain a large number of electric dipoles that
become polarized in the presence of an electric field. The charge separation caused by the
polarization of the dielectric is proportional to the external voltage and given by
q
ð
t
Þ¼
Cv
ð
t
Þ
Þ
where C represents the capacitance of the element. The unit of measure for capacitance
is the farad or farads (F), where 1 F
ð
9
:
23
¼
1 C/V. We use the symbol
C
to denote a capacitor;
10
6
F) or picofarads (1 pF
most capacitors are measured in terms of microfarads (1
m
F
¼
¼
10
12
F). Figure 9.26 illustrates a capacitor in a circuit.
Using the relationship between current and charge, Eq. (9.23) is written in a more useful
form for circuit analysis problems as
i
¼
dq
dt
¼
C
dv
ð
9
:
24
Þ
dt
The capacitance of a capacitor is determined by the permittivity of
the dielectric
10
12
F
(e
m
for air) that fills the gap between the parallel plates, the size of the
gap between the plates,
¼
8
:
854
d,
and the cross-sectional area of the plates,
A,
as
e
A
d
C
¼
ð
9
:
25
Þ
As described, the capacitor physically consists of two conducting surfaces that store
charge, separated by a thin insulating material that has a very large resistance. In actuality,
current does not flow through the capacitor plates. Rather, as James Clerk Maxwell
hypothesized when he described the unified electromagnetic theory, a displacement current
flows internally between capacitor plates, and this current equals the current flowing into
the capacitor and out of the capacitor. Thus, KCL is maintained. It should be clear from
Eq. (9.29) that dielectric materials do not conduct DC currents; capacitors act as open circuits
when DC currents are present.
i
+
−
v
C
FIGURE 9.26
Circuit with a capacitor.