Environmental Engineering Reference
In-Depth Information
A
I
h
B
A
L
I
(a)
(b)
Figure 4.7
The electric capacitor (a) and inductor (b) are devices for storing electrical energy.
the device.
10
If an increment
dQ
of charge is moved from the negative plate to the positive one
through the potential increase
φ
, via the circuit external to the capacitor, an amount of electrical
work
φ
dQ
is done in this process, increasing the capacitor free energy by the amount
dF
,
QdQ
C
1
2
C
Q
2
dF
=
φ
dQ
=
=
d
(
)
Q
2
2
C
=
2
C
(φ)
F
=
(4.9)
2
We may determine the free energies per unit volume and mass in terms of the electric field
E
=
φ/
h
in the capacitor as
2
E
2
2
F
V
=
(
A
/
h
)φ
=
2
Ah
E
2
2
f
=
(4.10)
ρ
the mass density (kg/m
3
) of the dielectric medium, and
where
f
is the free energy per unit mass,
ρ
we neglect the mass of the electrodes.
To obtain high-energy storage densities, we should choose a material with a high electric
permittivity
and an ability to withstand a high electric field
E
without breakdown—that is,
without conducting a current that would short-circuit the capacitor internally. Such materials are
composed of molecules that have a permanent electric dipole moment and that are not easily
ionized in the presence of strong electric fields. For example, polypropylene has a permittivity
10
The dimension of the electrical charge is the coulomb, and that of the capacitance is the farad
=
coulomb/volt.
The electric permittivity has the dimensions of farad/meter
=
coulomb/volt meter. (See Table A.1.)
