6
Electrochemical Supercapacitors for Energy Storage and Delivery
ΔV = Ed
(1.8)
Combining Equations (1.7) and (1.8), the following expression can be obtained:
Q d
ΔV =
+
ε 0 A
(1.9)
The electric difference between the two electrodes of a capacitor can be alternatively expressed as V rather than ΔV:
Q d
V =
+
ε 0 A
(1.10)
1.3 Capacitance Definition and Calculation
A typical capacitor consists of two conducting parallel plates separated by
a vacuum or dielectric material, as shown in Figures 1.1a and 1.3. When
charging a capacitor, the plates will have equal and opposite magnitudes of
charge. This indicates a zero net charge on the capacitor. Both plates are electrically conductive materials, so the uniform distributions of charge along
their surfaces are reached easily, giving a potential difference V. Charge Q
(Q = |Q + | + |Q |) and potential V are related to each other through propor–
tionality constant C:
Q = CV
(1.11)
A capacitor’s proportionality constant refers to its capacitance, and provides
a measurement of the amount of charge necessary to induce a specified
potential between the plates. The magnitude of capacitance is independent
of the charge accumulated across the plates in a linear capacitor. However,
this capacitance is dependent upon the geometry of the charged plates.
Capacitance is measured in farads (F) where 1 F = 1 coulomb/volt (C/V).
Combining Equations (1.10) and (1.11), capacitance can be expressed as
Q ε 0 A
C = =
V
d
(1.12)
Equation (1.12) demonstrates that capacitance is dependent on the dielectric
constant of the dielectric material, the electrode surface area, and the distance
between the two planar electrodes. However, Equation (1.12) is applicable