V
– +
V
– +
+q 3
C 3
C 2
C 1
–q 3
+q 2
–q 2
+q 1
–q 1
–q
+q
+q
+q
C 2
C 3
C 1
–q
–q
B
B
(a)
(b)
22
Electrochemical Supercapacitors for Energy Storage and Delivery
FIGURE 1.8
Electric circuit of single-loop capacitor connected in (a) series and (b) parallel.
Q = Q 1 + Q 2 + Q 3 … = (C 1 + C 2 + C 3 …)V o
(1.35)
Under a given potential and known total charge storage, the equivalent
capacitance (C Eq, parallel ) can be expressed as
Q
n
C
=
= ∑ C
Eq parallel
i
,
V
o
(1.36)
i=1
Capacitors connected in series to a voltage source with a potential difference
V o will experience an equivalent chain-reaction charging of each plate rather
than an equivalent potential across each capacitor. Therefore, each capacitor
will theoretically store an equal amount of charge. The potential difference
across the plates of each capacitor can be expressed as
Q
Q
Q
V =
;V =
;V =
; etc
(1.37)
1
2
3
C
C
C
1
2
3
From this, the sum of the potential across the series-wired capacitors should be