Cell Voltage, V
Cell Voltage, V
3.00
2.50
2.00
1.50
1.00
0.50
0.00
2I cell R esr
R esr = 5 Ω.cm 2
R esr = 0 Ω.cm
2
Charging
Discharging
0
5
10
15
20
25
30
35
40
45

Time, s

(a)

3.00
2.50
2.00
1.50
1.00
0.50
0.00
0
R p = 10000 Ω.cm
2
R p = 100 Ω.cm
2
Charging
Discharging
5
10
15
20
25
30
35
40
45
ΔV cell = I cell R p,2 (1 – exp(–
) – R p,1 (1 – exp(–
)
R p,1 C
T
dl
t
R p,2 C
T
dl
t
Time, s
(b)
77
Fundamentals of Electrochemical Double-Layer Supercapacitors
FIGURE 2.17
Calculated charging-discharging curves. (a) R esr is changed from 0.4 to 1.0 Ω.cm 2 with fixed R p
= 1000 Ω.cm 2 , C T
dl = 0.4 F.cm –2 , and I cell = 0.05 A.cm –2 . (b) R p is changed from 100 to 10000 Ω.cm 2
with fixed R esr = 0.5 Ω.cm 2 , C T
dl = 0.4 F.cm –2 , and I cell = 0.05 A.cm –2 . (c) I cell is changed from 0.05
to 0.1 Α.cm –2 with fixed R p = 100 Ω.cm 2 , C T
dl = 0.4 F.cm –2 , and R esr = 0.5 Ω.cm 2 . (d) C T
dl is changed
from 0.4 to 1.0 F.cm –2 with fixed R p = 10000 Ω.cm 2 , I cell = 0.05 A.cm –2 , and R esr = 0.05 Ω.cm 2 .
(continued)