4.50
t
ΔV cell = (I cell,2 – I cell,1 ) R esr + R p (1 – exp(–
))
C T
4.00
R p dl
3.50
3.00
I cell = 0.10 A/cm
2
2.50
I cell = 0.05 A/cm
2
2.00
1.50
1.00
0.50
0.00
0
5
10
15
Charging
20
25
30
Discharging
35
40
Time, s
(c)
3.00
t
t
ΔV cell = (I cell R p ) exp(–
) – exp(–
)
C T
C
T
R p dl,1
R p dl,2
2.50
C T
dl = 0.4 F/cm
2
2.00
1.50
C T
dl = 1.0 F/cm
2
1.00
0.50
Charging
Discharging
0.00
0
5
10
15
20
25
30
35
40
45
Time, s
(d)
Cell Voltage, V
Cell Voltage, V
78
Electrochemical Supercapacitors for Energy Storage and Delivery
FIGURE 2.17 (CONTINUED)
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 is changed
dl
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 .