1 24 electrostatic potential energy. 2 24-1 electrostatic potential energy
TRANSCRIPT
5
ji ij
ji
r
qkq
2
1
DA
AD
AD
DA
CA
AC
AC
CA
BA
AB
AB
BA
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
2
1
DC
CD
CD
DC
DB
BD
BD
DB
CB
BC
BC
CB
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
r
qkq
2
1
6
ji ij
ji
r
qkq
2
1
a
kq
a
kq
a
kq
a
kq
a
kq
a
kq 222222
222
1
a
kq
a
kq
a
kq
a
kq
a
kq
a
kq 222222
222
1
qqq ji
aarij 2,
Example with:
7
ji ij
ji
r
qkq
2
1
a
kq
a
kq
a
kq 222 2
2
22
2
1
a
kq
a
kq
a
kq 222 2
2
22
2
1
qqq ji
aarij 2,
Example with:
8
ji ij
ji
r
qkq
2
1
a
kq
a
kq
a
kq 222
2
a
kq
a
kq
a
kq 222
2
qqq ji
aarij 2,
Example with:
a
kq
a
kq
a
kq
a
kq
a
kq
2
22
22
22222
9
ji ij
ji
r
qkq
2
1
qqq ji
aarij 2,
Example with:
2
1
1
22
2
22
222
a
kq
a
kq
a
kq
242
2
1
4 22
a
kq
a
kq
17
rkE
12
2
1
R
REdrV 2
1
12
R
Rdrr
k 2
1ln2
R
Rrk
1
2ln2R
RkV
V
QC
LQ
V
L 12ln2 RRk
L
12ln2 RRk
L
12ln
2
RR
LC o
21
Ad
CV
volume
energyue
221
Energy Density Inside a Capacitor
Ad
dCE 2221
Ad
dE
d
A o22
21
221 Eu oe
Ex: Lab Capacitor, C = 1F, V = 6V, vol.=2x10-5 m3.
SI Unit: [J/m3]
36335
221
/10/000,900102
0.60.1mJmJ
mx
VFue
31033
8
/105.3104
104.1mJx
mx
Jxugasoline
about 35,000 higher than capacitor
23
Capacitors in “Parallel” Arrangement
CVQ
""12 VVVV BA
eqBA QQQ
BA QQ VCVCVC eqBA
eqBA CCC
Ex. FFFCeq 18126
24
eqBABA C
Q
C
Q
C
QVV
Capacitors in “Series” Arrangement
C
QV eqBA QQQ
Q = 0eqBA CCC
111
12
1
6
11
eqCEx.
FCeq 4
27
DielectricConstant K
• reduces E and V (E = Eo/K)
• C = KCo
• C = Capacitance with Dielectric
• Co = “Empty” Capacitor
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Ex. K’s
• vacuum: 1 exactly
• air: 1.00059
• paper: 3.7
• water: 80
• barium titanate: 1200
• potassium tantalate niobate (0 °C): 34,000
29
Supercapacitors
• porous structure
• surface areas much greater
• charge separation distance < 1 nm
• very high capacitance
30
Batteries
slow/special charging
limited # cycles with decreasing utility
short life
high energy density
poor low temp. performance
Capacitors
simple/fast charging
over 500,000 cycles at 100%
10 to 12 year life
low energy density
good low temp. perf.