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5 電容 Capacitance
National Ignition Facility
Explosions in Airborne Dust
5-1 電容與電容器
• 電容（ Capacitance ） • 平行板電容器 • C = ( F 法拉 ) K: 介電常數，真空 = 1 0: 真空電容率 A: 板面積 d : 兩板距
離
電位差電荷
V
qC
d
K 0
The Uses of Capacitors
As storehouses of electric potential energy
As vital elements in tuned circuits (radio and TV) and RAM chips
Charging a capacitor
5-2 Calculating the Capacitance
1) Put a charge q on the plates
2) Find E using Gauss’s Law
3) Find V between the plates
4) Calculate C by its definition
Calculating the electric field
EAqqAdE 00
Calculating the potential difference
)( VVVEdsV
sdEVV
if
f
iif
A parallel-plate capacitor
d
A
V
qC
EddsEEdsV
EAqd
0
0
0
A cylindrical capacitor
)/ln(
2or
)/ln(2
)ln(2
2
2
)2(
00
0
0
0
00
abL
C
ab
LC
a
b
L
q
r
dr
L
qEdsV
Lr
qE
rLEEAq
b
a
A spherical capacitor
4
4)
11(
4
4
4
1
)4(
0
00
20
20
200
ab
ab
V
qC
ab
abq
ba
q
r
drqEdsV
r
qE
rEEAq
b
a
An Isolated Sphere – the missing plate is a conducting sphere of infinite radius
)(b 4/1
4 00
Rba
aC
Ex.1 1.0 F 電容器
• d = 1.0mm
228
12
3
0
100~101.1
/1085.8
100.10.1
kmm
mF
mFCdA
Ex.2 a hyperbaric chamber
• Spark ： > 2000V
• fire ： > 0.20 mJ→
• Vf ： > 6000V
• Uf ： > 0.45 mJ
2 = , 1/ 2i i f fq CV C V U CV
Conducting floor
Ex.3 the threshold value Ut ( 150 mJ) required to ignite airborne grains.
20
3
0 0
4
4 , 1/ 2
2 2(150 10 )
4 4 (1.8m)
3.9 10 V
t
C R U CV
UV
R
5-3 Capacitors in parallel
等效電容
n
jjeq
eq
CC
CCCV
qC
VCCCqqqq
VCqVCqVCq
1
321
321321
332211
)(
, ,
5-4 Capacitors in series
等效電容
321
321
321321
33
22
11
1111
/1/1/1
1
)111
(
, ,
CCCC
CCCV
qC
CCCqVVVV
C
qV
C
qV
C
qV
eq
eq
Ex.4 Finding eq. capacitor
CVVVCq
qqC
qVVCq
CCCCCC
0.31)(
)( =
111 ,
121111
1231212
1212123123
3121232112
5-5 Storing Energy in an Electric Field
22
2
0
2
1
2
2
1
CVC
qU
C
qqdq
CdWW
qdC
qqdVdW
q
Ex.4 A RAM Chip
electrons108.1
1060.1
3.51055 619
15
C
VF
e
CV
e
qn
C = 55fF （ 10-15 ） V = 5.3 volt
Ex.5 電容式鍵盤
Ex.5 (cont)
• A = 9.50 10-5m2 ; k = 3.50 • 按鍵後 d 由 5.00mm 減為 0.150mm
• 按鍵前 C = 0.589PF
PFC 0.19
FPFd
k 120 106.19
電容式麥克風
Ex.6 defibrillator ( 除纖顫機 )
kW100s100.2
J200
J875)V5000)(F1070(2
1
2
1
3
262
t
UP
CVU
心跳停止病人之急救
1. 盡快求助2. 盡快給予先進的救命治療3. 盡快實行心肺復甦術
(CPR) 4. 盡快除纖顫
