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L
A
AQLQ
V
QC 0
0
Capacitors in series: ...1111
321
CCCCtot
Capacitors in parallel: ...321 CCCCtot
22
2
1
2
1Q
CCVW
faradC ][
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CapacitorsConsider two large metal plates which are parallel to each other and separated by a distance small compared with their width.
Area A
The field between plates is 0
E
VL
y
LdydyEbottomVtopVLL
y00 00
)]()([
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A
QLL
A
ALbottomVtopV
000
)]()([
0AQL
V
The capacitance is:
L
A
AQLQ
V
QC 0
0
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a
b
C1C3
C5C4
C2
C1=C5=8.4 F and C2=C3=C4=4.2 F The applied potential is Vab=220 V. a)What is the equivalent capacitance of the network
between points a and b? b) Calculate the charge on each capacitor and the
potential difference across each capacitor.
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ticselectrostainrdE 0
E
0 rdE
0 rdE
1E
2E
0)()( 2121 CDEABErdErdED
C
B
A
A
B C
D
!21 impossibleEE
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Electric field near the surface of a conductor
0
E
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L
A
AQLQ
V
QC 0
0
Capacitors in series: ...1111
321
CCCCtot
Capacitors in parallel: ...321 CCCCtot
22
2
1
2
1Q
CCVW
faradC ][
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Most capacitors have a non-conducting material, or dielectric, between their conducting plates. When we insert an uncharged sheet of dielectric between the plates, experiments show that the potential difference decreases to a smaller value V (we did this experiment last class !).
dielectricwithoutV
QC
00
dielectricwithV
QC
0CC
When the space between plates is completely filled by the dielectric, the ratio
0C
CK is called dielectric constant.
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Moore’s Law (1965): every 2 years the number of transistors on a chip is doubled
Smaller, Denser, Cheaper
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