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Physics is about nature. This course covers almost every concept related to physics. Important points in this lecture are: Electrostatic Energy and Capacitors, Electrostatic Energy, Capacitors, Using Capacitors, Energy in the Electric Field, Lifesaving Jolt, Defibrillator, Work Done, Configuration of a System, Charge Transfer
Typology: Slides
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Capacitor
Capacitor: pair of conductors carrying equal but opposite charges.
Usage: store electrical energy
Parallel-Plate Capacitor:2 conducting plates of area
A
separated by a
small distance
d
.
Plates are initially neutral.They’re charged by connecting to a battery.Charge transfer
plates are equal but oppositely charged.
Large
A
, small
d
E
0 outside.
0
inside
z
Far from the edges
0
z
^
ˆ
inside
d
z
d A
d A
Parallel-plate capacitor:
0
d
0
d C = Q
/
V
= capacitance
Parallel-plate capacitorSee Probs 41 & 42
^
^
farad
Practical capacitor ~
F ( 10
^6
F) or pF ( 10
^12
F )
^
0
C d
m
dV
dQ C
Charging / Discharging
dQ
dV
A capacitor consists of two circular metal plates of radius
R
= 12 cm,
separated by
d
= 5.0 mm. Find
(a) Its capacitance,(b) the charge on the plates, and(c) the stored energy when the capacitor is connected to a 12-V battery.
0
d
10
2
9
3
m
Vm
m
pF
(a) (b) (c)
pF
pC
2
pF
pJ
nJ
Computer memories: billions of 25 fF capacitors.Rectifiers: mFFuel-cells: 10
2
F
220-mFelectrolyticcapacitor
1 F
43 pF to 2.2 mF
Dielectrics: insulators containing molecular dipoles but no free charges.
Dielectric layer lowers V betweencapacitor plates by factor 1/
(
1).
0
A d
= dielectric constant
Molecular dipolesaligned by
E
0
.
Dipole fields oppose
E
. 0
Net field reduced to
E
=
E
0
/
.
Hence
V
=
V
0
/
.
Q
is unchanged, so
C
=
C
0
.
: 2 ~ 10 mostly
Working voltage V = Max safe potential < E
bkd
d
You need to replace a capacitor with one that can store more energy.Which will give you greater energy increase:(a) a capacitor with twice the capacitance and same working voltage as the old one,or (b) a capacitor with the same capacitance and twice the working voltage?
Two ways to connect 2 electronic components: parallel & series
Parallel:
Same
V
for both components
1
2
1
2
1
2
Series:
Same
I
(
Q
) for both components
1
2
1
2
1
2
1
2
or C
1
2
or C
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You’ve got two 10-
F capacitors rated at 15 V.
What are the capacitances & working voltages of their parallel & series combinations?Parallel :
working V
Series :
working V
1
2
1
2
You have 2 identical capacitors with capacitance
C
.
How would you connect them to get equivalent capacitances(a) 2
C
, and
(b) ½ C ?Which combination would have the higher working voltage?
parallel
series
San Francisco’s BART train:KE of deceleration stored as EE in ultracapacitor.Stored EE is used to accelerate train.
Capacitors deliver higher energymuch more quickly than batteries.Flash light:Battery charges capacitor,which then discharges to give flash.
Other examples:Defibrillator, controlled nuclear fusion, amusement park rides, hybrid cars, …
Charging a capacitor rearranges charges
energy stored in
E
Energy density = energy per unit volume
Parallel-plate capacitor:
2 Q 2
(^20)
2
A d
E
u
A d
Energy density :
2
2
0 2
2 0
2
0
1 2
0
is universal
2
0
1 2
E u
^
^
3
/
E u
m
2
0 1 2
dV
E