Transcript Chapter 27 Capacitance and Dielectrics

Chapter 27 Capacitance and
Dielectrics
第二十七章 電容及介電質
Capacitors
The uses of capacitors
Capacitor or condenser is a charge storage device. It is also an
energy storage device.
Capacitors have many uses beyond the energy or charge storage,
such as in tuning circuits, filter circuits, memories, etc.
What else can you think of?
Capacitance
Two isolated conductors of
any shape comprise a
capacitor. We call these two
conductors plates. When the
capacitor is charged, there
are equal amount but
opposite charges on the two
plates. The amount of
charge is proportional to the
potential difference between
them.
Q  CV
The proportionality constant
C is called capacitance.
Parallel-plate capacitor
Neglecting the edges, we have

E
0
d
V  Ed 
0
Q  A  (
0 A
The capacitance of a
parallel plate capacitor:
d
)V
C (
0 A
d
)
The unit of capacitance
The SI unit of capacitance is faraday (F).
1F  1C / V
How large is one faraday?
C (
0 A
d
)
 0  8.85 1012 F / m
If d = 10 m, then
1011 A
1F 
105
 A  106 m 2  1km  1km
Not easy to achieve!
Charging the capacitor
A cylindrical capacitor
C  2 0
ln(b / a)
A spherical capacitor
C  4 0
ab
ba
An isolated sphere
C  4 0 R
R
Sample problem 1
A storage capacitor on a random access memory (RAM) chip has a
capacitance of 55 fF. If the capacitor is charged to 5.3 V, how many
excess electrons are on its negative plate?
1.8  106 electrons
Some circuit symbols
Capacitors in parallel
Capacitors in series
Sample problem 2
Sample problem 3
Energy stored in a capacitor
dW  Vdq 
W 
Q
0
q
dq
C
q
Q2
dq 
C
2C
The work is stored as the potential
energy U in the capacitor.
Q2 1
U
 CV 2
2C 2
The medical defibrillator
C  70  F V  5000V
About ¼ of the stored energy is sent to
the patient during a period of 2.0 ms.
Energy stored in an electric field
1
1 0 A
1
2
2
U  CV  (
)( Ed )   0 E 2 ( Ad )
2
2 d
2
Neglecting the edges, Ad is the volume in which the electric field
is present.
Thus the energy density of the electric field is:
1
u  0E2
2
Sample problem 4
An isolated conducting sphere whose radius R is 6.85 cm has a
charge q = 1.25 nC. (a) How much potential energy is stored in the
electric field of this charged conductor? (b) What is the energy
density at the surface of the sphere?
(a) 103 nJ. (b) 25.4 J/m3.
Capacitor with a dielectric
++ ++ ++ +
V
    
A
C  0
d
A
C   0
d
C   Cair
Schematics of real capacitors
Capacitor with a dielectric
Space filled with a dielectric
material
For a point charge:
q
E
4 0 r 2
Just outside a conductor:
1

E
 0
Sample problem 5
A parallel-plate capacitor whose capacitance C is 13.5 pF is charged
by a battery to a potential difference V = 12.5 V between its plates.
The charging battery is now disconnected and a porcelain slab ( =
6.50) is slipped between the plates. What is the potential energy of
the capacitor-porcelain device, both before and after the slab is put
into place?
Ui = 1055 pJ and Uf = Ui/ = 160 pJ
Dielectrics: an atomic view
Induced dipole moment
Capacitance: an atomic view
E0 

0
   ind
E
0

E

  0
E0
 ind
 1



Sample problem 6
What is the electric field in (a) the gap between the plates and the
dielectric slab? (b) the dielectric slab? What is the capacitance?
Metal slab in a capacitor
Capacitor partially filled with a
dielectric
Sample problem 7
What is the ratio of the capacitance of the capacitor with dielectrics
shown below to that of the same capacitor without any dielectric?
Force exerted on a dielectric in a
capacitor
Force exerted on a dielectric in a
capacitor
Home work
Question (問題): 1, 6, 19
Exercise (練習題): 11, 16, 19
Problem (習題): 10, 20, 24, 38