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CHAPTER 4:
CAPACITANCE AND DIELECTRICS
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What and how
Khi cấp cứu trong các trường hợp liên quan đến tim mạch, các bác
sĩsửdụng một dụng cụnhưtrong hình bên dưới.
Dụng cụ đó tên là gì? Có tác dụng nhưthếnào khi cấp cứu?
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Learning goals
By studying this chapter, you will learn:
• The nature of capacitors, and how to calculate a quantity that
measures their ability to store charge.
• How to analyze capacitors connected in a network.
• How to calculate the amount of energy stored in a capacitor.
• What dielectrics are, and how they make capacitors more
effective.
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4.1 Capacitors and Capacitance
4.2 Capacitors in Series and Parallel
4.3 Energy Storage in Capacitors
and Electric-Field Energy
4.4 Dielectrics
4.5 Molecular Model of Induced Charge
4.6 Gauss’s Law in Dielectrics
Contents
4.1 CAPACITORS AND CAPACITANCE
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Definition of Capacitance (1)
A capacitor is formed by any two
conductors separated by an insulator (or a
vacuum)
A capacitor has charge :
- the conductor at higher potential: +
- the conductor at lower potential: −
Symbols of capacitor:
For a capacitor, the ratio of charge to potential difference
between the conductors does not change.
→capacitance : =
The SI unit of : farad (F)
1
F
=
1C
/
1V
(4.1)
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Definition of Capacitance (2)
↗ → ↗ → ↗ →Δ↗
→Capacitance is a measure of the ability of a capacitor to store
energy.
The value of the capacitance depends only on the shapes and
sizes of the conductors and on the nature of the insulating
material between them.
Typical devices:
: 10-6 F →10-12 F.
Commercial capacitors
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A capacitor stores charge at a potential difference . What
happens if the voltage applied to the capacitor by a battery is
doubled to 2?
A. The capacitance falls to half its initial value, and the
charge remains the same.
B. The capacitance and the charge both fall to half their
initial values.
C. The capacitance and the charge both double.
D. The capacitance remains the same, and the charge
doubles.
Test Your Understanding
→Điện dung của tụ điện phẳng:
=
=
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- Khi 1 bản tụnối với cực âm → −
- Khi 1 bản tụnối với cực dương → +
→
∝
area
and
∝
1
/
(4.2)
Xét hai bản tụ điện phẳng có diện tích và cách nhau khoảng .
→ Cường độ điện trường giữa hai bản tụ
=
=Q
A
- Hiệuđiện thếgiữa hai bản tụ:
= = Q
A
Calculating Capacitance: Plate Capacitors in Vacuum
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Unit of
From (4.2), we have:
=
The unit of : F, of : m, of : m2
→The other unit of : F/m
=8.85×10$%& C&/N·m& =8.85 × 10$%& F/m
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Trên bàn phím máy tính, mỗi phím là một tụ điện phẳng. Khi ấn
phím xuống dưới thì điện dung của tụsẽ:
A. Tăng B. Giảm C. Không đổi
Test Your Understanding
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Example: Properties of a parallel-plate capacitor
The plates of a parallel-plate capacitor in vacuum are 5.0 mm
apart and 2.0 m2in area. A 10.0-kV potential difference is applied
across the capacitor. Compute:
a) the capacitance;
b) the charge on each plate; and
c) the magnitude of the electric field between the plates.
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Example: A spherical capacitor
Two concentric spherical conducting shells are separated by
vacuum. The inner shell has total charge + and outer radius *
and the outer shell has charge − and inner radius *. Find the
capacitance of this spherical capacitor.
=
=4,**
*
−
*
Capacitance of this spherical capacitor:
(4.3)
The potential difference:
=−=
4,(1
*−1
*)
?
?
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A solid cylindrical conductor of radius
/
and charge
is coaxial
with a cylindrical shell of negligible thickness, radius 0(0 > /),
and charge −. Find the capacitance of this cylindrical capacitor
if its length is 2.
Electric field:
3=4
2,*
The potential difference :
=−=−5d78
=−53d*
=− 4
2,5d*
*
=−
2,2ln (0
/)
Capacitance of the cylindrical capacitor:
=
=
2,2
ln
(
0
/
)
Example: A cylindrical capacitor
(4.4)
We have: =− =;
&<=>?ln (
)
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Example: A cylindrical capacitor (2)
Suppose 0=2.0/for the cylindrical capacitor. You would like to
increase the capacitance, and you can do so by choosing to
increase either 2by 10%, or /by 10%. Which choice is more
effective at increasing the capacitance?
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Commercially available capacitors
4.2 CAPACITORS IN SERIES AND PARALLEL
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Capacitors in Series
- The magnitude of charge on all plates is the same
=%=&=⋯=A
→Equivalent capacitance:
1
BC
=
=1
%
+1
&
+⋯+ 1
A
=D1
E
E
- The potential difference:
=%+&+⋯+A
(4.5)
(4.6)
(4.7)
%&
%&
→Equivalent capacitance:
BC
=
=
%
+
&
+
⋯
+
A
=
D
E
E
- The potential difference is the same:
=%=&=⋯=A
- The magnitude of charge on all plates:
=%+&+⋯+A
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Capacitors in Parallel
(4.8)
(4.9)
(4.10)
%
&
%
&
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Equivalent Capacitance
Find the equivalent capacitance between /and 0 for the
combination of capacitors shown in Figure. All capacitances are
in microfarads.
