Capacitors

Ch06 Capacitors and Inductors 2
Capacitors and Inductors
• Introduction
• Capacitors
• Factors Affecting Capacitance
• Types Of Capacitors
• Charge in Capacitors
• Memory Effect
• Energy Storing in Capacitor
• Series and Parallel Capacitors

Introduction
• Resistor: a passive element which dissipates
energy only
• Two important passive linear circuit
elements:
1) Capacitor
2) Inductor
• Capacitor and inductor can store energy
only and they can neither generate nor
dissipate energy.

Michael Faraday (1971-1867)

Capacitors
• A capacitor consists of two conducting plates
separated by an insulator (or dielectric).
(F/m)
10
854
.
8
ε
12
0
0








 r
d
A
C

Factors Affecting Capacitance
• Three factors affecting the value of
capacitance:
1. Area: the larger the area, the greater the
capacitance.
2. Spacing between the plates: the smaller the
spacing, the greater the capacitance.
3. Material permittivity: the higher the permittivity,
the greater the capacitance.
d
A
C
ε


TYPES OF CAPACITORS
(a) Polyester capacitor, (b) Ceramic capacitor, (c)
Electrolytic capacitor
(d) Variable capacitors

Circuit Diagram

Charge in Capacitors
• The relation between the charge in plates and
the voltage across a capacitor is given below.
Cv
q 
C/V
1
F
1 
v
q Linear
Nonlinear

Voltage Limit on a Capacitor
• Since q=Cv, the plate charge increases as the
voltage increases. The electric field intensity
between two plates increases. If the voltage
across the capacitor is so large that the field
intensity is large enough to break down the
insulation of the dielectric, the capacitor is out
of work. Hence, every practical capacitor has a
maximum limit on its operating voltage.

I-V Relation of Capacitor
+
-
v
i
C
dt
dv
C
dt
dq
i
Cv
q 

 ,

Physical Meaning
dt
dv
C
i 
• when v is a constant voltage, then i=0; a constant voltage
across a capacitor creates no current through the capacitor, the
capacitor in this case is the same as an open circuit.
• If v is abruptly changed, then the current will have an infinite
value that is practically impossible. Hence, a capacitor is
impossible to have an abrupt change in its voltage except an
infinite current is applied.
+
-
v
i
C

Voltage On A Capacitor
• A capacitor is an open circuit to dc.
• The voltage on a capacitor cannot change
abruptly.
Abrupt change

Memory Effect
• The charge on a capacitor is an integration of
current through the capacitor. Hence, the
memory effect counts.
dt
dv
C
i   


t
idt
C
t
v
1
)
(
 

t
t
o
o
t
v
idt
C
t
v )
(
1
)
(
 
0
)
( 

v
 
C
t
q
t
v o
o /
)
(
)
( 
+
-
v
i
C

Energy Storing in Capacitor
dt
dv
Cv
vi
p 

 
 
 







t t
v
v
t
v
v
t
Cv
vdv
C
dt
dt
dv
v
C
pdt
w )
(
)
(
2
)
(
)
(
2
1
)
(
2
1
)
( 2
t
Cv
t
w 
C
t
q
t
w
2
)
(
)
(
2

)
0
)
(
( 

v +
-
v
i
C

Model of Practical Capacitor

Series and Parallel Capacitors
• The equivalent capacitance of N parallel-
connected capacitors is the sum of the
individual capacitance.
N
i
i
i
i
i 



 ...
3
2
1
dt
dv
C
dt
dv
C
dt
dv
C
dt
dv
C
i N




 ...
3
2
1
dt
dv
C
dt
dv
C eq
N
k
K 






 
1
N
eq C
C
C
C
C 



 ....
3
2
1

N
eq C
C
C
C
C
1
...
1
1
1
1
3
2
1






Series Capacitors
• The equivalent capacitance of series-
connected capacitors is the reciprocal of the
sum of the reciprocals of the individual
capacitances.
N
eq
t
N
t
eq
C
t
q
C
t
q
C
t
q
C
t
q
id
C
C
C
C
id
C
)
(
)
(
)
(
)
(
)
1
...
1
1
1
(
1
2
1
3
2
1








 
 






)
(
...
)
(
)
(
)
( 2
1 t
v
t
v
t
v
t
v N




2
1
1
1
1
C
C
Ceq


2
1
2
1
C
C
C
C
Ceq



Capacitors

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