Capacitors
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Transcript of Capacitors
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Capacitors
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Capacitors• A capacitor is a device that stores electric
charge.
• A capacitor consists of two conductors separated by an insulator.
• Capacitors have many applications:– Computer RAM memory and keyboards.– Electronic flashes for cameras.– Electric power surge protectors.– Radios and electronic circuits.
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Types of Capacitors
Parallel-Plate Capacitor Cylindrical Capacitor
A cylindrical capacitor is a parallel-plate capacitor that hasbeen rolled up with an insulating layer between the plates.
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Capacitors and Capacitance
Charge Q stored:
CVQ The stored charge Q is proportional to the potential
difference V between the plates. The capacitance C is the constant of proportionality, measured in Farads.
Farad = Coulomb / Volt
A capacitor in a simpleelectric circuit.
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Parallel-Plate Capacitor• A simple parallel-plate
capacitor consists of two conducting plates of area A separated by a distance d.
• Charge +Q is placed on one plate and –Q on the other plate.
• An electric field E is created between the plates.
+Q -Q
+Q -Q
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What is a capacitor?
• Electronic component• Two conducting surfaces separated by an insulating
material• Stores charge• Uses
– Time delays– Filters– Tuned circuits
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Capacitor construction
• Two metal plates• Separated by insulating
material• ‘Sandwich’ construction• ‘Swiss roll’ structure• Capacitance set by...
d
AC
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Defining capacitance
• ‘Good’ capacitors store a lot of charge…• …when only a small voltage is applied• Capacitance is charge stored per volt• Capacitance is measured in farads F
– Big unit so nF, mF and F are used
V
QC
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Graphical representation
Equating to the equation of a straight line
mxy
CVQV
QC
Q
V
Gradient term is the capacitance of the capacitor
Charge stored is directly proportional to the applied voltage
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Energy stored by a capacitor
• By general definition E=QV– product of charge and voltage
• By graphical consideration...
QVE2
1
Area term is the energy stored in the capacitor
Q
V
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Other expressions for energy
• By substitution of Q=CV
C
QE
CVE
QVE
2
2
2
1
2
12
1
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Charging a capacitor
• Current flow• Initially
– High• Finally
– Zero• Exponential model• Charging factors
– Capacitance– Resistance
I
t
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Discharging a capacitor
• Current flow• Initially
– High– Opposite to
charging• Finally
– Zero• Exponential model• Discharging factors
– Capacitance– Resistance
I
t
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Discharging a Capacitor
• Initially, the rate of discharge is high because the potential difference across the plates is large.
• As the potential difference falls, so too does the current flowing
• Think pressure
As water level falls, rate of flow decreases
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• At some time t, with charge Q on the capacitor, the current that flows in an interval t is:
I = Q/t
• And I = V/R• But since V=Q/C, we can say that
I = Q/RC• So the discharge current is proportional to
the charge still on the plates.
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• For a changing current, the drop in charge, Q is given by:
Q = -It (minus because charge Iarge at t = 0 and falls as t increases)
• So Q = -Qt/RC (because I = Q/RC)
• Or -Q/Q = t/RC
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V or Q
t
V or Q
t
Voltage and charge characteristics
• Charging Discharging
RCt
eQQ
0)1(0RC
teVV
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Dielectrics• A dielectric is an insulating material (e.g.
paper, plastic, glass).
• A dielectric placed between the conductors of a capacitor increases its capacitance by a factor κ, called the dielectric constant.
C= κCo (Co=capacitance without
dielectric)
• For a parallel-plate capacitor:d
A
d
AC 0
ε = κεo = permittivity of the material.
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Properties of Dielectric Materials• Dielectric strength is the maximum electric field that a
dielectric can withstand without becoming a conductor.• Dielectric materials
– increase capacitance.– increase electric breakdown potential of capacitors.– provide mechanical support.
MaterialDielectric Constant κ
Dielectric Strength (V/m)
air 1.0006 3 x 106
paper 3.7 15 x 106
mica 7 150 x 106
strontium titanate 300 8 x 106
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Practice Quiz
• A charge Q is initially placed on a parallel-plate capacitor with an air gap between the electrodes, then the capacitor is electrically isolated.
• A sheet of paper is then inserted between the capacitor plates.
• What happens to:a) the capacitance?b) the charge on the capacitor?c) the potential difference between the plates?d) the energy stored in the capacitor?
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Capacitors in Parallel
VC
VCCC
VCVCVC
QQQQ
eq
)( 321
321
321
...321 CCCCeq
Capacitors in Parallel:
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Capacitors in Series
eqC
Q
CCCQ
C
Q
C
Q
C
Q
VVVV
321
321
321
111
...1111
321
CCCCeq
For n capacitors in series:
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Circuit with Capacitors in Series and Parallel
a b
15 μF 3 μF
6 μF
What is the effective capacitance Cab between points a and b?
20 μF
C1 C2
C3
C4
Cab
?
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• Product of– Capacitance of the capacitor being charged– Resistance of the charging circuit– CR
• Symbol ‘Tau’• Unit seconds
Time constant
tCR
tQ
V
V
QCR
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When t equals tau during discharge
• At t = tau the capacitor has fallen to 37% of its original value.
• By a similar analysis tau can be considered to be the time taken for the capacitor to reach 63% of full charge.
37.00
10
0
0
eQQ
eQQ
eQQ
RCRC
RCt
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Graphical determination of tau
• V at 37%• Q at 37%• Compared to initial
maximum discharge
V
or
Q
t
RtC
RCt
t
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Logarithmic discharge analysis
• Mathematical consideration of discharge
• Exponential relationship • Taking natural logs
equates expression to ‘y=mx+c’
• Gradient is -1/Tau
0
0
0
0
ln1
ln
lnln
VtRC
V
RCtVV
eV
V
eVV
RCt
RCt
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Logarithmic discharge graph
lnV
t
Gradient term is the -1/Tau
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