SlideShare una empresa de Scribd logo
1 de 21
Descargar para leer sin conexión
Energy Storage Devices
Capacitors
Composed of two conductive plates separated by an
insulator (or dielectric).
Commonly illustrated as two parallel metal plates
separated by a distance, d.
C = ε A/d
where ε = εr εo
εr is the relative dielectric constant
εo is the vacuum permittivity
Effect of Dimensions
Capacitance increases with
increasing surface area of the plates,
decreasing spacing between plates, and
increasing the relative dielectric constant of the
insulator between the two plates.
Types of Capacitors
Fixed Capacitors
Nonpolarized
 May be connected into circuit with either terminal of
capacitor connected to the high voltage side of the circuit.
 Insulator: Paper, Mica, Ceramic, Polymer
Electrolytic
 The negative terminal must always be at a lower voltage than
the positive terminal
 Plates or Electrodes: Aluminum, Tantalum
Nonpolarized
Difficult to make nonpolarized capacitors that store a
large amount of charge or operate at high voltages.
Tolerance on capacitance values is very large
 +50%/-25% is not unusual
http://www.marvac.com/fun/ceramic_capacitor_codes.aspx
PSpice Symbol
Electrolytic
Pspice Symbols Fabrication
http://www.digitivity.com/articles/2008/11/choosing-the-right-capacitor.htm
Variable Capacitors
Cross-sectional area is changed as one set of plates
are rotated with respect to the other.
http://www.tpub.com/neets/book2/3f.htm
PSpice Symbol
Electrical Properties of a Capacitor
Acts like an open circuit at steady state when
connected to a d.c. voltage or current source.
Voltage on a capacitor must be continuous
There are no abrupt changes to the voltage, but there
may be discontinuities in the current.
An ideal capacitor does not dissipate energy, it takes
power when storing energy and returns it when
discharging.
Energy Storage
Charge is stored on the plates of the capacitor.
Equation:
Q = CV
Units:
Farad = Coulomb/Voltage
Farad is abbreviated as F
Sign Conventions
• The sign convention used with a
capacitor is the same as for a power
dissipating device.
• When current flows into the positive side
of the voltage across the capacitor, it is
positive and the capacitor is dissipating
power.
• When the capacitor releases energy back
into the circuit, the sign of the current will
be negative.
Charging a Capacitor
At first, it is easy to store charge in the capacitor.
As more charge is stored on the plates of the
capacitor, it becomes increasingly difficult to place
additional charge on the plates.
Coulombic repulsion from the charge already on the
plates creates an opposing force to limit the addition of
more charge on the plates.
 Voltage across a capacitor increases rapidly as charge is
moved onto the plates when the initial amount of charge on
the capacitor is small.
 Voltage across the capacitor increases more slowly as it
becomes difficult to add extra charge to the plates.
Adding Charge to Capacitor
The ability to add charge to a capacitor depends on:
the amount of charge already on the plates of the
capacitor
and
the force (voltage) driving the charge towards the
plates (i.e., current)
Discharging a Capacitor
At first, it is easy to remove charge in the capacitor.
Coulombic repulsion from charge already on the plates
creates a force that pushes some of the charge out of the
capacitor once the force (voltage) that placed the charge in
the capacitor is removed (or decreased).
As more charge is removed from the plates of the
capacitor, it becomes increasingly difficult to get rid of the
small amount of charge remaining on the plates.
Coulombic repulsion decreases as charge spreads out on the
plates. As the amount of charge decreases, the force needed
to drive the charge off of the plates decreases.
 Voltage across a capacitor decreases rapidly as charge is removed
from the plates when the initial amount of charge on the capacitor
is small.
 Voltage across the capacitor decreases more slowly as it becomes
difficult to force the remaining charge out of the capacitor.
Current-Voltage Relationships
∫=
=
=
=
1
1
t
t
CC
C
C
C
C
o
dti
C
v
dt
dv
Ci
dt
dq
i
Cvq
Power and Energy
dt
dv
Cvp
vip
C
CC
CCC
=
=
C
q
w
Cvw
C
CC
2
2
1
2
2
=
=
Capacitors in Parallel
Ceq for Capacitors in Parallel
i
4321eq
4321
4433
2211
4321
C CCCC
dt
dv
Ci
dt
dv
C
dt
dv
C
dt
dv
C
dt
dv
Ci
dt
dv
Ci
dt
dv
Ci
dt
dv
Ci
dt
dv
Ci
iiiii
eqin
in
in
+++=
=
+++=
==
==
+++=
Capacitors in Series
Ceq for Capacitors in Series
i
( ) ( ) ( ) ( )[ ] 1
4321eq
t
t
t
t4
t
t3
t
t2
t
t1
t
t4
4
t
t3
3
t
t2
2
t
t1
1
4321
1111C
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
idt
1
1
o
1
o
1
o
1
o
1
o
1
o
1
o
1
o
1
o
−
+++=
=
+++=
==
==
+++=
∫
∫∫∫∫
∫∫
∫∫
CCCC
C
v
CCCC
v
C
v
C
v
C
v
C
v
vvvvv
eq
in
in
in
General Equations for Ceq
Parallel Combination Series Combination
If P capacitors are in parallel,
then
If S capacitors are in series,
then:
1
1
1
−
=






= ∑
S
s s
eq
C
C∑=
=
P
p
Peq CC
1
Summary
Capacitors are energy storage devices.
An ideal capacitor act like an open circuit at steady state when a
DC voltage or current has been applied.
The voltage across a capacitor must be a continuous function;
the current flowing through a capacitor can be discontinuous.
The equations for equivalent capacitance for
capacitors in parallel capacitors in series
1
1
1
−
=






= ∑
S
s s
eq
C
C∑=
=
P
p
Peq CC
1
∫==
1
1
t
t
CC
C
C
o
dti
C
v
dt
dv
Ci

Más contenido relacionado

La actualidad más candente

Capacitors, how they work
Capacitors, how they workCapacitors, how they work
Capacitors, how they workcallr
 
Mechanism of-a-capacitor
Mechanism of-a-capacitorMechanism of-a-capacitor
Mechanism of-a-capacitorMasud Parvaze
 
Halderman ch046 lecture
Halderman ch046 lectureHalderman ch046 lecture
Halderman ch046 lecturemcfalltj
 
Functions and Application of Capacitor
Functions and Application of CapacitorFunctions and Application of Capacitor
Functions and Application of Capacitorbrassmile37
 
Definition of capacitance
Definition of capacitanceDefinition of capacitance
Definition of capacitanceAnaya Zafar
 
Capacitor and principle of capacitors
Capacitor and principle of capacitorsCapacitor and principle of capacitors
Capacitor and principle of capacitorsvibhu mehta
 
Parallel Plate capacitor
Parallel Plate capacitorParallel Plate capacitor
Parallel Plate capacitorphysicscatalyst
 
Series and parallel arrangement of capacitors
Series and parallel arrangement of capacitorsSeries and parallel arrangement of capacitors
Series and parallel arrangement of capacitorsphysicscatalyst
 
Chapter 24-capacitance
Chapter 24-capacitanceChapter 24-capacitance
Chapter 24-capacitanceAnaya Zafar
 
Capacitor experiment
Capacitor experimentCapacitor experiment
Capacitor experimentphilipkitheka
 
Capacitor aka condenser
Capacitor aka condenserCapacitor aka condenser
Capacitor aka condenserMahek1308
 
Triggatron gap
Triggatron gapTriggatron gap
Triggatron gapsarunkutti
 

La actualidad más candente (20)

Capacitors, how they work
Capacitors, how they workCapacitors, how they work
Capacitors, how they work
 
Capacitors
CapacitorsCapacitors
Capacitors
 
Capacitors
CapacitorsCapacitors
Capacitors
 
Capacitors
CapacitorsCapacitors
Capacitors
 
Mechanism of-a-capacitor
Mechanism of-a-capacitorMechanism of-a-capacitor
Mechanism of-a-capacitor
 
Halderman ch046 lecture
Halderman ch046 lectureHalderman ch046 lecture
Halderman ch046 lecture
 
Functions and Application of Capacitor
Functions and Application of CapacitorFunctions and Application of Capacitor
Functions and Application of Capacitor
 
Definition of capacitance
Definition of capacitanceDefinition of capacitance
Definition of capacitance
 
Capacitors
CapacitorsCapacitors
Capacitors
 
Charging C
Charging  CCharging  C
Charging C
 
Capacitor and principle of capacitors
Capacitor and principle of capacitorsCapacitor and principle of capacitors
Capacitor and principle of capacitors
 
Parallel Plate capacitor
Parallel Plate capacitorParallel Plate capacitor
Parallel Plate capacitor
 
Lesson 2 Capacitors
Lesson 2  CapacitorsLesson 2  Capacitors
Lesson 2 Capacitors
 
Series and parallel arrangement of capacitors
Series and parallel arrangement of capacitorsSeries and parallel arrangement of capacitors
Series and parallel arrangement of capacitors
 
Chapter 24-capacitance
Chapter 24-capacitanceChapter 24-capacitance
Chapter 24-capacitance
 
10 capacitors
10 capacitors10 capacitors
10 capacitors
 
Capacitor experiment
Capacitor experimentCapacitor experiment
Capacitor experiment
 
Introduction To Capacitance
Introduction To CapacitanceIntroduction To Capacitance
Introduction To Capacitance
 
Capacitor aka condenser
Capacitor aka condenserCapacitor aka condenser
Capacitor aka condenser
 
Triggatron gap
Triggatron gapTriggatron gap
Triggatron gap
 

Similar a Capacitors

Capacitors.ppt
Capacitors.pptCapacitors.ppt
Capacitors.pptAninDeb
 
General Physics- Electricity
General Physics- ElectricityGeneral Physics- Electricity
General Physics- ElectricitySaraLQ2
 
Chapter 5 B L Theraja Cylindrical Capacitor.pptx
Chapter 5 B L Theraja Cylindrical Capacitor.pptxChapter 5 B L Theraja Cylindrical Capacitor.pptx
Chapter 5 B L Theraja Cylindrical Capacitor.pptxabhisheksrivas124
 
Chapter 37
Chapter 37Chapter 37
Chapter 37mcfalltj
 
Capacitors with Dielectrics.ppt
Capacitors with Dielectrics.pptCapacitors with Dielectrics.ppt
Capacitors with Dielectrics.pptVara Prasad
 
3.3 Capacitors.ppt
3.3 Capacitors.ppt3.3 Capacitors.ppt
3.3 Capacitors.pptAninDeb
 
Generation of High D.C. Voltage (HVDC generation)
Generation of High D.C. Voltage (HVDC generation)Generation of High D.C. Voltage (HVDC generation)
Generation of High D.C. Voltage (HVDC generation)RP6997
 
Chapter_18_sec_1__Electric_Potential_and_Capacitance.ppt
Chapter_18_sec_1__Electric_Potential_and_Capacitance.pptChapter_18_sec_1__Electric_Potential_and_Capacitance.ppt
Chapter_18_sec_1__Electric_Potential_and_Capacitance.pptAmitKumarLal5
 
Elect principles -_capacitance
Elect principles -_capacitanceElect principles -_capacitance
Elect principles -_capacitancesdacey
 
Elect principles capacitance
Elect principles   capacitanceElect principles   capacitance
Elect principles capacitancesld1950
 

Similar a Capacitors (20)

Capacitors.ppt
Capacitors.pptCapacitors.ppt
Capacitors.ppt
 
Capacitors
CapacitorsCapacitors
Capacitors
 
General Physics- Electricity
General Physics- ElectricityGeneral Physics- Electricity
General Physics- Electricity
 
Capacitor
Capacitor Capacitor
Capacitor
 
Chapter 5 B L Theraja Cylindrical Capacitor.pptx
Chapter 5 B L Theraja Cylindrical Capacitor.pptxChapter 5 B L Theraja Cylindrical Capacitor.pptx
Chapter 5 B L Theraja Cylindrical Capacitor.pptx
 
Chapter 37
Chapter 37Chapter 37
Chapter 37
 
Basics of Capacitors
Basics of CapacitorsBasics of Capacitors
Basics of Capacitors
 
Capacitors
CapacitorsCapacitors
Capacitors
 
Capacitors with Dielectrics.ppt
Capacitors with Dielectrics.pptCapacitors with Dielectrics.ppt
Capacitors with Dielectrics.ppt
 
3.3 Capacitors.ppt
3.3 Capacitors.ppt3.3 Capacitors.ppt
3.3 Capacitors.ppt
 
Generation of High D.C. Voltage (HVDC generation)
Generation of High D.C. Voltage (HVDC generation)Generation of High D.C. Voltage (HVDC generation)
Generation of High D.C. Voltage (HVDC generation)
 
CAPACITORS.pptx
CAPACITORS.pptxCAPACITORS.pptx
CAPACITORS.pptx
 
Psps ppt
Psps pptPsps ppt
Psps ppt
 
Chapter_18_sec_1__Electric_Potential_and_Capacitance.ppt
Chapter_18_sec_1__Electric_Potential_and_Capacitance.pptChapter_18_sec_1__Electric_Potential_and_Capacitance.ppt
Chapter_18_sec_1__Electric_Potential_and_Capacitance.ppt
 
Elect principles -_capacitance
Elect principles -_capacitanceElect principles -_capacitance
Elect principles -_capacitance
 
Elect principles capacitance
Elect principles   capacitanceElect principles   capacitance
Elect principles capacitance
 
Capacitors.ppt
Capacitors.pptCapacitors.ppt
Capacitors.ppt
 
FFFF.ppt
FFFF.pptFFFF.ppt
FFFF.ppt
 
ggggg.ppt
ggggg.pptggggg.ppt
ggggg.ppt
 
cursoos.ppt
cursoos.pptcursoos.ppt
cursoos.ppt
 

Último

UNIT4_ESD_wfffffggggggggggggith_ARM.pptx
UNIT4_ESD_wfffffggggggggggggith_ARM.pptxUNIT4_ESD_wfffffggggggggggggith_ARM.pptx
UNIT4_ESD_wfffffggggggggggggith_ARM.pptxrealme6igamerr
 
Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)Bahzad5
 
EPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptxEPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptxJoseeMusabyimana
 
Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...
Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...
Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...Amil baba
 
sdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdf
sdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdfsdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdf
sdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdfJulia Kaye
 
IT3401-WEB ESSENTIALS PRESENTATIONS.pptx
IT3401-WEB ESSENTIALS PRESENTATIONS.pptxIT3401-WEB ESSENTIALS PRESENTATIONS.pptx
IT3401-WEB ESSENTIALS PRESENTATIONS.pptxSAJITHABANUS
 
Landsman converter for power factor improvement
Landsman converter for power factor improvementLandsman converter for power factor improvement
Landsman converter for power factor improvementVijayMuni2
 
Graphics Primitives and CG Display Devices
Graphics Primitives and CG Display DevicesGraphics Primitives and CG Display Devices
Graphics Primitives and CG Display DevicesDIPIKA83
 
Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...
Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...
Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...amrabdallah9
 
Nodal seismic construction requirements.pptx
Nodal seismic construction requirements.pptxNodal seismic construction requirements.pptx
Nodal seismic construction requirements.pptxwendy cai
 
Transforming Process Safety Management: Challenges, Benefits, and Transition ...
Transforming Process Safety Management: Challenges, Benefits, and Transition ...Transforming Process Safety Management: Challenges, Benefits, and Transition ...
Transforming Process Safety Management: Challenges, Benefits, and Transition ...soginsider
 
Design of Clutches and Brakes in Design of Machine Elements.pptx
Design of Clutches and Brakes in Design of Machine Elements.pptxDesign of Clutches and Brakes in Design of Machine Elements.pptx
Design of Clutches and Brakes in Design of Machine Elements.pptxYogeshKumarKJMIT
 
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...Amil baba
 
Multicomponent Spiral Wound Membrane Separation Model.pdf
Multicomponent Spiral Wound Membrane Separation Model.pdfMulticomponent Spiral Wound Membrane Separation Model.pdf
Multicomponent Spiral Wound Membrane Separation Model.pdfGiovanaGhasary1
 
Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...Apollo Techno Industries Pvt Ltd
 
Vertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptx
Vertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptxVertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptx
Vertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptxLMW Machine Tool Division
 
Phase noise transfer functions.pptx
Phase noise transfer      functions.pptxPhase noise transfer      functions.pptx
Phase noise transfer functions.pptxSaiGouthamSunkara
 

Último (20)

Présentation IIRB 2024 Chloe Dufrane.pdf
Présentation IIRB 2024 Chloe Dufrane.pdfPrésentation IIRB 2024 Chloe Dufrane.pdf
Présentation IIRB 2024 Chloe Dufrane.pdf
 
UNIT4_ESD_wfffffggggggggggggith_ARM.pptx
UNIT4_ESD_wfffffggggggggggggith_ARM.pptxUNIT4_ESD_wfffffggggggggggggith_ARM.pptx
UNIT4_ESD_wfffffggggggggggggith_ARM.pptx
 
Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)Lecture 1: Basics of trigonometry (surveying)
Lecture 1: Basics of trigonometry (surveying)
 
EPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptxEPE3163_Hydro power stations_Unit2_Lect2.pptx
EPE3163_Hydro power stations_Unit2_Lect2.pptx
 
Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...
Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...
Best-NO1 Best Rohani Amil In Lahore Kala Ilam In Lahore Kala Jadu Amil In Lah...
 
Présentation IIRB 2024 Marine Cordonnier.pdf
Présentation IIRB 2024 Marine Cordonnier.pdfPrésentation IIRB 2024 Marine Cordonnier.pdf
Présentation IIRB 2024 Marine Cordonnier.pdf
 
sdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdf
sdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdfsdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdf
sdfsadopkjpiosufoiasdoifjasldkjfl a asldkjflaskdjflkjsdsdf
 
IT3401-WEB ESSENTIALS PRESENTATIONS.pptx
IT3401-WEB ESSENTIALS PRESENTATIONS.pptxIT3401-WEB ESSENTIALS PRESENTATIONS.pptx
IT3401-WEB ESSENTIALS PRESENTATIONS.pptx
 
Landsman converter for power factor improvement
Landsman converter for power factor improvementLandsman converter for power factor improvement
Landsman converter for power factor improvement
 
Graphics Primitives and CG Display Devices
Graphics Primitives and CG Display DevicesGraphics Primitives and CG Display Devices
Graphics Primitives and CG Display Devices
 
Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...
Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...
Strategies of Urban Morphologyfor Improving Outdoor Thermal Comfort and Susta...
 
Nodal seismic construction requirements.pptx
Nodal seismic construction requirements.pptxNodal seismic construction requirements.pptx
Nodal seismic construction requirements.pptx
 
Litature Review: Research Paper work for Engineering
Litature Review: Research Paper work for EngineeringLitature Review: Research Paper work for Engineering
Litature Review: Research Paper work for Engineering
 
Transforming Process Safety Management: Challenges, Benefits, and Transition ...
Transforming Process Safety Management: Challenges, Benefits, and Transition ...Transforming Process Safety Management: Challenges, Benefits, and Transition ...
Transforming Process Safety Management: Challenges, Benefits, and Transition ...
 
Design of Clutches and Brakes in Design of Machine Elements.pptx
Design of Clutches and Brakes in Design of Machine Elements.pptxDesign of Clutches and Brakes in Design of Machine Elements.pptx
Design of Clutches and Brakes in Design of Machine Elements.pptx
 
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
Popular-NO1 Kala Jadu Expert Specialist In Germany Kala Jadu Expert Specialis...
 
Multicomponent Spiral Wound Membrane Separation Model.pdf
Multicomponent Spiral Wound Membrane Separation Model.pdfMulticomponent Spiral Wound Membrane Separation Model.pdf
Multicomponent Spiral Wound Membrane Separation Model.pdf
 
Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...Technology Features of Apollo HDD Machine, Its Technical Specification with C...
Technology Features of Apollo HDD Machine, Its Technical Specification with C...
 
Vertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptx
Vertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptxVertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptx
Vertical- Machining - Center - VMC -LMW-Machine-Tool-Division.pptx
 
Phase noise transfer functions.pptx
Phase noise transfer      functions.pptxPhase noise transfer      functions.pptx
Phase noise transfer functions.pptx
 

Capacitors

  • 2. Capacitors Composed of two conductive plates separated by an insulator (or dielectric). Commonly illustrated as two parallel metal plates separated by a distance, d. C = ε A/d where ε = εr εo εr is the relative dielectric constant εo is the vacuum permittivity
  • 3. Effect of Dimensions Capacitance increases with increasing surface area of the plates, decreasing spacing between plates, and increasing the relative dielectric constant of the insulator between the two plates.
  • 4. Types of Capacitors Fixed Capacitors Nonpolarized  May be connected into circuit with either terminal of capacitor connected to the high voltage side of the circuit.  Insulator: Paper, Mica, Ceramic, Polymer Electrolytic  The negative terminal must always be at a lower voltage than the positive terminal  Plates or Electrodes: Aluminum, Tantalum
  • 5. Nonpolarized Difficult to make nonpolarized capacitors that store a large amount of charge or operate at high voltages. Tolerance on capacitance values is very large  +50%/-25% is not unusual http://www.marvac.com/fun/ceramic_capacitor_codes.aspx PSpice Symbol
  • 7. Variable Capacitors Cross-sectional area is changed as one set of plates are rotated with respect to the other. http://www.tpub.com/neets/book2/3f.htm PSpice Symbol
  • 8. Electrical Properties of a Capacitor Acts like an open circuit at steady state when connected to a d.c. voltage or current source. Voltage on a capacitor must be continuous There are no abrupt changes to the voltage, but there may be discontinuities in the current. An ideal capacitor does not dissipate energy, it takes power when storing energy and returns it when discharging.
  • 9. Energy Storage Charge is stored on the plates of the capacitor. Equation: Q = CV Units: Farad = Coulomb/Voltage Farad is abbreviated as F
  • 10. Sign Conventions • The sign convention used with a capacitor is the same as for a power dissipating device. • When current flows into the positive side of the voltage across the capacitor, it is positive and the capacitor is dissipating power. • When the capacitor releases energy back into the circuit, the sign of the current will be negative.
  • 11. Charging a Capacitor At first, it is easy to store charge in the capacitor. As more charge is stored on the plates of the capacitor, it becomes increasingly difficult to place additional charge on the plates. Coulombic repulsion from the charge already on the plates creates an opposing force to limit the addition of more charge on the plates.  Voltage across a capacitor increases rapidly as charge is moved onto the plates when the initial amount of charge on the capacitor is small.  Voltage across the capacitor increases more slowly as it becomes difficult to add extra charge to the plates.
  • 12. Adding Charge to Capacitor The ability to add charge to a capacitor depends on: the amount of charge already on the plates of the capacitor and the force (voltage) driving the charge towards the plates (i.e., current)
  • 13. Discharging a Capacitor At first, it is easy to remove charge in the capacitor. Coulombic repulsion from charge already on the plates creates a force that pushes some of the charge out of the capacitor once the force (voltage) that placed the charge in the capacitor is removed (or decreased). As more charge is removed from the plates of the capacitor, it becomes increasingly difficult to get rid of the small amount of charge remaining on the plates. Coulombic repulsion decreases as charge spreads out on the plates. As the amount of charge decreases, the force needed to drive the charge off of the plates decreases.  Voltage across a capacitor decreases rapidly as charge is removed from the plates when the initial amount of charge on the capacitor is small.  Voltage across the capacitor decreases more slowly as it becomes difficult to force the remaining charge out of the capacitor.
  • 17. Ceq for Capacitors in Parallel i 4321eq 4321 4433 2211 4321 C CCCC dt dv Ci dt dv C dt dv C dt dv C dt dv Ci dt dv Ci dt dv Ci dt dv Ci dt dv Ci iiiii eqin in in +++= = +++= == == +++=
  • 19. Ceq for Capacitors in Series i ( ) ( ) ( ) ( )[ ] 1 4321eq t t t t4 t t3 t t2 t t1 t t4 4 t t3 3 t t2 2 t t1 1 4321 1111C idt 1 idt 1 idt 1 idt 1 idt 1 idt 1 idt 1 idt 1 idt 1 1 o 1 o 1 o 1 o 1 o 1 o 1 o 1 o 1 o − +++= = +++= == == +++= ∫ ∫∫∫∫ ∫∫ ∫∫ CCCC C v CCCC v C v C v C v C v vvvvv eq in in in
  • 20. General Equations for Ceq Parallel Combination Series Combination If P capacitors are in parallel, then If S capacitors are in series, then: 1 1 1 − =       = ∑ S s s eq C C∑= = P p Peq CC 1
  • 21. Summary Capacitors are energy storage devices. An ideal capacitor act like an open circuit at steady state when a DC voltage or current has been applied. The voltage across a capacitor must be a continuous function; the current flowing through a capacitor can be discontinuous. The equations for equivalent capacitance for capacitors in parallel capacitors in series 1 1 1 − =       = ∑ S s s eq C C∑= = P p Peq CC 1 ∫== 1 1 t t CC C C o dti C v dt dv Ci