www.bzupages.com saima asghar roll no.07-20 mudassir abbas roll no.07-34 aliya ashraf roll no.07-19...
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Saima AsgharSaima AsgharRoll No.07-20Roll No.07-20
Mudassir AbbasMudassir AbbasRoll No.07-34Roll No.07-34Aliya AshrafAliya Ashraf
Roll No.07-19Roll No.07-19Shafaq MehmoodShafaq Mehmood
Roll No.07-02Roll No.07-02
PRESENTATION PRESENTATION ONON
CAPACITERS.CAPACITERS.CONTENTS.CONTENTS.
1.History1.History2.Theory of operation2.Theory of operation
3.Capacitance3.Capacitance4.Energy storage4.Energy storage5.Eletric circuits5.Eletric circuits
6.Dc source6.Dc source7.Ac source7.Ac source
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HISTORYHISTORY In October 1745, In October 1745, Ewald Georg von KleistEwald Georg von Kleist of of
PomeraniaPomerania in in GermanyGermany invented the first invented the first recorded capacitor: a glass jar with water inside recorded capacitor: a glass jar with water inside as one plate was held on the hand as the other as one plate was held on the hand as the other plate. A wire in the mouth of the bottle received plate. A wire in the mouth of the bottle received charge from an electric machine, and released it charge from an electric machine, and released it as a spark.as a spark.
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In the same year, Dutch physicist In the same year, Dutch physicist Pieter van MusschenbroekPieter van Musschenbroek independently independently invented a very similar capacitor. It was named invented a very similar capacitor. It was named the the Leyden jarLeyden jar, after the , after the University of LeydenUniversity of Leyden where van Musschenbroek worked. where van Musschenbroek worked. Daniel GralathDaniel Gralath was the first to combine several was the first to combine several jars in parallel into a "battery" to increase the jars in parallel into a "battery" to increase the charge storage capacity.charge storage capacity.
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Theory of operation.Theory of operation.
A capacitor consists of two conductive electrodes, or plates, separated by a dielectric, which prevents charge from moving directly between the plates. Charge may however move from one plate to the other through an external circuit, such as a battery connected between the terminals.
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DielectricDielectric
Dielectricis placed between two conducting plates, each of area A and with a separation of d. . The simplest
practical capacitor consists of two wide, flat, parallel plates separated by a thin dielectric layer.
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CapacitanceCapacitance A capacitor's ability to store A capacitor's ability to store
charge is measured by its charge is measured by its capacitance , the ratio of the capacitance , the ratio of the amount of charge stored on each amount of charge stored on each plate to the voltage:plate to the voltage::
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EQUATIONEQUATION
For an ideal parallel plate capacitor with For an ideal parallel plate capacitor with a plate area and a plate separation :a plate area and a plate separation :
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Energy StorageEnergy Storage
When capacitor is uncharged,the When capacitor is uncharged,the potential diff. between plates is zero potential diff. between plates is zero & finaly becomes V than Q charges & finaly becomes V than Q charges is deposited on each plate thus the is deposited on each plate thus the average potiential diff. is average potiential diff. is
0+V/2=1/2V0+V/2=1/2V
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There for There for P.E=Energy=1/2qVP.E=Energy=1/2qV Using the relation q=CV for Using the relation q=CV for
capacitor we getcapacitor we get Energy=1/2CVEnergy=1/2CV22
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Electric circuitsElectric circuits When a capacitor is connected to a current source, charge When a capacitor is connected to a current source, charge
is transferred between its plates at a rate is transferred between its plates at a rate ii((tt) = d) = dqq((tt) / d) / dtt. . As the voltage between the plates is proportional to the As the voltage between the plates is proportional to the charge, it follows thatcharge, it follows that
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Conversely, if a capacitor is connected to a Conversely, if a capacitor is connected to a voltage source, the resulting displacement voltage source, the resulting displacement current is given bycurrent is given by
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For example, if one were to connect a 1000 µF For example, if one were to connect a 1000 µF capacitor to a voltage source, then increase the capacitor to a voltage source, then increase the sourced voltage at a rate of 2.5 Volts per sourced voltage at a rate of 2.5 Volts per second, the current flowing through the second, the current flowing through the capacitor would becapacitor would be
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DC sourcesDC sources
A simple resistor-capacitor circuit demonstrates charging of a capacitor.
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AC sourcesAC sources When connected to an alternating current (AC) When connected to an alternating current (AC)
voltage source, the voltage across the capacitor voltage source, the voltage across the capacitor varies sinusoidally asvaries sinusoidally as
vv((tt) = ) = VV0sin(ω00sin(ω0tt + φ), + φ),
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where ω0 = 2πf0 is the angular frequency of the source, V0 is the amplitude of the voltage and φ is the phase. The corresponding displacement current is therefore
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MUDASSIR ABBASMUDASSIR ABBASROLL NO. 07-34ROLL NO. 07-34
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CapacitorsCapacitors
Basic capacitor constructionBasic capacitor construction
Dielectric material
Plate 1
Plate 2The dielectric material is an insulator therefore no current flows through the capacitor
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CapacitorsCapacitors
Storing a charge Storing a charge between the platesbetween the plates
Electrons on the left Electrons on the left plate are attracted plate are attracted toward the positive toward the positive terminal of the voltage terminal of the voltage sourcesource
This leaves an excess This leaves an excess of positively charged of positively charged holesholes
The electrons are The electrons are pushed toward the pushed toward the right plateright plate
Excess electrons leave Excess electrons leave a negative chargea negative charge
+ -
+_
+ _
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Effect of Area on CapacitanceEffect of Area on Capacitance
Capacitance is directly proportional to the Capacitance is directly proportional to the amount of charge.amount of charge.
A larger plate will be able to hold more charge.A larger plate will be able to hold more charge. Capacitance is directly proportional to the plate Capacitance is directly proportional to the plate
area.area. If you double the plate area, you double the If you double the plate area, you double the
capacitance.capacitance.
d
AC
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Effect of Spacing on Effect of Spacing on Capacitance Capacitance
As plates are moved closer together, the force As plates are moved closer together, the force of attraction between the opposite charges is of attraction between the opposite charges is greater. (Electrostatic field increases)greater. (Electrostatic field increases)
Capacitance is inversely proportional to the Capacitance is inversely proportional to the distance between the plates.distance between the plates.
If we double the distance between the plates, If we double the distance between the plates, the capacitance becomes one-half as much.the capacitance becomes one-half as much.
d
AC
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Effect of Dielectric on Effect of Dielectric on CapacitanceCapacitance
If a dielectric other than air is used between the If a dielectric other than air is used between the plates, more charges can build up on the plates.plates, more charges can build up on the plates.
The factor by which the capacitance increases is The factor by which the capacitance increases is called the called the dielectric constantdielectric constant or the relative or the relative permittivity.permittivity.
PermittivityPermittivity is the measure of how easy it is to is the measure of how easy it is to establish or concentrate electric flux in a material.establish or concentrate electric flux in a material.
Leakage currentLeakage current is the small amount of current that is the small amount of current that passes or flows through the dielectric without passes or flows through the dielectric without damaging the dielectric.damaging the dielectric.
The type of dielectric used determines the permittivity The type of dielectric used determines the permittivity and leakage current in a capacitor.and leakage current in a capacitor.
d
AC
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Common DielectricsCommon Dielectrics
VacuumVacuum 1.01.0
AirAir 1.0041.004
MylarMylar 33
PaperPaper 4 to 64 to 6
MicaMica 4 to 84 to 8
GlassGlass 3.7 to 193.7 to 19
Alumina Alumina 9.99.9
CeramicsCeramics 5 to 18000 +5 to 18000 +
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Capacitors In SeriesCapacitors In Series
When the capacitors are connected in When the capacitors are connected in series, the total capacitance is less series, the total capacitance is less than the smallest capacitance value than the smallest capacitance value bcoz the effective plate separation bcoz the effective plate separation increases.increases.
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Series connected Capacitors always Series connected Capacitors always have the same Chargehave the same Charge. They do not the . They do not the same voltage unless the capacitors have same voltage unless the capacitors have the same Capacitance the same Capacitance CC. .
The Charge on the equivalent capacitor The Charge on the equivalent capacitor CCe is the e is the samesame as the charge on either as the charge on either capacitor. capacitor.
The Voltage across the equivalent The Voltage across the equivalent capacitor capacitor CCe is the e is the sumsum of the voltage of the voltage across both capacitors. across both capacitors.
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Consider a circuit having cap in seriesConsider a circuit having cap in series
Qtot = Q1 = Q2 =Q3………. =Qn----( 1Qtot = Q1 = Q2 =Q3………. =Qn----( 1
Acc to Kirchhoff’s lawAcc to Kirchhoff’s law
Vt = V1+V2+V3+V4………….+Vn------Vt = V1+V2+V3+V4………….+Vn------(2(2
We know thatWe know that
V = Q / CV = Q / C
Substituting the values…..Substituting the values…..
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Qt/Ct = Q1/C1+Q2/C2+Q3/C3+…..Qn/CnQt/Ct = Q1/C1+Q2/C2+Q3/C3+…..Qn/CnCharge on all Cap are equal,so Q can B Charge on all Cap are equal,so Q can B
cancalledcancalledSOSO1/Ct=1/C1+1/C2+1/C3+….1/Cn1/Ct=1/C1+1/C2+1/C3+….1/CnTaking the reciprocalTaking the reciprocalCt=1/1/C1+1/C2+1/C3+……1/CnCt=1/1/C1+1/C2+1/C3+……1/CnRESULT:RESULT: Total series capacitance is Total series capacitance is
always less than the smallest always less than the smallest capacitance.capacitance.
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When 2 capacitors R connected in When 2 capacitors R connected in series..series..
ThenThen
1/Ct= 1/C1 + 1/C21/Ct= 1/C1 + 1/C2 C1+C2/C1C2C1+C2/C1C2
Taking ReciprocalTaking Reciprocal
Ct = C1C2/C1+C2Ct = C1C2/C1+C2
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Capacitors In ParallelCapacitors In Parallel
When cap R connected in ||,the total When cap R connected in ||,the total capacitance is the sum of the capacitance is the sum of the individual capacitance bcoz the individual capacitance bcoz the effective plate area increase.effective plate area increase.
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According 2 kirchhoff’s rule,According 2 kirchhoff’s rule,
Qt = Q1+Q2+Q3+…….Qn -------(1Qt = Q1+Q2+Q3+…….Qn -------(1
We also know thatWe also know that
Q = CV -------( 2Q = CV -------( 2
ThenThen
CtVt = C1V1+C2V2+C3V3+CtVt = C1V1+C2V2+C3V3+……..CnVn---( 3……..CnVn---( 3
Since V is same So it could B cancalled,Since V is same So it could B cancalled,
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Then 3 becomes:Then 3 becomes:
Ct = C1+C2+C3+……………CCt = C1+C2+C3+……………C
RESULT: RESULT: The total parallel The total parallel capacitance is the sum of all the capacitance is the sum of all the capacitors in parallel.capacitors in parallel.
Capacitance of A Capacitance of A ||Plate Capacitor.||Plate Capacitor.
Consider a capacitor of 2 plates,each of Consider a capacitor of 2 plates,each of area A, separated by a distance d,the dist area A, separated by a distance d,the dist is so small so the Electric Field E b/w the is so small so the Electric Field E b/w the plates is uniform.Let the medium B air or plates is uniform.Let the medium B air or
vacuum.vacuum.
C = Q/V --------- ( 1C = Q/V --------- ( 1
Q is chargeQ is charge
V is Potential Diff..V is Potential Diff..
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The Electric Intensity E is related with The Electric Intensity E is related with distance d,distance d,
E = V/d ------------( 2E = V/d ------------( 2 Surface Density of charge on the plates isSurface Density of charge on the plates is σσ = Q/ = Q/εεA -----------( 3A -----------( 3 We know that electric Intensity b/w 2 We know that electric Intensity b/w 2
opposite charged plates isopposite charged plates is E =E =σσ / /εε----------------( 4----------------( 4
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Substituting the Values…Substituting the Values…
V/d = Q/A V/d = Q/A εε-----------------( 5-----------------( 5
Gives…Gives…
C = Q/V = A C = Q/V = A εε/d --------------------( 6/d --------------------( 6
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TYPES OF CAPACITORSTYPES OF CAPACITORS
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(a) Polyester capacitor, (b) Ceramic capacitor, (c) Electrolytic capacitor
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VARIABLE CAPACITORVARIABLE CAPACITOR
Variable capacitors
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APPLICATIONS OF APPLICATIONS OF CAPACITORSCAPACITORS
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Temporary power sourceTemporary power source
A capacitor provides “V” & “I” as long A capacitor provides “V” & “I” as long as its charge remains sufficuent.As as its charge remains sufficuent.As current drawn by the circuit charge current drawn by the circuit charge is removed from the capacitor & the is removed from the capacitor & the voltage decreases.voltage decreases.
For this reason,the storage capacitor For this reason,the storage capacitor can B used ascan B used as
Temporary power source… Temporary power source…
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Computer MemoriesComputer Memories
Dynamic memories in computers use Dynamic memories in computers use very tiny capacitors as the basic very tiny capacitors as the basic storage element for binary info,1s & storage element for binary info,1s & 0s.0s.
A charged capacitor can represent a A charged capacitor can represent a stored 1, & discharged capacitor stored 1, & discharged capacitor stored 0.stored 0.
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Signal FilterSignal Filter
Capacitors are essential to the operation of a Capacitors are essential to the operation of a class of a circuit called FILTER.That are class of a circuit called FILTER.That are used for selecting one ac signal with a used for selecting one ac signal with a certain specified frequency from a wide certain specified frequency from a wide range of signals.range of signals.
Common example is when U tune Ur radio or Common example is when U tune Ur radio or TV.TV.
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Variable CapacitorsVariable Capacitors
Used to tune a radio. Used to tune a radio. Have a set of stationary plates and a set of Have a set of stationary plates and a set of
movable plates which are ganged together and movable plates which are ganged together and mounted on a shaft.mounted on a shaft.
A trimmer or padder capacitor is used to make A trimmer or padder capacitor is used to make fine adjustments on a circuit.fine adjustments on a circuit.
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ANYANY