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CapacitorCapacitor
Engr. Faheemullah ShaikhLecturer,Department of Electrical Engineering.
Topic OutlineTopic Outline
Definition of Capacitance
Calculating Capacitance
Combinations of Capacitors
Energy Stored in a Charged Capacitor
Capacitors with Dielectrics
An Atomic Description of a Dielectric
Capacitance and DielectricCapacitance and Dielectric
Capacitors: Device that store electric charge
A capacitor consists of two conductors separated by an insulator.
Capacitance: Depends on its geometry and on the material, called a dielectric, that separates the conductors.
Definition of Capacitance Definition of Capacitance
Pictures from Serway & Beichner
A capacitor consists of two conductors (known as plates) carrying charges of equal magnitude but opposite sign.
A potential difference V exists between the conductors due to the presence of the charges.
What is the capacity of the device for storing charge at particular value of V?
Definition of Capacitance Definition of Capacitance
Experiments show the quantity of electric charge Q on a capacitor is linearly proportional to the potential difference between the conductors, that is Q ~ V. Or we write Q = C VThe capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between them:
C = Q
VSI Unit: farad (F), 1F = 1 C/V
Typical device have capacitances ranging from microfarad to picofarad.
Parallel-Plate CapacitorsParallel-Plate Capacitors
Pictures from Serway & Beichner
(a) The electric field between the plates of a parallel-plate capacitor is uniform near the center but non uniform near the edges.
(b) Electric field pattern of two oppositely charged conducting parallel plates.
Parallel - Plate Parallel - Plate CapacitorsCapacitors
A parallel-plate capacitor consists of two parallel conducting plates, each of area A, separated by a distance d. When the capacitor is charged, the plates carry equal amounts of charge. One plate carries positive charge, and the other carries negative charge. The plates are charged by connection to a
battery. Describe the process by which the plates get charged up.
CapacitorsCapacitors
Storing a charge between the plates
Electrons on the left plate are attracted toward the positive terminal of the voltage source
This leaves an excess of positively charged holes
The electrons are pushed toward the right plate
Excess electrons leave a negative charge
+ -
+_
+ _
Parallel-Plate CapacitorsParallel-Plate Capacitors
Two parallel metallic plates of equal area A separated by a distance d as shown.
One plate carries a charge Q and the other carries a charge –Q. And surface charge density of each plate is = Q/A.
A
d
If plates are large, then charges can distribute themselves over a substantial area, and the amount of charge that can be stored on a plate for a given potential diff increases as A is increased.
Thus we expect C to be proportional to A
C ~ A
Variation with A
Parallel-Plate CapacitorsParallel-Plate Capacitors
Variation with d
A
d
Potential difference ∆V constant across, E field increases as d decreases.
There is a potential difference of V volts between the plates, therefore the work in transferring 1 C of charge between the plates is V joules.
∆V = Ed
Air tank Analogy to Air tank Analogy to Charging a CapacitorCharging a Capacitor
Air tank Analogy to Air tank Analogy to Charging a CapacitorCharging a Capacitor
Capacitors ApplicationsCapacitors Applications
Types of capacitorsThe dielectric material
determines the type of capacitor
Common types of capacitors are:◦ Mica◦ Ceramic◦ Plastic film
Capacitors ApplicationsCapacitors Applications
Some capacitors are polarised, they can only be connected one way around
Electrolytic capacitors are polarised
Capacitors ApplicationsCapacitors Applications
Variable capacitors are used in communication equipment, radios, televisions and VCRs
They can be adjusted by consumers by tuning controls
Trimmers are internal adjusted capacitors that a consumer cannot adjust
Capacitors ApplicationsCapacitors Applications
These variable capacitors would be difficult to squeeze into your mobile phone and iPod
Current technology uses semi-conductor variable capacitors called varactors (varicaps)
Combinations of CapacitorsCombinations of Capacitors
Combinations of CapacitorsCombinations of Capacitors
Parallel Combination
The individual potential differences across capacitors connected in parallel are all the same and are equal to the potential difference applied across the combination.
Parallel Combination
Combinations of CapacitorsCombinations of Capacitors
When the capacitors are first connected, electrons transfer between wires and plates. Leave left plates positively charged and right plates negatively charged.
Energy source for this charge transfer is internal chemical energy stored in the battery.
Flow of charges ceases when the voltage across the capacitors is equal to that across the battery terminals.
Capacitors reach their maximum charge when the flow of charges ceases.
Parallel Combination
Combinations of CapacitorsCombinations of Capacitors
Let the maximum charges on the two capacitors Q1 and Q2.
Total charge Q stored by two capacitors is Q = Q1+Q2.
Voltage across are the same Q1=C1V, Q2=C2V
Define an equivalent capacitor having Ceq s.t. Q = CeqV
We have CeqV = C1V + C2V
And hence Ceq = C1 + C2 (for parallel combination)
In general Ceq = C1 + C2+ C3+ ………….. (for parallel combination)
Combinations of CapacitorsCombinations of Capacitors
Series Combination
Voltage V across battery terminals is split between two capacitors.
V = V1 + V2
Where V1 and V2 are potential diff across capacitors C1 and C2.
Suppose we have equivalent capacitor Ceq = Q/V
For each capacitor, we have V1 = Q/C1 and V2=Q/C2
Q/Ceq = Q/C1 + Q/C2
1/Ceq = 1/C1 + 1/C2 (series combination)
In general 1/Ceq = 1/C1 + 1/C2 + 1/C3 + ….. (series combination)
Example: Equivalent CapacitanceExample: Equivalent Capacitance
In parallel use C=C1+C2
In series use 1/C=1/C1+1/C2
6.00 F
20.00 F
2.50 F
8.50 F
20.00 F
In series use 1/C=1/C1+1/C2
5.965 F
Example: Equivalent CapacitanceExample: Equivalent Capacitance
In parallel use C=C1+C2
In parallel use C=C1+C2
In series use 1/C=1/C1+1/C2
Example: Equivalent Capacitance 26.22Example: Equivalent Capacitance 26.22
In series use 1/CB=1/C+1/C+1/C
In series use 1/CA=1/C+1/C C
C/2
C/3
In parallel use Ceq=C+C/2+C/3
Charging & Charging & Discharging of Discharging of
CapacitorCapacitor
Charging a capacitorCharging a capacitor
Current flow Initially
◦ HighFinally
◦ ZeroExponential modelCharging factors
◦ Capacitance◦ Resistance
I
t
Charging of CapacitorCharging of Capacitor
Time ConstantTime Constant
Discharging of CapacitorDischarging of Capacitor
Current flow Initially
◦ High◦ Opposite to
chargingFinally
◦ ZeroExponential modelDischarging factors
◦ Capacitance◦ Resistance I
t
Discharging of CapacitorDischarging of Capacitor
Energy Stored in Energy Stored in CapacitorCapacitor
Current Voltage Relationship in Current Voltage Relationship in Capacitor Capacitor
Capacitors with Capacitors with DielectricsDielectricsA dielectric is a non conducting material, such as rubber, glass, or waxed paper.
When a dielectric is inserted between the plates of a capacitor, the capacitance increases.
If the dielectric completely fills the space between the plates, the capacitance increases by a factor , which is called the dielectric constant.
Dielectric constant is a property of a material and varies from one material to another.
Dielectric StrengthDielectric Strength
For any given separation d, the maximum voltage that can be applied to a capacitor without causing a discharge depends on the dielectric strength (maximum electric field) of the dielectric.
If magnitude of the electric field in the dielectric exceeds the dielectric strength, then the insulating properties break down and the dielectric begins to conduct.
Dielectric Constant and Dielectric Strength of Dielectric Constant and Dielectric Strength of Various Materials at Room TemperatureVarious Materials at Room Temperature
Material Dielectric Constant Dielectric Strength (V/m)
Air (dry) 1.00059 3 x 106
Bakelite 4.9 24 x 106
Fused quartz 3.78 8 x 106
Neoprene rubber 6.7 12 x 106
Nylon 3.4 14 x 106
Paper 3.7 16 x 106
Polystyrene 2.56 24 x 106
Polyvinyl Chloride 3.4 40 x 106
Porcelain 6 12 x 106
Pyrex Glass 5.6 14 x 106
Silicone Oil 2.5 15 x 106
Strontium Titanate 233 8 x 106
Teflon 2.1 60 x 106
Vacuum 1.00000 -
Water 80 -
Capacitors with Dielectric MaterialCapacitors with Dielectric Material
What are the advantages of dielectric material in a capacitor?
• Increase the capacitance
• Possible mechanical support between the plates, which
allows the plates to be close together without touching,
thereby decreasing d and increasing C.
Case Study ProblemsCase Study Problems
Already we have calculated while deriving the mathematical relationship of capacitor