Capacitor Engr. Faheemullah Shaikh Lecturer, Department of Electrical Engineering

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