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CHAPTER 12

Capacitance

8/4/2019 Jack Ppt 12


Learning Outcomes

y Describe the nature of an electric field.

y Explain the relationships among electric

field, electric flux, electric flux density, and

potential difference.

y Explain how the electric charges in a

dielectric behave in the presence of an electricfield.

y Describe the construction of various

capacitors.

8/4/2019 Jack Ppt 12


Learning Outcomes

y Define capacitance in terms of the charge on

the plates of a capacitor and the voltage

across it.

y Calculate the capacitance of a capacitor

given the dielectric and the area and spacing

of the plates.y Calculate the total capacitance of capacitors

in parallel and the equivalent capacitance of

capacitors in series.

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12-1 Electric Fields

y An electric field is that region in which a

charge is acted upon by an electric force.

y The strength (intensity) of an electric field is

the force the field exerts on a unit of charge.

y The symbol for electric field strength is E .

y The units for electric field strength are

newtons per coulomb, which are equivalent

to volts per metre.

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Thus,

where E is the strength of the electric field in

newtons per coulomb, F is the force in newtons,and Q is the charge in coulombs.

Q

F E !Q

F

E !

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electric line of force (electric flux line)

the path along which a massless, electrically

charged particle would move in an electric field

Note that the lines of force are directed away from the

positive charge and toward the negative charge.

Figure 12-1 Electric fields surrounding point electric charges

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Fig 12-2 shows the electric fields around two

parallel conductors and between two concentric

(coaxial) conductors; these configurations havenumerous applications in radio, television, and

computer telecommunications.

Figure 12-2 Electric field between (a) parallel conductor s; (b) coaxial conductor s

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electric flux (= )

the electric field passing through a given

surface (defined as equivalent to electriccharge)

electric flux density (D)

the electric flux per unit area

y If an electric field is uniform over a given

area, A, then the flux density for that area is

A

Q

A

D !!

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dielectric

an electrical insulator

dielectric strength

the electric field strength required to

break down a dielectric

dielectric absorption

a small potential difference that remains

across some dielectrics after the removal

of an electric field

Key Ter ms

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12-2 Dielectrics

The atoms in a dielectric

become polarized whenthe electrons in each

atom are displaced

toward the positive plateand are no longer

centered on the nucleus.Figure 12-4 Effect of an electric field

on a dielectric

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12-3 Capacitance

capacitor

a component that can store electric charge

capacitance (C )

the property of an electric circuit that

opposes any charge in the voltage acrossthat circuit

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12-3 Capacitance

farad (F)

the SI unit of capacitance

y A farad is equal to one coulomb per volt.

y A circuit has a capacitance of 1 F when a

charge of 1 C raises the potential difference by

1 V: 1 F = 1 C/V.

where C is the capacitance, Q is the charge, and V is the

potential difference.

V

QC !

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12-4 Capacitors

y Parallel-plate capacitors are made of two

metal plates with air between them, or of a

ceramic disc coated with metal (Fig 12-7(a)).

y Some capacitors consist of interleaved

parallel plates with air or mica dielectric (Fig

12-7(b)).

y Some capacitors consist of two long strips

of aluminum foil interleaves with strips of a

dielectric, rolled up (Fig 12-7(c)).

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12-4 Capacitors

Figure 12-7 Construction of capacitor s

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12-4 Capacitors

y Capacitors are rated with a working voltage,

the maximum voltage that can be applied

across a capacitor without risk of damaging it.

y An electrolytic capacitor has aluminum foil

plates with an electrolyte between them, and a

thin aluminum oxide coating for the dielectric.

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12-5 Factors Governing Capacitance

y The capacitance of parallel plates is directly

proportional to their area and inversely

proportional to their spacing.

y The capacitance of parallel plates depends

on the type of dielectric between plates.

y The permittivity (� ) of a material is thecapacitance between opposite faces of a unit

length and cross section of the material,

measured in farads per metre.

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12-5 Factors Governing

Capacitance

For parallel plates,

whereC

is the capacitance in farads,�

is thepermittivity in farads per metre, A is the area of

each plate in square metres, and d is the distance

between plates in metres.

D

AC I

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12-6 Dielectric Constant

relative permittivity (dielectric constant)

the ratio of the permittivity of a material to the

permittivity of free space

y The equation for the capacitance of any

parallel-plate capacitor is

where C is the capacitance in farads, k is the dielectric

constant, A is the area of each plate, and d is the distance

between plates.

d Ak C 0I

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12-7 Capacitors in Parallel

The total capacitance of capacitors in parallel is

the sum of all the individual capacitances.

C T= C 1 + C 2 + C 3 + · · ·

Figure 12-9 Capacitor s in parallel

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12-8 Capacitors in Series

yWhen we connect capacitors in series, the

plates that are connected directly to each other

are charged by electrostatic induction.

electrostatic induction

separation of charge on a body

in an electric fieldFigure 12-10 Capacitor s in

series

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y The equivalent capacitance of series

capacitors is

y This is the same form as the equation for the

equivalent resistance of resistors in parallel.

y To simplify calculations for parallel resistors

we considered conductance; for capacitors in

series we can use elastance.

. 321/1/1/1

1C C C

C eq

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y Elastance (S ) is the opposition of material to

the setting up of electric lines of force in an

electric insulator or dielectric, measured inreciprocal farads (F ±1).

y It is the reciprocal of permittivity.

where S is elastance in reciprocal farads and C is

capacitance in farads.

C S 1!

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y An electric field is that region in which an

electric charge is acted upon by an electric

force.

y The strength of an electric field at a

certain point is the electric force acting on a

charge at that point divided by the quantityof the charge.

y The flux density of an electric field is the

electric flux per unit area.

Summary

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y The electric field between parallel

conductive plates is uniform except near

the edges.

y Dielectric strength indicates the electric

field strength that a dielectric can

withstand.y Capacitance opposes change and can

store charge.

Summary

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y The maximum voltage that a capacitor

can withstand is expressed as its working

voltage.

y Capacitance is the ratio of the charge on

the plates of a capacitor to the voltage

across it.y Capacitance is proportional to the area of

the plates and inversely proportional to the

spacing fo the plates of a capacitor.

Summary

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y Capacitance is dependent on the type of

dielectric in the capacitor.

y Permittivity is the capacitance of a unit

length and cross section of a material.

y The total capacitance of capacitors

connected in parallel is the sum of all theindividual capacitances.

Summary

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y The equivalent capacitance of capacitors

connected in series is the reciprocal of the

sum of the reciprocals of the individualcapacitances.

Summary

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