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CIRCUIT ELEMENT: CAPACITOR

PROF SIRIPONG POTISUKPROF. SIRIPONG POTISUK

ELEC 308

Types of Circuit Elements

Two broad types of circuit elements

A ti l t bl f ti l t i Active elements - capable of generating electric energy from nonelectric energy (chemical, mechanical, nuclear, etc.)

e.g. generators, batteries, operational amplifiers

Passive elements – consume or store energy i d f h l i h i ireceived from other elements in the circuit

e.g. resistors, capacitors, inductors

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Capacitors

consists of two conducting (metal) plates separated by an insulating gapan insulating gap

Circuit symbol with reference

voltage and current assignment

Physics of the Capacitor

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Example

If the voltage of 10 V applied to the capacitor induces 25 mC charge on its plates, what is the capacitance of the mC charge on its plates, what is the capacitance of the capacitor in Farads?

Physics of the Capacitor

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The capacitance can be significantly increased by filling the gap between the plates with so-called dielectric materials.

Physics of the Capacitor

g p p

Air

+Q

Dielectric

+Q

-Q -Q

Relative Permittivity of Selected Materials

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Example

Determine the plate size of a square parallel-plate air-gap capacitor that has the capacitance of 1 F and air gap capacitor that has the capacitance of 1 F and plate spacing of 1 mm.

Example

A parallel-plate capacitor has the plate size of 500 μm × 200 μm. The plates are separated by 2 μm thick dielectric film μ p p y μwith relative permittivity εr = 10. What is the capacitance of this capacitor in Farads?

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Physics of the Capacitor

Accumulation of charges on the plates is not instantaneous → the voltage across the terminals of a capacitor cannot g pchange abruptly

Gradual rise or fall in voltage is referredto as the charging and discharging of thecapacitor

Physics of the Capacitor

The transition period known as the transient state

During transient, the amount of charge changes with time During transient, the amount of charge changes with time → a flow of electric current

As time progresses until VC = VB , charging stops and the steady state is reached with no current flow

→ Capacitor acts like an open circuit to DC voltage

Q = CV

Q = 0

Time

QC = CVC

Transient state

Steady state

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Q = 0

QC = CVC

Transient state

Steady state

VCIVB

Time

TimeTime

Electrical Characteristics

v-i characteristics:

dvdQ 1∫t

The instantaneous power delivered to the capacitor is

dtdvC

dtdQi C

C == )(1)( ∫ +=t

oc

o

tvdiC

tv τ

tddvCvvip ==

The energy stored in the capacitor is

[ ])()(21

21)( 22)(

)(

2o

tv

tv

t

t

t

t

tvtvCvCdddvvCdpw

ooo

−==== ∫∫ ττ

ττ

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Energy Stored in Capacitor

Capacitance is the circuit property that accounts for energy stored in electric fields established by the accumulated ycharge on both plates

The E field is the Coulomb force per unit charge directed from positive to negative charge and distributed as shown

Effect of Dielectric on the E field

Alignment of dipoles in the dielectric (Polarization)

→ A flow of ‘displacement’ current→ A flow of displacement current

The more dipoles the dielectric material contains, the more additional charges it induces on the capacitor plates

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Example

Calculate the amount of charge stored on a 3-pF capacitor with 20 V across it. Find also the energy stored in it.with 20 V across it. Find also the energy stored in it.

Example

The voltage across 0.5 nF capacitor changes with time as shown. What is the current through the capacitor?shown. What is the current through the capacitor?

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Example

The current as shown flows through an initially uncharged 1-mF capacitor . Calculate the voltage across it at t = 2 ms1 mF capacitor . Calculate the voltage across it at t 2 msand t = 5 ms.

Example

Obtain the energy stored in each capacitor under DC steady-state conditionssteady state conditions

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For steady-state conditions with DC sources, capacitorsbehave as open circuits.

Series Capacitance Combination

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Parallel Capacitance Combination

Example

For the circuit shown, find the voltage across each capacitor.

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Electrolytic Capacitors

High capacitance per unit volume

Only voltages of proper polarity should be applied Only voltages of proper polarity should be applied (polarized capacitors)

One plate is oxide-coated metallic aluminum or tantalum immersed in the electrolytic solution

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Ceramic Capacitors (Non-polarized)

High-voltage Capacitors

11 kV capacitors

Capacitor bank

Ultra-capacitor battery

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Variable Capacitors

Capacitance of the variable air capacitor is changed by turning the shaft at the end of the unitby turning the shaft at the end of the unit.

Semiconductor technology allows making variable capacitor without moving parts, e.g., semiconductor diode capacitance is controlled by applied voltage