ED I UNIT NOTES

8/13/2019 ED I UNIT NOTES

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UNIT I - PASSIVE CIRCUIT COMPONENTSIntroduction Resistors - Fixed &Variable resistor Color coding Tolerance -

Series and Parallel connection. Capacitors - Basic structure and symbol Fixed &

Variable capacitors issipation !actor Series and parallel connection. Inductors:Inductance o! t"e coil Fixed & Variable inductors Inducti#e reactance $nergy

stored in an inductor % !actor utual inductance Series and Parallel connection

RESISTORS:

Resistors ' R () are t"e most !undamental and commonly used o! all t"e electronic

components) to t"e point *"ere t"ey are almost ta+en !or granted. T"ere are many

di!!erent Types of Resistorsa#ailable to t"e electronics constructor) !rom #ery small

sur!ace mount c"ip resistors up to large *ire *ound po*er resistors.

T"e principal ,ob o! a resistor *it"in an electrical or electronic circuit is to resist '"ence

t"e name resistor() regulate or to set t"e !lo* o! electrons 'current( t"roug" t"em by usingt"e type o! conducti#e material !rom *"ic" t"ey are composed. Resistors can also be

connected toget"er in #arious series and parallel combinations to !orm resistor net*or+s

*"ic" can act as #oltage droppers) #oltage di#iders or current limiters *it"in a circuit.

Typical Resistor

Resistors are Passi#e e#ices) t"at is t"ey contain no source o! po*er or ampli!icationbut only attenuate or reduce t"e #oltage or current signal passing t"roug" t"em. T"is

attenuation results in electrical energy being lost in t"e !orm o! "eat as t"e resistor resists

t"e !lo* o! electrons t"roug" it.

T"en a potential di!!erence is re/uired bet*een t"e t*o terminals o! a resistor !or current

to !lo*. T"is potential di!!erence balances out t"e energy lost. 0"en used in C circuits

t"e potential di!!erence) also +no*n as a resistors #oltage drop) is measured across t"e

terminals as t"e circuit current !lo*s t"roug" t"e resistor.

ost resistors are linear de#ices t"at produce a #oltage drop across t"emsel#es *"en an

electrical current !lo*s t"roug" t"em because t"ey obey 1"m2s 3a*) and di!!erent #alues

o! resistance produces di!!erent #alues o! current or #oltage. T"is can be #ery use!ul in

$lectronic circuits by controlling or reducing eit"er t"e current !lo* or #oltage produced

across t"em.


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T"ere are many t"ousands o! di!!erent Types of Resistorsand are produced in a #ariety

o! !orms because t"eir particular c"aracteristics and accuracy suit certain areas o!

application) suc" as 4ig" Stability) 4ig" Voltage) 4ig" Current etc) or are used as

general purpose resistors *"ere t"eir c"aracteristics are less o! a problem. Some o! t"e

common c"aracteristics associated *it" t"e "umble resistor are5 Temperature

Coefficiet! Vo"ta#e Coefficiet! Noise! $re%uecy Respose! Po&eras *ell

as Temperature Rati#! P'ysica" Si(eand Re"ia)i"ity.

In all $lectrical and $lectronic circuit diagrams and sc"ematics) t"e most commonly used

symbol !or a !ixed #alue resistor is t"at o! a 6ig-6ag type line *it" t"e #alue o! its

resistance gi#en in 1"ms) 7. Resistors "a#e !ixed resistance #alues !rom less t"an one

o"m) ' 897 ( to *ell o#er tens o! millions o! o"ms) ' :9;7 ( in #alue. Fixed resistors

"a#e only one single #alue o! resistance) !or example 9;;72sbut #ariable resistors

'potentiometers( can pro#ide an in!inite number o! resistance #alues bet*een 6ero and

t"eir maximum #alue.

Sta*ar* Resistor Sym)o"s

T"e symbol used in sc"ematic and electrical dra*ings !or a Resistor can eit"er be a 6ig-

6ag type line or a rectangular box.

ll modern !ixed #alue resistors can be classi!ied into !our broad groups5

Carbon Composition Resistor - ade o! carbon dust or grap"ite paste) lo* *attage

#alues

Film or Cermet Resistor - ade !rom conducti#e metal oxide paste) #ery lo* *attage

#alues

0ire-*ound Resistor - etallic bodies !or "eatsin+ mounting) #ery "ig" *attage

ratings Semiconductor Resistor - 4ig" !re/uency


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t"is section #ery large so I s"all limit it to t"e most commonly used) and readily a#ailable

general purpose types o! resistors.

Compositio Type Resistors

Car)o Resistorsare t"e most common type o! Compositio Resistors. Carbon

resistors are a c"eap general purpose resistor used in electrical and electronic circuits.

T"eir resisti#e element is manu!actured !rom a mixture o! !inely ground carbon dust or

grap"ite 'similar to pencil lead( and a non-conducting ceramic 'clay( po*der to bind it all

toget"er.

Carbon Resistor

T"e ratio o! carbon dust to ceramic 'conductor to insulator( determines t"e o#erall

resisti#e #alue o! t"e mixture and t"e "ig"er t"e ratio o! carbon) t"e lo*er t"e o#erall

resistance. T"e mixture is molded into a cylindrical s"ape *it" metal *ires or leads are

attac"ed to eac" end to pro#ide t"e electrical connection as s"o*n) be!ore being coated

*it" an outer insulating material and colour coded mar+ings to denote its resisti#e #alue.

Car)o Resistor

T"e Car)o Composite Resistoris a lo* to medium type po*er resistor *"ic" "as a

lo* inductance ma+ing t"em ideal !or "ig" !re/uency applications but t"ey can also

su!!er !rom noise and stability *"en "ot. Carbon composite resistors are generally

pre!ixed *it" a CR notation 'eg) CR9;+7 ( and are a#ailable in $= ' > ?;@ tolerance

'accuracy( () $9? ' > 9;@ tolerance( and $?A ' > B@ tolerance( pac+ages *it" po*er

ratings !rom ;.9?B or 9


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Carbon composite resistors are #ery c"eap to ma+e and are t"ere!ore commonly used in

electrical circuits. 4o*e#er) due to t"eir manu!acturing process carbon type resistors

"a#e #ery large tolerances so !or more precision and "ig" #alue resistances) fi"m type

resistorsare used instead.

$i"m Type Resistors

T"e generic term $i"m Resistor consist o!Metal Film) Carbon FilmandMetal Oxide

Filmresistor types) *"ic" are generally made by depositing pure metals) suc" as nic+el)

or an oxide !ilm) suc" as tin-oxide) onto an insulating ceramic rod or substrate.

Film Resistor

T"e resisti#e #alue o! t"e resistor is controlled by increasing t"e desired t"ic+ness o! t"e

deposited !ilm gi#ing t"em t"e names o! eit"er t"ic+-!ilm resistors or t"in-!ilm

resistors. 1nce deposited) a laser is used to cut a "ig" precision spiral "elix groo#e type

pattern into t"is !ilm. T"e cutting o! t"e !ilm "as t"e e!!ect o! increasing t"e conducti#e or

resisti#e pat") a bit li+e ta+ing a long lengt" o! straig"t *ire and !orming it into a coil.

T"is met"od o! manu!acture allo*s !or muc" closer tolerance resistors '9@ or less( as

compared to t"e simpler carbon composition types. T"e tolerance o! a resistor is t"e

di!!erence bet*een t"e pre!erred #alue 'i.e) 9;; o"ms( and its actual manu!actured #alue

i.e) 9;.= o"ms) and is expressed as a percentage) !or example B@) 9;@ etc) and in our

example t"e actual tolerance is .=@. Film type resistors also ac"ie#e a muc" "ig"er

maximum o"mic #alue compared to ot"er types and #alues in excess o! 9;7 '9;

illion 7Ds( are a#ailable.

$i"m Resistor


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Meta" $i"m Resistors"a#e muc" better temperature stability t"an t"eir carbon

e/ui#alents) lo*er noise and are generally better !or "ig" !re/uency or radio !re/uency

applications. Meta" O+i*e Resistors"a#e better "ig" surge current capability *it" a

muc" "ig"er temperature rating t"an t"e e/ui#alent metal !ilm resistors.

not"er type o! !ilm resistor commonly +no*n as a T'ic, $i"m Resistoris

manu!actured by depositing a muc" t"ic+er conducti#e paste o! CERamic and METal)

called Cermet) onto an alumina ceramic substrate. Cermet resistors "a#e similar

properties to metal !ilm resistors and are generally used !or ma+ing small sur!ace mount

c"ip type resistors) multi-resistor net*or+s in one pac+age !or pcb2s and "ig" !re/uency

resistors. T"ey "a#e good temperature stability) lo* noise) and good #oltage ratings but

lo* surge current properties.

Meta" $i"m Resistorsare pre!ixed *it" a FR notation 'eg FR9;;+7( and a CF !or

Carbon Film types. etal !ilm resistors are a#ailable in $?A '>B@ & >?@

tolerances() $E= '>9@ tolerance( and $9E?'>;.B@) >;.?B@ & >;.9@ tolerances(

pac+ages *it" po*er ratings o! ;.;B '9


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0ire*ound Resistor

not"er type o! *ire *ound resistor is t"e Po&er ire &ou* Resistor. T"ese are "ig"

temperature) "ig" po*er non-inducti#e resistor types generally coated *it" a #itreous or

glass epoxy enamel !or use in resistance ban+s or C motor


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ire &ou* Resistor

0ire *ound resistor types are pre!ixed *it" a 04 or 0 notation 'eg 049;7( and

are a#ailable in t"e 04 aluminum clad pac+age '>9@) >?@) >B@ & >9;@ tolerance( or

t"e 0 #itreous enameled pac+age '>9@) >?@ & >B@ tolerance( *it" po*er ratings !rom

90 to ;;0 or more.

Resistor Tutoria" Summary

T"en to summari6e) t"ere are many di!!erent types o! resistor a#ailable !rom lo* cost)

large tolerance) general purpose carbon type resistors t"roug" to lo* tolerance) "ig" cost)

precision !ilm resistors as *ell as "ig" po*er) *ire *ound ceramic resistors. resistor

regulates) impedes or sets t"e !lo* o! current t"roug" a particular pat" or it can impose a

#oltage reduction in an electrical circuit. T"e resisti#e #alue o! a resistor) its ability to

limit current !lo* is measured in 1"m2s ' 7 ( ranging !rom less t"an one 1"m eac" to

many millions o! 1"m2s) 'ega-1"m2s(. Resistors can be o! a !ixed #alue) !or exampleO

9;; 1"ms) '9;;7( or #ariable as in ; to 9;;72s.

resistor *ill al*ays "a#e t"e same resistance #alue no matter *"at t"e !re/uency o! t"e

supply !rom C to #ery "ig" !re/uencies and all resistors "a#e one t"ing in common)

t"eir resisti#e #alue in 1"m2s in a circuit *ill 30S be positi#e in nature and ne#er

negati#e.

T"e uses and applications o! a resistor *it"in an electrical or electronic circuit are #ast

and #aried) but a resistor can commonly used !or purposes suc" as current limiting)

pro#iding appropriate control #oltage to semiconductors suc" as bipolar transistors)

protecting 3$s or ot"er semiconductor de#ices !rom excessi#e current. d,usting or

limiting t"e !re/uency response in an audio or !ilter circuit. Pulling up or pulling do*n


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t"e #oltage at t"e input pin o! a digital logic c"ip or by controlling a #oltage at a point in

a circuit by placing t*o resistors in series to create a #oltage di#ider net*or+.

In t"e next tutorial about Resistors) *e *ill loo+ at t"e di!!erent *ays o! identi!ying t"e

resisti#e #alue o! t"e di!!erent types o! !ixed resistors *it" t"e most common met"od o!

identi!ication being t"e use o!Co"our Co*esand colour bands around t"e body o! t"e

resistor.

Resistor Co"our Co*e

0e sa* in t"e pre#ious tutorial t"at t"ere are many di!!erent types o! Resistorsa#ailable

and t"at t"ey can be used in bot" electrical and electronic circuits to control t"e !lo* o!

current or #oltage in many di!!erent *ays. Hut in order to do t"is t"e actual resistor needs

to "a#e some !orm o! resisti#e or resistance #alue. Resistors are a#ailable in a range

o! di!!erent resistance #alues !rom !ractions o! an 1"m ' 7 ( to millions o! 1"ms.

1b#iously) it *ould be impractical to "a#e a#ailable resistors o! e#ery possible #alue !or

example) 97)?7) 7) A7 etc) because literally "undreds o! t"ousands) i! not millions o!

di!!erent resistors *ould need to exist to co#er all t"e possible #alues. Instead) resistors

are manu!actured in *"at are called pre!erred #alues *it" t"eir resistance #alue printed

onto t"eir body in coloured in+.

A Coloured Hands

T"e resistance #alue) tolerance) and *attage rating are generally printed onto t"e body o!

t"e resistor as numbers or letters *"en t"e resistors body is big enoug" to read t"e print)

suc" as large po*er resistors. Hut *"en t"e resistor is small suc" as a 9


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resistors colour code mar+ings are al*ays read one band at a time starting !rom t"e le!t

to t"e rig"t) *it" t"e larger *idt" tolerance band oriented to t"e rig"t side indicating its

tolerance. Hy matc"ing t"e colour o! t"e !irst band *it" its associated number in t"e digit

column o! t"e colour c"art belo* t"e !irst digit is identi!ied and t"is represents t"e !irst

digit o! t"e resistance #alue. gain) by matc"ing t"e colour o! t"e second band *it" its

associated number in t"e digit column o! t"e colour c"art *e get t"e second digit o! t"e

resistance #alue and so on as illustrated belo*O

T'e Sta*ar* Resistor Co"our Co*e C'art.


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T'e Resistor Co"our Co*e Ta)"e.

Co"our /i#it Mu"tip"ier To"erace

Hlac+ ; 9

Hro*n 9 9; > 9@

Red ? 9;; > ?@

1range 9);;;

ello* A 9;);;;

reen B 9;;);;; > ;.B@

Hlue = 9);;;);;; > ;.?B@

Violet Q 9;);;;);;; > ;.9@

rey

0"ite E

old ;.9 > B@

Sil#er ;.;9 > 9;@

Gone > ?;@

Ca"cu"ati# Resistor Va"ues

T"e Resistor Co"our Co*esystem is all *ell and good but *e need to understand "o* to

apply it in order to get t"e correct #alue o! t"e resistor. T"e le!t-"and or t"e most

signi!icant coloured band is t"e band *"ic" is nearest to a connecting lead *it" t"e

colour coded bands being read !rom le!t-to-rig"t as !ollo*s5

igit) igit) ultiplier K Colour) Colour x 9;colour in 1"m2s '72s(

For example) a resistor "as t"e !ollo*ing coloured mar+ings5

ello* Violet Red K A Q ? K A Q x 9;?K AQ;;7 or A+Q.

T"e !ourt" and !i!t" bands are used to determine t"e percentage tolerance o! t"e resistor.

Resistor tolerance is a measure o! t"e resistors #ariation !rom t"e speci!ied resisti#e #alue

and is a conse/uence o! t"e manu!acturing process and is expressed as a percentage o! its

nominal or pre!erred #alue.


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Typical resistor tolerances !or !ilm resistors range !rom 9@ to 9;@ *"ile carbon resistors

"a#e tolerances up to ?;@. Resistors *it" tolerances lo*er t"an ?@ are called precision

resistors *it" t"e or lo*er tolerance resistors being more expensi#e. ost !i#e band

resistors are precision resistors *it" tolerances o! eit"er 9@ or ?@ *"ile most o! t"e !our

band resistors "a#e tolerances o! B@) 9;@ and ?;@. T"e colour code used to denote t"e

tolerance rating o! a resistor is gi#en as5

Hro*n K 9@) Red K ?@) old K B@) Sil#er K 9; @

I! resistor "as no !ourt" tolerance band t"en t"e de!ault tolerance *ould be at ?;@.

It is sometimes easier to remember t"e resistor colour code by using mnemonics or

p"rases t"at "a#e a separate *ord in t"e p"rase to represent eac" o! t"e Ten L T*o

colours in t"e code. 4o*e#er) t"ese sayings are o!ten #ery crude but ne#er t"e less

e!!ecti#e !or remembering t"e resistor colours. 4ere are ,ust a !e* o! t"e more cleaner

#ersions but many more existO

Resistors i Series

Indi#idual resistors can be connected toget"er in eit"er a series connection) a parallel

connection or combinations o! bot" series and parallel toget"er) to produce more complex

resistor net*or+s *"ose e/ui#alent resistance is a combination o! t"e indi#idual resistors.

T"en complicated resistor net*or+s or impedances can be replaced by a single e/ui#alent

resistor) R$%or impedance) $%. Go matter *"at t"e combination or complexity o! t"e

resistor net*or+ is) all resistors obey t"e same basic rules de!ined by O'm0s

1a&and 2irc'off0s Circuit 1a&s.

Resistors i Series.

Resistors are said to be connected in Series) *"en t"ey are daisy c"ained toget"er in a

single line. Since all t"e current !lo*ing t"roug" t"e !irst resistor "as no ot"er *ay to go

it must also pass t"roug" t"e second resistor and t"e t"ird and so on. T"en) resistors in

series "a#e a Commo Curret!lo*ing t"roug" t"em as t"e current t"at !lo*s t"roug"

one resistor must also !lo* t"roug" t"e ot"ers as it can only ta+e one pat". T"en t"e

amount o! current t"at !lo*s t"roug" a set o! resistors in series *ill be t"e same at all

points in a series resistor net*or+. For exampleO

In t"e !ollo*ing example t"e resistors R9) R?and Rare all connected toget"er in series

bet*een points and H.
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Series Resistor Circuit

s t"e resistors are connected toget"er in series t"e same current passes t"roug" eac"

resistor in t"e c"ain and t"e total resistance) RTo! t"e circuit must be e%ua"to t"e sum o!

all t"e indi#idual resistors added toget"er. T"at is

and by ta+ing t"e indi#idual #alues o! t"e resistors in our simple example abo#e) t"e total

e/ui#alent resistance) R$%is t"ere!ore gi#en asO

R$%K R9L R?L R K 9+7 L ?+7 L =+7 K E+7

So *e see t"at *e can replace all t"ree indi#idual resistors abo#e *it" ,ust one single

e/ui#alent resistor *"ic" *ill "a#e a #alue o! E+7.

0"ere !our) !i#e or e#en more resistors are all connected toget"er in a series circuit) t"e

total or e/ui#alent resistance o! t"e circuit) RT*ould still be t"e sum o! all t"e indi#idual

resistors connected toget"er and t"e more resistors added to t"e series) t"e greater t"e

e/ui#alent resistance 'no matter *"at t"eir #alue(.

T"is total resistance is generally +no*n as t"e E%ui3a"et Resistaceand can be de!ined

as5 a single value of resistance that can replace any number of resistors in series

without altering the values of the current or the voltage in the circuit". T"en t"e e/uation

gi#en !or calculating total resistance o! t"e circuit *"en connecting toget"er resistors in

series is gi#en asO


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Series Resistor E%uatio

RtotalK R9L R?L RL ..... Rnetc.

Gote t"en t"at t"e total or e/ui#alent resistance) RT"as t"e same e!!ect on t"e circuit as

t"e original combination o! resistors as it is t"e algebraic sum o! t"e indi#idual

resistances. 1ne important point to remember about resistors in series net*or+s) t"e total

resistance ' RT( o! any t*o or more resistors connected toget"er in series *ill al*ays

be 4REATERt"an t"e #alue o! t"e largest resistor in t"e c"ain. In our example

abo#e RTK E+7 *"ere as t"e largest #alue resistor is only =+7.

Series Resistor Vo"ta#e

T"e #oltage across eac" resistor connected in series !ollo*s di!!erent rules to t"at o! t"e

series current. 0e +no* !rom t"e abo#e circuit t"at t"e total supply #oltage across t"e

resistors is e/ual to t"e sum o! t"e potential di!!erences across

R9) R?and R) VHK VR9L VR?L VRK EV.

sing O'm0s 1a&) t"e #oltage across t"e indi#idual resistors can be calculated asO

Voltage across R9K IR9K 9m x 9+7 K 9V

Voltage across R?K IR?K 9m x ?+7 K ?V

Voltage across RK IRK 9m x =+7 K =V

gi#ing a total #oltage VHo! ' 9V L ?V L =V ( K EV *"ic" is e/ual to t"e #alue o! t"e

supply #oltage. T"en t"e sum o! t"e potential di!!erences across t"e resistors is e/ual to

t"e total potential di!!erence across t"e combination and in our example t"is is EV.

T"e e/uation gi#en !or calculating t"e total #oltage in a series circuit *"ic" is t"e sum o!

all t"e indi#idual #oltages added toget"er is gi#en asO

T"en series resistor net*or+s can also be t"oug"t o! as #oltage di#iders and a series

resistor circuit "a#ingNresisti#e components *ill "a#e G-di!!erent #oltages across it

*"ile maintaining a common current.

Hy using O'm0s 1a&) eit"er t"e #oltage) current or resistance o! any series connected

circuit can easily be !ound and resistor o! a series circuit can be interc"anged *it"out

a!!ecting t"e total resistance) current) or po*er to eac" resistor.
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E+amp"e No5

sing 1"ms 3a*) calculate t"e e/ui#alent series resistance) t"e series current) #oltage

drop and po*er !or eac" resistor in t"e !ollo*ing resistors in series circuit.

ll t"e data can be !ound by using O'm0s 1a&) and to ma+e li!e a little easier *e can

present t"is data in tabular !orm.

Resistace Curret Vo"ta#e Po&er

R9K 9;7 I9K ?;;m V9K ?V P9K ;.A0

R?K ?;7 I?K ?;;m V?K AV P?K ;.0

RK ;7 IK ?;;m VK =V PK 9.?0

RTK =;7 ITK ?;;m VSK 9?V PTK ?.A0

T"en !or t"e circuit abo#e) RTK =;7) ITK ?;;m) VSK 9?V and PTK ?.A0

T'e Potetia" /i3i*er Circuit

0e can see !rom t"e abo#e example) t"at alt"oug" t"e supply #oltage is gi#en as 9? #olts)

di!!erent #oltages) or #oltage drops) appear across eac" resistor *it"in t"e series net*or+.

Connecting resistors in series li+e t"is across a single C supply #oltage "as one ma,orad#antage) di!!erent #oltages appear across eac" resistor. T"e amount o! #oltage drop is

determined by t"e resistors #alue only because as *e no* +no*) t"e current t"roug" a

series circuit is common. T"is ability to generate di!!erent #oltages produces a #ery

"andy circuit called a Potetia"or Vo"ta#e /i3i*er Net&or,.
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T"e series circuit s"o*n abo#e is a simple potential di#ider *"ere t"ree #oltages ?V) AV

and =V are produced !rom a single 9?V supply. 2irc'off0s Vo"ta#e 1a&states t"at the

supply voltage in a closed circuit is equal to the sum of all the voltage drops (! around

the circuit and t"is can be used to good e!!ect as t"is allo*s us to determine t"e #oltage

le#els o! a circuit *it"out !irst !inding t"e current.

T"e basic circuit !or a potential di#ider net*or+ 'also +no*n as a #oltage di#ider( !or

resistors in series net*or+s is s"o*n belo*.

Potetia" /i3i*er Net&or,

In t"is circuit t"e t*o resistors are connected in series across Vin) *"ic" is t"e po*er

supply #oltage connected to t"e resistor) R9) *"ere t"e output #oltage Voutis t"e #oltage

across t"e resistor R?*"ic" is gi#en by t"e !ormula. I! more resistors are connected in

series to t"e circuit t"en di!!erent #oltages *ill appear across eac" resistor *it" regards to

t"eir indi#idual resistance R '1"ms la* IxR( pro#iding di!!erent #oltage points !rom a

single supply. 4o*e#er) care must be ta+en *"en using t"is type o! net*or+ as t"e

impedance o! any load connected to it can a!!ect t"e output #oltage. For example)

Suppose you only "a#e a 9?V C supply and your circuit *"ic" "as an impedance o!

B;7 re/uires a =V supply. Connecting t*o e/ual #alue resistors) o! say B;7 eac")

toget"er as a potential di#ider net*or+ across t"e 9?V *ill do t"is #ery nicely until you

connect your load circuit to t"e net*or+. T"e loading e!!ect o! t*o resistances connected

toget"er in parallel c"anges t"e ratio o! t"e t*o resistances altering t"e #oltage drop and

t"is is demonstrated belo*.
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Resistors i Para""e"

Resistors are said to be connected toget"er in Para""e" *"en bot" o! t"eir terminals are

respecti#ely connected to eac" terminal o! t"e ot"er resistor or resistors. nli+e t"e

pre#ious series circuit) in a parallel resistor net*or+ t"e current can ta+e more t"an one

pat". Since t"ere are multiple pat"s !or t"e supply current to !lo* t"roug") t"e current is

not t"e same at all points in a parallel circuit. 4o*e#er) t"e #oltage drop across all o! t"e

resistors in a parallel resisti#e net*or+ is t"e same. T"en) Resistors i Para""e""a#e

a Commo Vo"ta#eacross t"em and t"is is true !or all parallel connected elements.

So *e can de!ine a parallel resisti#e circuit as one *"ere t"e resistor are connected to t"e

same t*o points 'or nodes( and is identi!ied by t"e !act t"at it "as more t"an one current

pat" connected to a common #oltage source. T"en in our parallel resistor example belo*

t"e #oltage across resistor R9e/uals t"e #oltage across resistor R?*"ic" e/uals t"e

#oltage across Rand *"ic" e/uals t"e supply #oltage. T"ere!ore) !or a parallel resistor

net*or+ t"is is gi#en asO

In t"e !ollo*ing resistors in parallel circuit t"e resistors R9) R?and Rare all connected

toget"er in parallel bet*een t"e t*o points and H as s"o*n.

Para""e" Resistor Circuit

In t"e pre#ious series resistor net*or+ *e sa* t"at t"e total resistance) RTo! t"e circuit

*as e/ual to t"e sum o! all t"e indi#idual resistors added toget"er. For resistors in parallel

t"e e/ui#alent circuit resistance RTis calculated di!!erently.


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4ere) t"e reciprocal ' 9


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T"e !i#e resisti#e net*or+s abo#e may loo+ di!!erent to eac" ot"er) but t"ey are all

arranged as Resistors i Para""e".

E+amp"e No5

Find t"e total resistance) RTo! t"e !ollo*ing resistors connected in a parallel net*or+.

T"e total resistance RTacross t"e t*o terminals and H is calculated asO

T"is met"od o! calculation can be used !or calculating any number o! indi#idual

resistances connected toget"er *it"in a single parallel net*or+. I! "o*e#er) t"ere are only

t*o indi#idual resistors in parallel t"en a muc" simpler and /uic+er !ormula can be used

to !ind t"e total resistance #alue) and t"is is gi#en asO


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Currets i a Para""e" Resistor Circuit

T"e total current) ITin a parallel resistor circuit is t"e sum o! t"e indi#idual currents

!lo*ing in all t"e parallel branc"es. T"e amount o! current !lo*ing in eac" parallel

branc" is not necessarily t"e same as t"e #alue o! t"e resistance in eac" branc"

determines t"e current *it"in t"at branc". For example) alt"oug" t"e parallel combination

"as t"e same #oltage across it) t"e resistances could be di!!erent t"ere!ore t"e current

!lo*ing t"roug" eac" resistor *ould de!initely be di!!erent as determined by 1"ms 3a*.

Consider t"e t*o resistors in parallel abo#e. T"e current t"at !lo*s t"roug" eac" o! t"e

resistors ' IR9and IR?( connected toget"er in parallel is not necessarily t"e same #alue as

it depends upon t"e resisti#e #alue o! t"e resistor. 4o*e#er) *e do +no* t"at t"e current

t"at enters t"e circuit at point ust also exit t"e circuit at point H. 2irc'off0s Curret

1a&s.states t"at the total current leaving a circuit is equal to that entering the circuit #

no current is lost. T"us) t"e total current !lo*ing in t"e circuit is gi#en asO

ITK IR9L IR?

T"en by using O'm0s 1a&) t"e current !lo*ing t"roug" eac" resistor can be calculated

asO

Current !lo*ing in R9K VS R9K 9?V ??+7 K ;.BABm or BABu

Current !lo*ing in R?K VS R?K 9?V AQ+7 K ;.?BBm or ?BBu

gi#ing us a total current IT!lo*ing around t"e circuit asO

ITK ;.BABm L ;.?BBm K ;.m or ;;u.

T"e e/uation gi#en !or calculating t"e total current !lo*ing in a parallel resistor circuit

*"ic" is t"e sum o! all t"e indi#idual currents added toget"er is gi#en asO

ItotalK I9L I?L I..... L In

T"en parallel resistor net*or+s can also be t"oug"t o! as a current di#ider because t"e

current splits or di#ides bet*een t"e #arious branc"es and a parallel resistor circuit

"a#ingNresisti#e net*or+s *ill "a#e G-di!!erent current pat"s *"ile maintaining a

common #oltage. Parallel resistors can also be interc"anged *it"out c"anging t"e total

resistance or t"e total circuit current.
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Vo"ta#e /i3i*er

0e +no* !rom t"e pre#ious tutorials t"at by connecting toget"er resistors in series across

a potential di!!erence *e can produce a #oltage di#ider circuit gi#ing ratios o! #oltages

*it" respect to t"e supply #oltage across t"e series combination. T"is t"en produces

a Vo"ta#e /i3i*ernet*or+ t"at only applies to resistors in series as parallel resistors

produce a current divider networ$. Consider t"e circuit belo*.

Vo"ta#e /i3isio

T"e circuit s"o*s t"e principal o! a #oltage di#ider circuit *"ere t"e output #oltage drops

across eac" resistor) R9) R?) R and RA are re!erenced to a common point. For any

number o! resistors connected toget"er in series t"e total resistance) RT o! t"e circuit

di#ided by t"e supply #oltage Vs *ill gi#e t"e circuit current as I K Vs


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Vo"ta#e /i3i*er E%uatio

0"ere) V'x(is t"e #oltage to be !ound) R'x(is t"e resistance producing t"e #oltage) RTis

t"e total series resistance and VSis t"e supply #oltage.

T"en by using t"is e/uation *e can say t"at t"e #oltage dropped across any resistor in a

series circuit is proportional to t"e magnitude o! t"e resistor and t"e total #oltage dropped

across all t"e resistors must e/ual t"e #oltage source as de!ined by 2irc'off0s Vo"ta#e

1a&. So by using t"e Vo"ta#e /i3i*er E%uatio) !or any number o! series resistors t"e

#oltage drop across any indi#idual resistor can be !ound.

T"us !ar *e "a#e seen t"at #oltage is applied to a resistor or circuit and t"at current !lo*s

t"roug" and around a circuit. Hut t"ere is a t"ird #ariable *e can also apply to resistors

and resistor net*or+s. Po*er is a product o! #oltage and current and t"e basic unit o!

measurement o! po*er is t"e *att.

In t"e next tutorial about Resistors) *e *ill examine t"e po*er dissipated 'consumed( by

resistance in t"e !orm o! "eat and t"at t"e total po*er dissipated by a resisti#e circuit)

*"et"er it is series) parallel) or a combination o! t"e t*o) *e simply add t"e po*ers

dissipated by eac" resistor.

Resistor Po&er Rati#

0"en an electrical current passes t"roug" a resistor) electrical energy is lost by t"e

resistor in t"e !orm o! "eat and t"e greater t"is current !lo* t"e "otter t"e resistor *ill get.

T"is is +no*n as t"e Resistor Po&er Rati#. Resistors are rated by t"e #alue o! t"eir

resistance and t"e po*er in *atts t"at t"ey can sa!ely dissipate based mainly upon t"eir

si6e. $#ery resistor "as a maximum po*er rating *"ic" is determined by its p"ysical si6e

as generally) t"e greater its sur!ace area t"e more po*er it can dissipate sa!ely into t"e

ambient air or into a "eatsin+.

resistor can be used at any combination o! #oltage '*it"in reason( and current so long

as its issipating Po*er Rating is not exceeded *it" t"e resistor po*er rating

indicating "o* muc" po*er t"e resistor can con#ert into "eat or absorb *it"out any

damage to itsel!. T"e Resistor Po&er Rati#is sometimes called t"e!esistors %attage

!atingand is de!ined as the amount of heat that a resistive element can dissipate for an

indefinite period of time without degrading its performance&
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T"e po*er rating o! resistors can #ary a lot !rom less t"an one tent" o! a *att to many

"undreds o! *atts depending upon its si6e) construction and ambient operating

temperature. ost resistors "a#e t"eir maximum resisti#e po*er rating gi#en !or an

ambient temperature o! LQ;oC or belo*.

$lectrical po*er is t"e rate in time at *"ic" energy is used or consumed 'con#erted into

"eat(. T"e standard unit o! electrical po*er is t"e att) symbol and a resistors po*er

rating is also gi#en in 0atts. s *it" ot"er electrical /uantities) pre!ixes are attac"ed to

t"e *ord 0att *"en expressing #ery large or #ery small amounts o! resistor po*er.

Some o! t"e more common o! t"ese areO

E"ectrica" Po&er Uits

nit Symbol Value bbre#iation

milli*att m0 9


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T"e abo#e po*er triangle is great !or calculating t"e po*er dissipated in a resistor i! *e

+no* t"e #alues o! t"e #oltage across it and t"e current !lo*ing t"roug" it. Hut *e can

also calculate t"e po*er dissipated by a resistance by using O'm0s 1a&. 1"ms la*

allo*s us to calculate t"e po*er dissipation gi#en t"e resistance #alue o! t"e resistor. Hy

using 1"ms 3a* it is possible to obtain t*o alternati#e #ariations o! t"e abo#e expression

!or t"e resistor po*er i! *e +no* t"e #alues o! only t*o) t"e #oltage) t"e current or t"e

resistance as !ollo*sO

U P K V x I Po*er K Volts x mps

U P K I?x R Po*er K Current? x 1"ms

U P K V? R Po*er K Volts? 1"ms

T"e electrical po*er dissipation o! any resistor in a C circuit can be calculated using

one o! t"e !ollo*ing t"ree standard !ormulasO

0"ereO

V is t"e #oltage across t"e resistor in Volts

I is in current !lo*ing t"roug" t"e resistor in mperes

R is t"e resistance o! t"e resistor in 1"m2s '7(

s t"e dissipated resistor po*er rating is lin+ed to t"eir p"ysical si6e) a 9


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#alue are also a#ailable in di!!erent po*er or *attage ratings. Carbon resistors) !or

example) are commonly made in *attage ratings o! 9


25/76

in t"e circuit. T"is type o! resistor is used in test measuring e/uipment and controlled

po*er supplies.

T"e larger *ire *ound po*er resistors are made o! corrosion resistant *ire *ound onto a

porcelain or ceramic core type !ormer and are generally used to dissipate "ig" inrus"

currents suc" as t"ose generated in motor control) electromagnet or ele#ator


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Capacitors

Wust li+e t"e Resistor)t"e Capacitor) sometimes re!erred to as a Co*eser) is a simple

passi#e de#ice. T"e capacitor is a component *"ic" "as t"e ability or capacity to store

energy in t"e !orm o! an electrical c"arge producing a potential di!!erence ''taticoltage( across its plates) muc" li+e a small rec"argable battery. In its basic !orm) a

capacitor consists o! t*o or more parallel conducti#e 'metal( plates *"ic" are not

connected or touc"ing eac" ot"er) but are electrically separated eit"er by air or by some

!orm o! insulating material suc" as paper) mica) ceramic or plastic and *"ic" is

commonly called t"e capacitors /ie"ectric.

Typical Capacitor

T"e conducti#e metal plates o! a capacitor can be eit"er s/uare) circular or rectangular) or

t"ey can be o! a cylindrical or sp"erical s"ape *it" t"e general s"ape) si6e and

construction o! a parallel plate capacitor depending on its application and #oltage rating.

0"en used in a direct current or C circuit) a capacitor c"arges up to its supply #oltage

but bloc+s t"e !lo* o! current t"roug" it because t"e dielectric o! a capacitor is non-

conducti#e and basically an insulator. 4o*e#er) *"en a capacitor is connected to an

alternating current or C circuit) t"e !lo* o! t"e current appears to pass straig"t t"roug"t"e capacitor *it" little or no resistance.

I! a C #oltage is applied to t"e capacitors conducti#e plates) a current is unable to !lo*

t"roug" t"e capacitor itsel! due to t"e dielectric insulation and an electrical c"arge builds

up on t"e capacitors plates *it" electrons producing a positi#e c"arge on one and an

e/ual and opposite negati#e c"arge on t"e ot"er plate.

T"is !lo* o! electrons to t"e plates is +no*n as t"e capacitors C'ar#i# Curret*"ic"

continues to !lo* until t"e #oltage across bot" plates 'and "ence t"e capacitor( is e/ual to

t"e applied #oltage Vc. t t"is point t"e capacitor is said to be !ully c"arged *it"electrons. T"e strengt" or rate o! t"is c"arging current is at its maximum #alue *"en t"e

plates are !ully disc"arged 'initial condition( and slo*ly reduces in #alue to 6ero as t"e

plates c"arge up to a potential di!!erence across t"e capacitors plates e/ual to t"e applied

supply #oltage and t"is is illustrated belo*.
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Capacitor Costructio

T"e parallel plate capacitor is t"e simplest !orm o! capacitor. It can be constructed using

t*o metal or metallised !oil plates at a distance parallel to eac" ot"er) *it" its capacitance

#alue in Farads) being !ixed by t"e sur!ace area o! t"e conducti#e plates and t"e distance

o! separation bet*een t"em. ltering any t*o o! t"ese #alues alters t"e t"e #alue o! its

capacitance and t"is !orms t"e basis o! operation o! t"e #ariable capacitors.

lso) because capacitors store t"e energy o! t"e electrons in t"e !orm o! an electrical

c"arge on t"e plates t"e larger t"e plates and


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T"e property o! a capacitor to store c"arge on its plates in t"e !orm o! an electrostatic

!ield is called t"eCapacitaceo! t"e capacitor. Got only t"at) but capacitance is also t"e

property o! a capacitor *"ic" resists t"e c"ange o! #oltage across it.

T'e Capacitace of a Capacitor

T"e unit o! capacitance is t"e $ara*'abbre#iated to F( named a!ter t"e Hritis" p"ysicist

ic"ael Faraday and is de!ined as a capacitor "as t"e capacitance o! Oe $ara**"en a

c"arge o! Oe Cou"om)is stored on t"e plates by a #oltage o! Oe 3o"t.

Capacitance) C is al*ays positi#e and "as no negati#e units. 4o*e#er) t"e Farad is a #ery

large unit o! measurement to use on its o*n so sub-multiples o! t"e Farad are generally

used suc" as micro-!arads) nano-!arads and pico-!arads) !or example.

Sta*ar* Uits of Capacitace

icro!arad 'XF( 9XF K 9


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Capacitace of a Para""e" P"ate Capacitor

T"e capacitance o! a parallel plate capacitor is proportional to t"e area) o! t"e plates

and in#ersely proportional to t"eir distance or separation) d 'i.e. t"e dielectric t"ic+ness(

gi#ing us a #alue !or capacitance o! C K +'


30/76

material bet*een t"e plates is t"en t"e product o! t"e permitti#ity o! !ree space 'Yo( and

t"e relati#e permitti#ity 'Yr( o! t"e material being used as t"e dielectric and is gi#en asO

Comp"e+ Permitti3ity

s t"e permitti#ity o! !ree space) Yois e/ual to one) t"e #alue o! t"e complex permitti#ity

*ill al*ays be e/ual to t"e relati#e permitti#ity. Typical units o! dielectric

permitti#ity) Y or dielectric constant !or common materials areO Pure Vacuum K 9.;;;;)

ir K 9.;;;B) Paper K ?.B to .B) lass K to 9;) ica K B to Q) 0ood K to and etal

1xide Po*ders K = to ?; etc.

T"is t"en gi#es us a !inal e/uation !or t"e capacitance o! a capacitor asO

1ne met"od used to increase t"e o#erall capacitance o! a capacitor is to interlea#e more

plates toget"er *it"in a single capacitor body. Instead o! ,ust one set o! parallel plates) a

capacitor can "a#e many indi#idual plates connected toget"er t"ereby increasing t"e

area) o! t"e plate. For example) a capacitor *it" 9; interlea#ed plates *ould produce E

'9; - 9( mini capacitors *it" an o#erall capacitance nine times t"at o! a single parallel

plate.


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odern capacitors can be classi!ied according to t"e c"aracteristics and properties o!

t"eir insulating dielectricO

3o* 3oss) 4ig" Stability suc" as ica) 3o*-Z Ceramic) Polystyrene.

edium 3oss) edium Stability suc" as Paper) Plastic Film) 4ig"-Z Ceramic.

Polari6ed Capacitors suc" as $lectrolytic2s) Tantalum2s.

Vo"ta#e Rati# of a Capacitor

ll capacitors "a#e a maximum #oltage rating and *"en selecting a capacitor

consideration must be gi#en to t"e amount o! #oltage to be applied across t"e capacitor.

T"e maximum amount o! #oltage t"at can be applied to t"e capacitor *it"out damage to

its dielectric material is generally gi#en in t"e data s"eets asO 0V) '*or+ing #oltage( or

as 0V C) 'C *or+ing #oltage(. I! t"e #oltage applied across t"e capacitor becomes

too great) t"e dielectric *ill brea+ do*n '+no*n as electrical brea+do*n( and arcing *ill

occur bet*een t"e capacitor plates resulting in a s"ort-circuit. T"e *or+ing #oltage o! t"ecapacitor depends on t"e type o! dielectric material being used and its t"ic+ness.

T"e C *or+ing #oltage o! a capacitor is ,ust t"at) t"e maximum C #oltage and G1T

t"e maximum C #oltage as a capacitor *it" a C #oltage rating o! 9;; #olts C cannot

be sa!ely sub,ected to an alternating #oltage o! 9;; #olts. Since an alternating #oltage "as

an r.m.s. #alue o! 9;; #olts but a pea+ #alue o! o#er 9A9 #olts[. T"en a capacitor *"ic" is

re/uired to operate at 9;; #olts C s"ould "a#e a *or+ing #oltage o! at least ?;; #olts.

In practice) a capacitor s"ould be selected so t"at its *or+ing #oltage eit"er C or C

s"ould be at least B; percent greater t"an t"e "ig"est e!!ecti#e #oltage to be applied to it.

not"er !actor *"ic" a!!ects t"e operation o! a capacitor is /ie"ectric 1ea,a#e.

ielectric lea+age occurs in a capacitor as t"e result o! an un*anted lea+age current

*"ic" !lo*s t"roug" t"e dielectric material. enerally) it is assumed t"at t"e resistance o!

t"e dielectric is extremely "ig" and a good insulator bloc+ing t"e !lo* o! C current

t"roug" t"e capacitor 'as in a per!ect capacitor( !rom one plate to t"e ot"er.

4o*e#er) i! t"e dielectric material becomes damaged due excessi#e #oltage or o#er

temperature) t"e lea+age current t"roug" t"e dielectric *ill become extremely "ig"

resulting in a rapid loss o! c"arge on t"e plates and an o#er"eating o! t"e capacitor

e#entually resulting in premature !ailure o! t"e capacitor. T"en ne#er use a capacitor in a

circuit *it" "ig"er #oltages t"an t"e capacitor is rated !or ot"er*ise it may become "ot

and explode.


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Itro*uctio to Capacitors Summary

T"e ,ob o! a capacitor is to store c"arge onto its plates. T"e amount o! electrical c"arge

t"at a capacitor can store on its plates is +no*n as its Capacitace#alue and depends

upon t"ree main !actors.

T"e sur!ace area) o! t"e t*o conducti#e plates *"ic" ma+e up t"e capacitor)

t"e larger t"e area t"e greater t"e capacitance.

T"e distance) d bet*een t"e t*o plates) t"e smaller t"e distance t"e greater t"e

capacitance.

T"e type o! material *"ic" separates t"e t*o plates called t"e dielectric) t"e

"ig"er t"e permitti#ity o! t"e dielectric t"e greater t"e capacitance.

T"e dielectric o! a capacitor is a non-conducting insulating material) suc" as

*axed paper) glass) mica di!!erent plastics etc) and pro#ides t"e !ollo*ing

ad#antages.

T"e dielectric constant is t"e property o! t"e dielectric material and #aries !rom

one material to anot"er increasing t"e capacitance by a !actor o! +.

T"e dielectric pro#ides mec"anical support bet*een t"e t*o plates allo*ing t"e

plates to be closer toget"er *it"out touc"ing.

Permitti#ity o! t"e dielectric increases t"e capacitance.

T"e dielectric increases t"e maximum operating #oltage compared to air.

Capacitors can be used to bloc+ C current *"ile passing audio signals) pulses) or

alternating current) or ot"er time #arying *a#e !orms. T"is ability to bloc+ C currents

enables capacitors to be used to smoot" t"e output #oltages o! po*er supplies) to remo#e

un*anted spi+es !rom signals t"at *ould ot"er*ise tend to cause damage or !alse

triggering o! semiconductors or digital components. Capacitors can also be used to ad,ust

t"e !re/uency response o! an audio circuit) or to couple toget"er separate ampli!ier stages

t"at must be protected !rom t"e transmission o! C current.

t C a capacitor "as in!inite impedance 'open -circuit() at #ery "ig" !re/uencies a

capacitor "as 6ero impedance 's"ort-circuit(. ll capacitors "a#e a maximum *or+ing

#oltage rating) its 0V C so select a capacitor *it" a rating at least B;@ more t"an t"e

supply #oltage.


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Types of Capacitor

T"ere are a #ery) #ery large #ariety o! di!!erent types of capacitora#ailable in t"e

mar+et place and eac" one "as its o*n set o! c"aracteristics and applications) !rom #ery

small delicate trimming capacitors up to large po*er metal-can type capacitors used in

"ig" #oltage po*er correction and smoot"ing circuits. T"e comparisons bet*een t"e t"e

di!!erent types of capacitoris generally made *it" regards to t"e dielectric used bet*een

t"e plates. 3i+e resistors) t"ere are also #ariable types o! capacitors *"ic" allo* us to

#ary t"eir capacitance #alue !or use in radio or !re/uency tuning type circuits.

Commercial types o! capacitor are made !rom metallic !oil interlaced *it" t"in s"eets o!

eit"er para!!in-impregnated paper or ylar as t"e dielectric material. Some capacitors

loo+ li+e tubes) t"is is because t"e metal !oil plates are rolled up into a cylinder to !orm a

small pac+age *it" t"e insulating dielectric material sand*ic"ed in bet*een t"em. Small

capacitors are o!ten constructed !rom ceramic materials and t"en dipped into an epoxy

resin to seal t"em. $it"er *ay) capacitors play an important part in electronic circuits so

"ere are a !e* o! t"e more common types o! capacitor a#ailable.

/ie"ectric Capacitor

/ie"ectric Capacitorsare usually o! t"e #ariable type *ere a continuous #ariation o!

capacitance is re/uired !or tuning transmitters) recei#ers and transistor radios. Variable

dielectric capacitors are multi-plate air-spaced types t"at "a#e a set o! !ixed plates 't"e

stator #anes( and a set o! mo#able plates 't"e rotor #anes( *"ic" mo#e in bet*een t"e

!ixed plates. T"e position o! t"e mo#ing plates *it" respect to t"e !ixed plates determines

t"e o#erall capacitance #alue. T"e capacitance is generally at maximum *"en t"e t*o

sets o! plates are !ully mes"ed toget"er. 4ig" #oltage type tuning capacitors "a#e

relati#ely large spacings or air-gaps bet*een t"e plates *it" brea+do*n #oltages reac"ing

many t"ousands o! #olts.

Varia)"e Capacitor Sym)o"s


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Ra*ia" 1ea* Type

A+ia" 1ea* Type

T"e !ilm and !oil types o! capacitors are made !rom long t"in strips o! t"in metal !oil *it"

t"e dielectric material sand*ic"ed toget"er *"ic" are *ound into a tig"t roll and t"en

sealed in paper or metal tubes.

Film Capacitor

T"ese !ilm types re/uire a muc" t"ic+er dielectric !ilm to reduce t"e ris+ o! tears or

punctures in t"e !ilm) and is t"ere!ore more suited to lo*er capacitance #alues and larger

case si6es.


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etali6ed !oil capacitors "a#e t"e conducti#e !ilm metali6ed sprayed directly onto eac"

side o! t"e dielectric *"ic" gi#es t"e capacitor sel!-"ealing properties and can t"ere!ore

use muc" t"inner dielectric !ilms. T"is allo*s !or "ig"er capacitance #alues and smaller

case si6es !or a gi#en capacitance. Film and !oil capacitors are generally used !or "ig"er

po*er and more precise applications.

Ceramic Capacitors

Ceramic Capacitorsor /isc Capacitorsas t"ey are generally called) are made by

coating t*o sides o! a small porcelain or ceramic disc *it" sil#er and are t"en stac+ed

toget"er to ma+e a capacitor. For #ery lo* capacitance #alues a single ceramic disc o!

about -=mm is used. Ceramic capacitors "a#e a "ig" dielectric constant '4ig"-Z( and

are a#ailable so t"at relati#ely "ig" capacitances can be obtained in a small p"ysical si6e.

Ceramic Capacitor

T"ey ex"ibit large non-linear c"anges in capacitance against temperature and as a result

are used as de-coupling or by-pass capacitors as t"ey are also non-polari6ed de#ices.

Ceramic capacitors "a#e #alues ranging !rom a !e* pico!arads to one or t*o micro!arads

but t"eir #oltage ratings are generally /uite lo*.

Ceramic types o! capacitors generally "a#e a -digit code printed onto t"eir body to

identi!y t"eir capacitance #alue in pico-!arads. enerally t"e !irst t*o digits indicate t"e

capacitors #alue and t"e t"ird digit indicates t"e number o! 6ero2s to be added. For

example) a ceramic disc capacitor *it" t"e mar+ings 9; *ould indicate 9; and 6ero2s

in pico-!arads *"ic" is e/ui#alent to 9;);;; pF or9;nF.

3i+e*ise) t"e digits 9;A *ould indicate 9; and A 6ero2s in pico-!arads *"ic" is e/ui#alentto 9;;);;; pFor 9;;nF and so on. T"en on t"e image o! a ceramic capacitor abo#e t"e

numbers 9BA indicate 9B and A 6ero2s in pico-!arads *"ic" is e/ui#alent to 9B;);;;

pF or 9B;nF. 3etter codes are sometimes used to indicate t"eir tolerance #alue suc" asO W

K B@) Z K 9;@ or K ?;@ etc.


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E"ectro"ytic Capacitors

E"ectro"ytic Capacitorsare generally used *"en #ery large capacitance #alues are

re/uired. 4ere instead o! using a #ery t"in metallic !ilm layer !or one o! t"e electrodes) a

semi-li/uid electrolyte solution in t"e !orm o! a ,elly or paste is used *"ic" ser#es as t"e

second electrode 'usually t"e cat"ode(. T"e dielectric is a #ery t"in layer o! oxide *"ic"

is gro*n electro-c"emically in production *it" t"e t"ic+ness o! t"e !ilm being less t"an

ten microns. T"is insulating layer is so t"in t"at it is possible to ma+e capacitors *it" a

large #alue o! capacitance !or a small p"ysical si6e as t"e distance bet*een t"e plates) d is

#ery small.

$lectrolytic Capacitor

T"e ma,ority o! electrolytic types o! capacitors are Po"arise*) t"at is t"e C #oltage

applied to t"e capacitor terminals must be o! t"e correct polarity) i.e. positi#e to t"e

positi#e terminal and negati#e to t"e negati#e terminal as an incorrect polarisation *ill

brea+ do*n t"e insulating oxide layer and permanent damage may result. ll polarised

electrolytic capacitors "a#e t"eir polarity clearly mar+ed *it" a negati#e sign to indicate

t"e negati#e terminal and t"is polarity must be !ollo*ed.

E"ectro"ytic Capacitorsare generally used in C po*er supply circuits due to t"eir large

capacitances and small si6e to "elp reduce t"e ripple #oltage or !or coupling and

decoupling applications. 1ne main disad#antage o! electrolytic capacitors is t"eir

relati#ely lo* #oltage rating and due to t"e polarisation o! electrolytic capacitors) it

!ollo*s t"en t"at t"ey must not be used on C supplies. $lectrolytic2s generally come in

t*o basic !orms5 A"umium E"ectro"ytic Capacitorsand Tata"um E"ectro"ytic

Capacitors.


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E"ectro"ytic Capacitor

5. A"umium E"ectro"ytic Capacitors

T"ere are basically t*o types o! A"umiium E"ectro"ytic Capacitor) t"e plain !oil type

and t"e etc"ed !oil type. T"e t"ic+ness o! t"e aluminium oxide !ilm and "ig" brea+do*n

#oltage gi#e t"ese capacitors #ery "ig" capacitance #alues !or t"eir si6e. T"e !oil plates o!

t"e capacitor are anodi6ed *it" a C current. T"is anodi6ing process sets up t"e polarity

o! t"e plate material and determines *"ic" side o! t"e plate is positi#e and *"ic" side is

negati#e.

T"e etc"ed !oil type di!!ers !rom t"e plain !oil type in t"at t"e aluminium oxide on t"e

anode and cat"ode !oils "as been c"emically etc"ed to increase its sur!ace area andpermitti#ity. T"is gi#es a smaller si6ed capacitor t"an a plain !oil type o! e/ui#alent #alue

but "as t"e disad#antage o! not being able to *it"stand "ig" C currents compared to t"e

plain type. lso t"eir tolerance range is /uite large at up to ?;@. Typical #alues o!

capacitance !or an aluminum electrolytic capacitor range !rom 9uF up to AQ);;;uF.

$tc"ed !oil electrolytic2s are best used in coupling) C bloc+ing and by-pass circuits

*"ile plain !oil types are better suited as smoot"ing capacitors in po*er supplies. Hut

aluminium electrolytic2s are polarised de#ices so re#ersing t"e applied #oltage on t"e

leads *ill cause t"e insulating layer *it"in t"e capacitor to become destroyed along *it"

t"e capacitor. 4o*e#er) t"e electrolyte used *it"in t"e capacitor "elps "eal a damagedplate i! t"e damage is small.

Since t"e electrolyte "as t"e properties to sel!-"eal a damaged plate) it also "as t"e ability

to re-anodi6e t"e !oil plate. s t"e anodi6ing process can be re#ersed) t"e electrolyte "as

t"e ability to remo#e t"e oxide coating !rom t"e !oil as *ould "appen i! t"e capacitor *as

connected *it" a re#erse polarity. Since t"e electrolyte "as t"e ability to conduct


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electricity) i! t"e aluminum oxide layer *as remo#ed or destroyed) t"e capacitor *ould

allo* current to pass !rom one plate to t"e ot"er destroying t"e capacitor) so be a*are.

8. Tata"um E"ectro"ytic Capacitors

Tata"um E"ectro"ytic Capacitorsand Tata"um Bea*s) are a#ailable in bot" *et '!oil(

and dry 'solid( electrolytic types *it" t"e dry or solid tantalum being t"e most common.

Solid tantalum capacitors use manganese dioxide as t"eir second terminal and are

p"ysically smaller t"an t"e e/ui#alent aluminium capacitors. T"e dielectric properties o!

tantalum oxide is also muc" better t"an t"ose o! aluminium oxide gi#ing a lo*er lea+age

currents and better capacitance stability *"ic" ma+es t"em suitable !or use in bloc+ing)

by-passing) decoupling) !iltering and timing applications.

lso) Tata"um Capacitorsalt"oug" polarised) can tolerate being connected to a re#erse

#oltage muc" more easily t"an t"e aluminium types but are rated at muc" lo*er *or+ing

#oltages. Solid tantalum capacitors are usually used in circuits *"ere t"e C #oltage is

small compared to t"e C #oltage. 4o*e#er) some tantalum capacitor types contain t*o

capacitors in-one) connected negati#e-to-negati#e to !orm a non-polarised capacitor !or

use in lo* #oltage C circuits as a non-polarised de#ice. enerally) t"e positi#e lead is

identi!ied on t"e capacitor body by a polarity mar+) *it" t"e body o! a tantalum bead

capacitor being an o#al geometrical s"ape. Typical #alues o! capacitance range !rom

AQnF to AQ;uF.

A"umiium 9 Tata"um E"ectro"ytic Capacitor

$lectrolytic2s are *idely used capacitors due to t"eir lo* cost and small si6e but t"ere are

t"ree easy *ays to destroy an electrolytic capacitorO

1#er-#oltage - excessi#e #oltage *ill cause current to lea+ t"roug" t"e dielectric

resulting in a s"ort circuit condition.


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Re#ersed Polarity - re#erse #oltage *ill cause sel!-destruction o! t"e oxide layer

and !ailure.

1#er Temperature - excessi#e "eat dries out t"e electrolytic and s"ortens t"e li!e

o! an electrolytic capacitor.

Capacitor C'aracteristics

T"ere are a be*ildering array o! capacitor c"aracteristics and speci!ications associated

*it" t"e "umble capacitor and reading t"e in!ormation printed onto t"e body o! a

capacitor can sometimes be di!!icult especially *"en colours or numeric codes are used.

$ac" !amily or type o! capacitor uses its o*n uni/ue identi!ication system *it" some

systems being easy to understand) and ot"ers t"at use misleading letters) colours or

symbols. T"e best *ay to !igure out *"at a capacitor label means is to !irst !igure out

*"at type o! !amily t"e capacitor belongs to *"et"er it is ceramic) !ilm) plastic or

electrolytic.

$#en t"oug" t*o capacitors may "a#e exactly t"e same capacitance #alue) t"ey may "a#e

di!!erent #oltage ratings. I! a smaller rated #oltage capacitor is substituted in place o! a

"ig"er rated #oltage capacitor) t"e increased #oltage may damage t"e smaller capacitor.

lso *e remember !rom t"e last tutorial t"at *it" a polarised electrolytic capacitor) t"e

positi#e lead must go to t"e positi#e connection and t"e negati#e lead to t"e negati#e

connection ot"er*ise it may again become damaged. So it is al*ays better to substitute

an old or damaged capacitor *it" t"e same type as t"e speci!ied one. n example o!

capacitor mar+ings is gi#en belo*.

Capacitor C'aracteristics

T"e capacitor) as *it" any ot"er electronic component) comes de!ined by a series o!

c"aracteristics. T"ese Capacitor C'aracteristicscan al*ays be !ound in t"e datas"eets

t"at t"e capacitor manu!acturer pro#ides to us so "ere are ,ust a !e* o! t"e more

important ones.


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5. Nomia" Capacitace! 6C7

T"e nominal #alue o! t"e Capacitace) C o! a capacitor is measured in pico-Farads 'pF()

nano-Farads 'nF( or micro-Farads '\F( and is mar+ed onto t"e body o! t"e capacitor as

numbers) letters or coloured bands. T"e capacitance o! a capacitor can c"ange #alue *it"

t"e circuit !re/uency '46( y *it" t"e ambient temperature. Smaller ceramic capacitors

can "a#e a nominal #alue as lo* as one pico-Farad) ' 9pF ( *"ile larger electrolytic2s can

"a#e a nominal capacitance #alue o! up to one Farad) ' 9F (. ll capacitors "a#e a

tolerance rating t"at can range !rom -?;@ to as "ig" as L;@ !or aluminium electrolytic2s

a!!ecting its actual or real #alue. T"e c"oice o! capacitance is determined by t"e circuit

con!iguration but t"e #alue read on t"e side o! a capacitor may not necessarily be its

actual #alue.

8. or,i# Vo"ta#e! 6V7

T"e or,i# Vo"ta#eis t"e maximum continuous #oltage eit"er C or C t"at can be

applied to t"e capacitor *it"out !ailure during its *or+ing li!e. enerally) t"e *or+ing

#oltage printed onto t"e side o! a capacitors body re!ers to its C *or+ing #oltage) ' 0V-

C (. C and C #oltage #alues are usually not t"e same !or a capacitor as t"e C

#oltage #alue re!ers to t"e r.m.s. #alue and G1T t"e maximum or pea+ #alue *"ic" is

9.A9A times greater. lso) t"e speci!ied C *or+ing #oltage is #alid *it"in a certain

temperature range) normally - ;]C to L Q;]C.

ny C #oltage in excess o! its *or+ing #oltage or an excessi#e C ripple current may

cause !ailure. It !ollo*s t"ere!ore) t"at a capacitor *ill "a#e a longer *or+ing li!e i!

operated in a cool en#ironment and *it"in its rated #oltage. Common *or+ing C

#oltages are 9;V) 9=V) ?BV) BV) B;V) =V) 9;;V) 9=;V) ?B;V) A;;V and 9;;;V and

are printed onto t"e body o! t"e capacitor.

. To"erace! 6;@( !or "ig"er #alue capacitors generally "ig"er t"an 9;;pF. T"e tolerance

#alue is t"e extent to *"ic" t"e actual capacitance is allo*ed to #ary !rom its nominal#alue and can range any*"ere !rom -?;@ to L;@. T"us a 9;;\F capacitor *it" a >?;@

tolerance could legitimately #ary !rom ;\F to 9?;\F and still remain *it"in tolerance.

Capacitors are rated according to "o* near to t"eir actual #alues t"ey are compared to t"e

rated nominal capacitance *it" coloured bands or letters used to indicated t"eir actual

tolerance. T"e most common tolerance #ariation !or capacitors is B@ or 9;@ but some

plastic capacitors are rated as lo* as >9@.


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=. 1ea,a#e Curret

T"e dielectric used inside t"e capacitor to separate t"e conducti#e plates is not a per!ect

insulator resulting in a #ery small current !lo*ing or lea+ing t"roug" t"e dielectric dueto t"e in!luence o! t"e po*er!ul electric !ields built up by t"e c"arge on t"e plates *"en

applied to a constant supply #oltage. T"is small C current !lo* in t"e region o! nano-

amps 'n( is called t"e capacitors 1ea,a#e Curret. 3ea+age current is a result o!

electrons p"ysically ma+ing t"eir *ay t"roug" t"e dielectric medium) around its edges or

across its leads and *"ic" *ill o#er time !ully disc"arging t"e capacitor i! t"e supply

#oltage is remo#ed.

0"en t"e lea+age is #ery lo* suc" as in !ilm or !oil type capacitors it is generally

re!erred to as insulation resistance ' Rp( and can be expressed as a "ig" #alue resistance

in parallel *it" t"e capacitor as s"o*n. 0"en t"e lea+age current is "ig" as inelectrolytic2s it is re!erred to as a lea+age current as electrons !lo* directly t"roug" t"e

electrolyte.

Capacitor lea+age current is an important parameter in ampli!ier coupling circuits or in

po*er supply circuits) *it" t"e best c"oices !or coupling and


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>. or,i# Temperature! 6T7

C"anges in temperature around t"e capacitor a!!ect t"e #alue o! t"e capacitance because

o! c"anges in t"e dielectric properties. I! t"e air or surrounding temperature becomes to

"ot or to cold t"e capacitance #alue o! t"e capacitor may c"ange so muc" as to a!!ect t"e

correct operation o! t"e circuit. T"e normal *or+ing range !or most capacitors is

-;]C to L9?B]C *it" nominal #oltage ratings gi#en !or a or,i# Temperatureo! no

more t"an LQ;]C especially !or t"e plastic capacitor types.

enerally !or electrolytic capacitors and especially aluminium electrolytic capacitor) at

"ig" temperatures 'o#er LB]C t"e li/uids *it"in t"e electrolyte can be lost to

e#aporation) and t"e body o! t"e capacitor 'especially t"e small si6es( may become

de!ormed due to t"e internal pressure and lea+ outrig"t. lso) electrolytic capacitors can

not be used at lo* temperatures) belo* about -9;]C) as t"e electrolyte ,elly !ree6es.

?. Temperature Coefficiet! 6TC7

T"e Temperature Coefficieto! a capacitor is t"e maximum c"ange in its capacitance

o#er a speci!ied temperature range. T"e temperature coe!!icient o! a capacitor is

generally expressed linearly as parts per million per degree centigrade 'PP


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@. Po"ari(atio

Capacitor Po"ari(atiogenerally re!ers to t"e electrolytic type capacitors but mainly t"e

luminium $lectrolytic2s) *it" regards to t"eir electrical connection. T"e ma,ority o!

electrolytic capacitors are polari6ed types) t"at is t"e #oltage connected to t"e capacitor

terminals must "a#e t"e correct polarity) i.e. positi#e to positi#e and negati#e to negati#e.

Incorrect polari6ation can cause t"e oxide layer inside t"e capacitor to brea+ do*nresulting in #ery large currents !lo*ing t"roug" t"e de#ice resulting in destruction as *e

"a#e mentioned earlier.

T"e ma,ority o! electrolytic capacitors "a#e t"eir negati#e) -#eterminal clearly mar+ed

*it" eit"er a blac+ stripe) band) arro*s or c"e#rons do*n one side o! t"eir body as

s"o*n) to pre#ent any incorrect connection to t"e C supply.

Some larger electrolytic2s "a#e t"eir metal can or body connected to t"e negati#e terminal

but "ig" #oltage types "a#e t"eir metal can insulated *it" t"e electrodes being broug"t

out to separate spade or scre* terminals !or sa!ety.

lso) *"en using aluminium electrolytic2s in po*er supply smoot"ing circuits care

s"ould be ta+en to pre#ent t"e sum o! t"e pea+ C #oltage and C ripple #oltage !rom

becoming a re#erse #oltage.

. E%ui3a"et Series Resistace! 6ESR7

T"e E%ui3a"et Series Resistaceor ESR) o! a capacitor is t"e C impedance o! t"e

capacitor *"en used at "ig" !re/uencies and includes t"e resistance o! t"e dielectric

material) t"e C resistance o! t"e terminal leads) t"e C resistance o! t"e connections tot"e dielectric and t"e capacitor plate resistance all measured at a particular !re/uency and

temperature.

$SR odel


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In some *ays) $SR is t"e opposite o! t"e insulation resistance *"ic" is presented as a

pure resistance 'no capaciti#e or inducti#e reactance( in parallel *it" t"e capacitor. n

ideal capacitor *ould "a#e only capacitance but $SR is presented as a pure resistance

'less t"an ;.97( in series *it" t"e capacitor '"ence t"e name $/ui#alent Series

Resistance() and *"ic" is !re/uency dependant ma+ing it a GIC /uantity.

s $SR de!ines t"e energy losses o! t"e e/ui#alent series resistance o! a capacitor it

must t"ere!ore determine t"e capacitor2s o#erall I?R "eating losses especially *"en used

in po*er and s*itc"ing circuits. Capacitors *it" a relati#ely "ig" $SR "a#e less ability to

pass current to and !rom its plates to t"e external circuit because o! t"eir longer c"arging

and disc"arging RC time constant. T"e $SR o! electrolytic capacitors increases o#er time

as t"eir electrolyte dries out. Capacitors *it" #ery lo* $SR ratings are a#ailable and are

best suited *"en using t"e capacitor as a !ilter.

s a !inal note) capacitors *it" small capacitances 'less t"an ;.;9 uF( generally do not

pose muc" danger to "umans. 4o*e#er) *"en t"eir capacitances start to exceed ;.9 uF)

touc"ing t"e capacitor leads can be a s"oc+ing experience. Capacitors "a#e t"e ability to

store an electrical c"arge in t"e !orm o! a #oltage across t"emsel#es e#en *"en t"ere is

no circuit current !lo*ing) gi#ing t"em a sort o! memory *it" large electrolytic type

reser#oir capacitors !ound in tele#ision sets) p"oto !las"es and capacitor ban+s potentially

storing a let"al c"arge.

s a general rule o! t"umb) ne#er touc" t"e leads o! large #alue capacitors once t"e

po*er supply is remo#ed. I! you are unsure about t"eir condition or t"e sa!e "andling o!

t"ese large capacitors) see+ "elp or expert ad#ice be!ore "andling t"em.

Capacitace a* C'ar#e

0e sa* in t"e pre#ious tutorials t"at a Capacitorconsists o! t*o parallel conducti#e

plates 'usually a metal( *"ic" are pre#ented !rom touc"ing eac" ot"er 'separated( by an

insulating material called t"e dielectric. 0e also sa* t"at *"en a #oltage is applied to

t"ese plates an electrical current !lo*s c"arging up one plate *it" a positi#e c"arge *it"

respect to t"e supply #oltage and t"e ot"er plate *it" an e/ual and opposite negati#e

c"arge.

T"en) a capacitor "as t"e ability o! being able to store an electrical c"arge % 'units

in Cou"om)s( o! electrons. 0"en a capacitor is !ully c"arged t"ere is a potential

di!!erence) p.d. bet*een its plates) and t"e larger t"e area o! t"e plates and


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T"e Capacitors ability to store t"is electrical c"arge ' % ( bet*een its plates is

proportional to t"e applied #oltage) V !or a capacitor o! +no*n capacitance in Farads.

Capacitance C is al*ays positi#e and ne#er negati#e. T"e greater t"e applied #oltage t"e

greater *ill be t"e c"arge stored on t"e plates o! t"e capacitor. 3i+e*ise) t"e smaller t"e

applied #oltage t"e smaller t"e c"arge. T"ere!ore) t"e actual c"arge% on t"e plates o! t"e

capacitor and can be calculated asO

C'ar#e o a Capacitor

0"ereO % 'C"arge) in Coulombs( K C 'Capacitance) in Farads( x V 'Voltage) in Volts(

It is sometimes easier to remember t"is relations"ip by using pictures. 4ere t"e t"ree

/uantities o! %)C and V "a#e been superimposed into a triangle gi#ing c"arge at t"e top*it" capacitance and #oltage at t"e bottom. T"is arrangement represents t"e actual

position o! eac" /uantity in t"e Capacitor Charge!ormulas.

and transposing t"e abo#e e/uation gi#es us t"e !ollo*ing combinations o! t"e same

e/uationO

nits o!O % measured in Coulombs) V in #olts and C in Farads.


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T"en !rom abo#e *e can de!ine t"e unit o! Capacitaceas being a constant o!

proportionality being e/ual to t"e coulomb


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Para""e" P"ate Capacitor

0e "a#e said pre#iously t"at t"e capacitance o! a parallel plate capacitor is proportionalto t"e sur!ace area and in#ersely proportional to t"e distance) d bet*een t"e t*o plates

and t"is is true !or dielectric medium o! air. 4o*e#er) t"e capacitance #alue o! a

capacitor can be increased by inserting a solid medium in bet*een t"e conducti#e plates

*"ic" "as a dielectric constant greater t"an t"at o! air.

Typical #alues o! epsilon Y !or #arious commonly used dielectric materials

areO ir K 9.;) Paper K ?.B - .B) lass K - 9;) ica K B - Q etc.

T"e !actor by *"ic" t"e dielectric material) or insulator) increases t"e capacitance o! t"e

capacitor compared to air is +no*n as t"e /ie"ectric Costat) ',(. + is t"e ratio o! t"epermitti#ity o! t"e dielectric medium being used to t"e permitti#ity o! !ree space

ot"er*ise +no*n as a #acuum. T"ere!ore) all t"e capacitance #alues are related to t"e

permitti#ity o! #acuum. dielectric material *it" a "ig" dielectric constant is a better

insulator t"an a dielectric material *it" a lo*er dielectric constant. ielectric constant is

a dimensionless /uantity since it is relati#e to !ree space.


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E+amp"e No5

parallel plate capacitor consists o! t*o plates *it" a total sur!ace area o! 9;; cm?. 0"at

*ill be t"e capacitance in pico-Farads) 'pF( o! t"e capacitor i! t"e plate separation is ;.?

cm) and t"e dielectric medium used is air.

t"en t"e #alue o! t"e capacitor is AApF.

C'ar#i# 9 /isc'ar#i# of a Capacitor

Consider t"e !ollo*ing circuit.

ssume t"at t"e capacitor is !ully disc"arged and t"e s*itc" connected to t"e capacitor

"as ,ust been mo#ed to position . T"e #oltage across t"e 9;;u! capacitor is 6ero at t"is

point and a c"arging current ' i ( begins to !lo* c"arging up t"e capacitor until t"e

#oltage across t"e plates is e/ual to t"e 9?# supply #oltage. T"e c"arging current stops

!lo*ing and t"e capacitor is said to be !ully-c"arged.

T"en) Vc K Vs K 9?#.


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1nce t"e capacitor is !ully-c"arged in t"eory it *ill maintain its state o! #oltage c"arge

e#en *"en t"e supply #oltage "as been disconnected as t"ey act as a sort o! temporary

storage de#ice. 4o*e#er) *"ile t"is may be true o! an ideal capacitor) a real capacitor

*ill slo*ly disc"arge itsel! o#er a long period o! time due to t"e internal lea+age currents

!lo*ing t"roug" t"e dielectric. T"is is an important point to remember as large #alue

capacitors connected across "ig" #oltage supplies can still maintain a signi!icant amount

o! c"arge e#en *"en t"e supply #oltage is s*itc"ed 1FF.

I! t"e s*itc" *as disconnected at t"is point) t"e capacitor *ould maintain its c"arge

inde!initely) but due to internal lea+age currents !lo*ing across its dielectric t"e capacitor

*ould #ery slo*ly begin to disc"arge itsel! as t"e electrons passed t"roug" t"e dielectric.

T"e time ta+en !or t"e capacitor to disc"arge do*n to Q@ o! its supply #oltage is +no*n

as itsTime Costat.

I! t"e s*itc" is no* mo#ed !rom position to position H) t"e !ully c"arged capacitor

*ould start to disc"arge t"roug" t"e lamp no* connected across it) illuminating t"e lamp

until t"e capacitor *as !ully disc"arged as t"e element o! t"e lamp "as a resisti#e #alue.

T"e brig"tness o! t"e lamp and t"e duration o! illumination *ould ultimately depend

upon t"e capacitance #alue o! t"e capacitor and t"e resistance o! t"e lamp 't K C x R(.

T"e larger t"e #alue o! t"e capacitor t"e brig"ter and longer *ill be t"e illumination o!

t"e lamp as it could store more c"arge.

Curret t'rou#' a Capacitor

T"e current t"at !lo*s t"roug" a capacitor is directly related to t"e c"arge on t"e plates as

current is t"e rate o! !lo* o! c"arge *it" respect to time. s t"e capacitors ability to store

c"arge '%( bet*een its plates is proportional to t"e applied #oltage 'V() t"e relations"ip

bet*een t"e current and t"e #oltage t"at is applied to t"e plates o! a capacitor becomesO

Curret-Vo"ta#e 6I-V7 Re"atios'ip

s t"e #oltage across t"e plates increases 'or decreases( o#er time) t"e current !lo*ing

t"roug" t"e capacitance deposits 'or remo#es( c"arge !rom its plates *it" t"e amount o!

c"arge being proportional to t"e applied #oltage. T"en bot" t"e current and #oltage

applied to a capacitance are !unctions o! time and are denoted by t"e
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symbols) i't(and #'t( 4o*e#er) !rom t"e abo#e e/uation *e can also see t"at i! t"e

#oltage remains constant) t"e c"arge *ill become constant and t"ere!ore t"e current *ill

be 6ero[. In ot"er *ords) no c"ange in #oltage) no mo#ement o! c"arge and no !lo* o!

current. T"is is *"y a capacitor appears to bloc+ current !lo* *"en connected to a

steady state C #oltage.

T'e $ara*

0e no* +no* t"at t"e ability o! a capacitor to store a c"arge gi#es it its capacitance

#alue C) *"ic" "as t"e unit o! t"e $ara*! $. Hut t"e !arad is an extremely large unit on its

o*n ma+ing it impractical to use) so submultiple2s or !ractions o! t"e standard Farad unit

are used instead. To get an idea o! "o* big a Farad really is) t"e sur!ace area o! t"e plates

re/uired to produce a capacitor *it" a #alue o! one Farad *it" a reasonable plate

separation o! ,ust 9mm operating in a #acuum and rearranging t"e e/uation !or

capacitance abo#e *ould beO

K Cd .BpF


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Con#ert t"e !ollo*ing capacitance #alues !rom a( 88$to u$) b( .8u$to $)

c( >>p$to u$.

a( ??nF K ;.;??uF

b( ;.?uF K ?;;nF

c( BB;pF K ;.;;;BBuF

0"ile one Farad is a large #alue on its o*n) capacitors are no* commonly a#ailable *it"

capacitance #alues o! many "undreds o! Farads and "a#e names to re!lect t"is o! Super

capacitors or ltra capacitors. T"ese capacitors are electroc"emical energy storage

de#ices *"ic" utili6e a "ig" sur!ace area o! t"eir carbon dielectric to deli#er muc" "ig"er

energy densities t"an con#entional capacitors and as capacitance is proportional to t"e

sur!ace area o! t"e carbon) t"e t"ic+er t"e carbon t"e more capacitance it "as.

3o* #oltage '!rom about .BV to B.BV( super capacitors are capable o! storing large

amounts o! c"arge due to t"eir "ig" capacitance #alues as t"e energy stored in a capacitor

is e/ual to 9


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so t"e energy stored in t"e 9;;uF capacitor circuit abo#e is calculated asO

T"e next tutorial in our section about Capacitors) *e loo+ at Capacitor Co"our

Co*esand see t"e di!!erent *ays t"at t"e capacitance and #oltage #alues o! t"e capacitor

are mar+ed onto its body.

Capacitor Co"our Co*es

enerally) t"e actual #alues o! Capacitance) Voltage or Tolerance are mar+ed onto t"e

body o! t"e capacitors in t"e !orm o! alp"anumeric c"aracters. 4o*e#er) *"en t"e #alue

o! t"e capacitance is o! a decimal #alue problems arise *it" t"e mar+ing o! a ecimal

Point as it could easily not be noticed resulting in a misreading o! t"e actual #alue.

Instead letters suc" as p 'pico( or n 'nano( are used in place o! t"e decimal point to

identi!y its position and t"e *eig"t o! t"e number.

For example) a capacitor can be labelled as) nAQ K ;.AQnF) AnQ K A.QnF or AQn K AQnF

and so on. lso) sometimes capacitors are mar+ed *it" t"e capital letter Z to signi!y a

#alue o! one t"ousand pico-Farads) so !or example) a capacitor *it" t"e mar+ings

o! 9;;Z *ould be 9;; x 9;;;pF or 9;;nF.

To reduce t"e con!usion regarding letters) numbers and decimal points) an International

colour coding sc"eme *as de#eloped many years ago as a simple *ay o! identi!ying

capacitor #alues and tolerances. It consists o! coloured bands 'in spectral order( +no*n

commonly as t"e Capacitor Co"our Co*esystem and *"ose meanings are illustrated

belo*O
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Capacitor Co"our Co*e Ta)"e

Colourigit

igit

H

ultiplier

Tolerance

'T( : 9;p!

Tolerance

'T( 8 9;p!

Temperature

Coe!!icient

'TC(Hlac+ ; ; x9 > ?;@ > ?.;pF

Hro*n 9 9 x9; > 9@ > ;.9pF -x9;-=

Red ? ? x9;; > ?@ > ;.?BpF -QBx9;-=

1range x9);;; > @ -9B;x9;-=

ello* A A x9;);;; > A@ -??;x9;-=

reen B B x9;;);;; > B@ > ;.BpF -;x9;-=

Hlue = = x9);;;);;; -AQ;x9;

-=

Violet Q Q -QB;x9;-=

rey x;.;9L;@)-

?;@

0"ite E E x;.9 > 9;@ > 9.;pF

old x;.9 > B@

Sil#er x;.;9 > 9;@

Capacitor Vo"ta#e Co"our Co*e Ta)"e

ColourVoltage Rating 'V(

Type W Type Z Type 3 Type Type G

Hlac+ A 9;; 9; 9;

Hro*n = ?;; 9;; 9.=

Red 9; ;; ?B; A B

1range 9B A;; A;

ello* ?; B;; A;; =. =

reen ?B =;; 9= 9B

Hlue B Q;; =; ?;


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Violet B; ;;

rey E;; ?B ?B

0"ite 9;;; ?.B

old ?;;;

Sil#er

Capacitor Vo"ta#e Referece

Type W - ipped Tantalum Capacitors.

Type Z - ica Capacitors.

Type 3 - Polyester


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T"e Capacitor Co"our Co*esystem *as used !or many years on unpolarised polyester

and mica moulded capacitors. T"is system o! colour coding is no* obsolete but t"ere are

still many old capacitors around. Go*adays) small capacitors suc" as !ilm or dis+ types

con!orm to t"e HS9B? Standard and its ne* replacement) HS $G =;;=?) *ere t"e

colours "a#e been replaced by a letter or number coded system.

enerally t"e code consists o! ? or numbers and an optional tolerance letter code to

identi!y t"e tolerance. 0"ere a t*o number code is used t"e #alue o! t"e capacitor only is

gi#en in pico!arads) !or example) AQ K AQ pF and 9;; K 9;;pF etc. t"ree letter code

consists o! t"e t*o #alue digits and a multiplier muc" li+e t"e resistor colour codes in t"e

resistors section.

For example) t"e digits AQ9 K AQ^9; K AQ;pF. T"ree digit codes are o!ten accompanied

by an additional tolerance letter code as gi#en belo*.

Capacitor To"erace 1etter Co*es Ta)"e

3etter H C F W Z

ToleranceC 89;pF >pF ;.9 ;.?B ;.B 9 ?

C :9;pF >@ ;.B 9 ? B 9; ?; L;-?;

Consider t"e capacitor belo*O

T"e capacitor on t"e le!t is o! a ceramic disc type capacitort"at "as t"e code AQW printed onto its body. T"en t"e A K

9stdigit) t"e Q K ?nddigit)

t"e is t"e multiplier in pico-Farads) pF and t"e letter W is t"e

tolerance and t"is translates toO

AQpF ^ 9);;; ' 6ero2s( K AQ);;; pF ) AQnF or ;.;AQ uF

t"e W indicates a tolerance o! L


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Capacitor 1etter Co*es Ta)"e

Picofara*

6p$7

Naofara*

6$7

Microfara*

6u$7Co*e

Picofara*

6p$7

Naofara*

6$7

Microfara*

6u$7Co*e

9; ;.;9 ;.;;;;9 9;; AQ;; A.Q ;.;;AQ AQ?

9B ;.;9B ;.;;;;9B 9B; B;;; B.; ;.;;B B;?

?? ;.;?? ;.;;;;?? ??; B=;; B.= ;.;;B= B=?

;.; ;.;;;; ; =;; =. ;.;;= =?

AQ ;.;AQ ;.;;;;AQ AQ; 9;;;; 9; ;.;9 9;

9;; ;.9 ;.;;;9 9;9 9B;;; 9B ;.;9B 9B

9?; ;.9? ;.;;;9? 9?9 ??;;; ?? ;.;?? ??

9; ;.9 ;.;;;9 99 ;;; ;.;

9B; ;.9B ;.;;;9B 9B9 AQ;;; AQ ;.;AQ AQ

9; ;.9 ;.;;;9 99 =;;; = ;.;= =

??; ;.?? ;.;;;?? ??9 9;;;;; 9;; ;.9 9;A

; ;. ;.;;; 9 9B;;;; 9B; ;.9B 9BA

AQ; ;.AQ ;.;;;AQ AQ9 ?;;;;; ?;; ;.? ?BA

B=; ;.B= ;.;;;B= B=9 ??;;;; ??; ;.?? ??A

=; ;.= ;.;;;= =9 ;;;; ; ;. A

QB; ;.QB ;.;;;QB QB9 AQ;;;; AQ; ;.AQ AQA

?; ;.? ;.;;;? ?9 =;;;; =; ;.= =A

9;;; 9.; ;.;;9 9;? 9;;;;;; 9;;; 9.; 9;B

9B;; 9.B ;.;;9B 9B? 9B;;;;; 9B;; 9.B 9BB

?;;; ?.; ;.;;? ?;? ?;;;;;; ?;;; ?.; ?;B

??;; ?.? ;.;;?? ??? ??;;;;; ??;; ?.? ??B

;; . ;.;; ? ;;;;; ;; . B

T"e next tutorial in our section about Capacitors) *e loo+ at connecting

toget"er Capacitor i Para""e"and see t"at t"e total capacitance is t"e sum o! t"e

indi#idual capacitors.
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Capacitors i Para""e"

Capacitors are said to be connected toget"er in parallel *"en bot" o! t"eir terminals are

respecti#ely connected to eac" terminal o! t"e ot"er capacitor or capacitors. T"e #oltage

' Vc ( connected across all t"e capacitors t"at are connected in parallel is TDE SAME.

T"en) Capacitors i Para""e""a#e a common #oltage supply across t"em gi#ing

VC9K VC?K VCK VHK 9?V

In t"e !ollo*ing circuit t"e capacitors) C9) C?and Care all connected toget"er in a

parallel branc" bet*een points and H as s"o*n.

0"en capacitors are connected toget"er in parallel t"e total or e/ui#alent

capacitance) CTin t"e circuit is e/ual to t"e sum o! all t"e indi#idual capacitors added

toget"er. T"is is because t"e top plate o! capacitor) C9is connected to t"e top plate

o! C?*"ic" is connected to t"e top plate o! Cand so on. T"e same is also true o! t"e

bottom plates. T"en it is t"e same as i! t"e t"ree sets o! plates *ere touc"ing eac" ot"er

and e/ual to one large single plate t"ereby increasing t"e e!!ecti#e plate area in m?.

Since capacitance) C is related to plate area ' C K Y


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and t"is can be re-*ritten asO

T"en *e can de!ine t"e total or e/ui#alent circuit capacitance) CTas being t"e sum o! all

t"e indi#idual capacitances add toget"er gi#ing us t"e generali6ed e/uation o!

Para""e" Capacitors E%uatio

0"en adding toget"er capacitors in parallel) t"ey must all be con#erted to t"e same

capacitance units) *"et"er it is uF) nF or pF. lso) *e can see t"at t"e current !lo*ing

t"roug" t"e total capacitance #alue)CTis t"e same as t"e total circuit current) iT

0e can also de!ine t"e total capacitance o! t"e parallel circuit !rom t"e total stored

coulomb c"arge using t"e % K CV e/uation !or c"arge on a capacitors plates. T"e total

c"arge %Tstored on all t"e plates e/uals t"e sum o! t"e indi#idual stored c"arges on eac"

capacitor t"ere!ore)


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s t"e #oltage) ' V ( is common !or parallel connected capacitors) *e can di#ide bot"

sides o! t"e abo#e e/uation t"roug" by t"e #oltage lea#ing ,ust t"e capacitance and by

simply adding toget"er t"e #alue o! t"e indi#idual capacitances gi#es t"e total

capacitance) CT. lso) t"is e/uation is not dependant upon t"e number o! Capacitors i

Para""e"in t"e branc") and can t"ere!ore be generali6ed !or any number o!G parallel

capacitors connected toget"er.

E+amp"e No5

So by ta+ing t"e #alues o! t"e t"ree capacitors !rom t"e abo#e example) *e can calculate

t"e total e/ui#alent circuit capacitance CTas beingO

CTK C9L C?L C K ;.9uF L ;.?uF L ;.uF K ;.=uF

1ne important point to remember about parallel connected capacitor circuits) t"e total

capacitance ' CT( o! any t*o or more capacitors connected toget"er in parallel *ill

al*ays be 4REATERt"an t"e #alue o! t"e largest capacitor in t"e group as *e are

adding toget"er #alues. So in our example abo#e CTK ;.=uF *"ereas t"e largest #alue

capacitor is only ;.uF.

0"en A) B) = or e#en more capacitors are connected toget"er t"e total capacitance o! t"e

circuit CT*ould still be t"e sum o! all t"e indi#idual capacitors added toget"er and as *e

+no* no*) t"e total capacitance o! a parallel circuit is al*ays greater t"an t"e "ig"est

#alue capacitor. T"is is because *e "a#e e!!ecti#ely increased t"e total sur!ace area o! t"e

plates. I! *e do t"is *it" t*o identical capacitors) *e "a#e doubled t"e sur!ace area o! t"e

plates *"ic" inturn doubles t"e capacitance o! t"e combination and so on.


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E+amp"e No8.

Calculate t"e combined capacitance in micro-Farads 'uF( o! t"e !ollo*ing capacitors

*"en t"ey are connected toget"er in a parallel combinationO

a( t*o capacitors eac" *it" a capacitance o! AQnF

b( one capacitor o! AQ;nF connected in parallel to a capacitor o! 9uF

a( Total Capacitance)

CTK C9L C? K AQnF L AQnF K EAnF or ;.;EAuF

b( Total Capacitance)

CTK C9L C? K AQ;nF L 9uF

t"ere!ore) CTK AQ;nF L 9;;;nF K 9AQ;nF or 9.AQuF

So) t"e total or e/ui#alent capacitance) CTo! a circuit containing Capacitors i

Para""e"is t"e sum o! t"e all t"e indi#idual capacitances added toget"er and in our next

tutorial about Capacitors) *e loo+ at connecting toget"erCapacitors i Seriesand t"e

a!!ect t"is combination "as on t"e circuits total capacitance) #oltage and current.

Capacitors i Series

Capacitors are said to be connected toget"er in series *"en t"ey are e!!ecti#ely daisy

c"ained toget"er in a single line. T"e c"arging current ' iC( !lo*ing t"roug" t"e

capacitors is TDE SAME!or all capacitors as it only "as one pat" to !ollo*

and iTK i9K i?K ietc. T"en) Capacitors i Seriesall "a#e t"e same current so eac"

capacitor stores t"e same amount o! c"arge regardless o! its capacitance. T"is is because

ED I UNIT NOTES

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