Chapter27 Student

7/25/2019 Chapter27 Student

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Chapter 27. Current andChapter 27. Current and

ResistanceResistanceA PowerPoint Presentation byA PowerPoint Presentation by

Paul E. Tippens, Professor ofPaul E. Tippens, Professor ofPhysicsPhysics

Southern Polytechnic StateSouthern Polytechnic State

UniersityUniersity

!2""7


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#b$ecties%#b$ecties% After co&pletin'After co&pletin'this &odule, you should bethis &odule, you should be

able to%able to%( )e*ne)e*ne electric currentelectric currentandand

electro&otie forceelectro&otie force..

( +rite and apply+rite and apply #h&s law#h&s lawto circuitsto circuitscontainin' resistance and e&f.containin' resistance and e&f.

( )e*ne)e*ne resistiityresistiity of a &aterial andof a &aterial and

apply for&ulas for its calculation.apply for&ulas for its calculation.

( )e*ne and apply the concept of)e*ne and apply the concept of

te&perature coe-cient of resistancete&perature coe-cient of resistance..


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Electric CurrentElectric Current

Electric currentElectric current is theis the

rate of the /ow of char'erate of the /ow of char'e

00throu'h a cross1sectionthrou'h a cross1section

AA in a unit of ti&ein a unit of ti&e tt..

QI

t=

QI

t=

1C1 A

1 s=

1C1 A

1 s=

#ne#ne a&perea&

pereAAis char'e /owin'is char'e /owin'

at the rate of oneat the rate of one coulo&b percoulo&b per

secondsecond..

AA

11+ire+ire

00

tt


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E3a&ple 4.E3a

&ple 4.The electric current inThe electric current ina wire is 5 A. 6ow &any electronsa wire is 5 A. 6ow &any electrons/ow past a 'ien point in a ti&e of/ow past a 'ien point in a ti&e of s8 s8

9 5 A 9 5 A

;q

I q It

t

= =

;q

I q Itt

= =


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Conentional CurrentConentional Current

&a'ine a char'ed capacitor with&a'ine a char'ed capacitor with Q = CVQ = CVthat is allowed tothat is allowed to

dischar'e.dischar'e.Electron /ow%Electron /ow%TheThe

direction of edirection of e11 /owin'/owin'

fro& : to .fro& : to .Conentional current%Conentional current%The &otion of ;The &otion of ;

fro& to : has sa&efro& to : has sa&e

e.

11

1

Electron/ow

1 1

e1

Conentional/ow


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CurrentCurrent

The number of charges that pass through the area in timeThe number of charges that pass through the area in timettN = n(|N = n(|vv||t)(|A|)t)(|A|)

The total charge that passes through is q times this numberThe total charge that passes through is q times this number

q = qnq = qnvv AAtt

The current I =The current I =q/q/ tt

Current , I = qnCurrent , I = qn v Av A

Current Density , J = I /A = qnCurrent Density , J = I /A = qn vv


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Current DensityCurrent Density

The current density (associated with one type of chargeThe current density (associated with one type of charge

carriers) is defined as a product of the drift velocity, thecarriers) is defined as a product of the drift velocity, the

concentration of charge carriers and the charge of the carriers:concentration of charge carriers and the charge of the carriers:

J

J vd

=nq


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Electric Current in a ConductorElectric Current in a Conductor

In a conductor, current density is proportional to the electricIn a conductor, current density is proportional to the electricfield vectorfield vector

J E= (h!"s law)(h!"s law)

The constant of proportionalityThe constant of proportionality is called the conductivityis called the conductivityof the conductor.of the conductor.

#nder a steady flow of charged particles#nder a steady flow of charged particles

along a conductor, the current across anyalong a conductor, the current across any

cross section of the conductor has thecross section of the conductor has thesa!e value$sa!e value$

II

II

II

%e assign this value to the current in the%e assign this value to the current in the

conductor$conductor$


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Electro&otie BorceElectro&otie Borce

AA source of electro&otie force =e&f>source of electro&otie force =e&f>is a deice that uses che&ical,is a deice that uses che&ical,

&echanical or other ener'y to proide&echanical or other ener'y to proide

the potential di


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+ater Analo'y to EDB+ater Analo'y to EDB

&ow

pressure

Pump%ater

'igh

pressure

alve%ater

low

Constriction

Source ofEDB

Resistor

'igh

potential

&ow

potential

*witch

E

RI

1

TheThe source of e&fsource of e&f=pu&p> proides the=pu&p> proides the

olta'eolta'e=pressure> to force=pressure> to force electronselectrons=water> throu'h electric=water> throu'h electric resistanceresistance

=narrow constriction>.=narrow constriction>.


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Electrical Circuit Sy&bolsElectrical Circuit Sy&bols

Electrical circuitsElectrical circuitsoften contain one oroften contain one or

&ore resistors 'rouped to'ether and&ore resistors 'rouped to'ether and

attached to an ener'y source, such asattached to an ener'y source, such as

a battery.a battery.The followin' sy&bols are oftenThe followin' sy&bols are often

used%used%

+ - + -- + - + -

+round attery-+

-esistor


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Electric ResistanceElectric Resistance

Suppose we apply a constant potentialSuppose we apply a constant potentialdi


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#h&s Gaw#h&s Gaw

#h&s law#h&s lawstates that the currentstates that the current throu'h a 'ien conductor is directlythrou'h a 'ien conductor is directly

proportional to the potential di


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E3a&ple 2.E3a&ple 2. +hen a+hen a 1@1@battery isbattery is

connected to a li'ht, a current ofconnected to a li'ht, a current of 55&A&Ais obsered. +hat is theis obsered. +hat is theresistance of the li'ht *la&ent8resistance of the li'ht *la&ent8

Source ofEDB

R

I

1

V = 3 @

5 &A


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A&&eterA&&eter@olt&eter@olt&eter RheostatRheostatSourceSource

of EDBof EDB

-heostat

A

Gaboratory Circuit Sy&bolsGaboratory Circuit Sy&bols

@ .!f

-

+


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Bactors A


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Bactors A

. The. The te&perature Tte&perature Tof the &aterial.of the &aterial.The hi'her te&peratures usuallyThe hi'her te&peratures usually

result inresult in hi'herhi'herresistances.resistances.

. The Hind of. The Hind of &aterial&aterial. ron has &ore. ron has &ore

electrical resistance than aelectrical resistance than a

'eo&etrically si&ilar copper'eo&etrically si&ilar copperconductor.conductor.

RRoo R I RR I R

oo

RRiiI RI RccCopperCopper ronron


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Resistiity of a DaterialResistiity of a Daterial

TheThe resistivityresistivity is a property of ais a property of a&aterial that deter&ines its electrical&aterial that deter&ines its electrical

resistanceresistance RR..Recallin' thatRecallin' that RRis directlyis directly

proportional to len'thproportional to len'th LLandandinersely proportional to areainersely proportional to areaAA,,

we &ay write%we &ay write%

or

L RA

R A L = = or

L RA

R A L = =

The unit of resistiity is theThe unit of resistiity is the oh&1&eteroh&1&eter

==

&>


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E3a&ple .E3a&ple .+hat+hat len'thlen'thLLof copper wireof copper wire

is re;uired to produce ais re;uired to produce a & & resistor8resistor8Assu&e the dia&eter of the wire isAssu&e the dia&eter of the wire is 44

&&&& and that the resistiityand that the resistiity of copper isof copper is4.72 3 4"4.72 3 4"1J1J ..&&..

LR

A=

LR

A=

Re;uired len'th is%Re;uired len'th is%


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Te&perature Coe-cientTe&perature Coe-cient

Bor &ost &aterials, the resistanceBor &ost &aterials, the resistance RRchan'es in proportion to the initialchan'es in proportion to the initial

resistanceresistance Roand to the chan'e inand to the chan'e in

te&peraturete&perature tt..

/R R t = /R R t = Chan'e inChan'e in

resistance%resistance%

TheThe te&perature coe-cient ofte&perature coe-cient of

resistance,resistance, is the chan'e in resistanceis the chan'e in resistance

per unit resistance per unit de'reeper unit resistance per unit de'reechan'e of te&perature.chan'e of te&perature.

/

/

1; #nits:

C

R

R t

=

/

/

1; #nits:

C

R

R t

=


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E3a&ple .E3a&ple . The resistance of a copperThe resistance of a copperwire iswire is ."" &."" &atat 2"2"""CC. +hat will be its. +hat will be its

resistance if heated toresistance if heated to J"J"""CC8 Assu&e8 Assu&ethatthat 9 "."" ?C9 "."" ?Coo..


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ConductiityConductiity

AA ConductiityConductiity &easures of a&aterialKs ability to conduct anelectric current

1 1 or

= =

1 1 or

= =


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Electric PowerElectric Power

Electric powerElectric powerPP is the rate at whichis the rate at whichelectric ener'y is e3pended, or worH perelectric ener'y is e3pended, or worH per

unit of ti&e.unit of ti&e.

V q

V

To char'e C% +orH 9To char'e C% +orH 9

;@;@ and

or! qV q" I

t t t= = =

SubstituteSubstitute q = It ,q = It ,

then%then%VIt"

t= P = VI

I


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Calculatin' PowerCalculatin' Power

Usin' #h&s law, we can *nd electricUsin' #h&s law, we can *nd electric

powerpowerfro& any two of the followin'fro& any two of the followin'

para&eters%para&eters% currentcurrent II,, olta'eolta'eVV, and, andresistanceresistanceRR..#h&s law%#h&s law% V = IRV = IR

0

0; ; V" VI " I R "R

= = =

0

0; ;V

" VI " I R "R

= = =


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E3a&ple M.E3a&ple M. A power tool is rated atA power tool is rated at N AN Awhen used with a circuit that proideswhen used with a circuit that proides

42"[email protected]"1@.+hat power is used in operatin'+hat power is used in operatin'this tool8this tool8

E3a&ple 5.E3a&ple 5. A M""1+ heater draws aA M""1+ heater draws acurrent of 4" A. +hat is the resistance8current of 4" A. +hat is the resistance8


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Su&&ary of Bor&ulasSu&&ary of Bor&ulas

QIt

=QIt

= 1C1 A1 s

=1C1 A1 s

=Electriccurrent%Electriccurrent%

; ;V V

I V IR R

R I

= = =; ;V V

I V IR R

R I

= = =

#h&s Gaw#h&s Gaw

1 volt-esistance: 1 oh!

1 a!pere=

1 volt-esistance: 1 oh!

1 a!pere=


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Te&perature coe-cient ofresistance%

Te&perature coe-cient ofresistance%

Su&&ary =Cont.>Su&&ary =Cont.>

orL RARA L

= = orL RARA L

= =

/

/

1; #nits:

C

R

R t

=

/

/

1; #nits:

C

R

R t

=

00; ;

V" VI " I R "

R= = =

00; ;

V" VI " I R "

R= = =

/R R t =

ResistiityResistiityofof

&aterials%&aterials%

ResistiityResistiityofof

&aterials%&aterials%

ElectricPower P:

ElectricPower P:


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C#OCGUS#O% Chapter 27C#OCGUS#O% Chapter 27

Current and ResistanceCurrent and Resistance

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Chapter27 Student

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