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Co py r ight © 2002,1997,1993by TheMcGr aw-HillCom panies,Inc.Allr ightsr eserved.Manuf acturedin

theUnitedStatesofAm er ica.Exce ptasper m ittedundertheUnitedStatesCo py r ightActof1976,nopar tofthispu blicationm ay ber e pr oducedordistr i butedin any f or m orby any means,orstor edinadata base

orr etr ievalsy stem ,withoutthepr iorwr ittenper m issionofthepu blisher .

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tr adem ar kowner ,withnointentionofinf r ingem entof thetr adem ar k .Wher esuchdesignationsa ppearin

thisbook ,they havebeenpr intedwithinitialca ps.

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TER MSOFUSE

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THEWOR KISPR OVIDED"ASIS."McGR AW-HILLA NDITSLICE NSOR SMAK ENO

GUAR A NTEESORWAR R A NTIESASTOTHEACCUR ACY,ADEQUACYORCOMPLETE NESS

OFORR ESULTSTOBEOBTAI NEDFR OMUSI NGTHEWOR K ,I NCLUDI NGA NY

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Continued 

Element name Abrev iation Atomic number Atomiceight*

Lead Pb 8 2Lithium Li 3 7

Lutetium Lu 7 1

Magnesium Mg 1 2

Manganese Mn 2 5

Mendelev ium* Md 1 2

Mercury Hg 8 2

Molydenum Mo 4 9

Neodyium Nd 6 1Neon Ne 1 2

Neptunium* Np 9 2

Nickel Ni 2 5

Niobium Nb 4 9

Nitrogen N 7 1

Nobelium* No 1 2

Osmium Os 7 1

Oxen O 8 1

 Palladium Pd 4 1

 Phosphorus P 1 3

 Platinum Pt 7 1

 Plutonium* Pu 9 2

 Polonium Po 8 2

 Potassium K 1 3

 Praseodyium Pr 5 1

 Promethium Pm 6 1

 Protactinium Pa 9 2

Radium Ra 8 2

Radon Rn 8 2

Rhenium Re 7 1

Rhodium Rh 4 1

Rubidium Rb 3 8

Ruthenium Ru 4 1

Samarium Sm 6 1

Scandium Sc 2 4Selenium Se 3 8

Silicon Si 1 2

Silver A 4 1

Sodium Na 1 2

t ontiu

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Continued 

Element name Abrev iation Atomic number Atomiceight*

Tin Sn 5 1Titanium Ti 2 4

Tungsten W 7 1

Unnilhex ium* Unh 1

Unnilpentium* Unp 1

Unnilquadium* Unq 1

Uranium U 9 2

Vanadium V 2 5

Xenon Xe 5 1Ytterbium Yb 7 1

Yttrium Y 3 8

Zinc Zn 3 6

Zirconium Zr 4 9

*ost ommon isotope.he umofthe numberof rotons ndthe numberof neutrons inthe nucleus.ostelements

haveother isotopes ithdifferent tomiceights.

*heseelements tomic numbersor arger)re not ound in nature,ut re uman-ade.

1 A nearlyodelofthe

atom,developed boutthe

year endered 

electrons ike lanets nd 

the nucleus ikethe un in

miniature olar ytem.

Electric harge ttraction

kepttheelectrons rom

fly ing wy

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8 Direct-urrent ircuit nalyis

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 Problem

In ig.there re esistors.ive of them ave lues of ,nd the other ive

have luesof .he ower ource is dc.hat istheoltage crossoneofthe

1 resistors?rossoneofthe resistors?

First,indthetotal esistance: R ( 5 ( 5 5 1 1 .hen

findthe urrent: I E/ 1 0 1Ahis isthe urrentthrougheach

ofthe esistors inthe ircuit.

If n 1 ,then n I(n) 0 1 1.

If n 2 ,then n I(n) 0 2 2.

You can check to see wether all of these voltages add up to the supplyvoltage.

There re ive esistors ith crosseach,or totalof ;there re lso ive e-

sistors ith crosseach,or totalof .othe umoftheoltages crossthe

i t i

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 Problem

In ig.upposeeachofthetwo esistors elowoint as lueof ,nd all three esistors bove re .he urrent through each resistor is

mAhat isthe urrentthrough nyofthe resistors,ssuming it isequallydis-

Kirchhoff econd aw 9

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tributed?hat istheoltage,then,cross nyofthe resistors?

Thetotal urrent into is AA 1his ust ediv idedthree

wyequallymongthe resistors.herefore,the urrentthrough nyoneofthem

 is 0 3A

Theoltage cross nyoneof the resistors is ound yhm aw E IR

  0 1 3.

Kirchhoff econd aw

The umof lltheoltages,sou o round ircuit rom ome ixed oint nd eturn

there romtheoppositedirection,ndtaking olarity into ccount, is lwyero.

This ight ound trange.urelythere isoltage inour electric air dryer,or a-

dio,or omputer.es,there is,etweendifferent oints.ut no oint an ave n MFw ith espect to itself.his is o imple that it lmost aughable.oint in ircuit is

alwy hortedoutto itself.

What irchhoff eallys ay ing,en e ote is econd aw is ore eneral

versionofthe econd ndthird oints rev iouslyentioned.e easonedthatoltage

cannot ppearoutof nowere, nor an it nish.lthe otentialdifferences ust al-

anceout in nyircuit, no atter owomplicated nd no atter owanyranches

there re.

This is Kirchhoff econd aw A n lternative name ight ethe awof conser-

vtionofoltage.

Considerthe uleoue lreadyearned bout eries ircuits:heoltages cross ll

the indiv idual esistors dduptothe upplyoltage.es,theydo,utthe olaritiesofthe

EMFs crossthe esistors reoppositetothatofthe atteryhis is how n in ig.t

a ubtlething.ut it ecomes lear en eries ircuit isdraw n ith llthe omponents,

 includingthe atteryorother MF ource, in ine itheachother,s in ig.

 Probleme e tot edi o i u o et e ou e i to e ue o nd

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