eletrica_p13q09

]udstêa ><

]udstêa ><

 _‚

 _‚

 2>=:

 2>=:

m)

m)





 6 6    ==2299∜∜∫ ∫ ((∗ ∗ ::∜∜

_{++}

 + +



 ∜ ∜))





66    <<



∫ 

∫ 

_{++}

 + +









 6 6    <<

 ∫∫   =−



_{++}

 + +

  =−22

22 

66    <<

22  − −2222||



_{++}

 + +





 6 6    <<

22 ∜∜:: − −



00:: 2

 222:: 2

22

 2





22:: 2−

 2−00:: 2

 2

66 ∗  ∗ ::22 ∜ ∜22−−==22∜∜22∗ ∗ ::22 ∜ ∜22==22∜∜22



22:: 2−

 2−00::22  66 ∗  ∗ :∜

:∜22





 6 6    <<

22 ∜∜::  ∗ ∗ :∜



:∜22

22 6 :6 :



 ∜ ∜  ==99∗ ∗ ::22

??





 6 :(=28 ∜

 6 :(=28 ∜∗ ∗ 2)2)∜∜  ==99∗ ∗ :::>¾:>¾

00   6 4:?,?2

  6 4:?,?2  ==99∗ ∗ ::??





 6 ,

 6 ,  

  



 6 , 

 6 , 

 6  6 



 ∜ ∜



 6  

 6  

b)

b)





 6  6 ::



 ∜ ∜  ==99∗ ∗ ::22

00   6 :(=28

  6 :(=28∗ ∗ 2)2)  ==99−−∗ ∗ ::??





 6 ,

 6 ,  

  



 6 , 

 6 , 

 6  6 



 ∜ ∜



 6  

 6  

Mbmlxa vajç lrí dejaetrmr ms

Mbmlxa vajç lrí dejaetrmr ms

`÷vl`ms/rdspastms `as mcueas metlhas

`÷vl`ms/rdspastms `as mcueas metlhas

rdidrdetds î dssm qudstêa.

rdidrdetds î dssm qudstêa.

RDJAFDE@MFAZ IARPDFDEPD

RDJAFDE@MFAZ IARPDFDEPD

]TD CDLM PA@MZ DCMZ! 

]TD CDLM PA@MZ DCMZ! 

Jmsa mle`m tdeom iljm`a jaf `÷vl`ms, jaesuctd m

Jmsa mle`m tdeom iljm`a jaf `÷vl`ms, jaesuctd m

rdidrçejlm

rdidrçejlm

tdúrljm le`ljm`m

tdúrljm le`ljm`m pmrm dssm

pmrm dssm qudstêa, em

qudstêa, em

^CMELCOM @D RDIDRÇEJLMZ.

^CMELCOM @D RDIDRÇEJLMZ.

Yajç tmfbìf pa`drí imzdr a sdu jafdetírla, jrlme`a

Yajç tmfbìf pa`drí imzdr a sdu jafdetírla, jrlme`a

uf túplja eava `m sdhuletd iarfm7

uf túplja eava `m sdhuletd iarfm7

]udstêa - ^ravm - Plpa `d Jafdetírla

]udstêa - ^ravm - Plpa `d Jafdetírla

Pdrdfas : tlpas `d jafdetírla7

Pdrdfas : tlpas `d jafdetírla7

@÷vl`m

@÷vl`m

- ì uf `÷vl`m rdcmjlaem`m m rdsacuèêa `m

- ì uf `÷vl`m rdcmjlaem`m m rdsacuèêa `m

qudstêa;

qudstêa;

Drra

Drra

- ì uf passævdc drra qud vajç l`detliljau em

- ì uf passævdc drra qud vajç l`detliljau em

rdsacuèêa;

rdsacuèêa;

Jafpcdfdeta

Jafpcdfdeta

- ì ufm absdrvmèêa qud mhrdhm em

- ì ufm absdrvmèêa qud mhrdhm em

rdsacuèêa `m qudstêa jafa, par dxdfpca, ufm autrm

rdsacuèêa `m qudstêa jafa, par dxdfpca, ufm autrm

iarfm `d rdsacvç-cm au ufm autrm

iarfm `d rdsacvç-cm au ufm autrm

rdidrçejlm pmrm dcm

rdidrçejlm pmrm dcm

Detêa, sd vajç iar jafdetmr uf `÷vl`m em qudstêa >:

Detêa, sd vajç iar jafdetmr uf `÷vl`m em qudstêa >:

`m pravm `d 2>=0, vml jrlmr uf túplja jaf a sdhuletd

`m pravm `d 2>=0, vml jrlmr uf túplja jaf a sdhuletd

tætuca7

tætuca7

>: - 2>=0 - @÷vl`m

>: - 2>=0 - @÷vl`m

LEPDRMGM D RDZ^AE@M AZ JAFDEPÍRLAZ...

LEPDRMGM D RDZ^AE@M AZ JAFDEPÍRLAZ...

YAJÇ LRÍ M^RDE@DR FTLPA IMWDE@A LZZA 7)

YAJÇ LRÍ M^RDE@DR FTLPA IMWDE@A LZZA 7)

@×YL@MZ

@×YL@MZ

^ravm 2>=:

^ravm 2>=:

 _‚

 _‚

 ]udstêa ><

 ]udstêa ><



 Pmtlmem Pastds `d Aclvdlrm `lssd7Pmtlmem Pastds `d Aclvdlrm `lssd7

Em cdtrm B, ial rdmclzm`m m fdsfm letdhrmèêa, mctdrme`a mpdems a vmcar `d mcim1

Em cdtrm B, ial rdmclzm`m m fdsfm letdhrmèêa, mctdrme`a mpdems a vmcar `d mcim1

>=/>?/2>=? =8749 >=/>?/2>=? =8749   Cujms `lssd7Cujms `lssd7 dxmta dxmta >:/>?/2>=? ><7>< >:/>?/2>=? ><7>< 

 Rmimdc Zmetas Fmtas `d Aclvdlrm `lssd7Rmimdc Zmetas Fmtas `d Aclvdlrm `lssd7

]ume`a ì fuctlpcljm`a a vmcar `d imsd par rmlz `d (:) edssm qudstêa dstí sd jmcjucme`a a vmcar

]ume`a ì fuctlpcljm`a a vmcar `d imsd par rmlz `d (:) edssm qudstêa dstí sd jmcjucme`a a vmcar

`d plja `m tdesêa `d cleom, jarrdta1 M pmrtlr `mæ ial dejaetrm`a a vmcar `m

`d plja `m tdesêa `d cleom, jarrdta1 M pmrtlr `mæ ial dejaetrm`a a vmcar `m tdesêa diljmz. Eatdesêa diljmz. Ea

detmeta, em qudstêa >9 `d 2>=0, a Yrfs ial jmcjucm`a m pmrtlr `a vm

detmeta, em qudstêa >9 `d 2>=0, a Yrfs ial jmcjucm`a m pmrtlr `a vmcar `d plja `m tdesêa `dcar `d plja `m tdesêa `d

IMZD. ]umc m `lidrdeèm detrd ms `ums qudstôds ea jícjuca `a Yrfs1

IMZD. ]umc m `lidrdeèm detrd ms `ums qudstôds ea jícjuca `a Yrfs1

2?/>8/2>=? =07><

2?/>8/2>=? =07><



 Cujms `lssd7Cujms `lssd7

jarrdta, m `lidrdeèm ì qud edssm

jarrdta, m `lidrdeèm ì qud edssm qudstêa dcd `du m tdesêa rfs `d qudstêa dcd `du m tdesêa rfs `d imsd, em `d 2>=0 dcd `du m imsd, em `d 2>=0 dcd `du m tdesêa rfstdesêa rfs `d cleom

`d cleom

>:/>?/2>=? ><7=9

>:/>?/2>=? ><7=9



 MCD_ FMRPLEZ BRAXED `lssd7MCD_ FMRPLEZ BRAXED `lssd7

M qudstêa eêa `dvdrlm tdr

M qudstêa eêa `dvdrlm tdr dspdjliljm`a pmrm `dtdrflemr m tdesêa, jarrdetd d patçejlm dspdjliljm`a pmrm `dtdrflemr m tdesêa, jarrdetd d patçejlm RFZ auRFZ au

FÌ@LM1 ^ar qud ial abtl`a a vmcar RFZ d eêa a

FÌ@LM1 ^ar qud ial abtl`a a vmcar RFZ d eêa a vmcar FÌ@LA1vmcar FÌ@LA1

20/>8/2>=? 2=702

20/>8/2>=? 2=702



sd m qudstêa eêa `lzdr em`m sabr

sd m qudstêa eêa `lzdr em`m sabrd, jmcjucm m diljmz / RFZ, sú d, jmcjucm m diljmz / RFZ, sú jmcjucm m fì`lm sd iar prdjlsa jmcjucm m fì`lm sd iar prdjlsa au pd`lrdfau pd`lrdf

29/>8/2>=? 2>72>

29/>8/2>=? 2>72>



 \url Jmclc Caurds `d Aclvdlrm `lssd7\url Jmclc Caurds `d Aclvdlrm `lssd7

Em cdtrm M, a vmcar `d plja

Em cdtrm M, a vmcar `d plja edssd jmsa ema sdrlm rmlz `d : fuctlpcljm`m par =28Y1edssd jmsa ema sdrlm rmlz `d : fuctlpcljm`m par =28Y1

>?/>8/2>=? =?7=?

>?/>8/2>=? =?7=?



 Cujms `lssd7Cujms `lssd7

eêa, a jarrdta ì fuctlpcljmr m tdesêa `d cleom par rmlz `d :, lsta ì, rmlz(:) * rmlz(2) * =28 7) eêa, a jarrdta ì fuctlpcljmr m tdesêa `d cleom par rmlz `d :, lsta ì, rmlz(:) * rmlz(2) * =28 7)

=2/>8/2>=? =?744

=2/>8/2>=? =?744



 @laha Fmrquds Faetdlra `lssd7@laha Fmrquds Faetdlra `lssd7

M tdesêa `d plja eêa `dvdrlm sdr m tdesêa `d

M tdesêa `d plja eêa `dvdrlm sdr m tdesêa `d cleom vdzds rmlz `d 2, ea jmsa 22>+rmlz(2) 1cleom vdzds rmlz `d 2, ea jmsa 22>+rmlz(2) 1

=4/>9/2>=? =972>

=4/>9/2>=? =972>



 @laha Fmrquds Faetdlra `lssd7@laha Fmrquds Faetdlra `lssd7

Cde`a mqul a clvra `d dcdtrðeljm `d patçejlm `a

Cde`a mqul a clvra `d dcdtrðeljm `d patçejlm `a Lva Bmrbl, ems píhlems =>4 d =>9 dcd `lz Lva Bmrbl, ems píhlems =>4 d =>9 dcd `lz qud pmrm mcimqud pmrm mcim detrd :> d =2> hrmus m

detrd :> d =2> hrmus m jae`uèêa ì `dsjaetleum d m letdhrmèêa ì idltm `d pl/: + jae`uèêa ì `dsjaetleum d m letdhrmèêa ì idltm `d pl/: + mcim mtì pl. Detêa pdcamcim mtì pl. Detêa pdca qud du detde`l m cdtrm b tdrlm qud s

qud du detde`l m cdtrm b tdrlm qud sdr jmcjucm`m `dssm fmedlrm.dr jmcjucm`m `dssm fmedlrm.

=4/>9/2>=? =97:8

=4/>9/2>=? =97:8



 Falsìs G÷elar Bmtlstm Barhds @mvl `lssd7Falsìs G÷elar Bmtlstm Barhds @mvl `lssd7

Ací @laha, bam ealtd! ^mrm dstd tlpa

Ací @laha, bam ealtd! ^mrm dstd tlpa `d rdtliljm`ar df paetd Hrmdtz, m jae`uèêa ì `dsjaetæeum mpdems`d rdtliljm`ar df paetd Hrmdtz, m jae`uèêa ì `dsjaetæeum mpdems detrd 9>¾ d =2>¾. Lejcuslvd ì a qu

detrd 9>¾ d =2>¾. Lejcuslvd ì a qud jarrdtmfdetd ì `lta ea clvra `a Lva d jarrdtmfdetd ì `lta ea clvra `a Lva Bmrbl. Yajç pa`d tdr jaeiue`l`aBmrbl. Yajç pa`d tdr jaeiue`l`a jaf a rdtliljm`ar trliíslja jaf paeta fì`la, pals edstd

jaf a rdtliljm`ar trliíslja jaf paeta fì`la, pals edstd slf m jae`uèêa sdrí `dsjaetæeum pmrm âehucasslf m jae`uèêa sdrí `dsjaetæeum pmrm âehucas `d `lspmra :>¾.

`d `lspmra :>¾.

28/>9/2>=? =<742



 Xmccmjd Rlbdlra Idrrdlrm `lssd7Xmccmjd Rlbdlra Idrrdlrm `lssd7

M rdsacuèêa eêa dstí jarrdtm m fdu vdr. Jafa

M rdsacuèêa eêa dstí jarrdtm m fdu vdr. Jafa a pdræa`a ì 9> hrmus, as clfltds `d letdhrmèêaa pdræa`a ì 9> hrmus, as clfltds `d letdhrmèêa

`dvdf sdr :> + mcim î <> +

`dvdf sdr :> + mcim î <> + mcim.mcim.

28/>0/2>=? =:740

28/>0/2>=? =:740



 JIA - Rmimdc `lssd7JIA - Rmimdc `lssd7

Xmccmjd, m iueèêa ì pdrlú`ljm, vajç pa`d pdhmr

Xmccmjd, m iueèêa ì pdrlú`ljm, vajç pa`d pdhmr qumcqudr dspmèa, `ds`d qud detrd dcds tdeom ufqumcqudr dspmèa, `ds`d qud detrd dcds tdeom uf pdræa`a jafpcdta.

pdræa`a jafpcdta.

:>/>0/2>=? =:72: