Que debemos saber de los decibeles?

Ksaritl plr? Qcgvc`lr Hcraäc Acstkggñj, YQ3HA

¼Suk `kfkdls scfkr `k gls `kaifkgks<

Qcgvc`lr Hcraäc Acstkggñj, YQ3HA

¼Sué `kfkdls scfkr `k gls `kaifkgks< Vkgcailjks, kokdpgls, kjnlquks, auc`rls aldpcrctivls y auc`rls `k rksÿdkjks

Qcgvc`lr Hcraäc Acstkggñj

Rchijc 6



IJPVL@[AAIÑJ Prcfcol `ks`k mcak yc tikdpl kj kg ãrkc `k kquipls `k rcìlaldujiacaiñj y kquipls `k VN, aldkjaé aldl duamls kj kg acdpl, `k dl`l prãatial, alj gc ksaukgc `k gc kxpkrikjaic `k gc vi`c (ñskc qukdcj`l kquipls, cghujcs vkaks), alj gl quk cghujls ncdigicrks y cdihls gk kxpgiacj c ujl…. Rkrl kggls cg ihucg quk yl tkjäcj gc kxpkrikjaic `k gc vi`c. Rlr pridkrc vkz vi gls @kaifkgks kj uj trcjsakptlr `k Fcj`c aiu`c`cjc, slgäc vkr gc chuoc ijìaãj`ldk kg jivkg `k rkakpaiñj `k ltrls kquipls kj di aui`c`, Qcj Qcgvc`lr, aldprkj`äc quk kjtrk dcs jivkg krc dcylr, pkrl jl scfic quk dk ijìacfc kxcatcdkjtk kstc dkì`c. Aljnlrdk dk dktäc dcs kj kg tkdc supk quk gls `kaifkgks jl slgl sk laupcfcj pcrc rkaifir gc ijtkjsi`c`, si jl pcrc ujc skrik `k dkì`cs `k? kgkatrñjiac, kgkatriai`c`, pltkjaic, kta. Y ac`c vkz dk skjtäc dcs cgkoc`l `k ujc kxpgiacaiñj rkcg. Aldl duamls kstuìk `kspués kj gc [jivkrsi`c`, y ksauamk ujcs pcgcfrcs quk dk sljcrlj ìnäaigks pkrl rkcgks ‗Kg Ijhkjikrl `k Kgkatriai`c`, Pkgkaldujiacailjks y

rcdcs cnijks, `kfk `k pkjscr kj uj duj`l kj @kaifkgks5 aldprkj`kr y kjtkj`kr pkrnkatcdkjtk, kstk tkdc. Yc quk quk su duj`l duj`l hirc cgrk`k`lr cgrk`k`lr `k kstcs uji`c`ks `k rknkrkjaic— tkjhl quk chrc`kakrgk Ijh. Ouãrkz, quk sus pcgcfrcs mly kj `äc cuj sihukj prkskjtks kj di acfkzc, y mcstc cmlrc sihl utigizcj`l gls @kaifkgks aljstcjtkdkjtk kj di prlnksiñj. Rlstkrilrdkjtk dk kjaljtré c uj aldpcókrl `k acrrkrc, y dk mizl ujc prkhujtc sijhugcr ‗¼Amcdfc, [`. kjtikj`k plr quk kxistkj gls `kaifkgks jkhctivls y aldl nujailjc kstc dkì`c kj gls kquipls<, yc quk yl mk prkhujtc`l kj gc kdprksc y jcìk dk scfk rksplj`kr —. —. Gk kxpgiquk slfrk gls `F, pkrl surhiñ di ù`c5 ‗Gc disdc prkhujtc quk dk miak mcak duaml tikdpl, kstc ks ujc prkhujtc aldÿj `kjtrl `kg acdpl alj dis algkhcs —. Ks plr ksl quk aldkjaé a ldkjaé c rkalpigcr ijnlrdcaiñj `k ìnkrkjtks nukjtks, pcrc trctcr `k mcakr uj `laudkjtl skjaiggl, alrtl y sidpgk `k gls @kaifgks. Kspkrl kstk dctkricg skc `k cyu`c, pcrc ustk`ks y sirvc pcrc `kscrrlggcr dkolr jukstrl skrviail prlnksiljcg, y quk cyu`kdls c duamls kxpkridkjtc`lrks, rcìlcniailjc`ls, téajials y prlnksiljcgks slfrk gls `F°s. Qcgvc`lr, YQ3HA

Dcig? ys3haBlutglle.ald , scgvc`lr.acstkggljBhdcig.ald 5 Qeypk? scgvc`lr.hcraic.acstkgglj Qñgl mcy uj fikj? kg aljlaidikjtl. Qñgl mcy uj dcg? gc ihjlrcjaic. Qñarctks (082 CA-199 CA) Nigñslnl Hrikhl. Rchijc 1



@kaifkg Kg `kaifkg nuk jldfrc`l plr Cgkxcj`kr Hrcmcd Fkgg5 sk utigizc pcrc dkìr Jivkgks, ijtkjsi`c`ks, pltkjaics, pkrl tcdfiéj sk utigizc kj skócgks, kgkatrñjiac y aldujiacaiñj. %, `F, `Fd y `F(»^) slj aljakptls idplrtcjtks quk tl`l téajial `k acdpl l Ijhkjikrl `kfkräc kjtkj`kr pkrnkatcdkjtk y skr acpcz `k trcfcocr alj kggls jlrdcgdkjtk. @k jl skr csä, sk kjaljtrcrã kj ujc agcrc `ksvkjtcoc ùrcjtk kg `kscrrlggl `k su trcfcol. Aucj`l kstls térdijls cpcrkakj kj ìsausiljks alj agikjtks l alj ltrls aldpcókrls, tkj`rã skrils prlfgkdcs pcrc akjtrcrsk kj kg prlfgkdc si kstã laupc`l prkhujtãj`lsk si 1 `F sihjiniac uj ncatlr `k 6 l `k 0 (u ltrc alsc) l si gls `kaifkgks slj `k vcglr jkhctivl -1`F, c quk alrrksplj`krã kstc dchjitu`. Dkrkak gc pkjc kg ksnukrzl `k rkviscr kstls aljakptls `k vkz kj aucj`l y ncdigicrizcrsk alj kggls. Aucj`l sk utigizcj nñrdugcs y uji`c`ks, sk mcj skhui`l gls kstãj`crks ijtkrjcailjcgks nioc`ls kj gc IQL 13 y kj gc IKA 68 3 (tcdfiéj sk ijìacj gls acsls kj gls quk ks ujc prãatiac aldÿj kg `ksvicrsk `k kstls kstãj`crks).

¼Rcrc quk utigizcdls gls `kaifkgils< Gls @kaifkgil, puk`kj kdpgkcrsk pcrc `ksarifir kg rkjìdikjtl ij`kpkjìkjtkdkjtk `kg ^lgtcok l Rltkjaic `k lpkrcaiñj `k ujc cpgiacaiñj, plr tcjtl, ks ujc kspkainiacaiñj `k uj rkjìdikjtl hkjérial, si kj uj sistkdc prkskjtc uj cplrtk c gc skócg l jivkg `k kjtrc`c (Hcjcjaic), kstc ks kxprksc`c aldl uj vcglr plsitivl y tl`l gl aljtrcril pcscräc alj uj vcglr jkhctivl kj `kaifkgks, yc quk skrã ujc ctkjucaiñj kj gc scgi`c `kg sistkdc, aucj`l sk tkjhc uj vcglr kj `kaifkgks `k 2, rkprkskjtc quk kg sistkdc jl cplrtc ji ctkjÿc, c gcs skócgks, tcjtl `k kjtrc`c aldl `k scgi`c

3

IKA 68 ks kg kstãj`cr `k gc Aldisiñj Kgkatrltéajiac Ijtkrjcailjcg slfrk gc Acrtc `k gls sädflgls quk sk utigizcj kj gc tkajlglhäc kgéatriac.

Rchijc 0



¼Rlr qué utigizcdls gls `kaifkgils kj jukstrls aãgaugls< Gls ijhkjikrls tkjkdls quk trcfcocr alj jÿdkrls tl`ls gls `äcs, y kstls jÿdkrls puk`kj skr duy hrcj`ks l duy pkqukóls. Kj gc dcylräc `k gls acsls, gl quk ks dãs idplrtcjtk ks gc rkgcaiñj kjtrk `ls dchjitu`ks quk alrrksplj`krãj c gc disdc uji`c` `k dkì`c. Rlr kokdpgl, ujc kstcaiñj fcsk `k tkgknljäc dñvig puk`k trcjsditir ujc pltkjaic `k =2X cprlxidc`cdkjtk (hcjcjaic `k gc cjtkjc ijagui`c). Gls tkgénljls dñvigks sñgl rkaifkj ujls 2.222222226 X, gl quk supljk uj 2.222222226;% `k gc pltkjaic trcjsditi`c. Qikdprk quk mcyc quk trcfcocr alj rcjhls judérials hrcj`ks, ks aljvkjikjtk utigizcr kg glhcritdl `k ksls jÿdkrls. Rlr kokdpgl, gc kstcaiñj fcsk `k jukstrl kokdpgl trcjsditk ujc pltkjaic `k +09 `Fd dikjtrcs quk kg tkgénljl dñvig rkaifk ‑;8 `Fd, prlùaikj`l ujc ìnkrkjaic kj pltkjaic `k +09 `Fd ‑ (-;8 `Fd) 4 32> `F. Ltrl kokdpgl? si aljkatcdls `ls cdpginiac`lrks kj acsac`c alj hcjcjaics `k 36 y 3> rkspkativcdkjtk, lftkjkdls ujc hcjcjaic tltcg `k 36 x 3> 4 396. Kj térdijls glhcrätdials, gls `ls cdpginiac`lrks tikjkj ujc hcjcjaic `k 32.= `F y 36 `F, rkspkativcdkjtk, prlùaikj`l ujc hcjcjaic tltcg `k 32.= `F + 36 `F 4 66.= `F, quk ks duaml dãs nãaig `k acgaugcr. Aucj`l trcfcocdls alj `kaifkgils, gls vcglrks slj duaml dãs nãaigks `k dcjipugcr. Ks duaml dãs skjaiggl sudcr y rkstcr `kaifkgils `k acfkzc quk dugtipgiacr y ìviìr vcglrks gijkcgks. Kstc ks gc prijaipcg rczñj plr gc quk prknkridls utigizcr `kaifkgils kj jukstrls aãgaugls.

¼Suk vkjtcoc tikjk utigizcr kg @kaifkg< Kg @kaifkg sk acgaugc kj ujc ksacgc glhcrätdiac `kniji`c, quk pkrditk gcs kspkainiacailjks `kg rkjìdikjtl c trcvés `k uj cdpgil rcjhl `k gc skócg `k rknkrkjaic, skc ^lgtcok l pltkjaic, plr kokdpgl Gls @kaifkgks puk`kj sudcrsk l rkstcrsk (dugtipgiacj`l y ìviìkj`l kj sus alrrkspljìkjtks rkgcailjks), ncaigitcj`l `k ksk dl`l gls aãgaugls l slguailjks hrcniacs. Kg Fkg nuk lrihijcgdkjtk `kniji`l plr Cgkxcj`kr Hrcmcd Fkgg, pcrc dkìr rkgcailjks `k slji`l, kj gcs gäjkcs tkgkhrãniacs, gcs aucgks aljtcfcj alj ujc idpk`cjaic `k >22 lmds.

@knijiaiñj `k `F C pkscr `k quk kg glhcritdl kj fcsk 32 `k gc rkgcaiñj `k `ls jivkgks `k pltkjaic ks cìdkjsiljcg, tikjk uji`c`ks `k fkgils kj mljlr `kg ijvkjtlr `kg tkgénljl (Cgkxcj`kr Hrcmcd Fkgg). Rcrc lftkjkr acjti`c`ks dãs dcjkocfgks, utigizcdls kg `F (`kaifkgil) kj guhcr `kg fkgil. Rcrc kggl mcy quk dugtipgiacr plr 32 gls vcglrks kxprksc`ls kj fkgils (cg ihucg quk dugtipgiacdls plr dig ujc ìstcjaic si qukrkdls trcfcocr alj digädktrls kj guhcr `k alj dktrls).

 () 

Aldl yc sk mc dkjailjc`l cjtks, gc vkjtcoc `k uscr `kaifkgils ks quk sk puk`kj rkprkskjtcr gcs ìvkrscs skócgks quk jlrdcgdkjtk sk kjaukjtrcj kj ijhkjikräc utigizcj`l jÿdkrls dãs dcjkocfgks. Rchijc ;



Kokdpgl? R3 ks ihucg c 622 X y R6 ks ihucg c 322 dX. ¼Auãg ks su rkgcaiñj kj `F<

 () 

Rlr supukstl, cjtks `k ìviìr kstls jivkgks `k pltkjaic, mcy quk aljvkrtirgls c gc disdc uji`c`, X l dX. Qi ìviìdls ìrkatcdkjtk 622 kjtrk 322, kg rksugtc`l lftkji`l skrã ijalrrkatl. Mly kj `äc, sk utigizc kg glhcritdl kj fcsk 32 acsi `k nlrdc kxagusivc. Gc cfrkvicturc pcrc kstk glhcritdl ks gh. Kg cghujls gifrls `k tkxtl cjtihuls, sk puk`k kjaljtrcr gc utigizcaiñj `kg glhcritdl jcturcg, quk ks kg glhcritdl kj fcsk k (k 4 6.83= cprlxidc`cdkjtk). Kj kstc jltc `k cpgiacaiñj sñgl sk utigizcrã kg glhcritdl kj fcsk 32, quk cfrkvicrkdls aldl gh `k cquä kj c`kgcjtk. Pcdfiéj ks plsifgk aljvkrtir `kaifkgils c uji`c`ks gijkcgks. Rridkrl mcy quk aljvkrtir gls `F c fkgils ìviìkj`l kg vcglr plr 32. Rlstkrilrdkjtk, mcy quk kgkvcr 32 (`c`l quk kstcdls utigizcj`l kg glhcritdl kj fcsk 32) c ksc pltkjaic?

    Kokdpgl? c4 61`F, ¼aucjtl ks R 3 / R6< @kspuks `k acgaugcr pridkrl 61/3246.1, plstkrilrdkjtk sustituidls gls `ctls y lftkjkdls?

    

     

Mldlhkjki`c` `k ainrcs Qi tldcdls glhcritdls c judkrls duy hrcj`ks y/l duy pkqukóls, sk vkrc quk kg rksugtc`l `k ksc lpkrcaiñj dctkdctiac frij`c acjti`c`ks auyls judkrls `k ainrcs slj sidigcrks. C gl sudl mcfrc ìnkrkjaic kj gls sihjls, gl quk ijìacrc gl sihuikjtk? Qihjl plsitivl? judkrl aljsi`krc`l :3 Qihjl jkhctivl? judkrl aljsi`krc`l 73 Kokdpgls? Glh 3,222,222,222 4 +9 Glh 2.222223 4 -> @k dcjkrc quk alj gc utigizcaiñj `kg `kaifkg ks plsifgk lpkrcr dctkdãtiacdkjtk uj vcglr duy hrcj`k l duy pkqukól l cdfls sidugtcjkcdkjtk, sij tkjkr gc jkaksi`c` `k rkaurrir c judkrls quk plr su acjti`c` `k ainrcs mcricj plal prcatial su dcjkol.

¼Sué sihjiniac `Fd< Qi rknkridls uj jivkg `k pltkjaic crfitrcril c ujc acjti`c` nioc `k rknkrkjaic, lftkjkdls ujc acjti`c` cfslgutc c pcrtir `k ujc rkgcaiñj glhcrätdiac `k pltkjaics. Gc acjti`c` `k rknkrkjaic dãs aldÿjdkjtk utigizc`c kj tkgkaldujiacailjks y rcìlnrkaukjaic ks 3 dX (gc digésidc pcrtk `k 3 X). Rchijc >



Qlfrk ;2 lmds. Kstc acjti`c` `k rknkrkjaic sk `ksihjc cócìkj`l ujc d (`k dX) c `F lftkjiéj`lsk `Fd. Gc rkgcaiñj `k pltkjaics kjtrk R3 y R6 sk aljvikrtk kj ujc rkgcaiñj kjtrk R3 y 3 dX, ijìaãj`lsk kj `Fd.

 ) ( Qkhÿj kg kstãj`cr IKA 68, kxistk ltrc nlrdc `k ksarifir kstc nñrdugc. Gls jivkgks sk rkprkskjtcj alj gc gktrc G y kg vcglr `k rknkrkjaic sk `kfk ijìacr `k nlrdc kxpgäaitc. Gc nñrdugc quk`c `k gc sihuikjtk nlrdc?

 )   (

Qk ksarifiräc GR/3dX 4 8 `F, plr kokdpgl. Qkhÿj gc IKA 68 jl kstã pkrditi`l utigizcr gc kxprksiñj 8 `Fd. Aldl ks duaml dãs aldÿj ksarifir `Fd, skrã éstc gc kxprksiñj quk sk utigizcrã kj kstc jltc `k cpgiacaiñj. Rcrc tkjkr ujc i`kc `k gls ñr`kjks `k dchjitu` quk sk dcjkocj, cquä mcy cghujls kokdpgls? kg rcjhl `k gc pltkjaic `k scgi`c `k uj hkjkrc`lr `k skócg vc `ks`k gls ‑302 `Fd c +62 `Fd l `ks`k 2.23 pX c 2.3 X. Gcs kstcailjks fcsk `k tkgknljäc dñvig trcjsditkj c +01 `Fd l 62 X. Gls tkgénljls dñvigks trcjsditkj `k +32 `Fd c +11 `Fd l `ks`k 32 dX c 6 X. Gls trcjsdislrks `k ìnusiñj `k rcìl y tkgkvisiñj lpkrcj alj jivkgks `k scgi`c `k +82 `Fd c +92 `Fd l `ks`k 32 eX c 3 DX.

¼Sué ks uj jivkg< Aldl vidls cjtkrilrdkjtk, kg tkrdijl `Fd aljggkvc gc rknkrkjaic c uj jivkg `k pltkjaic `k 3 dX. Ltrcs acjti`c`ks `k rknkrkjaic utigizc`cs jlrdcgdkjtk slj 3 X, 3 ^, 3 »^ y tcdfiéj 3 C l 3 »C. Qk `ksihjcj aldl `F (X), `F (^), `F (»^), `F (C) y `F (»C), rkspkativcdkjtk, l kj dkì`cs `k ijtkjsi`c` `k acdpl, `F (X/d 6), `F (^/d), `F (»^/d), `F (C/d) y `F (»C/d). Aldl kj kg acsl `k gls `Fd, gc nlrdc aljvkjailjcg `k ksarifir kstcs uji`c`ks `FX, `F^, `F»^, `FC, `F»C, `FX/d 6, `F^/d, `F »^/d, `FC/d y `F »C/d sk `ksväcj `kg kstãj`cr, pkrl skrãj gcs utigizc`cs kj kstc jltc `k cpgiacaiñj. C pcrtir `k gls vcglrks vcglrk s rkgctivls `k gc pltkjaic R3 (tkjsiñj [3) rknkri`ls c gc pltkjaic pl tkjaic R6 (tkjsiñj [6), sk lftikjkj gls vcglrks cfslgutls utigizcj`l gls vcglrks `k rknkrkjaic cjtkrilrdkjtk aitc`ls. Kstls vcglrks cfslgutls tcdfiéj sk aljlakj aldl jivkgks. [j jivkg `k 32 `Fd sihjiniac uj vcglr quk ks 32 `F ` F dcylr quk 3 dX, y uj jivkg `k. ` k. 38`F »^ sk alrrksplj`k alj uj vcglr quk ks 38 `F dkjlr quk 3 `F»^. Aucj`l sk trcfcoc alj kstls vcglrks, ks idplrtcjtk tkjkr kj aukjtc si slj dchjitu`ks `k pltkjaic l `k tkjsiñj. Cghujls kokdpgls `k dchjitu`ks `k pltkjaic slj sl j gc pltkjaic, gc kjkrhäc, gc rksistkjaic, gc nihurc `k rui`l y gc `kjsi`c` `k pltkjaic. Gcs dchjitu`ks `k tkjsiñj (tcdfiéj aljlai`cs aldl dchjitu`ks `k acdpl) ijaguykj gc tkjsiñj, gc alrrikjtk, gc ijtkjsi`c` `k acdpl kgéatrial, gc ijtkjsi`c` `k acdpl dchjétial y kg alkniaikjtk `k rkngkxiñj. Rchijc 8



¼Auãg ks gc ìnkrkjaic kjtrk gls `kaifkgils `k tkjsiñj y gls `kaifkgils `k pltkjaic< Rcrc kdpkzcr, ks jkakscril lgvi`crsk `k tl`l gl quk sk mcyc lä`l cakrac `k gls `kaifkgils `k tkjsiñj y `k pltkjaic. Qñgl kxistk uj tipl `k `kaifkgil, y rkprkskjtc gc rkgcaiñj kjtrk `ls jivkgks `k pltkjaic R3 y R6. Rlr supukstl, sk puk`k kxprkscr aucgquikr jivkg `k pltkjaic aldl ujc tkjsiñj si sk aljlak gc rksistkjaic.

            

Qk puk`k kxprkscr gc rkgcaiñj glhcrätdiac aldl sihuk?

      ()     [tigizcj`l gcs sihuikjtks rkhgcs, ()           Lftkjkdls (utigizcj`l glh pcrc rknkrirjls cg glhcritdl kj fcsk 32)?       ()       ()()  Lfsérvksk kg sihjl dkjls cjtks `kg térdijl `k gc rksistkjaic. Kj gc dcylräc `k gls acsls, gc rksistkjaic `k rknkrkjaic ks gc disdc pcrc cdfls jivkgks `k pltkjaic, V3 4 V6. Rlr gl tcjtl?

   Qk puk`k sidpginiacr kj?   

Aljsi`krcj`l V3 4 V6

Csä sk kxpgiac plr qué sk utigizc kg 32¸g2h pcrc rkgcailjks `k pltkjaic y kg 62¸g2h pcrc rkgcailjks `k tkjsiñj. JLPC Duy idplrtcjtk? Kstc nñrdugc sñgl ks vãgi`c si V3 4 V6. Qi, aldl laurrk kj cghujcs lacsiljks kj tkgkvisiñj, jkaksitcdls tkjkr kj aukjtc gc aljvkrsiñj `k 8; lmds c ;2 lmds, mcy quk aljsi`krcr gc rkgcaiñj kjtrk gcs rksistkjaics. Gc aljvkrsiñj c vcglrks gijkcgks sk rkcgizc `k gc disdc dcjkrc. Rcrc rkgcailjks `k tkjsiñj, sk `kfk ìviìr kg vcglr kjtrk 62 yc quk utigizcdls [ 6 y `kaifkgils.

  ⁀    ⁀ 

Rchijc =



Dchjitu` `k rkgcaiñj `F Kg `kaifkg kj su nlrdc fãsiac, ks gc kxprksiñj dãs hkjkrcg `k kstuìl aldl dchjitu` `k rkgcaiñj. Gcs kaucailjks dãs kdpgkc`cs pcrc gls pcrãdktrls kgéatrials? pltkjaic, tkjsiñj y alrrikjtk, alrrksplj`kj c gcs kaucailjks fãsiacs, `k gc gky `k lmds. `Fr K   dfé u d  ñ      ufä ‗— 

quk ks uj vcglr `k pltkjaic `k rknkrkjaic l rkgctivl cg lrihkj `kg sistkdc l airauitl cjcgizc`l (c gc kjtrc`c `kg disdl).

   

R ks gc pltkjaic dkì`c kj uj pujtl aucgquikrc `k uj sistkdc l airauitl aucj`l sk kjväc ujc skócg kj kg lrihkj `kg disdl R lrihkj ks g pltkjaic `k skócg kj kg lrihkj `kg airauitl l sistkdc, dkì`l kj gc disdc uji`c` quk R. Qi sk vcräc gc pltkjaic ijykatc`c kj kg lrihkj `kg airauitl, gls `Fr pkrdcjkakrãj aljstcjtks k ij`kpkjìkjtks `kg jivkg `k gc skócg ijykatc`c. Ks `kair quk gls `Fr slj ujc acrcatkrästiac prlpic `kg airauitl l sistkdc y jl vcräcj dikjtrcs jl vcrié gc Hcjcjaic l ctkjucaiñj `k ac`c kgkdkjtl `kg disdl. `Fw Ks ltrl tipl `k `kaifkg `lj`k gc pltkjaic `k rknkrkjaic 3Xctt

   

Qu kquivcgkjaic alj gls `Fd ks? 3`FX 4 12 `Fd `Fe Qk utigizc dcylrdkjtk `lj`k gls jivkgks gls jivkgks `k pltkjaic kj oukhl slj kgkvc`ls, tcgks aldl gcs rk`ks `k ìstrifuaiñj kgéatriac. Kg vcglr `k rknkrkjaic ks 3 Eiglwctt.

   

`Fp Qk utigizc dcylrdkjtk `lj`k gls jivkgks gls jivkgks `k pltkjaic `k skócgks duy pkqukócs, `c`l quk gc pltkjaic `k rknkrkjaic ks 3 pialwctt.

   

`Fdl Kj kstk acsl kg sufäjì  ‗d—  u v  c `k gc skócg rknkri`l c 3 digiXctt. K ufä ‗—  qu  d  u v    d d  

kg lrihkj `kg airauitl.

Rchijc 9



Ks `kair kg `Fdl ks uj jivkg `k pltkjaic `k ujc skócg rknkri`l kj ac`c pujtl cg vcglr jldijcg `k gc skócg `k kjtrc`c. Rlr kokdpgl -62 `F plr `kfcol `kg vcglr kxistkjtk kj kg lrihkj `kg airauitl l sistkdc. `Fdlp Ks kg vcglr `kg rui`l dkìl kj gc nlrdc pslnldétriac (c trcvés `k uj nigtrl alj ä  uñ m ≍ u) y rknkri`l cg jivkg `k gc skócg `k prukfc kj ìaml pujtl. `F» (Qistkdcs `k Aldujiacailjks) Ks ujc uji`c` `k cdpgic cpgiacaiñj kj kg ãrkc `k gcs aldujiacailjks, pcrtiaugcrdkjtk kj kg cjãgisis `k prlpchcaiñj `k skócgks kgkatrldchjétiacs kj kg kspcail gifrk. Kg vcglr `k gc skócg `k rknkrkjaic ks kg `k ujc ijtkjsi`c` `k acdpl kgéatrial `k 3 diarl ^/d (3»^/d).Kj cghujls crtäaugls y/l pufgiacailjks sukgk aljnujìr kg `Fu (quk alrrksplj`k c Pkgknljäc) alj `F» (Qistkdc `k Aldujiacailjks) plr gc ijagusiñj `k gc  ‗u— y    hh ‗du— (»). Q f  ñ  x  

kxprksiñj cjcgizc`c pcrc ìnkrkjaicr alrrkatcdkjtk gc uji`c` `k dkì`c dkjailjc`c. Qk utigizc kg `F» pcrc niocr gls gäditks `k gcs ãrkcs `k alfkrturc `k gls acjcgks `k tkgkvisiñj l `k gcs kdislrcs `k rcìlìnusiñj pÿfgiac `k CD y ND, `ktkrdijcj`l kg jivkg `kg acdpl kgéatrial dkì`l kj »^/d kj ìaml pujtl. Ãrkc `k alfkrturc `k gls acjcgks > cg 31? 88 `F» 4 82=2 »^/d `F^ Kxprksc gc rkspukstc kj `kaifkgks `k uj diarñnljl c ujc nrkaukjaic `ktkrdijc`c. Kg Jivkg `k rknkrkjaic `k 2 `F ks ihucg c 3^ (2 `F^) aucj`l sk slfrk uj diarñnljl ujc prksiñj caÿstiac `k 3 ìjc/ad 6

   

`Fd^ Ks ujc uji`c` `k dkì`c, surhi`c pcrc kstcfgkakr ujc uji`c` `k rknkrkjaic pcrc AAP^ l Pkgkvisiñj plr acfgk. K ^  ñ    3 d^ f u d  8; ℮

        

Vkaukr`k quk gc idpk`cjaic `k gls acfgks, tcjtl `k AAP^, aldl Pkgkvisiñj plr acfgk uz 8;℮  d.

`Fi Qk utigizc pcrc kxprkscr gc hucjcaic `k ujc cjtkjc rkspkatl `k uj rcìc`lr isltrñpial. Kj gcs cjtkjcs ìrkaailjcgks, kstc hcjcjaic ks nujai ñ  ãhu ν  ñ. Kg vcglr `k `Fi alrrksplj`k c gc hcjcjaic `k ujc cjtkjc i`kcg (tkñriac) quk irrcìc gc pltkjaic rkaifi`c `k uj ìsplsitivl cg quk kstã aljkatc`l, y cg aucg tcdfiéj trcjsditk gcs skócgks rkaifi`cs `ks`k kg kspcail, sij aljsi`krcr ji pérì`cs ji hcjcjaics kxtkrjcs l cìailjcgks `k pltkjaics

  @ñj`k?

RrC? Rltkjaic rcìc`c plr ujc cjtkjc RrVI? Rltkjaic rcìc`c plr uj rcìc`lr isltrñpial Rchijc 32



`F` Aldl rcìc`lr Isltrñpial ks ujc cfstrcaaiñj dctkdãtiac `kniji`c pcrc plsifigitcr gls aãgaugls rkspkativls, ks usucg rknkrir gc hucjcaic `k ujc cjtkjc aucgquikrc, rkspkatl `kg cgujc ltrc `k ncatifgk rkcgizcaiñj prcatiac. Rcrc kggl sk kdpgkc uj ìplgl `k dkìc lj`c aldl rknkrkjaic. Rcrc aljvkrtir `Fi c `F` y

   @ñj`k?

viakvkrsc, sk kdpgkc sihuikjtk nlrdugc?

`F` 4 `Fi + 6.3;

RrC ? Rltkjaic rcìc`c plr ujc cjtkjc Rr@C/6? Rltkjaic rcìc`c plr uj rcìc`lr isltrñpial

Lftkjkr `kaifkgks `k ujc pltkjaic `k rknkrkjaic 

  

gc





 



Auc`rl rksudkj `k aljvkrsiñj ^-`F-R`F-`F^- `Fη^



Aljvkrtir `F c Rltkjaic kj Xctts  



 





  

^lgtcok c pcrtir `k rksistkjaic `k Vknkrkjaic (Vksistkjaic skhÿj kg airauitl `k idpk`cjaic) 

 

 



UT

 

@kaifkgks c pcrtir ^lgtcok `k rknkrkjaic 

  





 





Aljvkrtir Xctts c `Fη^ 

  





 



U∖ T  

 

   





Aljvkrtir `Fd c η^lgtils 

 

+

  

 

  UT 

 

Ctkjucaiñj y hcjcjaic Gc nujaiñj gijkcg `k trcjsnkrkjaic c ij `k uj airauitl `k `ls pukrtls rkprkskjtc gc rkgcaiñj kjtrk gc pltkjaic `k scgi`c y gc pltkjaic `k kjtrc`c.

Nih. 3? Airauitl `k `ls pukrtls

       Rchijc 33



Gc nujaiñj `k trcjsnkrkjaic jlrdcgdkjtk sk kspkainiac kj `F?

            UT T      Qi gc pltkjaic `k scgi`c R6 `k uj airauitl `k `ls pukrtls ks dcylr quk gc pltkjaic `k kjtrc`c R3, kjtljaks gc rkgcaiñj glhcrätdiac kjtrk R6 y R3 ks plsitivc. Kstl sk aljlak aldl cdpginiacaiñj l hcjcjaic. Qi gc pltkjaic `k scgi`c R6 `k uj airauitl `k `ls pukrtls ks dkjlr quk gc pltkjaic `k kjtrc`c R3, kjtljaks gc rkgcaiñj glhcrätdiac kjtrk R6 y R3 ks jkhctivc. Kstl sk aljlak aldl ctkjucaiñj l pérì`c (sk lditk kg sihjl dkjls).

      UT      

Rcrc gc kvcgucaiñj `k gc rkgcaiñj `k pltkjaics l `k gc rkgcaiñj `k tkjsiljks c pcrtir `k gls vcglrks kj `kaifkgils sk utigizcj gcs sihuikjtks nñrdugcs?

  ⁀ 

L

  ⁀ 

Rcrc Vlut 4 Vij

Gls cdpginiac`lrks aljvkjailjcgks aljsihukj hcjcjaics `k mcstc 02 `F kj ujc slgc ktcpc, gl quk sk alrrksplj`k alj rkgcailjks `k tkjsiñj `k mcstc 322 vkaks y rkgcailjks `k pltkjaic `k mcstc 32222 vkaks. Rcrc vcglrks dcylrks kxistk kg rikshl `k quk kg cdpginiac`lr lsaigk. Qk puk`kj lftkjkr hcjcjaics dãs kgkvc`cs aljkatcj`l vcrics ktcpcs kj skrik. Gc lsaigcaiñj sk puk`k kvitcr utigizcj`l ujc cpcjtcggcdikjtl c`kauc`l. Gls ctkjuc`lrks dãs aldujks tikjkj vcglrks `k 1 `F, > `F, 32 `F y 62 `F. Kstl sk alrrksplj`k alj rkgcailjks `k tkjsiñj `k 2.8, 2.;, 2.1 y 2.3 l rkgcailjks `k pltkjaic `k 2.;, 2.6;, 2.3 y 2.23. Kj kstk acsl tcdfiéj sk puk`kj aljkatcr kj acsac`c vcrils ctkjuc`lrks pcrc lftkjkr vcglrks `k ctkjucaiñj supkrilrks. Qi sk ijtkjtc lftkjkr ctkjucailjks supkrilrks alj ujc slgc ktcpc, kxistk rikshl `k quk sk prlùzacj ìcnljäcs.

Aljkxiñj kj skrik `k airauitls `k `ls pukrtls Kj kg acsl `k ujc aljkxiñj kj skrik (acsac`c) `k airauitls `k `ls pukrtls, sk puk`k acgaugcr nãaigdkjtk gc hcjcjaic tltcg (l gc ctkjucaiñj tltcg) sudcj`l gls vcglrks kj `kaifkgils.

Nih. 6? Aljkxiñj kj acsac`c `k airauitls `k `ls pukrtls Gc hcjcjaic tltcg sk acgaugc `k gc sihuikjtk nlrdc?

     

Rchijc 36



Kokdpgl? Nih. 6 dukstrc gcs ktcpcs `k kjtrc`c `k uj rkakptlr. Gc hcjcjaic tltcg sk acgaugc `k gc sihuikjtk dcjkrc? c 4

-2.8 `F + 36 `F - 8 `F + 61 `F 4 68.1 `F.

Aljvkrsiñj `k `kaifkgils c plrakjtcok y viakvkrsc K éd ‗ — h ‗ —.  3% h  éd   u

vcglr. 3 % `k x 4 2,23 x

⋋

Cg utigizcr plrakjtcoks, ks jkakscril nlrdugcrsk gl sihuikjtk? • ¼Kd u v  ñ   < • ¼Kd   u  %x `k ujc acjti`c` l uj %x dãs l dkjls `k ujc

acjti`c`< Pcg y aldl sk mc dkjailjc`l cjtkrilrdkjtk, gcs dchjitu`ks `k tkjsiñj slj? tkjsiñj, alrrikjtk, ijtkjsi`c` `k acdpl y alkniaikjtk `k rkngkxiñj, plr kokdpgl. Gcs dchjitu`ks `k pltkjaic ijaguykj gc pltkjaic, rksistkjaic, nihurc `k rui`l y `kjsi`c` `k pltkjaic.

Aljvkrsiñj `k % `k tkjsiñj c `kaifkgils y viakvkrsc Kg tcjtl plr aikjtl x% `k ujc dchjitu` `k tkjsiñj sk aljvikrtk c `kaifkgils `k gc sihuikjtk nlrdc?

   

Kj ltrcs pcgcfrcs? Rcrc lftkjkr kg vcglr x% kj `kaifkgils, sk `kfk aljvkrtir pridkrl kg vcglr x `kg plrakjtcok c uj jÿdkrl rcailjcg ìviìéj`lgl plr 322. Rcrc aljvkrtir c `kaifkgils, sk dugtipgiac kg glhcritdl `kg jÿdkrl rcailjcg plr 62 (dchjitu` `k tkjsiñj). Kokdpgl? Csudikj`l quk gc tkjsiñj `k scgi`c `k uj airauitl `k `ls pukrtls ks ihucg cg 1% `k gc tkjsiñj `k kjtrc`c, ¼auãg ks gc ctkjucaiñj kj `F<

( )     

Rcrc aljvkrtir kg vcglr kj `F c plrakjtcok?

 ⁀

Kokdpgl? Acgaugcr gc tkjsiñj `k scgi`c `k uj ctkjuc`lr `k 1 `F aldl plrakjtcok `k gc tkjsiñj `k kjtrc`c. Gc tkjsiñj `k scgi`c `k uj ctkjuc`lr `k 1 `F ks ihucg cg 83% `k gc tkjsiñj `k kjtrc`c. Jltc? Aldl rkalr`crc gc ctkjucaiñj sihjiniac vcglrks kj `kaifkgils jkhctivls.

Aljvkrsiñj `k % `k pltkjaic c `kaifkgils y viakvkrsc Kg tcjtl plr aikjtl x% `k ujc dchjitu` `k pltkjaic sk aljvikrtk c `kaifkgils `k gc sihuikjtk nlrdc? Rchijc 31



(  )  Rcrc lftkjkr kg vcglr x% kj `kaifkgils, sk `kfk aljvkrtir pridkrl kg vcglr x `kg plrakjtcok c uj jÿdkrl rcailjcg ìviìéj`lgl plr 322. Rcrc aljvkrtir c `kaifkgils, sk dugtipgiac kg glhcritdl `kg jÿdkrl rcailjcg plr 32 (dchjitu` `k pltkjaic). Kokdpgl? Csudikj`l quk gc pltkjaic `k scgi`c `k uj airauitl `k `ls pukrtls ks ihucg cg 1% `k gc pltkjaic `k kjtrc`c, ¼auãg ks gc ctkjucaiñj kj `F<

  (  ) Rcrc aljvkrtir kg vcglr kj `F c plrakjtcok?

⁀   

Kokdpgl? Acgaugcr gc pltkjaic `k scgi`c `k uj ctkjuc`lr `k 1 `F aldl plrakjtcok `k gc tkjsiñj `k kjtrc`c.

∖    

Gc pltkjaic c gc scgi`c `k uj ctkjuc`lr `k 1 `F ks gc ditc` ;2% `k gc pltkjaic `k kjtrc`c. Jltc? Aldl cjtkrilrdkjtk, ctkjucaiñj sihjiniac vcglrks kj `kaifkgils jkhctivls

Aljvkrsiñj `k % `k tkjsiñj dãs l dkjls c `kaifkgils [j x% dãs l dkjls `k uj vcglr sihjiniac quk cócìdls l rkstcdls kg plrakjtcok cg vcglr `k ijiail. Rlr kokdpgl, si gc tkjsiñj `k scgi`c [6 `k uj cdpginiac`lr `kfk skr uj x% supkrilr c gc tkjsiñj `k kjtrc`c k jtrc`c [3, kg aãgaugl sk rkcgizc `k gc sihuikjtk dcjkrc?

       ( (   )

Qi gc tkjsiñj `k scgi`c ks dkjlr quk gc tkjsiñj `k kjtrc`c kjtljaks x skrã uj vcglr jkhctivl. Rcrc gc aljvkrsiñj c `kaifkgils sk utigizc gc sihuikjtk nñrdugc?

(  ) 

Jltc? [tigizcr kg ncatlr `k 62, pcrc dchjitu`ks `k tkjsiñj. Kokdpgl? Gc tkjsiñj `k scgi`c `k uj cdpginiac`lr ks 36.6% supkrilr c gc tkjsiñj `k kjtrc`c. ¼Auãg ks gc hcjcjaic kj `kaifkgils< Lfsérvksk quk ijagusl alj vcglrks `k plrakjtcok pkqukóls, kg aãgaugl `kg tcjtl plr aikjtl dãs `k ujc acjti`c` `c aldl rksugtc`l uj vcglr kj `kaifkgils ìnkrkjtk quk kg aãgaugl `kg tcjtl plr aikjtl dkjls. 62% dãs `c aldl rksugtc`l +3.;= `F 62% dkjls `c aldl rksugtc`l -3.90 `F

Aljvkrsiñj `k % `k pltkjaic dãs l dkjls c `kaifkgils Rcrc pltkjaic sk cpgiac gc sihuikjtk nñrdugc? Rchijc 30



      ( (   ) Rcrc gc aljvkrsiñj c `kaifkgils sk utigizc gc sihuikjtk nñrdugc?        (   ) 

Jltc? [tigizcr kg ncatlr `k 32 pcrc dchjitu`ks `k pltkjaic. Kokdpgl? Gc pltkjaic `k scgi`c `k uj ctkjuc`lr ks 62% dkjlr quk gc pltkjaic `k kjtrc`c. ¼Auãg ks gc ctkjucaiñj kj `kaifkgils<

       (   )

Cg ihucg quk kj kg acsl `kg aãgaugl alj tkjsiljks, kg aãgaugl `kg tcjtl plr aikjtl dãs `k ujc acjti`c` `c aldl rksugtc`l uj vcglr kj `kaifkgils ìnkrkjtk quk kg aãgaugl `kg tcjtl plr aikjtl dkjls.

[tigizcaiñj `k vcglrks kj `F kj gls aãgaugls Kj kstc skaaiñj sk `ksarifk añdl sudcr jivkgks `k pltkjaic y tkjsiñj kj `kaifkgils.

Qudc `k jivkgks `k pltkjaic ¼12 `Fd + 12 `Fd 4 >2 `Fd< ¡Rlr supukstl quk jl! Qi aljvkrtidls kstls jivkgks c vcglrks gijkcgks, rksugtc lfvil quk 3 X + 3 X 4 6 X, quk slj 11 `Fd y jl >2 `Fd. Rkrl kstl ks vkr`c` sñgl si gls jivkgks `k pltkjaic kj gls vcglrks ijstcjtãjkls jl tikjkj ujc rkgcaiñj `k ncsk aljstcjtk. Jltc? Ks jkakscril aljvkrtir gls jivkgks `k pltkjaic glhcrätdials c vcglrks gijkcgks cjtks `k sudcrgls. Ks dãs prãatial trcfcocr alj vcglrks kj `kaifkgils `kspués `k rkcgizcr gc sudc, plr gl quk jlrdcgdkjtk sk aljvikrtkj `k jukvl c `Fd. Kokdpgl? Qk `kskc sudcr trks skócgks R3, R6 y R1 alj jivkgks `k 2 `Fd, +1 `Fd y -> `Fd. ¼Auãg ks gc pltkjaic tltcg<

              ∖          Cg aljvkrtirgl `k jukvl kj `kaifkgils, sk lftikjk?

) ( Gc pltkjaic tltcg ks ;.36`Fd Rchijc 3;



Ruk`k quk kj kstk dldkjtl surhk, gc sihuikjtk prkhujtc, ¼si gc uji`c` lrihijcgdkjtk kstc kj `Fd, skric dãs nãaig, sudcrgc kj nlrdc ìrkatc<, si [`. rkcgizc gc lpkrcaiñj ìrkatc, 2 `Fd, +1 `Fd y -> `Fd, kg vcglr rksugtcjtk, sudc`l kj nlrdc gijkcg ks -1`Fd, kstl ìnikrk kjlrdkdkjtk `k gc rkspukstc cjtkrilr, gl aucg ks ijalrrkatl, yc quk aldl aldprkj`krã gcs skócgks `k pltkjaic aucj`l sk sudc su dchjitu` gijkcg, hkjkrc ujc pltkjaic rksugtcjtk, kg aucg kstk rkprkskjtc ujc rknkrkjaic kj uji`c`ks `Fd, ks plr kstc rczñj quk gc lpkrcaiñj sk rkcgizc pridkrl aljvirtiéj`lgcs, pcrc gukhl pcscrgcs c gc rknkrkjaic kj `Fd. Rkrl aldl téajial l ijhkjikrl `kg ãrkc, aldprkj`k quk kstk ks uj acsl mipltétial.

Dkì`c `k skócgks akrac `kg jivkg `k rui`l [jc `k gcs tcrkcs dãs aldujks ks gc `k dkìr skócgks `éfigks akracjcs cg jivkg `k rui`l `k uj ijstrudkjtl `k dkì`c, aldl uj rkakptlr l uj cjcgizc`lr `k kspkatrl. Kg ijstrudkjtl `k dkì`c dukstrc gc sudc tltcg `kg rui`l ijmkrkjtk y gc pltkjaic `k gc skócg, cujquk i`kcgdkjtk sñgl `kfkräc dlstrcr gc pltkjaic VDQ `k gc skócg, quk ks gl quk jlrdcgdkjtk laurrk cg utigizcr uj dkì`lr `k pltkjaic. Kj kg acsl `k uj cjcgizc`lr `k kspkatrl ks jkakscril cativcr kg `ktkatlr VDQ. Rridkrl sk `ktkrdijc kg jivkg `k rui`l ijmkrkjtk Rr `kg ijstrudkjtl `k dkì`c `kscativcj`l gc skócg. @kspués, sk di`k gc skócg alj kg rui`l Rtlt. Qk puk`k lftkjkr gc pltkjaic R `k gc skócg rkstcj`l gls vcglrks gijkcgks. Kokdpgl? Kg jivkg `k rui`l Rr `k uj dkì`lr `k pltkjaic ks ihucg c -82 `Fd. Aucj`l sk cpgiac ujc skócg, kg jivkg cudkjtc mcstc Rtltcg 4 ->; `Fd. ¼Auãg ks gc pltkjaic `k gc skócg kj `Fd<

  ∖    ∖        (  ) Gc pltkjaic `k gc skócg R ks ->>.> `Fd.

Rchijc 3>



Qk puk`k lfskrvcr quk sij rkcgizcr jijhujc aldpkjscaiñj, kg rui`l `kg ijstrudkjtl `k dkì`c prlvlacrã uj krrlr `k 3.> `F, quk ks uj vcglr rkgctivcdkjtk kgkvc`l pcrc uj ijstrudkjtl `k dkì`c `k prkaisiñj. JLPCQ? Dcjkocr vcglrks kj `kaifkgils ks duaml dãs skjaiggl si sk dkdlrizcj ujls aucjtls vcglrks, c pcrtir `k gls aucgks sk puk`kj lftkjkr ltrls. Qk puk`k sidpginiacr kg prlfgkdc rk`lj`kcj`l mcaic crrifc l mcaic cfcol cghujls `k gls rksugtc`ls pcrc quk skc dãs nãaig rkalr`cr kstcs ainrcs. Pl`l gl quk mcy quk mcakr ks dkdlrizcr gls vcglrks cprlxidc`ls, plr kokdpgl, uj ncatlr `k 6 kj pltkjaic sk alrrksplj`k alj 1 `F (kj guhcr `kg vcglr kxcatl `k 1.26 `F). 1 `F jl sk alrrksplj`k kxcatcdkjtk alj ujc rkgcaiñj `k pltkjaic `k 6 y > `F jl sk alrrksplj`k kxcatcdkjtk alj ujc rkgcaiñj `k pltkjaic `k 0. Qij kdfcrhl, jlrdcgdkjtk sk utigizcj kstcs sidpginiacailjks yc quk cplrtcj ujc prkaisiñj suniaikjtk kj gls aãgaugls. Qi sk jkaksitc acgaugcr alj prkaisiñj gc sudc `k `ls vcglrks kspkainiac`ls kj `kaifkgils, pridkrl mcy quk aljvkrtir gcs acjti`c`ks c dchjitu`ks gijkcgks, sudcrgcs y plstkrilrdkjtk aljvkrtir kg rksugtc`l c `kaifkgils. Kokdpgls? Qupljhcdls quk sk `kskcj sudcr gls sihuikjtks jivkgks `k pltkjaic? ->2 `Fd y ->> `Fd. Rcrc kggl, sk rkstcj cdfcs acjti`c`ks lftkjiéj`lsk ujc ìnkrkjaic `k > `F. Aucj`l tkjkdls pltkjaics kj Digi ^lgtils, Diarl^lgtils y/l Xctts kjtrk ltrls, y tkjkdls cghÿj airauitl ctkjuc`lr `k > `F, scfrkdls quk cg vcglr `k kjtrc`c gk quitcrkdls gc ditc `k gc ditc` `k pltkjaic, ñskc kg rksugtc`l skrã uj aucrtl `k gc pltkjaic `k rknkrkjaic `k su kjtrc`c. Prcfcocr alj `kaifkgks cg prijaipil rksugtc uj plal aljnusl, pkrl kj gc prãatiac aljstcjtk `kg téajial l Ijhkjikrl `k gcs rcdcs c nijks `k pltkjaic y tkgkaldujiacailjks ks aljstcjtk su utigizcaiñj

Rchijc 38



Cghujcs ainrcs ÿtigks Gcs sihuikjtks ainrcs tcdfiéj puk`kj skr ÿtigks c gc mlrc `k rkcgizcr gls aãgaugls? 31 `Fd sk alrrksplj`k alj [VDQ 4 3 ^ slfrk ;2 ℮ 2 `Fd sk alrrksplj`k alj [VDQ 4 2.660 ^ slfrk ;2 ℮ 328 `F (»^) sk alrrksplj`k alj 2 `Fd slfrk ;2 ℮ 362 `F (»^) sk alrrksplj`k alj 3 ^ -380 `Fd ks gc pltkjaic `k rui`l r ui`l térdial alj uj cjaml `k ` k fcj`c `k 3 Mz c ujc tkdpkrcturc cprlxidc`c 62 ²A (>= ²N).

Ltrcs dchjitu`ks `k rknkrkjaic Mcstc cmlrc, mkdls utigizc`l aldl dchjit u   3 dX y ;2 Ω  ij kdfcrhl, mcy sistkdcs quk utigizcj rknkrkjaics ìstijtcs, aldl kj tkgkvisiñj quk sk uscj 8; Ω y  ÿ   d    >22 Ω. G d  VN  >2 Ω d d     d  >22 Ω   K  

sk utigizcj `kdcsic`l. Qij kdfcrhl, ks fcstcjtk skjaiggl c`cptcr gcs nñrdugcs c kstcs jukvcs rknkrkjaics.

V

R2

[2

Jltc

;2 Ω

3 dX

2.660 ^

Ijhkjikräc VN

>2 Ω

3 dX

2.60; ^

Ijhkjikräc VN (cjtihuc)

8; Ω

3 dX

2.680 ^

Ijhkjikräc P^

>22 Ω

3 dX

2.88; ^

Caÿstiac

>22 Ω

3.>> dX

3.222 ^

Kstãj`cr [QC

Rrkaisiñj, plsiailjks `kaidcgks ¼Auãjtcs plsiailjks `kaidcgks sk `kfkräcj utigizcr pcrc kspkainiacr vcglrks kj `kaifkgils< Qi sk cudkjtc uj jivkg `k pltkjaic x kj 2.23 `F, kg vcglr gijkcg vcräc `k gc sihuikjtk nlrdc?

 +    

Kstl ks kquivcgkjtk c uj cudkjtl `k pltkjaic `kg 2.61%. Kj kg acsl `k tkjsiñj, kg acdfil ks `kg 2.33%. Kstk acdfil `k jivkg ks aldpcrcfgk c gcs nguatucailjks jlrdcgks `kg rksugtc`l `k dkì`c. Rlr gl tcjtl, jl tikjk skjti`l kspkainiacr vcglrks kj `kaifkgils alj aijal l dãs `kaidcgks scgvl kj aljtc`cs lacsiljks.

Rchijc 3=



Pcfgc `k % `k pérì`cs kj `F Rkrì`c Rkrì`c Rkrì`c Rkrì`c Rkrì`c Rkrì`c Rkrì`c Rkrì`c `F plrakjtucg `F plrakjtucg `F plrakjtucg `F plrakjtucg 6.2 18 % 0.2 >2 % >.2 8; % 2.6 0% 6.6 19 % 0.6 >6 % 8.2 =2 % 2.0 =% 6.0 06 % 0.0 >1 % =.2 =0 % 2.> 31 % 6.> 0; % 0.> >; % 9.2 =8 % 2.= 38 % 6.= 08 % 0.= >8 % 32.2 92 % 3.2 63 % 1.2 ;2 % ;.2 >= % 62.2 99 % 3.6 60 % 1.6 ;6 % ;.6 82 % 12.2 322 % 3.0 68 % 1.0 ;0 % ;.0 83 % 02.2 322 % 3.> 12 % 1.> ;> % ;.> 81 % 3.= 11 % 1.= ;= % ;.= 80 %

Vknkrkjaic `k gls Xctts

Rchijc 39



Qlfrk gls vcglrks kj `F kjtrk y gc rkgcaiñj `k pltkjaic / Pkjsiñj Aldl sk puk`k vkr ks duaml dãs nãaig sudcr gcs uji`c`ks kj `kaifkg quk ujc dugtipgiacaiñj aldpgkoc, kokdpgl alj `F kj pltkjaic? 3222

6222

4 6 x ; x 322 4 32 x 32 x 32 4 32 x 322 4 6 x 3222

4: 4: 4: 4:

1 `F + 8 `F + 62 `F 32 `F + 32 `F + 32 `F 32 `F + 62 `F 1 `F + 12 `F

4 12 `F 4 12 `F 4 12 `F 4 11 `F

Ltrc nlrdc `k rkgcailjcr? = `F 4 1 `F + ;`F 4: 6x14> (Gc hcjcjaic rkgcailjc`c pcrc = `F ks dÿgtipgl `k > cprlxidc`cdkjtk) Aucj`l gcs idpk`cjaics `k `k pltkjaic tcjtl `k kjtrc`c aldl scgi`c slj gcs disdcs, gc aljvkrsiñj `k pltkjaic c tkjsiñj slgl fcstcrc kj dugtipgiacrgl plr 6 kg vcglr `k pltkjaic y lftkjkdls gc rkgcaiñj `k tkjsiñj, skhÿj gc sihuikjtk rkgcaiñj? 6 x `F (tkjsiñj) 4 `F (pltkjaic) Auc`rl `k rkgcaiñj dÿgtipgl, pltkjaic y t kjsiñj kj `F

Dÿgtipgl x6 x1 x0 x; x= x 32 x 322 x 3.222 x 32.222 x 322.222 x 3.222.222

`F (kj Rltkjaic) 1 `F ; `F > `F 8 `F 9 `F 32 `F 62 `F 12 `F 02 `F ;2 `F >2 `F

`F (kj Pkjsiñj) > `F 32 `F 36 `F 30 `F 3= `F 62 `F 02 `F >2 `F =2 `F 322 `F 362 `F

Jltc? `F Pkjsiñj 4 6 x `F Rltkjaic, slgl pcrc kg disdl vcglr `k idpk`cjaic `k uj sistkdc l airauitl. ^cglrks rkgcailjc`ls c uj `F dkì`lr `k skócg ijtkrjc kj gls kquipls

"Q"4Q-Dktkr Q-2 Q-3 Q-6 Q-1 Q-0 Q-; Q-> Q-8 Q-= Q-9 Q-9 +32`F Q-9 +62`F Q-9 +12`F Q-9 +02`F

`F (Pkjsiñj) -;0 `F -0= `F -06 `F -1> `F -12 `F -60 `F -3= `F -36 `F -> `F Vknkrkjaic +32 `F +62 `F +12 `F +02 `F

Qkócg `k rkakpaiñj 2.6 diarl-^lgtils 2.0 diarl-^lgtils 2.= diarl-^lgtils 3.; diarl-^lgtils 1 diarl-^lgtils > diarl-^lgtils 36.; diarl-^lgtils 6; diarl-^lgtils ;2 diarl-^lgtils 2.3 digi-^lgtils 2.1 digi-^lgtils 3 digi-^lgtils 1 digi-^lgtils 32 digi-^lgtils Rchijc 62



Fifgilhrcnäc U3T ¼`F l jl `F< Vlm`k & Qamwcrz, Dcräc Oidéjkz, dcyl `k 622> @P-DO-223-2>. @P-DO-2 23-2>. U6T Xieipkìc www.wieipkìc.lrh www.wieipkìc.lrh.. U1T Dcjucg pcrc kg Vcìlcniailjc`l AVCQ, Kg Qcgvc`lr, cfrig `k 622;. U0T Kg `kaifkg acrcatkrästiacs y cpgiacailjks, Ijh. Kùcr`l O. Dkjsl, Vkvistc tkgkhrãniac kgkatrñjiac, pufgiacaiñj kjkrl `k3991. U;T Gc pãhijc `k Rikrrl, Cjtkjjc Hcij, Q-Dktkr, Vcìl/Qihjcg rkplrt mttp?//pchks.ijtjkt.du/ijhkpru/`kaifkg.mtd

Rchijc 63

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