Campos Variables en El Tiempo
August 10, 2022 | Author: Anonymous | Category: N/A
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NKBQJ^ WKPIK@DM^ ML MD XIMBQJ Md bktmrikd mstuhikhj fkstk kfjrk pmrtmlmnm kd nksj mspmnikd hm njrrimltms njlstkltms (NH) y nkreks mdéntrinks mstëtinks, qum nrmkl nkbpjs bkelétinjs y mdéntrinjs tkb`iél njlstkltms ml md timbpj m ilhmpmlhimltms mltrm sâ. Kfjrk njrrmspjlhm md mstuhij hm dks nkreks y njrrimltms vkrik`dms njl md timbpj, hm bkyjr iltmrés prëntinj. Dks nkreks y njrrimltms vkrik`dms njl md timbpj ilhunml nkbpjs vkrik`dms ml md timbpj y simbprm knjpdkhjs mltrm mddjs. mddjs . Kb`js nkbpjs mstkrël prmsmltms kd mxistir ulj hm mdd mddjs js y sjl ddkbkhjs nkbpjs mdmntrjbkelétinjs hilëbinjs j vkrik`dms ml md timbpj. Djs nkbpjs mdéntrinjs y bkelétinjs sm iltmrnjlmntkl y md knjpdkbimltj mltrm mddjs prjhunm jlhks mdmntrjbkelétinks nkpknms hm vikokr k trkvés hmd mspknij di`rm y ml bmhijs bktmrikdms. Dks jlhks mdmntrjbkelétinks, qum ilnduyml jlhks dubiljsks, rkyjs V, jlhks ilgrkrrjoks, rkyjs ekbbk y jlhks hm rkhij. Ml md nksj mstëtinj hjlhm
2 1,
sm utidizkrjl md pribmr pkr hm dks mnuknijlms hm Bkxwmdd
pkrk mstuhikr gmlþbmljs mdéntrinjs y md smeulhj pkrk klkdizkr gmlþbmljs bkelétinjs, ml md nksj hilëbinj
≡1,
sm timlm qum njlsihmrkr md knjpdkbimltj qum mxistm mltrm djs nkbpjs
mdéntrinjs y bkelétinjs, tkd njbj dj mxprmskl dk smeulhk y nukrtk mnuknijlms hm dk tk`dk?
Njbj sm vm ml dk tk`dk, dks mnuknijlms ; y > hm dk dmy hm Ekuss sieuml simlhj vëdihks tkltj ml nkbpjs hilëbinjs njbj mstëtinjs. Dk smeulhk y nukrtk mnuknijlms hm Bkxwmdd si sm vm dk iltmrhmpmlhmlnik mltrm djs nkbpjs. Ml md nkbpj hilëbinj sm fkrë md mstuhij hm mstks hjs ÿdtibks mnuknijlms? Dmy hm Gkrkhky y Dmy hm Kbpmrm.
DMY HM GKPKHKY Mstk dmy hintk qum ul nkbpj bkelétinj qum vkrâk njl md timbpj emlmrk ul nkbpj mdéntrinj vkrik`dm ml md timbpj. ]l nkbpj bkelétinj vkrik`dm ml md timbpj prjhunm ul vjdtkom ilhunihj (vjdtijs) ddkbkhj gumrzk mdmntrjbjtriz (gmb) nkpkz hm prjhunir ulk njrrimltm ml ul nirnuitj nmrrkhj, mstm prjnmsj sm njljnm njbj ilhunniþl mdmntrjbkelétink.
0
(;) Mnukniþl emlmrkd
Md gduoj bkelétinj ms md gduoj qum nruzk k trkvés hm nukdquimr supmrginim nuyj pmrâbmtrj smk ulk trkymntjrik nmrrkhk y hШ/ht ms dk rkzþl hm nkb`ij hm hinfj gduoj njl rmspmntj kd timbpj. Md sielj bmljs sieligink qum md vjdtkom ilhunihj kntÿk pkrk prjhunir ul gduoj qum sm jpjlm kd nkb`ij hmd gduoj qum dj prjhunm, mstj sm njljnm njbj Dmy hm Dmlz. Md mgmntj hm dk dmy hm Dmlz sm mbpdmk pkrk prmhmnir dk pjdkrihkh hm djs vjdtkoms ilhunihjs ml djs hmvklkhjs hmd trklsgjrbkhjr.
Gmb
Dk njrrimltm ml dk mspirk simbprm nirnudk ml ulk hirmnniþl qum sm jpjlm kd nkb`ij hmd gduoj bkelétinj Χ (t) Χ (t) qum dk prjhuoj. Md vjdtkom ilhunihj prjhunm ulk njrrimltm njrr imltm ilhunihk i n, njrrimltm qum k su vmz nrmk ul nkbpj bkelétinj ilhunihj (@ ilh). Ms ibpjrtkltm rmnjrhkr qum md nkbpj bkelétinj ilhunihj sm jpjlm kd nkb`ij hm @(t) y lj lmnmskrikbmltm k @(t) pjr sâ sjdj, mstjs nkb`ijs pumhml smr ml bkelituh j hirmnniþl.
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@ (t), pjr dk dmy hm Gkrkhky ilhunm ulk njrrimltm In. @ (t) nkbpj vkrik`dm ml md
Mstk njrrimltm nrmk ul nkbpj bkelétinj ilhunihj Ш¸
timbpj, pksk k trkvés hm hm ulk
qum sm jpjlm kd nkb`ij hmd gduoj jrieilkd hm @ (t). ^i
trkymntjrik nmrrkhk N (mspirk)
timlm ulk k`mrturk ml mstk pumhm bmhirsm ulk gmb j j vjdtkom kd njdjnkr ulk nkrek mxtmrlk nirnudk In.
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JPIEML HM DJ^ NKBQJ^ MDMNXPINJ^ WKPIK@DM^ W KPIK@DM^ Qkrk qum nirnudm ulk njrrimltm ml ul njlhuntjr ms lmnmskrik dk kpdinkniþl hm ul nkbpj mdéntrinj qum momrzk ulk gumrzk qum j`dieum k nirnudkr djs mdmntrjlms di`rms hmd bktmrikd njlhuntjr. Mstm nkbpj mdéntrinj ms jrieilkhj pjr dk gumrzk mdmntrjbjtriz (gmb). Ml md mstuhij hm dk mdmntrjstëtink vibjs md nkbpj mdéntrinj nrmkhj pjr dks nkreks mdéntrinks mstëtinks. ^il mb`krej mxistml jtrjs nkbpjs mdéntrinjs nrmkhjs pjr ulk gumrzk mdmntrjbjtriz njbj emlmrkhjrms mdéntrinjs, pidks, `ktmrâks `ktmrâks qum sjl gumltms hm gumrzk mdmntrjbjtriz qum njlvimrtml dk mlmreâk lj mdéntrink ml mdéntrink. Ml mstjs tipjs hm nkbpjs mdéntrinjs ml ulk trkymntjrik nmrrkhk sm nubpdm qum?
(0)
Higmrmlniks mltrm md nkbpj mdéntrinj vkrik`dm njl md timbpj y md nkbpj mdmntrjstëtinj. Ml mdmntrjstëtink, dk iltmerkd hm dâlmk hk duekr k ulk higmrmlnik hm pjtmlnikd3 ml djs nkbpjs vkrikltms njl md timbpj, md rmsudtkhj ms ulk gmb j ul vjdtkom. ]l nkbpj mdéntrinj jrieilkhj pjr ulk histri`uniþl hm nkrek mstëtink emlmrk ulk
higmrmlnik hm pjtmlnikd nmrj k dj dkrej hm ulk trkymntjrik nmrrkhk. Ml md nkbpj mdéntrinj vkrik`dm ml ulk trkymntjrik nmrrkhk ms ieukd k dk gumrzk mdmntrjbjtriz j vjdtkom. Hm dj kltmrijr njb`ilklhj (;) y (0) y sustituymlhj md Ш pjr dk mxprmsiþl iltmerkd hmd nkbpj @ pjr dk higmrmlnikd hm supmrginim sm j`timlm?
(>)
Hjlhm ^ ms dk supmrginim mlnmrrkhk pjr dk trkymntjrik nmrrkhk D. hШ/ht pumhm hm`mrsm k trms nkusks? Dk vkrikniþl hmd gduoj ml md timbpj hШ/ht k. ]lk mspirk giok (ërmk njlstkltm ml md timbpj) ml ul nkbpj @ vkrik`dm ml md timbpj `. ]lk mspirk bþvid (ërmk vkrik`dm ml md timbpj) ml ul nkbpj @ mstëtinj n. ]lk mspirk bþvid (ërmk vkrik`dm ml md timbpj) ml ul nkbpj @ vkrik`dm ml md timbpj
Nksj k Mnukniþl hm ilhunniþl trklsgjrbkhjrk Mstk gjrbk hm dk dmy hm Gkrkhky hk dk gmb ilhunihk pjr ul nkbpj bkelétinj vkrik`dm ml md timbpj ml ul nirnuitj j mspirk giok, mstm ms md prilnipij hm gulnijlkbimltj hmd trklsgjrbkhjr. Njbj md ërmk hm dk supmrginim mstk giok (^ njlstkltm) sjdj vkrâk md nkbpj @ (
) dk mnukniþl sm rmhunm k? (8) Dmy hm Gkrkhky ml gjrbk iltmerkd
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Ml djs trklsgjrbkhjrms rmkdms sm uskl `j`ilkhjs hm L vumdtks pkrk kubmltkr md vjdtkom ilhunihj, ksâ njbj lÿndmjs gmrrjbkelétinjs pkrk kubmltkr hm bklmrk njlsihmrk`dm md gduoj bkelétinj ml md nirnuitj. Dk vkrikniþl hmd gduoj bkelétinj Ш sm djerk pjr dk njrrimltm vkrik`dm ml md timbpj I (t) ml md pribkrij hmd trklsgjrbkhjr. (=) Qkrk L vumdtks ml md nirnuitj, sm ilhunm bkyjr vjdtkom
Kpdinkniþl hm dk dmy hm Gkrkhky ml md nirnuitj hmd trklsgjrbkhjr hm ; vumdtk ml md smnulhkrij. Dk njrrimltm vkrik`dm I (t) prjhunm ul gduoj bkelétinj vkrik`dm @ (t). ( t). Mstm gduoj iltmrsmntk dk supmrginim mlnmrrkhk pjr md nirnuitj gioj hmd smnulhkrij (mspirk) ilhunimlhj ul vjdtkom ml éd (gmb) tkb`iél vkrik`dm ml md timbpj W (t)
Kpdinklhj md tmjrmbk hm ^tjcms Kpdinklhj ^tjcms k dk iltmerkd iltmerkd hm dâlmk nmrrkhk hm dk m mnukniþl nukniþl (8), (8), sm j`timlm dk gjrbk higmrmlnikd hm dk Dmy hm Gkrkhky?
(7) Dmy hm Gkrkhky ml gjrbk higmrmlnikd
Nksj `. Mnukniþl emlmrkhjrk Nuklhj ulk nkrek mdéntrink [ sm bumvm k ulk vmdjnihkh v ml bmhij hm ul nkbpj bkelétinj @, ulk gumrzk bkelétink ms momrnihk sj`rm dk nkrek hkhk pjr dk mnukniþl hm Djrmltz?
Hmspmoklhj [, sm j`timlm ul nkbpj mdéntrinj mquivkdmltm jrieilkhj pjr dk gumrzk bkelétink
=
Dk gumrzk bkelétink sj`rm dk nkrek ml bjvibimltj prjhunm ul nkbpj mdéntrinj mquivkdmltm qum momrnmrâk ulk gumrzk mdéntrink sj`rm dk nkrek [. Nuklhj ul nkbpj ms emlmrkhj pjr md bjvibimltj hm pkrtânudks nkrekhks ml bmhij hmd nkbpj @ sm ddkbk nkbpj mdéntrinj bþvid Mb y ms pmrpmlhinudkr kd pdklj qum njltimlm v y @.
Njbj ul njlhuntjr mstë njbpumstj hm lubmrjsks nkreks di`rms, mstks nkreks kd bjvmrsm k trkvés hm ul nkbpj bkelétinj @, dk gumrzk bkelétink nrmk md nkbpj mdéntrinj bþvid Mb qum k su vmz emlmrk ul vjdtkom j gmb mltrm djs hjs mxtrmbjs hmd njlhuntjr. ^imbprm qum ulk hmlsihkh hm gduoj bkelétinj @ njrtm ul njlhuntjr, sm ilhunm ul vjdtkom mltrm djs tmrbilkdms k y ` hmd njlhuntjr hkhj pjr dk mnukniþl emlmrkhjrk?
Ml md nksj hm ul njlhuntjr qum sm bumvm ml ul nkbpj bkelétinj njlstkltm sm pumhm ksjnikr ulk iltmlsihkh hm nkbpj mdéntrinj hm bjvibimltj hkhk pjr Mb 2 v Õ @ k nkhk pkrtm hmd njlhuntjr bþvid nuklhj mstjs gjrbkl pkrtm hm ul nirnuitj nmrrkhj y mvkdukr dk gmb rmsudtkltm pjr bmhij
^imlhj dk iltmerkniþl kdrmhmhjr hmd nirnuitj nmrrkhj njbpdmtj pjr mombpdj ulk mspirk. Mstk gmb ms dk qum mstë prmsmltm ml djs emlmrkhjrms y bjtjrms.
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Emlmrkhjr mspirk bþvid (rjtjr) y nkbpj @ uligjrbm uligjrbm
Emlmrkhjr. Njlhuntjr gioj (mstktjr) y nkbpj @ vkrik`dm (rjtjr)
Nksj n. ]lk mspirk bþvid (ërmk vkrik`dm ml md timbpj) ml ul nkbpj @ vkrik`dm ml md timbpj ^i dk hmlsihkh hm gduoj bkelétinj tkb`iél nkb`ik njl md timbpj, mltjlnms sm hm`ml ilnduir kb`ks njltri`unijlms, dk gmb hm trklsgjrbkhjr y dk gmb hm bjvibimltj?
^m hk dk smpkrkniþl hm dk gmb ml hjs pkrtms, ulk hm`ihk k dk rkzþl hm nkb`ij hm @ njl md timbpj y dk jtrk kd bjvibimltj hmd nirnuitj. Dk dmy hm Gkrkhky smeÿl dk kpdinkniþl prëntink sm hjs usk pumhm su gjrbk iltmerkd jpkrk emlmrkd. Mstks mxprmsijlms sjl mquivkdmltms y nukdquimrk hm dks mbpdmkrsm hmtmrbilkr mstjs vjdtkoms ilhunihjs.
^i dk `j`ilk sm njbpjlm hm L vumdtks, djs térbiljs hm djs dkhjs hmrmnfjs hm dks mnuknijlms hm`mrël budtipdinkrsm pjr L.
5
DMY HM KBQMPM Bkxwmdd kermej ul lumvj térbilj k dk mnukniþl hm dk dmy hm Kbpmrm pkrk njrrmeir dk ilnjbpkti`idihkh qum sm prmsmltk`k mltrm dk mnukniþl hm dk njltiluihkh hm dk nkrek y md rjtknijlkd hm F nuklhj djs nkbpjs sjl vkrik`dms ml md timbpj. Dk mnukniþl hm dk njltiluihkh ilhink qum dk hivmremlnik hm dk hmlsihkh hm njrrimltm ms ieukd k dk vkrikniþl hm dk nkrek vjdubétrink rmspmntj kd timbpj (ml ulk supmrginim nmrrkhk md sielj bmljs sieligink hisbiluniþl hm dk nkrek hmltrj hm dk supmrginim)?
Ml nkbpjs mstëtinjs
2 1
mltjlnms,
⋍ ̍ 2 1
Ml nkbpjs mstëtinjs mstk mnukniþl mxpdink ml gjrbk bktmbëtink pjrqum lj pumhm fk`mr knubudkniþl hm nkrek ml ul ljhj (dmy hm Cirnffjgg hm ljhjs), tjhk dks dâlmks hm hmlsihkh hm njrrimltm qum mltrk ml ieukd k dk qum skdm pjr mddj dk hivmremlnik ms nmrj.
O
Dk dmy hm Kbpmrm ml nkbpjs bkelétinjs ml gjrbk higmrmlnikd ilhink?
^i kpdinkbjs dk hivmremlnik k mstk ÿdtibk mnukniþl pkrk vmriginkr njl dk mnukniþl hm njltiluihkh, pjr nëdnudj vmntjrikd sk`mbjs qum dk hivmremlnik hm ul rjtknijlkd ms NMPJ. Ml mstm nksj hm nkbpjs mstëtinjs sm nubpdm pjrqum kb`js sjl NMPJ.
Qmrj ml md nksj hm nkbpjs vkrik`dms lj sunmhm ksâ, yk qum dk mnukniþl hm dk njltiluihkh ms higmrmltm hm nmrj, hm kddâ surem dk ilnjbpkti`idihkh qum Bkxwmdd njrriem iltrjhunimlhj md tmrbilj hm hmlsihkh hm njrrimltm hm hmspdkzkbimltj Oh qum sm nubpdm pkrk tjhjs nksjs tkltj nkbpjs mstëtinjs njbj vkrik`dms ml md timbpj
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Njl mstk njrrimltm sm njbpdmtkl djs trms tipjs hm hmlsihkh hm njrrimltm njljnihks fkstk kfjrk? Dk hmlsihkh hm njrrimltm hm njlhunniþl, qum sjl prjhunihks pjr md bjvibimltj hm nkreks mdéntrinks ml ulk rmeiþl njl hmlsihkh lmtk hm nkrek ludk, emlmrkdbmltm dk njrrimltm qum njljnmbjs njbj md bjvibimltj hm mdmntrjlms di`rms ul njlhuntjr j nk`dm. Dks sjdunijlms mdmntrjdâtinks (`ktmrâks), njrrimltms ml smbinjlhuntjrms. Xkb`iél sjl njrrimltms hm njlhunniþl.
Dk hmlsihkh hm njrrimltm hm njlvmnniþl, qum ms md bjvibimltj hm dk hmlsihkh hm nkrek vjdubétrink. Mstk ms prjhunihk pjr md bjvibimltj hm pkrtânudks nkrekhjs ml njrrimltms j gduojs k trkvés hm ul mspknij (eksms j dâquihjs). Xkb`iél sjl sm ilnduym md bjvibimltj gâsinj hm j`omtjs nkrekhjs pjr mombpdj ul vihrij nkrekhj pjr grjtkbimltj ml bjvibimltj.
Kb`ks sm rmprmsmltkl rmprmsmltkl pjr O Dk hmlsihkh hm njrrimltm hm hmspdkzkbimltj, hmspdkzkbimltj ,
,
Mstks sjl njrrimltms prjhuntj hm ul nkbpj mdéntrinj vkrik`dm njl md timbpj. ^jl ibpjrtkltms k kdtks grmnumlniks y ml bktmrikdms himdéntrinjs Mxistml ml tjhj njlhuntjr ibpmrgmntj qum ddmvk ulk njrrimltm hm njlhunniþl vkrikltm njl md timbpj sil mb`krej ml grmnumlniks bmljrms k ;1;; Fz, dk njrrimltm hm hmspdkzkbimltj ml bmtkdms pumhm ieljrkrsm. Ml md nksj hm himdéntrinjs dk njrrimltm hm njlhunniþl ms bâlibk j nmrj, bimltrks qum dk njrrimltm hm hmspdkzkbimltj lulnk pumhm ieljrkrsm. Ml grmnumlnik hm 71Fz, tjhk dk njrrimltm qum pksk k trkvés hm ul njlhmlskhjr ml ul nirnuitj hm NK ms njrrimltm hm hmspdkzkbimltj. Ml mstk sm ilnduym dk njrrimltm hm nkreks diekhks j pjdkrizkniþl. Dk njrrimltm tjtkd sm j`timlm hm dk subk hm dks njrrimltms hm njlhunniþl y hmspdkzkbimltj, mxprmskhk pjr dk dmy hm Kbpmrms ml gjrbk iltmerkd.
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QPJQKEKNIJL HM JLHK Dks jlhks ml bjvibimltj trklspjrtkl mlmreâk hm ul pultj k jtrj, hm kddâ md iltmrés ml md mstuhij hm su prjpkekniþl ml md mspknij. ]lk nkrkntmrâstink msmlnikd hm ulk jlhk qum sm prjpkek ms qum ms ulk pmrtur`kniþl kutjsustmltk`dm hmd bmhij k trkvés hmd nukd vikok. ^i mstk pmrtur`kniþl vkrâk njbj ulk gulniþl hm ulk vkrik`dm mspknikd ms ulk jlhk ulihibmlsijlkd. ]lk jlhk `ihibmlsijlkd sm prjpkek hm ul dkhj k jtrj hm ulk supmrginim, su pmrtur`kniþl pmrtur`kn iþl sm hmsnri`m bmhikltm hjs vkrik`dms mspknikdms. ]lk jlhk trihibmlsijlkd sm prjpkek k trkvés hm ul vjdubml y su pmrtur`kniþl ms ulk gulniþl hm dks trms vkrik`dms mspknikdms. Dks jlhks trihibmlsijlkd trihibmlsijlkdms ms khjptkl bunfks gjrbks higmrmltms3 ilnduyml jlhks pdklks, jlhks nidâlhrinks y jlhks msgérinks. ]lk jlhk pdklk sm nkrkntmrizk pjr ulk pmrtur`kniþl qum ml ul pultj hkhj ml md timbpj timlm prjpimhkhms uligjrbms k trkvés hm ul pdklj ilgilitj pmrpmlhinudkr k dk hirmnniþl hm prjpkekniþl hm dk jlhk.
Jlhk ulihibmlsijlkd njl vmdjnihkh hm prjpkekniþl u, njbj md hmspdkzkbimltj vmrtinkd hm dk numrhk
Jlhk `ihibmlsijlkd, njbj md bjvibimltj hmd keuk kd krrjokr ulk pimhrk
Jlhk trihibmlsijlkd
Dk Mnukniþl hm Jlhk Qdklk Emlmrkd Dk mnukniþl emlmrkd hm jlhk hmsnri`m njbj ms dk prjpkekniþl (kvklnm y/j rmtrjnmsj) hm dk jlhk ml md mspknij. Dk mnukniþl msnkdkr hm jlhk hm ulk hibmlsiþl mstë hkhk pjr dk mxprmsiþl?
2 G
(;)
Dk prjpkekniþl ms md mom _ (ml mstm nksj). nksj) . Hjlhm v ms dk vmdjnihkh hm gksm hm dk jlhk m G rmprmsmltk ulk gulniþl. Mstk ms dk mnukniþl qum sm kpdink kd bjvibimltj hm dks jlhks mdmntrjbkelétinks pdklks njljnihks njbj Jlhks Xrklsvmrskdms Mdmntrjbkelétinks (XMB).
;1
^jdunijlms hm Jlhk Qdklk ml njjrhmlkhks rmntkleudkrms Dk hmsnripniþl bktmbëtink hm ulk jlhk, fknm usj hm dks hmrivkhks pkrnikdms. Dk sjduniþl hm dk mnukniþl hm jlhk hmsnri`m dk jlhk ml si, pjr mddj sm hm`m `usnkr ulk mxprmsiþl bktmbëtink qum sktisgkek dk mnukniþl hm jlhk (;)
Mstk mnukniþl timlm sjdunijlms hm dk gjrbk?
+∐ 22 2
Jlhk qum vikok fknik ktrës -_ Jlhk qum vikok fknik khmdkltm +_ ^jduniþl hm jlhk
Kb`ks hirmnnijlms Kb`ks hirmnnijlms
2 2
Hjlhm y sjl gulnijlms kr`itrkriks. Mstks rmprmsmltkl jlhks qum vikokl njl vmdjnihkh ml dks hirmnnijlms hmd mom +_ y „ y „_ _ rmspmntivkbmltm. Mstks gulnijlms g y e mxprmskhks ml gulniþl hmd timbpj pumhml smr hm dk gjrbk?
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Dks pjsi`dms sjdunijlms k dk mnukniþl (;) mxprmskhks njbj gulnijlms smljihkdms (njl hmpmlhmlnik krbþlink njl md timbpj), njbj pjr mombpdj dks smûkdms hm njrrimltm kdtmrlk NK sjl dks sieuimltms?
∐ 2 + 2 2 2
2
2
2
2
2
Hjlhm ω ms dk grmnumlnik kleudkr ml rkh/se y c ms md lÿbmrj hm jlhk c2ω/ ml rkh/b Njlsihmrklhj njbj sjduniþl ulk jlhk qum sm prjpkek fknik khmdkltm gjrbk njbpdmok?
∐ + 2 ∐
si tjbkbjs dk
Dk nukd sm bumstrk njbj ulk njb`ilkniþl hm dks gjrbks hm smlj y njsmlj, bmhikltm md usj hm dk ihmltihkh hm Mudmr?
2 2 2 2
ζ 2
Xjbklhj dk pkrtm ibkeilkrik Xjbklhj dk pkrtm rmkd
^m j`smrvk qum sm pumhm tjbkr dk pkrtm rmkd j ibkeilkrik, pjr dj qum sm hmbumstrk qum tjhks dks kltmrijrms gulnijlms sjl sjdunijlms hm jlhk pdklk. ^m pumhm mdmeir nukdquimrk hm mddks pkrk su rmprmsmltkniþl.
;;
MN]KNIÞL HM JLHK MDMNXPJBKELÉXINK MDMNXPJBKELÉXINK Dk mnukniþl hm jlhk mdmntrjbkelétink sm hmrivk hm dks mnuknijlms hm Bkxwmdd. Nuklhj sm njlsihmrkl jlhks mdmntrjbkelétinks ml md mspknij di`rm sm j`smrvk qum md bmhij nkrmnm hm gumltms ( y O21) Ml mstks njlhinijlms, dks mnuknijlms hm Bkxwmdd sþdj sm pumhml msnri`ir ml térbiljs hm M y F ml dk sieuimltm gjrbk,
2 1
^m prmsupjlm dk mxistmlnik hm ulk jlhk pdklk uligjrbm ml dk qum kb`js nkbpjs, M y F, sm mlnumltrkl ml md pdklj trklsvmrskd, ms hmnir, md pdklj nuyk pmrpmlhinudkr ms dk hirmnniþl hm prjpkekniþl.
Jlhks Xrklsvmrskdms Mdmntrjbkelétinks (XMB). - Dks jlhks pdklks sþdj timlml njbpjlmltms hm nkbpj trklsvmrskdms k dk hirmnniþl hm prjpkekniþl. Dks jlhks mdmntrjbkelétinks sieuml mstm pktrþl pjr mddj sjl njljnihks Jlhks Xrklsvmrskdms Mdmntrjbkelétinks (XMB) yk qum sm prjpkekl ml ul sjdj pdklj (dks njbpjlmltms hm M y F mstël njltmlihks ml ul sjdj pdklj). Mstks jlhks rmprmsmltkl tjhj md mspmntrj ml dks kpdinknijlms fjy njljnihks?
;0
Ml dk gieurk sieuimltm, dk prjpkekniþl hm dk jlhk ms ml dk hirmnniþl hm _. Xkltj md nkbpj mdéntrinj M njbj md nkbpj bkelétinj F sjl pmrpmlhinudkrms k dk hirmnniþl hm prjpkekniþl _. Md nkbpj bkelétinj @ ms pmrpmlhinudkr kd nkbpj mdéntrinj M, ml dk jrimltkniþl hjlhm md prjhuntj vmntjrikd M x @ sm mlnumltrk ml dk hirmnniþl hm dk prjpkekniþl hm dk jlhk.
Dk mnukniþl hm jlhk hmd nkbpj mdmntrjbkelétinj ml md mspknij di`rm ms?
Y dk vmdjnihkh hm prjpkekniþl ms ieukd k N qum hmljtk dk vmdjnihkh hm dk duz ml md mspknij di`rm?
Dk sjduniþl hm ulk mnukniþl hm jlhk hmpmlhm hmd tipj hm jlhk klkdizkhk. Qkrk dks jlhks mdmntrjbkelétinks XMB sm ksubm gulnijlms silusjihkdms njl ulk grmnumlnik mspmnâgink, sm msnri`m dk sjduniþl hm (0) ml dk gjrbk hm smljs qum sm prjpkekl fknik hmdkltm. Njlsihmrklhj mstm fmnfj dk sjduniþl bktmbëtink pkrk dks mnuknijlms (0) njrrmspjlhimltm k jlhks pdklks qum sm prjpkekl fknik hmdkltm?
Qkrk md nkbpj mdéntrinj ms? Qkrk md nkbpj bkelétinj?
2 2 ⅅ ⅅ
Ms md lÿbmrj hm jlhk ml md mspknij di`rm mxprmskhj ml 2 ω/n sm iltmrprmtkrë njbj ulk grmnumlnik
mspknikd, qum ml mstm nksj bihm md njrribimltj ml gksm pjr ulihkh hm histklnik k dj dkrej hm dk hirmnniþl z ml rkh/b.
;>
ms dk grmnumlnik rkhiël, qum bihm md njrribimltj hm gksm pjr ulihkh hm timbpj3 timlm ulihkhms hm rkh/s . Ml ilstkltms sunmsivjs dk nurvk smljihkd sm prjpkek ml hirmnniþl z pjsitivk tmlmbjs mltjlnms ulk jlhk vikomrk. ω
Mstks mnuknijlms sjl gjrbks ilstkltëlmks rmkdms hmd nkbpj mdéntrinj y bkelétinj. Mddks sjl dks rmprmsmltknijlms bktmbëtinks hm dj qum sm bihm hm bklmrk mxpmribmltkd.
PMDKNIJLM^ HM QJXMLNIK MLMPEÂK ML JLHK^ MDMNXPJBKELÉX MDMNXPJBKELÉXINK^ INK^ Dks jlhks mdmntrjbkelétinks pjrtkl mlmreâk nuklhj vikokl k trkvés hmd mspknij vknâj. Fky ulk hmlsihkh hm mlmreâk ksjnikhk njl kb`js nkbpjs mdéntrinj y bkelétinj. Dk tksk hm trklspjrtm hm mlmreâk pjr ulihkh hm ërmk ms hmsnritk pjr md vmntjr ddkbkhj vmntjr hm Qjyltile.
QPJQKEKNIJL QPJQKEKNI JL HM JLHK^ MDMNXPJBKELMXINK MDMNXPJBKELMXINK^ ^ ML DILMK^ HM XPKL^BI^IJL
Qkrk dk trklsbisiþl mginimltm hm pjtmlnik hm pultj k pultj ms lmnmskrij euikr dk mlmreâk hmshm dk gumltm fkstk dk nkrek. Dks jlhks XMB euikhks ml ulk dâlmk hm trklsbisiþl sjl bës mginimltms qum dks qum sm prjpkekl ml ul bmhij himdéntrinj idibitkhj njbj md kirm. Dk jlhk XMB ms md bjhj hjbilkltm ml dks dâlmks hm trklsbisiþl qum utidizkl hjs j bës njlhuntjrms. ^m rmquimrml kd bmljs hjs njlhuntjrms pkrkpumhm mstk`dmnmr md bjhj XMB, qum sm trklsbitir ml hivmrsks grmnumlniks fkstk ddmekr ilndusj k dk grmnumlnik 1 Fz (nh). Dk tmjrâk hm nkbpjs ms ibpjrtkltm pkrk md hismûj hm dks dâlmks hm trklsbisiþl nuklhj ms hm iltmrés hmtmrbilkr dk iltmlsihkh bëxibk hmd nkbpj pjr md mgmntj njrjlk y rupturk pjr vjdtkom. ]lk nkrkntmrâstink sj`rmskdimltm njbÿl mltrm dks dâlmks XMB ms qum sm njbpjlml hm hjs supmrginims njlhuntjrks pkrkdmdks. Qjr dj emlmrkd dks jlhks XMB ml ulk dâlmk hm trklsbisiþl sjl nkrkntmrizkhks nkrkntmr izkhks ml gulniþl hm dks jlhks hm vjdtkom y njrrimltm ml duekr hm djs nkbpjs mdéntrinjs y bkelétinjs pjr smr gënidbmltm bmhi`dms, bimltrks qum djs nkbpjs sm ilgimrml hm msks bmhinijlms.
;8
DILMK HM XPKL^BI^IJL ]lk dâlmk hm trklsbisiþl ms ul nirnuitj hm nuktrj tmrbilkdms, hjs tmrbilkdms hm mltrkhk pkrk dk gumltm (mbisjr) y hjs pkrk dk nkrek (rmnmptjr).
_D
Djs tipjs hm dâlmks hm trklsbisiþl ml bjhj XMB sjl?
QKPKBMXPJ^ MDMNXPINJ^ HM ]LK DILMK HM XPKL^BI^IJL Djs pkrëbmtrjs rmprmsmltktivjs hm nukdquimr sistmbk hm pjtmlnik sjl nuktrj?
P? Dk rmsistmlnik njb`ilkhk hm kb`js njlhuntjrms pjr ulihkh hm djleituh, ml Ω/b. Hmpmlhm Ω/b. Hmpmlhm dk rmsistivihkh hm djs njlhuntjrms
D? Dk ilhuntklnik njb`ilkhk hm kb`js njlhuntjrms pjr ulihkh hm djleituh, ml F/b. F/b . Ximlm qum vmr pjr dk ilhuntklnik ksjnikhk kd nkbpj bkelétinj prjhunihj pjr dk njrrimltm vkrik`dm qum nirnudk pjr md njlhuntjr
E? Dk njlhuntklnik hmd bmhij kisdkltm pjr ulihkh hm djleituh, ml ^/b. Dk njlhuntklnik hm hmsvikniþl E, sm utidizk pkrk bjhmdkr dk njrrimltm hm guek k trkvés hmd himdéntrinj qum sm puhimrk prmsmltkr k dj dkrej hm dk dâlmk. Dk njlhuntklnik timlm ml numltk dks njrrimltms hm guek tkltj hm djs kisdkhjrms qum sjstimlml k dks dâlmks kérmks njbj dks pérhihks jnksijlkhks pjr djs mdmntrjlms kd skdtkr k trkvés hmd kirm. Dk njlhuntklnik hmpmlhm hm lubmrjsjs gkntjrms, mltrm mddjs djs ndibëtinjs y djs bmhijkb`imltkdms, gkntjrms higânidms hm prmhmnir y qum lj sm bkltimlml njlstkltms k dj dkrej hm tjhk dk dâlmk.
N? Dk nkpknitklnik hm djs hjs njlhuntjrms pjr ulihkh hm djleituh, ml G/b. Njbj dk dâlmk mstë gjrbkhk pjr hjs j bës njlhuntjrms smpkrkhjs pjr ul himdéntrinj, njlstituym, pjr tkltj, ul njlhmlskhjr nuyk nkpknihkh hmpmlhm hmd ërmk hm djs njlhuntjrms, su smpkrkniþl y dk njlstkltm himdéntrink hmd bktmrikd qum djs smpkrk. Mstjs pkrëbmtrjs pumhml kerupkrsm hm gjrbk djleituhilkd (rmsistmlniks m ilhuntklniks), j `iml hm gjrbk trklsvmrskd (njlhuntklniks y nkpknitklniks).
;=
Djs pkrëbmtrjs sjl gulnijlms hm? ;. Hibmlsijlms hm dk smnniþl trklsvmrskd hm dk dâlmk 0. Bktmrikdms hm djs nukdms mstël fmnfjs djs njlhuntjrms y md bktmrikd kisdkltm mltrm mddjs. Qjr mombpdj ml ulk dâlmk kérmk md bktmrikd kisdkltm ms md kirm
Ͻj, δj y
djs njlhuntjrms tmlhrël
ώr, δr
]LGD]MLNIK HM DK DJLEIX]H HM DILMK ML DK JLHK Djs nirnuitjs jrhilkrijs njbj djs qum sm mstuhikl ml dk tmjrâk hm nirnuitjs sm rmprmsmltkl njl pkrëbmtrjs hisnrmtjs njlnmltrkhjs, pjrqum djs mdmbmltjs sm u`inkl k histklniks njrtks y md rmtkrhj hm timbpj ml rmnjrrmrdjs ms hmsprmnik`dm, dj qum ekrkltizk qum md vjdtkom ml dk nkrek mstë ml gksm prmnisk njl md vjdtkom hm dk gumltm? D
K
≆
1
@
‰ 2
_ K¸
@¸
Dks erklhms histklniks mxistmltms mltrm dk gumltm y dk nkrek ml ulk dâlmk hm trklsbisiþl timlml ul ibpkntj ml dk njrrimltm y md vjdtkom prmsmltm ml md nirnuitj. Md rmtkrhj hm timbpj ml rmnjrrmr tjhjs djs mdmbmltjs hmshm dk gumltm fkstk nkrek jnksijlk ulk higmrmlnik ml md vjdtkom y dk njrrimltm pjr md rmtkrhj. Dk skdihk md vjdtkom mltrm dks tmrbilkdms @@ tmlhrë ul rmtrksj njl rmspmntj k djs tmrbilkdms KK¸ pjr ul timbpj hm hm smeulhjs.
/
¸
K
D 2 Cb hm dâlmk
@ _
K¸
@¸
Qjr mombpdj? ]lk dâlmk hm trklsbisiþl NK k 71Fz, pjr smr ulk jlhk XMB sk`mbjs qum vikok kprjxibkhkbmltm k dk vmdjnihkh hm dk duz n2 >x;1 6 b/s, md vjdtkom hm dk gumltm timlm ul hmspdkzkbimltj ilinikd hm 2 91j
;7 D 2 Cb hm dâlmk
K
@ _
K¸
@¸
t21 ‰ 2 sml2 sml0 .91j 2 sml0 .91j ‰ 2 sml sml191j 2 Md vjdtkom ml dk gumltm ml md timbpj
ms?
Njbpkrmbjs njbj ilgduym dk djleituh hm dk dâlmk ml md vjdtkom, ml ul nirnuitj jrhilkrij jrhilkr ij njl ulk djleituh 2 ;b hmshm dk gumltm k dk nkrek, md vjdtkom ml dk nkrek ml md timbpj smrë?
‰ 2 sml sml 2 smlml00 //
t21
‰ 2 sml0.71 1 >;1; 91j 2 ‰ 2 sml sml 2 smlml00 // j21,99998= ‰ 2 sml0.71 1 =11111 91 >;1 / 20 2 gkntjr hm gksm
Ml ulk dâlmk hm =11cb
Md gkntjr hmtmrbilkltm ms dk bkelituh hm . Dk vmdjnihkh hm prjpkekniþl hm ulk jlhk vikomrk mstë rmdknijlkhk njl dk grmnumlnik g y dk djleituh hm jlhk γ bmhikltm dk gþrbudk? Mltjlnms,
^m ddkbk
Wkdjrms bkyjrms k 1,1; ml md gkntjr hm gksm j`diekl k njlsihmrkr dk ilgdumlnik hm dk dâlmk hm trklsbisiþl ml md hmspdkzkbimltj hm dk gksm ksâ njbj dks jlhks rmgdmokhks pjr dk nkrek fknik dk gumltm. K bkyjrms grmnumlniks grmnumlniks hmd mspmntrj mdmntrjbkelétinj mdmntrjbkelétinj mstm gkntjr ms hm subk ibpjrtklnik pjr md rmtkrhj hm timbpj.
NDK^IGINKNIJL HM DK^ DILMK^ ^MEßL ^] DJLEIX]H ]lk vmz hmtmrbilkhk djs pkrëbmtrjs hm dk dâlmk, sm rmprmsmltk su nirnuitj mquivkdmltm pkrk hmtmrbilkr dk vkrikniþl hmd vjdtkom y njrrimltm hmshm su mbisiþl fkstk su rmnmpniþl j ml nukdquimr pultj hm dk dâlmk. Dk hivisiþl hm dks bisbks sm fknm ml gulniþl hm su djleituh?
;. Dâlmks hm djleituh njrtk (djleituh iilgmrijr lgmrijr k 61cb). ^jl dks qum trklsbitml mlmreâk mdéntrink k vjdtkoms bmljrms k 77 cW. Njl mstk djleituh pumhm hmsprmnikrsm md mgmntj prjhunihj pjr dk njlhuntklnik (mgmntj njrjlk y mgmntj kisdkhjr), ksibisbj md mgmntj nkpknitivj ms tkb`iél hm pmqumûj vkdjr, lj ilgduymlhj ml djs rmsudtkhjs.
;5
Md nirnuitj mquivkdmltm hm ulk dâlmk hm trklsbisiþl njrtk qumhk rmhunihj k ulk rmsistmlnik y ulk ilhuntklnik, njlmntkhks ml smrim y njlnmltrkhks ml md nmltrj hm dk dâlmk. Mstm tipj hm bjhmdj sm rmsumdvm njl djs prilnipijs hm dk tmjrâk hm nirnuitjs.
0. Dâlmk hm djleituh bmhik (djlei (djleituhms tuhms njbp njbprmlhihks rmlhihks mltrm 61cb y 081cb) ^jl dks qum trklsbitml mlmreâk mdéntrink k vjdtkoms hm trklsbisiþl y su`trklsbisiþl njl djleituh bmljr k 081 cb. Qkrk md nëdnudj hm dks dâlmks hm djleituh bmhik, k djs mgmntjs qum momrnml dk rmsistmlnik y dk ilhuntklnik, sm hm`m ilnduir md vkdjr hmd mgmntj hm dk nkpknitklnik, hm`ihj k qum njl mstks djleituhms yk mbpimzk k smr sieliginktivj. Dk njlhuntklnik sieum simlhj hm vkdjr buy rmhunihj y, hkhk dk higinudtkh pkrk su nëdnudj, pumhm hmsprmnikrsm. Mxistirë, pjr dj tkltj, ibpmhklnik y khbitklnik ml mstks dâlmks hm djleituh bmhik, kulqum sm smeuirël njlsihmrklhj kerupkhks j njlnmltrkhks. Mxistml hjs gjrbks hm kerupkr djs pkrëbmtrjs mdéntrinjs qum ilgduyml ml ulk dâlmk mdéntrink hm djleituh bmhik, lj kgmntklhj su mdmnniþl k dk nkdihkh hm djs rmsudtkhjs gilkdms.
Bétjhj hmd nirnuitj mquivkdmltm ml —X‒
•
Bétjhj hmd nirnuitj mquivkdmltm ml —ρ‒
Mstjs nirnuitjs sm rmsumdvml njl djs prilnipijs hm dk tmjrâk hm nirnuitjs qum njlsihmrk dk rmspumstk ilstkltëlmk ml tjhk dâlmk. Qkrk dâlmks njrtks k vjdtkoms supmrijrms 77 cW, njl djleituhms mltrm =1 y 61 cb, nuyj nëdnudj hm`mrë smr bës mxkntj hm`ml uskrsm djs nirnuitjs mquivkdmltms X j ρ. Ml Wmlmzumdk tmlmbjs dâlmks ml ;;=cW njl histklniks njrtks ml djs mldknms mltrm su`mstknijlms hm trklsbisiþl.
;6
>. Dâlmk hm djl djleituh eituh dkrek (bkyjr k 081cb) ^jl dks qum trklsbitml mlmreâk mdéntrink k vjdtkoms hm trklsbisiþl njl djleituhms bkyjrms k 081 cb. Ml dâlmks hm trklsbisiþl qum jpmrkl k 71Fz sm njlsihmrk qum djs pkrëbmtrjs mstël histri`uihjs uligjrbmbmltm k dj dkrej hm tjhk dk dâlmk. Qkrk dâlmks bkyjrms k 081cb dks dâlmks hm trklsbisiþl sm rmprmsmltkl njl pkrëbmtrjs histri`uihjs, njbj sm bumstrk ml dk gieurk sil ibpjrtkr dk gjrbk mspmnâgink hm dk dâlmk njlsihmrkhk (njlnéltrink, njlhuntjrms ilhivihukdms, pdknks). Mstm bjhmdj sm rmsumdvm kpdinklhj dk tmjrâk hm jlhks.
Dk dâlmk sm hivihm ml smnnijlms higmrmlnikdms pmqumûks, nkhk ulk rmprmsmltkhk pjr md nirnuitj mquivkdmltm
;9
MN]KNIJLM^ HM JLHK ML DILMK^ HM XPKL^BI^IJL DKPEK^ Md j`omtivj ml djs nëdnudjs hm dâlmks hm trklsbisiþl ms hmtmrbilkr njbj md vjdtkom y dk njrrimltm ml dk dâlmk vkrâk njl rmspmntj kd vkdjr njljnihj ml ulj hm sus mxtrmbjs.
Kpdinklhj dks dmyms hm Cirnffjgg Kpdinklhj Cirnffjgg kd nirnuitj mquivkdmltm mquivkdmltm hm hm ulk dâlmk hm trklsbisiþl njl njl njlhuntjrms njlhuntjrms ml dk hirmnniþl kd mom _ y hmrivklhj dks mnuknijlms rmsudtkltms sm j`timlml ul pkr hm mnuknijlms higmrmlnikdms njljnihks njbj mnuknijlms hm jlhk qum hmsnri`ml dk rkpihmz hm nkb`ij hmd vjdtkom y dk njrrimltm njl rmspmntj k dk hirmnniþl hm prjpkekniþl.
Hjlhm ;/b njlstkltm hm prjpkekniþl
2 2 2 ∟ ⦃ ⦄ ΰ λ
njlstkltm hm kbjrtieukniþl j ktmlukniþl (Lp/b)
njlstkltm hm gksm (rkh/b) hm dk dâlmk
^i njlsihmrkbjs qum dk gumltm ms smljihkd (NK), dk s jdun jdunii þl hm dks dks mnu kni knijlms jlms hm jlhk hm ulk dâlmk hm trklsbisiþl ms?
(>)
(8)
Md vkdjr hm
+ ∐ y
, sm nkdnudkl hm dks njlhinijlms ilinikdms ml md mxtrmbj hm dk dâlmk
01
Md pribmr térbilj hm dks mnuknijlms (>) y (8), sm rmgimrm k ulk jlhk qum sm prjpkek ml hirmnniþl +_ y md smeulhj dk prjpkekniþl „ prjpkekniþl „_. _. Dk tmlsiþl ml nukdquimr pultj hm dk dâlmk ms dk subk hm dk jlhk ilnihmltm y rmgdmokhk hm dk tmlsiþl ml kqumd pultj, dj bisbj sunmhm njl dk njrrimltm. Md rmsudtkhj ms ulk jlhk mstknijlkrik.
+ 2 ⦃Ω⦄ 2 +
2 ∟ 2
⦃ ⦄
b/s
IBQMHKLNIK NKPKNXMPÂ^XINK HM DK DÂLMK
NJL^XKLXM HM QPJQKEKNIÞL J HM XPKL^BI^IÞL
Xkltj dk njlstkltm hm prjpkekniþl njbj dk ibpmhklnik nkrkntmrâstink _j, hmpmlhml hm djs pkrëbmtrjs P, D, E, N y hm dk grmnumlnik hm jpmrkniþl hm dk dâlmk hm trksbisiþl. Dk vmdjnihkh hm jlhk
2
u y dk djleituh hm jlhk
mstël rmdknijlkhks pjr dks hmgilinijlms kuxidikrms?
2 2
HMXMPBILKNIJL HMXMPBILKNIJ L HM WJDXKOM Y NJPPIMLXM ML ]LK DILMK HM XPKL^B^IJL DKPEK Hm dks sjdunijlms hm jlhk (>) y (8) sm klkdizk md nksj hjlhm dk dâlmk hm ibpmhklnik _j tmrbilk ml ulk ibpmhklnik hm nkrek _D.. ^m uskl dks mnuknijlms (>) y (8) pkrk fkddkr md vkdjr hm dk tmlsiþl
y njrrimltm ml nukdquimr pultj hm dk dâlmk, sjdj sm lmnmsitkl dks njlhinijlms ilinikdms ml md mxtrmbj hm dk dâlmk pkrk nkdnudkr md vkdjr hm y ,
+ ∐
Njlhinijlms ilinikdms ml dk nkrek Dk dâlmk sm mxtimlhm ulk djleituh d mstë nkrkntmrizkhk pjr su ibpmhklnik _j y , tmrbilk ml ulk nkrek _D. Grmnumltmbmltm rmsudtk lmnmskrij hmtmrbilkr dk tmlsiþl y dk njrrimltm ml dks dâlmks,
njljnihjs djs pkrëbmtrjs hmd mxtrmbj hm rmnmpniþl, pkrk mddj sm pumhm mbpdmkr dks njlhinijlms tmrbilkdms hmd hm d mxtrmbj hm rmnmpniþl y sm sustituyml ml dks sjdunijlms hm tmlsiþl tmlsi þl y njrrimltm (>) y (8)? d-_
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P
IP
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WP _2d
_2 1
_D
0;
Hkhks dks njlhinijlms ml dk nkrek
+ 2 -
2 2 d ∐ 2 ∐ y
ml _2
^ustituymlhj mstjs vkdjrms ml (>) y (8)?
2 ∐ 2 ∐ Hjlhm
2 ∟
ms dk ibpmhklnik nkrkntmrâstink hm dk dâlmk y
hm prjpkekniþl.
2
ms dk njlstkltm
Dks mnuknijlms hkl djs vkdjrms hm W m I, ksâ njbj sus ëleudjs hm gksm ml nukdquimr pultj hm dk dâlmk ml gulniþl hm dk histklnik hmshm md mxtrmbj _ hm dk nkrek fknik dk gumltm, supumstjs njljnihjs Wj y Ij y djs pkrëbmtrjs hm dâlmk.
Mombpdj? Ml ulk dâlmk hm trklsbisiþl sil pérhihks, nkdnudm md vjdtkom y njrrimltm hm dk gieurk si ml dk nkrek sm bihm ulk tmlsiþl hm =1W
=1 Ω
h2 0.> γ
IP
_E _j2 ;11 Ω
WP
_D
=1 Ω
00
γ bmtrjs. Hkhj md vjdtkom ml dk nkrek, dk histklnik hmshm dk nkrek fknik dk gumltm _2 0.> 0.>γ Kpdinkbjs dk gþrbudk? gþrbudk?
WP _IP WP _IP WW 22 =1;11∕; 0 mm =1;11∕; 0 m∐ m∐ 25=m 0=m 0 0
Md pribmr térbilj ms ulk jlhk qum kvklzk hm dk nkrek fknik md emlmrkhjr y md smeulhj térbilj ms dk jlhk rmgdmokhk fknik dk nkrek.
Njbj ms ulk dâlmk sil pérhihks P2E21, mltjlnms λ21 y dk njlstkltm hm prjpkekniþl qumhk njbj . Hm dks mnuknijlms kuxidikrms fkddkbjs ΰ ?
2ΰ
ΰ 2 ξ_ 2 0.>γ 2o8.7ρ W25=m, 0=m∐, 20>,;57o5;,>095,50=o0>,557
W2;=,8=;o9=,;1=2 97,>= I 2 _;J WP 0_IP m WP 0_IP m∐ I 2 ;11; (5=m∐, 0=m∐,)20>,;57o5;,>095,50=o0>,557
-61,55 ⁱ W Mstm ms md vjdtkom ml dk mltrkhk hm dk dâlmk
I21,>19o1,8572 1,=76 ;00,99
ⁱ K K
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