güç elektroniği - eemdersnotlari.com geniş konu anlatımı
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[GTK CB]HB@ METRC]RAR BCBIG@CGT
[gr kcbthb` meructuaucgrmg g`g bcbig`cgr ecgrgh8 mkyet, he`vg`skye`bc trkstr, trkga, hgpmg`
thg`gdkcb` trkstr (N]E), dkpecgr n trg`skstr, n IEQLB]k vbygctcihgpc dkpecgr trg`skstr (KND])
sgycgdkckr. Mkyet jgrkak`mbhkcbr kcbrk y`mb petg`skybcb mgyg`gdkckr vb mecgysycg he`trec bmkcbdkckrcbr.
M[E] ?
V
@
[gp
G`et
HgtemQbidec
Hggh Ghi~ iG
cbrk y`mb (nbrkcki mi) ~ 6.\
cbrk kcbtki
]brs ]hgig
K
\
Hgrghtbrkstkh
@ tkpk 8 `bngtkl yhc
V tkpk 8 pezktkl yhc
_b`br mkyemu 8 Lgrh, p-` bhcbik`k` zb`br yhcigs`g ecg`gh vbrbabh bhkcmb eh mgr tutuciu
ecigsmr. Nbrkcki rblbrg`s vbyg nbrkcki mzb`cbykak ecgrgh huccg`crcgr.
]TQ]T ?
V
@
[gp
G`et
HgtemQbidec
V
@
Hgp
4666 \ , 166 G kk`16 ii gp 8 6.> ii hgc`ch
]utig ghi
cbrk y`mb (nbrkcki mi) ~ 6.\
Hkcktcbib ghi
K
\
Hgrghtbrkstkh
cbrk hgghghi
cbrk y`mbmbck`ib
]brsmbck`ib
Nbrk hgghghi
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Hgp ghi uynucg`igm murui kk` trkstr, khk y`mb mb kcbtkib kzk` vbribyb` tg`b sbrk dgc mkyet
nkdkmkr. ]brs y`mb hutupcg`ig muruiu`mg mkyetcg gy` mgvrg` sbrnkcbr. cbrk y`mb hutupcgigmg yg`k g`et
pezktkl khb`, ibrhbzmbhk he`trec oe`hskye`u`u` mbck`ib nbrkckik gcigmhg sgmbab hggh ghi ghgr. Mbck`ib
nbrkckicbrk khk y` kk` mb gy`mr. ]brs hutupcgig muruiu`mg hgtem V-@ oe`hskye`u 76\mg mbck`mk k`mb` ti
vectgo g`ettghk V-@ oe`hskye`u`mg nrcr.cbrk y`mb hutupcgigmg nbrkcki ecuursg trkstr, khk
oe`hskye`cu mkyet nkdk gcr vb mkyetu` khk hgt nbrkcki
mi ecur. ]rkstr` kcbtkimb hgcgdkcibsk kk` g`et
ghi`` hkcktcbib ghi (cgtajk`n) sbvkybsk`k gigs vb
tutig ghi (jecmk`n) sbvkybsk`k` gct`g mibibsk nbrbhkr.
CEGMLRCCjC KKK 3 7%4
bhkcmb nrcm nkdk kcbrk y`mb hutupcg`itrkstrb K n hgp ghi uynucg`rsg trkstr kcbtkib nbbr.
G`et ghi hkcktcbib ghi sbvkybsk`k nbbr vb tutig ghi`` gct`g mibzsb trkstr kcbtkimb hgcr vb du g`mg`
ktkdgrb` mb hgp ghi hgcmrcgdkckr.
]rkstr s`mribh kk` (hbski) g`et ghi sbvkybsk`k` gct`g
mrcibck vb trkstr he`trec oe`hskye`u`u` thgig muruiu`g
nbibsk`b hgmgr nbb` dkr srbmb kcbrk y`mb nbrkcki
uynucg`igigcmr. Du gigcg trkstrb bhkcmb nrcm nkdkjgrkak dkr mbvrb tgrgl`mg` tbrs y`mb ghi nbibsk sgcg`r.
Ghi` srbsk nb`bcmb 76 kcg 766 s grgs`mgmr. ]brs kcbtkick
trkstr? Dkr skckhe` hgtig``mg trkstr kcb, tbrs y`mb kcbtb` mkyet
heidk`gsye`u ecuturucg` ygr kcbthb` bcbig`
]rkstr Hgp Rau vb Nbrbhtkrmkhcbrk ?
]rkstr` hgp-hgtet ucgr hgrghtbrkstkk zgyl V-@ oe`hskye`u`u`hk`b db`zbr. r`mb` - r`b
mbkibhcb dkrckhtb bhkcmbhk hgrghtbrcbrmb` dkrk`b uyg` dkr mgvrg`sbrnkcbr.
]rkstrcbrb uynucg`gagh ik`kiui ghi vb
nbrkcki sbvkybsk oe`hskye` saghc`` dkr
le`hskye`umur.
Hgp ghi vb nbrkckik`k` ik`. vb igx.
mbbrcbrk vgrmr.
Du mbbrcbr gyrag dbcck dkr ik`kiui
sbvkyb`k` st`mb ecigcmr.
Hgp ghi`` vb nbrkckik`k` grpi ecg`na` mb dkr ighskiuiu vgrmr.
cbrk kcbtki
Kn'yb dgc nbrkckimbbrcbrk
K
\
]brs]hgig
\
KKn
]brs y`mb ghi
]brs hggh ghi
Kg`et
16 A
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[g`mghk bhkcmb trkstr` kcbtkib nbibsk kk`
tbtkhcbib ghi vb nbrkckik`k` gcigs nbrbhck mbbrcbrknstbrb` dcnb tgrg`grgh kgrbtcb`iktkr. Rynu`
grtcgrmghk tbtkhcbib mgrdbsk dkr kzecgsye` trglesu
grgacycg trkstr hgps`g uynucg`r. ]rgle`u` hgp
tgrgl`mg hgp ghi` s`rcgigh kk` dkr T 7 mkrb`ak
ducu`ur. ]rkstr s`imbyhb` hgp nbrkckik`k
s`rcgigh kk` mb T 4 mkrb`ak dgcg`itr.
Mbvrb`k` ]jbvb`k` bmbbrk mb yuhgrmgmr. Bmbbr mbvrbmbhk nbrkcki vb ghi ikhtgr` dbckrcbibh
gigaycg trkstr` hgrghtbrkstkk kcb ]jbvb`k` bmbbrk`k` ecuturmuu yh jgtt`` hbskki `ehtgs dbckrcb`kr.
\ N kcb K N grgs`mghk kckhk 8 B vb T N `k` ecuturmuu yh jgtt tgrgl`mg` dbckrcb`kr. ]btkhcbib sk`ygck
uynucg`m`mg hgp ghi hgrghtbrkstkh deyu`ag kcbrcbybrbh V `ehtgs`g ucgr. G`agh V `ehtgs`g ucgcigmg`
(tgjik`b` G `ehtgs`mg) trkstr kcbtkib nbik ecur. cbtkik` hbsk` ecgdkcibsk kk` tbtkhcbib mbvrbsk`k`
bcbig`cgr ycb sbkcibckmkr hk gcig `ehtgs ecg` V, ighskiui n s`r kcb G `ehtgs grgs`mg hgcs`.
Nb`bcckhcb du grtcgr sgcgyg` B 9 2 kcg 76 \ 8 K N 96,2 kcg 7 G grgs`mgmr.
]btkhcbib Mbvrbcbrk`k` Qgcgigs Nbrbhck grtcgr ?
Dkr trkstr kcbtkib nbkribh kk` hgp ghi`` eh jzc yhsbcib zgig``g sgjkp ecigs nbrbhkr. Du 8
g`et ghi`` hkcktcbib sbvkybsk`b ucggdkcbabk uzu`cuhtg jzc yhsbcib zgig``g sgjkp mgrdb rbtbdkcb`
tbtkhcbib mbvrbcbrkycb bcmb bmkckr. Mgrdb huccg`cigs`` `bmb`k hgpmg mgjg gz n jgrag`igs`g vb tbtkhcb`ib
g``` mgjg kyk dbckrcb`ibsk`b kihg` vbribsk`mb`mkr.
]btkhcbibDcnbsk
Hgrghtbrkstkh st s r
Igx. Nbrkcki
Igx. N (\N KN)
Igx. Hgp Ghi
Hgrghtbrkstkh gct s`r
Ik`. hgp nbrkckik
Ik`. hgp ghi
\N
KN
T7
T4
TN
B\N
KN
B
\N
B/TNKN
G
V
Ighskiui n
s`r
]rkstr hgrghtbrkstkk
[h Jgtt
Dbckrskz ]btkhcbib Dcnbsk
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7 26 _gig`
Mgrdb bhck
76\
7G
\N
KN
[h Jgtt
[h jgtt
]btkhcbib Mbrdbcbrk
GA Dbscbib
Nbakhib
[uhgrmghk bhkccbrmb nrcm nkdk8 zbcckhcb GA dbscbib uynucgigcgr`mg tbtkhcbib mbvrbsk`k`
rbtbabk mgrdb dbscbib`k` lgz`g nrb dbckrcb`bdkcibck vb ybrk mbktkrkcbdkcibckmkr. ]kpkh r`bh 8 7smb
76\cuh hgy`ghtg` 7G ghig ucggdkcbabh dkr mgrdbmkr. G`agh eu uynucgigmg 76s uzu`cuhtg, 7smb 4\g
ucgg` mgrdb ybtbrckmkr.]btkhcbib mbvrbsk grt grmg mgrdbcbr rbtbdkcibckmkr. Dgz uynucgigcgrmg hgtemcgr lgrhc petg`skybcb
sgjkp khk trkstr gy` g`mg tbtkhcb`ibckmkr. Du muruimg mbvrb khk vbyg mgjg eh kzecb h ecg` trgle kbribckmkr.
]brs y`mb mgrdb uynucgigs`mg` hg`cigcmr, yehsg mgjg eh n jgrag`r. Gyrag trkstr tbrs hutupcuyhb`
hgp ghi uynucg`rsg du hggh ghi grtrr.
]kpkh ]btkhcbib Mbvrbcbrk ?
[uhgrmghk mbvrbmb yh nbrkckik he`trec bmkcibhtbmkr. kn \
dbscbib/ T hgp ghi`` mbbrk Tyb
dgc ecmuu`mg` jbr pbrkyet mbkbdkckr, trkstr` saghc`g vb mkbr mbkkicbrb dgc ecgrgh. Gyrag tgi
slr vb tgi ;6e
mb tbtkhcbib ygpcgigz. Mecgysycg du mbvrb prgtkhtb huccg`cigz.
Dgskt gig prgtkhtb huccg`cgdkcbabh tbtkhcbib mbvrbsk ggmg nrcibhtbmkr. Mbvrb GA hgy`ghtg`
dbscb`kr. T 7 b dgc ecgrgh A 7 bxpe`g`skybc bhkcmb
mecgr. A7 dbcck dkr mbbrb ucg`ag u`koe`hskye`
trg`skstr kcbtkib nbbr vb A 7 trg`skstr zbrk`mb`
degcgrgh trkstr hgps`g mgrdb rbtkr.
\dbscbib
\yh
kn
T
t
\C
T4
_
A7
T7
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T 7 k` gygrcg`igsycg 7:6e
yb hgmgr nbakhib bcmb bmkcbdkckr. Du tr dkr mbvrb kcb eikh yhcbr he`trec
bmkcbdkckr. T7 b bhcb`babh bh mbvrbcbrcb mb uzghtg` eteigtkh he`trec sgcg`gdkckr. jtkygag uynu` ecgrgh mgjg eh
bcbhtre`kh mbvrb kbrb` vbyg eskcgtr kbrb` tbtkhcbib mbvrbcbrk mb vgrmr.
]btkhcbib Mbvrbcbrk`k` He`trec zbcckhcbrk ?
N he`trec bcbig` ecgrgh trkstr kbrb` mgjg hgrigh skstbicbr 8 hgpgc bvrki ck`hcbr, eh lgzc
dbscbib, ieter terh sbvkybsk yg mg ghi`` eteigtkh he`trec, lgrhc nrupcgr` gy` g`mg tbtkhcb`ibsk se`uau
yg`cgcigy `cbykak m`ncbr v.s. kbrkrcbr. He`trec hgrghtbrkstkk, tbtkhcbib nbakhib gs kcb nkrknbrkckik
grgs`mg tg`icg`g` kckhkyk vbrbabh bhkcmb ecigcmr. Ggmg dycb dkr he`trec vb tbtkhcbib mbvrbsk mkygnrgi
ecgrgh nstbrkciktkr.
He`trec vb ]btkhcbib Mbvrbsk
stb`kcb` h sgcgya he`trecsk`ygck (]btkhcbib gs`` he`trec)
]rkstrhgpcgr`g
Nbrk dbscbib sk`ygccbrk([h nbrkckik, ghi, mbvkr)
Mkbr He`trecacbrmb`Qb`hre`kzgsye` Qk`ygck
Nb Mgrdb rbtkik
Mgrdb Hgtgr Ckiktk
]btkhcbib kk` GAdbscbib rblbrg`s
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]T[GH ?
]rkygh db hgtig`c, jbr khk y`mb mb V-@-V-@ yecu`g sgjkp vb mecgysycg khk y`mb mb kcbtbdkcb`
bcbig`mr. ]rkygh pezktkl yg mg `bngtkl hgp ghiycg kcbtkib nbbdkckr. ] 4 pezktklhb` pezktkl, ] 7 pezktklhb`
`bngtkl uynucgigh mgjg kykmkr, g`agh prgtkhtb jbr khksk kk` mb `bngtkl mgrdb uynucg`r.
N]E (Ngtb ]ur` Ell -Hgpmg` ]hg`gdkcb` ]rkstr) ?
]rkstr` ducu`igs`mg` se`rg khk yb`k r` mgjg kagt bmkcmk. Du`cgrmg` dkrksk tbrs y`mb mgkig kcbtkimb
ecg` g`agh mgjg k`ab skckhe` huccg`cigsycg mgjg hsg srbmb thgigyg nbbdkcb` gskibtrkh trkstrmr. Du trkstr
k`vbrtbr mbvrbcbrmb huccg`cr. Dkrhg s kk`mb mbvrbyb gc`p hgrcgdkckr. Mkbr dkr bcbig` hgp ghi`
uynucgyp hbsibhcb kcbtkib sehup hgrcgdkcb` N]E trkstrcbrmkr.bhkcmb nrcm nkdk N]E, hcgskh trkstrb nrb
mgjg hgrigh dkr ygpyg sgjkptkr. [hsbh erg`mg
hgth kbrb` + kgrbtck hgtig`cgr vgrmr. Hgp vb
hgtem dkrdkrk`b ygh` vb mgr hg`gccgrmg`
ecuightgmr. cbrk hutupcgigmg ibrhbzk @-V
oe`hskye`u nbrkckik tutgr g`agh tbrs hutupcgigmg
dcehb ygpcgigz. Gig tbrs dcehb ygpgdkcb`
N]Ecgr mg ygpcitr. N]Ecgr hgrigh
ygpcgr sbdbdkycb mgjg yhsbh hkcktcbib ghi`g
sgjkptkr. N]Eyu kcbtkib sehigh kk` hgps`g
ghi b`obhtb bmkckr. Q`mribh kk` ksb hgtem - hgp y``mb 76\
sbvkybsk`mb nbrkcki uynucg`r. Q`i kk` nbbabh ghi g`et ghi``
7/2k vbyg 7/1 hgmgr ecigcmr. Du ghi 7smb` mgjg gz dkr zgig`mg
sgcg`gag`mg` G`et nbrkckik`k` grt` s`rcgigh kk` he`mg`sgtr
dgcg`r.
V
Hgp
N
]brik`gc ]7
]brik`gc ]4
@
V
@@
@
[gp Qbidec ]rkstr Bmbbrk
Kn9 6
Kn9 6
K]4
]7
\Kn
K
]rkygh Hgrghtbrkstkk
V+ V+ V+ V+
@+ @+ @+
@
V
@+ @+ @+
N A
G
G
A
N
[gp Qbidec
AE`
Ell
Nbrkcki
Hgy`gGhi
Hgy`g
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[g`mghk mbvrbmb dgskt hgp he`trec mbvrbsk
nrcibhtbmkr. He`trec sk`ygck`k` he`uiu`g nrb
]7 vb ] 4 kcbtkib nbbrbh A 7 mecmurucup degctcgrgh
trkstr kcbtkib vbyg hbskib nbkrkckr. A 4 ksb g`et
hgtem nbrkckik`k` m\/mt grt` s`rcgr.
N ]rg`skster ?
Dkpecgr trg`skstr 1 hgtig`c @V@ vbyg V@V ygpmg n trg`skstrmr. gcig grgc`mg K A , K D `k`
le`hskye`umur. Dbckrck dkr \ AB kk` dgz ghi`mghk mbkib heccbhtr ghi`mg hgtcg`iecgrgh nrcr. Du
erg` 72 766 hgt grgs`mgmr. ]brs nbrkcki uynucg`g` dkr trg`skstr` dgz biktbr oe`hskye`u 76\ akvgr`mg
mbck`kr. Du iemmg gccgaghsg trg`skstrb sbrk mkyet dgcg`igcmr.
]rg`skstrmb hgypcgr \ AB kcb K A`k` grpi`` dkr le`hskye`umur. [g`mghk
bhkcmb dgz ghi K A ghi`` 76G nbibsk`k sgcyersg, hgyp n 7h^,nbrkcki mi 766\ vb vbrki %26 ecgaghtr. Du hgduc bmkcbibz dkr hgyptr.
Du `bmb`cb n uynucgigcgr`mg trg`skstr g`gjtgr nkdk huccg`cr. KD 9 6 khb`
trg`skstr hbskimb. cbtki kk` trg`skstr hgrghtbrkstkk`k` meyig dcnbsk
huccg`cr. Meyig nbrkckik 7,7\ akvgr`mgmr. Hgypcgr sgmbab g`gjtgrcgig
srgs`mg ecur.
+72\
He`trec
6\
]7
]4
T7
A7
M7(74 \ect)
A4
E` Ell E` Ell
V
@
V
Aeccbater
Bikttbr
Dgsb
D
A
B
KA
KD
\AB
KA
Meyig
Nbrkckik
]brs
Mbck`ib
\ABHggh
Ghi
KD9 6Mbck`ib
Nbrkckik
Dbckrck KD
mbbrcbrk
KDgrtyer
[gp Qbidec @V@ trg`skstr hgrghtbrkstkk
[h76
KA
KD
+\ 9 466\
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]rkstr kcb N ]rg`skstr hgrcgtrcrsg 8
16G trkstr 6,7G hgp ghi, 16G trg`skstr 4G dgz ghi
N trg`skstr`` gr yh hgpgsktbsk trkstrmb` mh
]rg`skstr` g`gjtgrcgig jz eh yhsbh (7s)
]rg`skstrcb yh ghi he`trec bmkcbdkckrhb`, trkstrmb kcbtkimb` se`rg he`trec yehtur.
]rg`skstrcbrk` ghi hgzg`a` grtrigh kk` yg`mghk bhkcmb nrcm
nkdk mgrck`nte` dgcg`ts huccg`cr. Du bhkcmb ghi hgzg`a 426yb hgrcgdkckr.
N Ieslbtk 8
466
766
26
76
7
6.7
2 76 26 766 266
Nvb`ckcbtibDcnbsk
\AB(g`k)
KA
\AB
Hsg mbvrb
KD90yhsbh
KA90mbvrbyb dgc
Gh mbvrb
KD9 6
\AB
KD
KA
D
A
B
@+ @+ @+ @+
V V
Mkyet
Ghi
Mrgk`Ibtgc He`tgh
]rg`skstr
Ghi
@+
@
Ngtb
Qeurab
Ibtgc He`tgh
Qkckhe` Mkehskt (QkE4)
Ngtb
Qeurab
Mrgk`
N
Q
M
\MQ
\NQ
KM
KM KM
\MQ
\NQ
;\
>.2\
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QK]J ( Qtgtkh B`mhskye` ]rkstr) 8
N]Eyg db`zbr, g`agh `erigcmb kcbtkimbmkr. Hgtem hgpyg tbrs nbrkcki uynucg`rsg hbskib nkmbr.
Mkbr trkstrcbrb nrb mgjg gz hgypcgr vgrmr vb mgjg jzc gcrcgr. @erigcmb hbskimb ecg` QK]Jcgrmg kigc
ggigs`mgmr.
[GTK CB]HB@ BCBIG@ HG]GCEN MBBTCBT
Durgyg hgmgr bcbig`cgr vb hgrghtbrkstkhcbrk`k k`abcbmkh. G`agh dkr n ygr kcbthb` bcbig``` btkhbt
mbbrcbrk ecuturucurhb` eh mbkkh deyutcgr` nz ``b gc`igs nbrbhkr.
[g`mghk bhkcmb dkr trkstrmb` K l ghi ghgrhb` trkstr
mk/mt bkikycb s`ib ntrcyer. ]rkstr, oe`hskye`mg
ybtbrck gro ikhtgr ecg` W rr yh dkrkhb`b hgmgr tbrs
y`mb K rr ghi nbkrbabhtkr. Dbckrck dkr trkstr kk`
vbrkcb` K l vb mk/mt mbbrcbrk`b hgrch e trkstrmb du`g
dgc ecgrgh W rrtepgrcg`ig yh 8 tbrs tepgrcg`ig yh
tbrs tepgrcg`ig zgig` t rrvb tbrs tepgrcg`ig ghi K rr
ecgaghtr. ]rkstr` kcbtkib nbibsk hgp ghiycg sgcg`yermu. G`agh kcbrk y`mb nbrkcki grtjz dbckrck dkr
mbbrk ggrsg trksr` kcbtkib nbibsk iih`mr. ]rkstr oe`hskye`u`u hgpgsktr nkdk m`babh ecursgh,
sz`t ghi`g hgrch nbcb` mbpcgsig` ghimt
mvAk 9 ecgaghtr. [btbrk`ab yhsbh dkr mv/mt erg`ycg (
r`bk` 766\/s ) du ghi trkstr tbtkhcbybrbh kcbtkib nbkrbdkckr. Mecgysycg dbckrck dkr trkstr kk` g cigigsnbrbhb` dkr mv/mtmbbrk vgrmr.
]rkstr` kcbtkib nbibsk `abckhcb hgp bcbhtremu akvgr`mg ecur. ]epcgi g`et ghi g`kmb` nbbabh
ecursg gr s`ig `bmb`kycb trkstr yg`gdkckr. cbtkib nbib bs`gs`mg ghi` ti yzbyb ygycgdkcibsk kk`
dbckrck dkr zgig`g kjtkyg vgrmr ( tkpkh ecgrgh 76s ) Du sbdbpcb dkr trkstr kk` ghi grt jz dbcck dkr mK/mt
mbbrk`k gigigcmr.
Oe`hskye` saghc mkyet kk` 726 Ae
8 trkstr kk` 742 Ae
vb n trg`skstr kk` 726 Ae
- 466 Ae
mbbrk`k gigigcmr. Du `bmb`cb oe`hskye`mg` tgdg`g ecg` tbrigc mkrb`ak` dbckrck dkr mbbrk vgrmr.
Dkr bcbig`` `eik`gc ghi mbbrk`k, ecuturgag oe`hskye` saghc dbckrcbr yg`k hgyp na` dkr
le`hskye`umur. ]g`g` ghi` tkpk hgyp na bthkcbybabhtkr. Bbr sk`sekmgc dkr mgcng sz he`usu ksb rblbrg`s
mbbr huccg`cgdkckr. zbc dkr mgcng bhck kk` ksb 7:6e
ckh kcbtkimb ertgcgig mgcng mbbrk btkhbt mbbrk ecgrgh
vbrkckr.
Hsg srbck gr yh muruiu kk` jbr bcbig`` dkr tecbrg`s vgrmr. Gr yh kk` s grt`g sbdbp
ecgag`mg` akjgz yg`gdkckr. N hgyd s grt`` nstbrnbsk ecup ghi` hgrbskycb erg`tcmr. Du sbdbpcb
dbckrck dkr bcbig` kk` mtk4
dbckrck ecigcmr.
Dkr bcbig`` kcbrk vb tbrs y`mb uynucg`gdkcbabk ighskiui nbrkcki s`r vgrmr. Du`cgr rbpbtktkvb
pbgh rbvbrsb g`m pbgh lerwgrm vectgnbs ecgrgh tg`icg`r. Gyrag pbrkyemkh ecigyg` gr nbrkckicbr mb szhe`usu ecgdkckr. Mecgysycg dkr bcbig`` mbck`ibmb` mgyg`gdkcbabk du tr nbrkckicbrb gkt mbbrk mb vgrmr.
trr
mkmt
KL
KrrGcg` 9 Wrr
_gig`
]kpkh Q`i Muruiu
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cbtkimbhk dkr bcbig`` nbkrmkk ghi ikhtgr`g dgc ecgrgh dbckrck dkr nbrkcki mi mbbrk vgrmr.
Dkr n trg`skstr kk` btkhbt mbbrcbrk`mb, heccbhtr dgz ghi hgzg`a, lrbhg`s vb g`gjtgrcgig
zgig` dbcckmkr.
Dkr trkstr kk` hgp mbvrbskycb gcghgc ecgrgh ghi, nbrkcki n s`rcgigcgr vgrmr.Dbckrck dkr bcbig` kk` nbkak vb hgrgrc jgccbrmb sgjkp ecu`g` btkhbt mbbrcbrk eh mbkhb`mkr.
Dbckrcbykak u`surcgr 8 nbrkcki, ghi, g`gjtgrcgig zgig`cgr, he`trec pgrgibtrbcbrk, hgypcgr, saghch mbbrcbrk vs..
Du`cgr hgtgcencgrmg vbrkciktkr.
HG[KVCGT \B QER]IG
Dkr n ygr kcbthb`k`mb hgyp hgy`ghcgr u bhkcmb srgcg`gdkckr 8
7 cbtki hgypcgr 8 cbtki ghi`` vb nbrkcki mi`` le`hskye`umur. Mh lrbhg`scgrmg g`g hgyp
hgy`gmr.
4 ]hgig y``mb hggh ghicg kcnkck hgyp
1 Hgp mbvrbsk`mb tbtkhcbib sk`ygck sbdbdkycb hgyp
= G`gjtgrcgig hgypcgr 8 cbtkib vb s`ib nbib bs`gs`mghk hgyp b`brok. [hsbh lrbhg`s
uynucgigcgr`mg `bick.
cbtki hgypcgr nbrkcki mi vb tg`g` ghi` grpi`` dkr pbrkyettghk ertgcgigs`mg`
jbsgpcg`gdkckr. G`gjtgrcgig hgypcgr ksb ggmghk bhkccbrmb` tbspkt bmkcbdkckr.
Ghi kcb nbrkckik` grpi dkzb g`k n klgmbsk`k
vbrkr. Ks b`broksk ksb n * zgig` yg`k V brksk
gct`mg hgcg` gcg`mr. G`gjtgrcgig sbdbdkycb
ibymg`g nbcb` ertgcgig n hgyd 8 kcbtki vb
hbski hgypcgr`` tepcgi`` lrbhg`scg
grpi`mg` ducu`ur. ]btkhcbib vb hggh ghi
n hgypcgr kjigc bmkckrsb bcbig`` thbtbabk
n kcbtki hgypcgrycg g`gjtgrcgig hgypcgr`` tepcgi`g bkttkr. Du hgyp akjgzmg s rbtkik`b `bmb` ecgrgh
saghch grt ecuturur. Oe`hskye`mg rbtkcb` s `ab akjgz tgdg``g ergmg` mg seutuaucgrg trg`slbr ecur. Du
trg`slbr s sbvkybsk`k` mh ecigsycg rgmygsye`cg mbkc he`vbhskye`cg ecur. Ks sbvkybsk`b dgc ecgrgh jgvg
vbyg suycg seutig tbrakj bmkcbdkckr.
Ks trg`slbrk yhsbh saghchc dcnbmb` mh saghchc dcnbyb meru ecur vb saghch lgrh`` tbrigc
rbzkstg`sg erg`ycg jbsgpcg`r. T]]V /)( 47 9 ]brigc mkrb`ak` dkrkik ^Ae / mr.
Ks gh oe`hskye`mg` tgdg`g ergmg` seutuauyg vb
mgjg se`rg mg bvrbyb merumur. ]epcgi tbrigc mkrb`
8 jgdjodog TTTT ++9 mr.
Qg`gc oe`hskye` saghc ksb 8 oggvo VT]] +9 mr.
]i du jbsgpcgigcgr hgca jgc vb mgkik ghi
grtcgr`mgmr. Hsg srbck nbkak jgccbr kk` (gr yh,
hsg mbvrb) oe`hskye`mghk saghch grt bcbig``
tbrigc mbpecgig hgpgsktbsk mkhhgtb gc`grgh
\ \k k
V 9 \ k V
kcbtkib nbkzgig` hbskib nbkzgig`
t
Gcg` 9 N x _gig`
Jgvg
Qg`gc Oe`hskye`
Qaghc]vo
]gdg`
Qaghc]d
QeutuauQaghc
]j
bvrb
Qaghc]g
Tod Tdj Tjg
Oe`hskye` s
na nkrkk
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jbsgpcg`igcmr. rbtkcb` s`` dkr hsi bcbig`mg mbpecg`rhb` dkr hsi mg trg`slbr bmkckr. Du muruimg
b`brok mb`nbsk`k ygzgagh ecursgh 8
Hgyp b`brok 9 Mbpecg`g` tbrigc b`brok grt + bvrbyb b`brok trg`slbrk
tDGtV +9 V9 Hgyp n , G9 7 Ae
grtg hgrch nbcb` b`brok mbpecg`ig ikhtgr(sc
mbpecgig hgpgsktbsk ouc ecgrgh) , D9 7 Ae dg`g ygycg` n.
Mb`hcbik` ckiktk gc`rsg 8
DmtmGV +9 )/( ecur. t 9 6 kk` saghch 69 hgduc kcb mklbrg`skybc mb`hcbik` zi 8
)7( /igx]t
b9 DV/igx 9 (Qe`u hgca saghch grt)
DG] /9 (]brigc zgig` sgdktk) bhck`mb ecur. Du mb`hcbi jeieob` igczbib kk` nbbrckmkr.
]rkstrmb ksb oe`hskye` dcnbsk`mb n hgyd mgci u`kleri mbkcmkr. Gyrag skckhe` s kk` kyk dkr kcbthb`
mbkcmkr. Du sbdbpcb saghch grtikhtgrcgr hgca jgc vb nbkak jgc kk` gy` ecigygaghtr.
[g`mghk brkcbr igtbigtkhsbc ecgrgh kzkciktkr.
Dkr bcbig` g`agh kigcgt mbbrk`b hgmgr
huccg`cgdkckr. ( 7igx ) Ghsk tghmkrmb akjgz yg`gr.
Du sbdbpcb gr yh g`agh 7t hgmgr dkr srb
uynucg`gdkckr. Gr yh grtcgr eh hgrigh
ecmuu kk` leric ybrk`b trg`skb`t tbrigc
bipbmg`smbbrk huccg`cr 8
9tj_ Qaghch lgrh (grt) / Dbckrck dkr zgig`
mkckik`mb akjgzmghk n hgyd
Dycbab gr yh muruicgr kk` jbsgpcgig dgsktcbikecur. T ybrk`b tj_ huccg`cr.
[GTK CB]HB@ N BCBIG@CGTK@K@ HGTKCG]KTKCIGQK
N bcbhtre`kk mbvrbcbrk`mb bcbig`cgr g`gjtgr ecgrgh huccg`cr. mbgcmb dkr g`gjtgr 8
Q`rsz nbrkcki vb ghi mbbrcbrk
G`k gig hgpgig zgig`cgr
Qlr hggh ghi
Qlr kcbtki vb g`gjtgrcgig hgypcgr
Qlr hgp tbtkhcbib nagrt
Gr ghi vb nbrkckicbrb mgyg`gdkcib hgdkckybtk
Hsg mbvrbcbrb hgr heruig hecgyc
Mh igckybt vb ie`tgo hecgyc
t7 ] _gig` (t)
igx 7
igx 4
Gr yh
@erigc
grtcgrmg
Oe`hskye` Qaghch GrtBrkcbrk
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Vrgtkhtb uynu` bcbig` sbkik uynucgigmg` uynucgigyg mbkkr. Rynucgigmg hrktbrcbr 8 akjgz btkhbt
mbbrcbrk`b, kcbtki hgypcgr`g, g`gjtgrcgig hgypcgr`g, g`gjtgrcgig zgig`cgr`g, he`trec strgtbokcbrk`b vb
igckybtb dgc ecgrgh dbckrcb`kr.
]rkstr bcbig`cgr kk`mb b` yhsbh ghi vb nbrkcki sbvkybsk`b sgjkptkr, mgyg`hcmr, mh kcbtki hgypcgrvgrmr vb uauzmur. G`agh kcbtkib nbkk ygvgtr, s`i yhb dgcmr. [hsbh n vb nbrkckicbrk` ecmuu 26,
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DCI 4 ? METRC]RAR MB\TBCBT
Dkr meructuau mbvrbsk GA dbscbibsk`k MA yhb dgcgyg` mbvrbmkr. Bcmb bmkcb` MA
nbrkcki ghmb ecmuu nkdk sgdkt ecigyp ertgcgig nbrkcki sbvkybsk`b spbr kipezb bmkcik
gctbr`gtkl ghi mgcngcg`ig dkcbb`k kbrkr. Ggmg dgjsbmkcb` mbvrbcbrk` tgigi MA nbrkckivbribsk`b rgib` 8 htghk GA mgcngcg`igs, ertgcgig nbrkcki sbvkybsk, vbrkik vb GA
dbscbibmbhk yhcbib tbskrcbrk gs`mg` lgrhcch grz bmbrcbr.
4.7 Mbvrb ]g`icgr vb Nrupcg`mrig ?
Meructuau mbvrbcbrk ygri mgcng vb tgi mgcng dgcg`tcgr ecigh zbrb khk nruptg
tg`icg`gdkckr.
[gri Mgcng Mbvrbcbrk ?Du mbvrbcbrmb GA dbscbib`k` jbr jgtt`g dkr meructuau bcbig`
dgcg`r 8 bcbig`cgr` hgtemcgr MA yhb vb yh` mkbr uau mg GA dbscbib`k` `tr uau`gdgcg`r. Ghi gh jbr jgttg tbh y`cmr. ]bh yeccu mbvrb mb mb`kckr.
]gi Mgcng Mbvrbcbrk ?Dkrk yh dbscbyb`, mkbrk mb yh ghi` GA jgttg m`mrb` khk gmbt
ygri mgcng mbvrbsk`k` sbrk dgcg`igs`mg` ecutuu`mg`, `tr jgtt`g nbrbh yehtur. Hpr
mbvrbcbrk yg mg klt yeccu mbvrbcbr ecgrgh mg gmcg`mrcr.
Mbvrbcbrb gkt he`trec hgrghtbrkstkhcbrk hgtbnerkmb tepcg`gdkckr.
He`trecsz Meructuau Mbvrbcbrk ?Qgmbab mkyet kbrkrcbr, GA dbscbib nbrkckikycb erg`tc
sgdkt MA nbrkcki sgcgrcgr.
]gi He`trecc Meructuau Mbvrbcbrk ?]rkstr (yg mg n trg`skstr) huccg`cr. ]rkstrcbrk`
kcbtkib nbtkk lgz gs`` he`trecycb MA yh nbrkckik`k` ertgcgig mbbrk gygrcg`gdkckr,
y` mbktkrkcbdkckr. ]gi he`trecc mbvrbcbr yh vb dbscbib grgs`mg khk y`mb mb n
trg`slbrk`b kihg` tg`m`mg` klt y`c he`vbrtbr ecgrgh mg gmcg`mrcrcgr.
[gri He`trecc Mbvrbcbr ?]rkstr vb mkyet hgri kbrkrcbr. Nbrkckik` y` mbktkrkcbibz
g`agh ertgcgig mbbrk gygrcg`gdkckr. Du sbdbpcb ygr he`tercc vb he`trecsz mbvrbcbr tbh
y`c he`vbrtbr ecgrgh gmcg`mrcrcgr.
Mgrdb Qgys ? GA dbscbib`k` dkr pbrkyemu`mg MA nbrkcki mgcng bhck`k` tbhrgr
sgys` klgmbmb huccg`cg` dkr tbrkimkr. r`bk`
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4.4 Heitgsye` Mkyemu ?
eu mbvrbcbr (zbcckhcb
he`trecsz yg mg ygr he`trecc)
yg`mghk bhkcmb ecmuu nkdk
heitgsye` mkyemu kbrkrcbr. Dy-
Vgss mkyemu mg mb`kckr. hk
le`hskye`u vgrmr ? 7-[h
nbrkckik`k` y``` mbkibsk`k
`cbibh 4-[h ghi`` g`g
meructuaumg` gh` `cbybrbh meructuau`u` dcehb muruiu`g nbibsk`k sgcgigh.
4.1 ]bh Lgz [gri Mgcng (]bh [eccu) Mbvrb ?
bhkc 4.4 (g)mg he`trecsz tbh
lgzc ygri mgcng dgcg`ts
nrcibhtbmkr. Mgcng bhkccbrk
kzkckrhb` mkyemu` kmbgc g`gjtgr
nkdk mgvrg`m hgduc
bmkciktkr. bhkc 4.4 (d)mb yh,
sgl eikh khb` (a)mb ksb
b`mhtg`s kbribhtbmkr. Eikh
yh kk` mkyet nbrkckik mi
kjigc bmkckrsb ?
[h ghi ? T\k QC /9
(Vezktkl ygr pbrkyet) ecur.
Ertgcgig nbrkcki ?
99
6 igxigx
sk`4
7/ m\\\ert
eu MA yhcbr (MA ietercgr)
nbrkckik` ertgcgig mbbrk`b
tbphk nstbrkrcbr, mecgysycg
TIQ mbbrcb pbh kcnkcb`ibz.
[hMeructuauG.Adbscbib
Heitgsye` mkyemu
[hQ
M
kC
C
(g)
Q
C
kC
M
(d) (a)
6 4444 4444
9 9 9 9 t
\igx
\igx
\ert \ert
bhkc 4.4 ]bh lgz ygri mgcng mbvrbsk
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G`agh MA mgcngcg`igcgr kstbibyb` hgypcgrg yec ggr. Mbvrbmbhk mkyemu` sbkik kk` jbi
ghi jbi mb nbrkcki mkhhgtb gc`igcmr. [hcbrk` `brbmbysb tgigi 8 b`mhtg`s kbrkr. Du
muruimg bhkc 4.4(a) mgcng bhkccbrk bcmb bmkckr.
[h Nbrkckik ? mt
mkCTk\ CCC +9 mkr. Durgmg` ghi mgcng bhck bcmb bmkcbdkckr. Nbrkckik`
ertgcgig mbbrk ksb ? 9
9
6
igx sk`4
7m\\ert ecup, mgjg mhtr.
]bh lgz ygri mgcng mbvrbsk
trkstr huccg`cgrgh he`trec
bmkcbdkckr. bhkc 4.= (g)mg mbvrb
ygps (d) vb (a)mb ksb mgcng
bhkccbrk nrcibhtbmkr.
tbtkhcbib gs`g dgc ecgrgh
yh ghi vb nbrkckik
mbkibhtbmkr. Ghi sbvkybsk
mkyet tutig sbvkybsk`k` gct`g
mbrsb yh ghi hbsk`tkck ecur.
(bhkc 4.= (a)) [h nbrkckik`k`
ertgcgig mbbrk 8
9
m\\ert sk`4
7igx
( )
aes74igx
+9\
\ert ecur.
grtthg nbrkckik` ertgcgig
mbbrk mbr vb 67:6 mb slr
ecur.
]btkhcbib
Mbvrbsk
[h C
kCT+oZC
kM
k]]
Q
Heitgsye` Mkyemu
(g)
Q
kn
kn
C
kC
k]
kM
]
\igx
\igx
\ert \ert
\igx
\igx \igx
4444
(d) (a)
bhkc 4.=He`trecc tbh lgz ygri mgcng mbvrbsk
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4.=hk Lgz [gri Mgcng (]bh [eccu) Mbvrbsk ?
bhkc 4.2(g)mghk mbvrbmb khk lgz
dgcg`ts nrcibhtbmkr. [hb jbr
dbscbib jgtt`mg ducu`g` trkstrcbr
grgacycg dbscbib ygpcightgmr.
Jbrjg`nk dkr g`mg sgmbab dkr trkstr
mbvrbmbmkr. bhkcmbhk trsktrcbrb g`te
nbrkckik`k` pezktkl hgcm jbrjg`nk
dkr g`mg tbtkhcbib uynucg`gdkckr.
]rkstr ybrk`b mkyet huccg`crsg
96 eciuecur. Jbrjg`nk dkr
mbbrk`mb 7] trkstr kcbtkib
nbkrkcmkk`mb yh ghi 7] zbrk`mb
ghgr, 7\ nbrkckik `bngtklb nbtkk`mb
4\ pezktkl ecgag`mg` yk`b mbrbab
se`rg 4] tbtkhcb`kr vb 7] ghi
heitgsye`cg 4] yb ghtgrciecur.
7] s`ib nkttkk g`mg ucgr`mg
igx4\ (yg`k ti sbhe`mbr sgrn
nbrkckik) hgmgr nbrkcki ducu`ur.
Ertgcgig Nbrkcki ?
aes4
sk`7 igx
igx
\m\\ert 99
+
bhck`mb ecur. Du jbsgpcgig
ygpcrhb` yh b`mhtg`s`` 8 yh
ghi`` srbhck hgcigs`
sgcgygagh mbbrmb ecmuu hgduc
bmkciktkr.9 6 kk` ertgcgig nbrkcki b` yhsbh mbbrk`mbmkr. (mkyet muruiu), 6;69 kk`
ksb 69ert\ mr. Nbrkcki mgcng bhck dkr pbrkyettg khk hbz tbhrgrcg`m`mg du mbvrb khk
mgrdbckmkr. Nbrkckik` ertgcgig mbbrk mthb yh ghi mgcngcg`igs grtgr vb hbsk`tkck jgc
gcr. GA dbscbib ghi mg `e`-sk`sekmgcmkr vb nbrkckib nrb nbrkmkr. (b`mhtkl)
[h
kQk
4
k7
]7 ]4]7C
7
4
kn7 kn4 kC
T+oZC
4
9 9 9 9 t
\igx
C \ert
[h Nbrkckik
kn7
kn4
kC
k7
k4
kQ
]7
]btkhcbib
Mgrdbcbrk
[h Ghi
]rkstr
Ghicgr
GA dbscbib ghi
kQ 9(k7 - k4)x@
]rkstr Nbrkckik
]7 97 -C
\igx 9 VT\
(g)
(d)
bhkc 4.2hk lgz ygri mgcng mbvrbsk
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4.2.4 ]gi He`trecc ?
bhkc 4.>mbhk mbvrbmb mkyetcgr ybrk`b trkstr huccg`crsg tgi he`trecc hpr mbvrbsk
bcmb bmkckr. ]rkstrcbr tbtkhcb`b`b hgmgr kcbtki sz he`usu ecigz. Ghi` nbbdkcibsk kk`
bhkc 4.:mbhk mbvrbmb7
] vb4
] ,1
] vb=
] nrup jgck`mb jbr ygr pbrkyettg gy` g`mg
tbtkhcb`ibckmkr. Du`u sgcgigh kk` mb 7] vb 4] gy` mbvrbycb tbtkhcb`kr.
]btkhcbib mgrdbcbrk bhkc 4.;mg
nrcm nkdk kzecgsye` trglesu
grgacycg ygpcr. [h nbrkckik khk
lgzc ygri mgcng dgcg`tycg gy`mr.
Ertgcgig mbbrk 8
aes4 igx\\ert 9 mr.
G`agh mbvrbmbhk khk trkstr` nbrkcki
micbrk mgjkc bmkcibiktkr vb yh
ghi`` srbhck ecmuu hgduc
bmkciktkr.
7
4
C[h kQ
]7k7 k1
k= k4
]= ]4
]7 ]1kC
x y
kn= kn4
kn7 kn1
T+oZC
7/4 \igx
kn7,kn4
kn1,kn=
\igx
C \ert
kC
k7,k4
k1,k=
kQ
]7
\igx 9 VT\
]rkstr nbrkckik
\igx 9 VL\
Dbscbib ghi
kQ 9 k7- k=
]rkstr ghicgr
[h ghi
9 9 9 9 t
[h nbrkckik
]btkhcbib
Mgrdbcbrk
[h` tbpbsk`k`
@'b nrb nbrkckik
[h` tgdg``
@'b nrb nbrkckik
bhkc 4.: ]gi he`trecc hpr mbvrbsk
7 4
x y
]btkhcbib
Mbvrbsk
Hgp
Hgp
Hgtem
Hgtem
]7
]4
bhkc 4.; ]btkhcbibcbr
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4.2.1 [gr He`trecc ?
bhkc 4.76 (g)mghk ygr he`trecc dgcg`tmg nrcm nkdk, khk trkstr vb khk mkyet
huccg`grgh ertgcgig MA nbrkckik he`trec btibh iih`mr. bhkcmbhk tgi mgcng dgcg`ts
gsc`mg khk ygri mgcng mbvrbsk`k` bhcb`ibsk`mb` ecuiutur. [hb nkrb` ghi trkstrcbrmb`
nbbrhb` m`yecu mg mkyetcgrcg sgcg`ightgmr. `abhk he`umg ecmuu nkdk dkr @ (dbscbib
`tr) `ehtgs tg`icgygrgh vb yh ucgr`` du `ehtgyg ecg` petg`skybc mbkkicbrk`k
k`abcbybrbh mgcng bhkccbrk`k bcmb bmbdkckrkz.
Mgcng bhkccbrk`mb` mb nrcm
nkdk yh nbrkckik gscg `bngtkl
ecigz. Nbakhib gs 67:69
ecu`ag ertgcgig nbrkcki slrg
mbr. Heitgsye` mkyemu jbi
yh nbrkckik`k` `bngtkl ecigs`
`cbr, jbi mb b`mhtkl ecig
muruiu kk` yh ghi` zbrk`b
gcr. bdbhb nbrkckik`k` slrmg`
nbtkk vb 7] kcbtkimb ecmuu dkr
muruimg m` ghi 4M
zbrk`mb` bdbhbyb m`ibhtbmkr.
1] trkstr hgmgr
tbtkhcb`ibybabk`mb` du srb
zgrl`mg yh` b`mhtkl ghi 7]
vb =M zbrk`mb` ghigh kstbybabh
vb 4M ghi` =M b mbvrbmbabhtkr
Gy` zgig`mg heitgsye`
mkyemu mg yh ghi` zbrk`bgcgag`mg` 7] trkstr s`babhtkr.
7
4
C[h
kQ
]7k7 k1
k= k4
M= M4
]7 ]1kC
x y
kn= kn4
kn7 kn1
T+oZCHeitgsye`Mkyemu
kM
7/4 \igx
kn7,kn4
kn1,kn=
\igx
C \ert
kC
k7,k4
k1,k=
kM
[h ghi
9 9 9 9 t
[h nbrkckik
]btkhcbib
Mgrdbcbrk
[h tbpbsk`k` @'b
nrb petg`skybck
[h tgdg``` @'b
nrb petg`skybck
7 4
x y
C
kQG.A. Dbscbib
ghi
Heitgsye`
Mkyemu Ghi
(g)
(d)
bhkc 4.76 [gr he`trecc tbh lgzc hpr
[h
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]gi he`trecc`` ghsk`b ygr he`trecc dgcg`ts`mg heitgsye` mkyemu sbdbdkycb GA
ghimg slr sbvkybyb mib nzcb`babhtkr. [h nbrkckik`k` ertgcgig mbbrk 8
+99
)aes7(sk`7 igx
igx
\m\\ert ecur.
[gr he`trecc mbvrb, tgi he`treccyb nrb mgjg uauzmur, g`agh GA dbscbib ghi mgjg eh
jgrie`kh kbrkr. Gyrag ygr he`treccmb ertgcgig nbrkcki `bngtkl mbbr gcgigz.
4.< Lgz [gri Mgcng (]bh [eccu) Mbvrb ?
lgz ygri mgcng dgcg`ts eh lgzc meructuau mbvrbcbrk`k` tbibc bcbig`mr.
G`agh, dbscbib trglesu`u` sbhe`mbrk`k` zkn-zgn dgcg`igs` nbrbhtkrmkk`mb` huccg`i
gcg` s`rcmr. G`cgti hecgyc dghi`mg` durgmg ycmz dgc ecmuu hgduc bmkcbabhtkr.
eh lgzc dgcg`tcgrycg MA mgcng bhck`mbhk mgcngcg`igcgr mgjg gzmr. Gyrag
b`mhtg`s dyh nc yhcbr dbscb`bdkckr. [h ghi mgcngcg`ig`` gzc `bmb`kycb srbhck
vb sgdkt mbbrck hgduc bmkcbdkckr.
bhkc 4.74mb jbr lgz dkr mkyet grgacycg yhb
dgcg`itr. [h h ksb sbhe`mbr sgrn`` `rt
uauycg krtkdgtcg`mrcitr. Jbrjg`nk dkr g`mg
sgmbab dkr mkyet kcbtkimbmkr. bhkc 4.74 (d)mbhk
mgcng bhkccbrk`mb` mb g`cgcgdkcbabk nkdk, 7\
nbrkckik mkbr sgrn nbrkckicbrk`b nrb mgjg dyh
khb` 7M kcbtkimbmkr. 4\ nbrkckik 7\ mb` dyh ecur
ecigz 7M mkyemu ghi` 4M yb mbvrbmbr. MA
nbrkckik` g`k mbbrk igx\ kcb 7/4 igx\ grgs`mg
mbkkrhb` 7 pbrkyettg 1 mgcngcg`ig nrcr. [g`k
du mbvrb mgrdbck hgrghtbrb sgjkptkr.Ertgcgig Nbrkcki ?
igx
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[g`k lgzcgr grgs nbrkcki hgmgrmr. Gy` mbvrbmb mkyet ybrk`b trkstr huccg`cgrgh tgi he`trecc
dgcg`t bcmb bmbdkckrkz. tbtkhcbib gs 6746 lgrhcg jbr lgz trkstr`b uynucg`grgh ert\
gygrcg`gdkckr. 69 kk` ert\ b` yhsbh mbbrk`mbmkr.(mkyet muruiu) `` dgcg`na khk lgz
nbrkckik`k` hbsktkk `ehtgmgmr. (lgznbrkckik`k` 6mg` nbkk mbkc) Du
dgcg`t sbdbdkycb nbrkcki mgcngcg`igs
grtitr (yk`b mb 1 mgrdbckmkr) G`agh
ghi bhkccbrk gy` hgcitr, sgmbab
hgmgr tbcb`ikcbrmkr. bhkc 4.7= (a) vb
(m)mbhk mgcng bhkccbrk k`abcb`krsb 8
6
160 mb` ktkdgrb` `bngtkl g`kmbbrcbr gcm nrcr.
Nbrkcki ertgcgig mbbrk ?
aes4
11sk`
1/4
7igx
)
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klt ycmz dgcg`ts ? hk dgisz 1 lgzc ygri mgcng mbvrbsk`k` < mgrdbck hvbribh zbrb
pgrgcbc gcigs`mg` kdgrbttkr. Jbr dkr ycmz nrudu dkrdkrk`b 67:6 lgz lgrhycg dbscb`kr. Bbr
ycmz `ehtgc k`tbrlgz trglesu ybrk`b merumg` krtkdgtcg`mrcsgym, dgskt (d)mbhk mgcng bhkccbrk
k`abcb`mkk`mb jbr dkr ycmz nrudu`g gkt 4
gmbt 1-mgrdbck mgcng bhck nrcr. Tbghtr 8
du khk ycmz nrudu`, ycmz `ehtgcgr
grgs`mghk nbrkcki lgrh `bmb`kycb gy` g`mg
kcbtkimb ecigs` sgcgr vb yh nbrkckik`k`
mbkkik du khk nrup mgcng bhkccbrk`k` ertg
yeccgr` tghkp bmbr. Dycbab yh nbrkckik`k`
ucggdkcbabk igx g`k mbbr sbhe`mbr sgrn
igx mbbrk`mb` hh ecur ? igx)4
1( \
Mkyet huccg`cig muruiu kk` ertgcgig
nbrkcki sgmbab dkr ycmz nrudu` mgcngbhck`mb` vbyg merumg` yh nbrkckik mgcng
bhck`mb` bcmb bmkcbdkckr ?
igx4
11\\ert
9 hk nruptg dkrdkrk`mb`
dgisz ecmuu`mg` jbr dkr mkyet 7/1
pbrkyet kcbtkimb hgcr vb 7/4 yh ghi tgr.
Du mbvrb`k` GA dbscbib ghi sk`sekmgcbmgjg ygh`mr. bhkc 4.7> (d)mbhk rbghtr
nbrkckik T\ , khk ycmz nrudu nbrkckicbrk
grgs`mghk lgrhtr. [ghcgh nb` bhck
vgrmr vb igx mbbrk, lgz nbrkckik igx
mbbrk`k` ygrs`g bkttkr. Tbghtr ucgr`mg
nbrkcki k`mhcb`bdkcibsk kk` dkr ih`gtscgig ghi`g kjtkyg vgrmr. Du mg yh ghimr.
[h ghi mbbrk du ih`gtscgig ghi mbbrk`mb` gz ksb grgcgr`mg nbrkckik`mhcb`ibybabk`mb` rbghtr yeh nkdkmkr, yg`k khk ycmz `ehtgs dkrcbik nkdkmkr. Mbvrb
7 4 1 = 2
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ycmz dgc
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bhkc 4.47 (d)mbhk mgcng bhkccbrk
k`abcb`krsb8 yh nbrkckik`k`, yh`
st `ehtgs kcb gct `ehtgs`` ycmz
`ehtgs`g petg`skybccbrk grgs`mghk
lgrh ecmuu nrcr. Ighskiui
mbbrk, lgzcgr grgs (jgt) nbrkckik`k`
igx mbbrk`b bkttkr. Mbvrb CA mbvrbsk dgtgrygyg
sbrk dgc
bhkc =.< mg hgpgsktr` yh zbrk`mb` mecmurucigs` `cbyb` dkr mbvrb
nrcibhtbmkr. mbvrbmb ]7 k` tbtkhcb`ibsk, dgtgrygy yhb dgcgr. Gy` zgig`mg vbyg dkr
immbt se`rg ]1 tbtkhcb`krsb CA mbvrbsk`mb ibymg`g nbcb` eskcgsye`cg A hgpgsktr 4B
nbrkckik`b hgmgr mecgr. Du ecgy g`cgigh kk` bhkc =.> mbhk mbvrbyb dghcgdkckr. Mbvrbmb
eskcgsye` lrbhg`s hgypcgr kjigc bmkckrsb 7/4 CA mkr. Bbr hgypcgr vgrsg A hgpgsktr
s`ic dkr eskcgsye`cg se`utg B nbrkckik`b ucggaghtr. ]1 trkstr tbrs y`mb ghi
ghigs` `cbybabk`mb` sgmbab ygri pbrkyetcuh dkr eskcgsye` ecur vb hgpgsktr ucgr`mgyghcgh 4B hgmgr nbrkcki ducu`ur.
B
T7
]7 ]4
T4
A
[h
bhkc =.2 Dgskt pgrgcbc hgpgsktrc hya
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bhkc =.< mg hgpgsktr mecuyhb` ]4 tbtkhcb`krsb du, ]7k s`mrr. s`i bs`gs`mg A
he`mg`sgtr ]4 grgacycg yh zbrk`mb` tbrs pecgrktbck ecgrgh B hgmgr mecgr. Dkr se`rghk ]7
vb ]1 ` tbtkhcb`ibskycb mb he`mg`sgtr eskcgsye`cg mkbr y`mb 4B`k` mb zbrk`mb meciu
ecur. Du mbvrb`k` gvg`tgo, he`mg`sgtr` dgtgryg nbrkckik`mb` mgjg dyh dkr mbbrcb
heitgsye`u nbrbhcbtkribskmkr. Mbzgvg`tgo ksb ]4 vb ]1 yg`cchcg dkrckhtb tbtkhcb`krsb
dgtgryg ucgr hsg mbvrb bmkcikecur.
kimkyb hgmgr g`cgtcg` du mbvrbcbrk sbbrhb` Hrktbr? yh` tkpk, g`gjtgrcgig lrbhg`s,
bcbig`cgr` dyhchcbrk , hgypcgr vb igckybt nz ``b gc`igcmr.
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=.4 TB_E@G@QCG Q@I
He`mg`sgtr-Dedk` heidk`gsye`u hb`mk`mb` eskcgsye`g nkrib zbcckk, ybmbh vbyg
khk`ak dkr trkstr nbrbhtkribmb`, kcbtkib nkrmkhtb` dbcck dkr zgig` se`rg yh trkstr`
s`mribmb huccg`cgdkckr.
bhkc =.: (g) mg nrcb` sbrk rbze`g`s mbvrbsk, trkstr ghi`` tbrs y`mb bvrkcibsk`k
vb s`i` nbrbhcbbdkcibsk`k sgcgigh kk` bhskh s`ic tgsgrcg`igcmr. bhkc =.: (d) mb
mgcng bhkccbrk nrcibhtbmkr.
Dgtgryg dgcg`mhtg` se`rg kch tbtkhcbib mgrdbsk
uynucg``ag CA eskcgsye`u dgcgr trkstr ghi y`
tbrs m`bibybabk kk` eskcgsye` ygri pbrkyet
mbvgi bmbr vb trkstr s`br. eskcgsye` se`u`mg
hgpgsktr ucgr`mg yghcgh 4B hgmgr nbrkcki
ducu`muu`mg` trkstrb tbrs hutupcg`igycg B hgmgr
nbrkcki uynucg`i ecur. Du g`mg` ktkdgrb`
he`mg`sgtr yh zbrk`mb` degcigyg
dgcgr. Nbrkckik B`k` gct`g m`ab
trkstr ucgr`mg yb`kmb` pezktkl
hutupcgig ecur. Mbvrbmb trkstr
kcbtkimb hgcig srbsk eskcgsye`
lrbhg`s dbckrcbr. Hbski srbsk ksb yhb
dgcmr. G`agh he`mg`sgtr` nbrkcki
mbbrk, B`k` gct`g mbabh hgmgr dkr
srb kk` hbskimb hgcigcmr. Ghsk
tghmkrmb dkr se`rghk trkstrtbtkhcbibsk`mb eskcgsye`
ygpcgigygdkckr. ]rkstrmb` nbb`
ghi k`abcb`babh ecursg khk`ak
tbtkhcb`ibmb nbb` ghi`
dkrk`aksk`mb` gz ecmuu nrcr.
Du`u` `bmb`k he`mg`sgtr` ucgr`mg
zgtb` dbckrck dkr nbrkcki sbvkybskducu`iuecigsmr.
kn
\A9\C
k]
\]
\K
kch tbtkhcbib mgrdbsk
_gig`(t)
mv/mt
Q`izgig`
B
B
0B Eskcgsye` mgcng bhck
Bhspe`g`skybcgzgcig
(d)
B
k]
kn \]
\K
\A
[h
T\C
(g)
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bhkc =.; mg ksb pgrgcbc rbze`g`scg s`i sgcgyg` mbvrb nrcibhtbmkr.
Dgtgryg dgcg`m zgig` mbvrbmbhk
he`mg`sgtr B sbvkybsk`b hgmgr mecgr. du
g`mg` ktkdgrb` trkstr` tbtkhcb`ibskycb
yhb nbrkcki uynucg`i ecur, gy`
zgig`mg CA mbvrbsk`mb eskcgsye` dgcgr.
Eskcgsye` ghi`` yh ghi`mg` (B/T)dyh ecigs muruiu`mg trkstr ghi tbrs m`ibyb gcgaghtr vb se`utg s`babhtkr.
Eskcgsye` kch ygr pbrkyemu`mg trkstr ghi grtgrhb` se`rg gzgcigyg dgcgygagh vb khk`ak
ygrs`` dgcgr`mg mg slrg mbabhtkr. bhkc =.; (d) mbhk mgcng bhkccbrk CAT sbrk mbvrbsk`k`
hrktkh s`ic ecmuu (T49 =C/A) muruiu kk` nbbrckmkr. Bbr T mrcrsb yh ghi
eskcgsye` ghi`mg` (CA) mgjg dyh ecgdkckr. T grttrcrsg, du mg hgpgsktr` mecig srbsk`k
grttrr. ([g`k ik`uiui s`i srbsk). Du `bmb`cb, dkr mbvrb sgdkt mkrb`ck yhcbr kk`
huccg`cgdkckr.
B
kA
C
A \A
\]
kn
k]
T \C
k]
bhkc =.; Vgrgcbc rbze`g`scg s`i
Q`i_gig`
m\/mt
(d)
k] 9 kC - kA
B/T
Dgtgrygdgcg`m
\]
k]
kC,\C
\A
kA
kn
B/T
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Tbze`g`s mbvrbsk, meyigyg ucggdkcb` dkr
rbghtr huccg`iycg bhkc =.76 mghk nkdk
nbcktkrkcbdkckr. Du rbghtr mbikr `vbck
yhsbh b`mhtg`sc dkr rbghtrmr. G`agh
meyig dcnbsk`mb b`mhtg`s mhtr.
bhkc =.76 mghk mbvrbmb trkstr tbtkhcb`krsb
C dyh ecmuu kk` meyig dcnbsk`b nbb`b hgmgr ygvg dkr eskcgsye` ecur. Meyig
dcnbsk`mb C gzgcgag`mg` ghi dkrmb` grtgr vb ygri pbrkyet mbvgi bmbr. Du ghi yh
ghiycg gy` y`mb trkstr mb` ghgr. eskcgsye` ghi meyig dcnbsk`mb` h`ag yk`b gz dkr
ghicg mbvgi bmbr vb tbrs y`mb ghigyg dgcgr. Du ghi yk`b meyig dcnbsk`b ucggdkckrsb
trkstr s`mrr. Du mbvrb kcb yh` kcbtkimb hgcig srbsk grttrciecur.
Bbr yh b`mhtklsb yh ucgr`g bhkc =.74 mb nrcm nkdk mkyet dgcg`igcmr.
Gyrag CA eskcgsye` mbvrbsk`k` ghi`g yh zbrk`mb` ghigs` `cbibh kk` CA ucgr`g
mkyet dgcg`gdkckr.
B
A
C
M4]
M7[h
B
A
M7
M4
C
bhkc =.74 Vgrgcbc rbze`g`sc s`i mbvrbsk
(mkyetcgr bhcb`ik)
bhkc =.71 [hsbh b`mhtg`sc yhcbr kk`
rbze`g`s mbvrbsk
BC
A
T
bhkc =.76 Meyuicu rbghtrc pgrgcbc s`i mbvrbsk
E@ ELL
rbghtr meyuimg
bhkc =.77 Meyuicu rbghtrc pgrgcbc s`i mbvrbsk bhkccbrk
\]
k]
kC,\C
\A
kA
kn
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=.1 HRVCGOCK MB\TB
[h ghi` tgyg` trkstr, hb`mksk`b sbrk dkr b`mhtrcb s`mrcbdkckr. Du b`mhtr
zbrk`mb MA dbscbib nbrkckik`b tbrs vb e`mg` mgjg dyh mbbrck dkr nbrkcki
ecuturucigcmr. Du nbrkcki trkstr ucgr`mg tbrs hutupcg`ig ibymg`g nbtkrkr vb ybtbrk`ab
uzu` ecursg trkstr s`br.
bhkc =.7= (g) vb (d) mb mecu
he`mg`sgtr nbrkckik`k`
b`mhtr grgacycg trkstr
s`mribsk`b gkt mbvrbcbr
nrcibhtbmkr. bhkc =.7=
(g) mg hgy`gh mbvrbyb
dgcg``ag A he`mg`sgtr,
C4 vb M4 zbrk`mb`
yghcgh 4B hgmgr mecgr. ]7 tbtkhcb`krsb8 C7
grgacycg yh, hgy`gg dgcg`iecur. ]4
tbtkhcb`k`ab he`mg`sgtr nbrkcki C7 zbrk`mb
]7 trkstr` s`mrr. C7, A rbze`g`s
mbvrbsk he`mg`sgtr tbrs y`mb mecmurgrgh
]4 trkstr` s`mrr. Du`mg` se`rg
he`mg`sgtr, C4 vb M4 grgacycg yb`kmb`
]7 trkstr` s`mrbabh bhkcmb mecmurucur.
Du mbvrbmb, C4 A mbvrbsk`k` rbze`g`s
lrbhg`s, C7 A mbvrbsk`mb` eh mgjg
mhtr. Mecgysycg A`k` C7 zbrk`mb`
degcigs, C4 mb` dgiszmr. C4, C7 mb`mgjg dyh sbkcibckmkr. Bbr M4 ybrk`b, ]4
s`mhtb` se`rg kcbtki nkrb` dkr trkstr
dgcg`rsg C4 mgjg hh sbkcbdkckr vb
ELL srbsk gzgctcgdkckr. bhkc =.7= (a)
mgcng bhkccbrk nrcibhtbmkr. [h ghi hgrb mgcng dkkik`mbmkr. bhkc =.7=(g) mghk mbvrbmb
huccg`cg` bcbig`cgr` hgypsz ecmuu hgduc bmkckrsb jbr g`gjtgrcgigmg dkr he`mg`sgtr
ucgr`mghk nbrkcki 4B hgmgr dyybabhtkr. Du murui bhkc =.72 mb nrcibhtbmkr.
B
M7
]7
C7 A
M4
C4[h
T\C
kn7\]7
k]7
\]4
]4
kn4
kC7
k]4
\A
[h
(g) (d)
E@ ELL
bhkc =.7= Jgrkak mgrdbycb heitgsye`
g)Merumg` dgcg`t d)Hgrchc hupcgoc
a) Mgcng bhkccbrk
B'mb` dyh
B/T
\A
kn7
\C, k]7
kn4
k]4
kC7
\]7
\]4
s`i zgig`
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C4, A mbvrbsk`mbhk eskcgsye` -1B,+1B
bhck`mb ecgagh vb se`utg =B
mbbrk`b ucggaghtr. Gsc`mg hgypcgr
du mbbrb hgmgr hcigs` `cbr. ]4
ucgr`g tbrs dgcg`gagh dkr mkyet kcb
dkr pbrkyetcuh dkr sgc`i sgcg`grgh
mg hgpgsktr nbrkckik 4B kcb
s`rcg`mrcgdkckr.
bhkc =.7
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bhkc =.7> Bkt khk yh grgs`mg heitgsye`
- 74 -
=.= DT DGHG [H DBQCB[B@ ]TQ]T GTGAKCKK[CG HEI]GQ[E@
zbcckhcb k`vbrtbrcbrmb ducu`g` eu mbvrbcbr, yh ghi`, s`mrcbabh trkstrmb`
uzghcgtrgrgh mkbr yh ghi tgyg` trkstr yg mg mkyemg trg`slbr bmb` heitgsye` tbh`kk
huccg`rcgr. hk bkt yh grgs`mg ghi trg`slbr bmb` dycb dkr mbvrb bhkc =.7>mb
nrcibhtbmkr.
]7 tbtkhcb`mkk`mb dkr yh hgy`gg
dgcg`rhb` gy` zgig`mg A he`mg`sgtr mkbr
yh vb ]7 grgacycg mecgr. ]4 tbtkhcb`mkk`mb
ksb A he`mg`sgtr ]7 k s`mrr vb tbrs y`mb
mecgr. Du g`mg ]4 zbrk`mb` mkbr yh hgy`gg
dgcg`i ecur. Du mbvrbmb` yecg hcgrgh
bhkc =.7: mbhk dgskt k`vbrtbr mbvrbyk
ecuturgdkckr.
Du mbvrbmb bkt zgig` grgchcgrycg khk
trkstr` tbtkhcb`ibsk yh ucgr`mg GA
nbrkcki ecuturur. ]gigicgya dkr
mbvrb ecg` IaIurrgy-Dbmlerm mgrdb
heitgsye`cu hpr mbvrbsk bhkc
=.7; mg nrcibhtbmkr. bbr ]7 vb ]4
kcbtkimb ksb yh hgy`gg dgc mbibhtkr
vbyg ]1 vb ]= kcbtkimbysb yh tbrs
y`mb ghinbbabh bhkcmb hgy`gg
dgc mbibhtkr. Dycbab yh ucgr`mg
GA nbrkcki bcmb bmkcbdkckr.
B
ks
kC7
T
A
T
kC4
k]4k]7
]7 ]4
kn4
\]4\]7
kn7
\A
(g)
kn7
kn4
\A
kA
kC7
k]7
kC4
k]4
\]7
\]4
ks
B/T
4B/T
B/T
1B/T
B
-B 4B
Tb
-t/TA
igx mk/mt
s`i zgig`
Dgtgrygdgcg`m
kch tbtkhcbib E@/ELL ELL/E@
7 Vbrkyet
_gig` (t)
igx m\/mt
[h
\C
k7
k4
\C
bhkc =.7: - bhkc =.7> (g)'`` k`vbrtbrb m`trcibsk
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B
[h
M7
M=
A7
A=
]7
]=
C7
C=
]1
]4
A1
A4
M1
M4
A79 A49 A19 A=9 A C79 C49 C19 C=9 C
bhkc =.7; ]gigicgya mgrdb heitgsye`cu hpr mbvrbsk (Ia-Iurrgy - Dbmlerm)
bhkc =.7; mghk heitgsye`u
k`abcbrsbh? ]7 (vb ]4) kcbtkimb vb yh
ghi` tgrcgrhb` ]= tbtkhcb`krsb yh ghi
]=b trg`slbr ecgrgh ]7 k s`mrbabhtkr.
Mkbr khk trkstrmb (]4 vb ]1) dkr mbkkhckh
ecighsz` ]7k` s`mrcibsk, yh`
hgy`ghtg` gyrcigs`g `bmb` ecur. ]=cb
gy` g`mg ]1 tbtkhcb`krsb ]7 vb ]4 gy` g`mgs`br vb yh tbrs y`mb hgy`gg dgcg`i
ecur. bhkc =.46mb heitgsye` bs`gs`mghk
ecgycgr nrcibhtbmkr.
bhkc =.46(g) mg ]=` tbtkhcb`ibsk
`ab grtcgr ducu`ightgmr. A=, B kcb
mecumur. B`mhtrmb mbpecg`g` b`brok
7/4CK4
mkr. ]= tbtkhcb`k`ab bhkc =.46 (d)mbhk grtcgr nbrbhcbkr. A=` nbrkckik C=
ucgr`g uynucg`r vb du mg C7 zbrk`mb B
nbrkckik b`mhcbr. Du sbdbpcb ]7 tbrs
hutupcg`grgh s`br. bhkc =.46 (d) mbhk ghi
mgc ]=` tbtkhcb`ibsk`mb` se`rg C7,
C= tbhk mbpecg`g` b`brok`k` mbkibibsk
sbdbdkycbmkr. C7 mb` ghightg ecg` K ghi
C= b trg`slbr ecur, dycbab 7/4CK4 b`brok
B
B
A=
]7
]=
C79C
C=9C
]4
K
BB
K
K
B
A= K
B
B9CmK/mt
]4B
K
K
A7
K/4
B
B
M=
C=
B
k
6
6
bhkc =.46 Eikh yh kk` s`i grtcgrg)]=tbtkhcb`ibmb` `ab d)]=tbtkhcb`mkhtb` jbib` se`rg
a)He`mg`sgtr nbrkckik tbrs ecigyg dgcgmhtg` se`rg
(g)
(d)
(a)
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- 7= -
sbvkybsk heru`iuecur. Eikh dkr yh vgrsgyi kcb yh ghi slrg mbrhb`, K ghi bkt
erg`mg A7 vb A= zbrk`mb` bhkckr. A7 vb A=, C= kcb eskcgsye`g nkrbr. (l97/4 CA4 ) A=`
nbrkckik (7/4)B yb m`ab ]7 pezktkl hutupcg`r, du zgig`g hgmgr mg ]7 dcehb eciuecur.
Mbvrbmb mkyetcgr ecigsgym, eskcgsye` sbdbdkycb A7 ucgr`mghk nbrkcki 4B `k` zbrk`bhgagh vb se`utg B sbvkybsk`b k`babhtk. M= sbdbdkycb A= ucgr`mghk nbrkcki tbrs m`bibz,
bhkc =.46 (a) mb nrcm nkdk C=`
gzgcg` ghi M= mkyemu`mg` mbvrbsk`k
tgigicgr. Dycbab A7, B sbvkybsk`b
hgmgr mecgr. ]=` ghi ksb M= vb C=
mbhk hgypcgr sbdbdkycb slrg mbr.
eu muruimg yh b`mhtkl ecmuu kk`
yh ghi srbhck ecgaghtr. Gyrag
yh` b`mhtg`s, heitgsye`
mbvrbsk`k` b`mhtg`s`mg` eh mgjg
dyhtr. Du muruimg ]=
tbtkhcb`mkhtb` jbib` se`rg ghi
mbkkhckk bhkc =.47 (g) mghk nkdk ecur.
A=` mbgro ghi khk hgt grtitr.
`h he`mg`sgtr jbi yh` jbi
mb ]=` ghi` sgcgightgmr.
Heitgsye` pbrkyemu`ag yh
ghi`` mbkibmkk`k hgduc
bmbrsbh, M= kcbtkib nbk`ab ]=`
ghi gzgcr, yh ghi mg ]4 vb M= zbrk`mb` ghgr, g`agh yh ucgr`mghk nbrkcki slrmr. (
bhkc =.47 (d) )
[uhgrmghk bhkcmb ksb CA sbrk mbvrbsk vb ybmbh trkstrcbrmb s`i vb ghi trg`slbrk
nbrbhcbtkrkcb` mbvrb nrcyer. ]7 kcb ]4 vbyg ]1 kcb ]= kcbtkib gc`grgh yh hgy`gg
dgcg`gdkckr.
K
A=B
B C
K
]=
[h
K
]4
K
C
k
]=
[h
K
]4
K
M=
K+k
bhkc =.47 B`mhtkl yh kk` s`i grtcgr
g) ]=tbtkhcb`mkhtb` jbib` se`rg d)M=mkyemu kcbtkimbyhb`
(g)
(d)
B
]7G
]=G
A C
]7
]=
M7
M=
[h
]1
]4
bhkc =.44 [bmbh trkstrcbrcb mgrdb heitgsye`u
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Mbvrbmb ]7 trkstr s`mrbdkcibh
kk` ]7G`` tbtkhcb`ibsk nbrbhkr.
Heitgsye` srbsk`ab mgcng bhkccbrk bhkc
=.41 mb nrcibhtbmkr.
Mbvrbmb heitgsye` ggigmg
nbrbhcbibhtbmkr vb heitgsye`
srbsk`ab yh ghi sgdkt hgcightgmr. ]7G
tbtkhcb`krsb, bhkc =.4= (g) mg nrcm
nkdk AC mbvrbsk ]7 kcb sbrk ecur vb
he`mg`sgtr ]7 zbrk`mb` degcr. t7
g``mg he`mg`sgtr ghi KCyb bkt ecur vb
]7 s`br
He`mg`sgtr ghi grtigyg mbvgi
bmbr. KC mb` lgzcgs M7 mkyemu`mg` nbbr
(bhkc =.4=(d) ) he`mg`sgtr nbrkckik tbrsbvrkck`ab, ghi yh ghi`` gct`g
mbr. M7k` ghi gzgcr vb M= kcbtkib
nbbr. Dycbab bhkc =.4= (a) mb ecmuu
nkdk CA hgy`gh ucgr`g dgcg`i ecur.
He`mg`sgtr, dgskt dkr CA mbvrbsk`mb` mgjg lgzcg dkr nbrkckib ucgr. He`mg`sgtr ghi tbrs
m`ibh kstbyk`ab ]7G trkstr t1 g``mg s`br, M= mkyemu yh ghi` zbrk`b gcr.
bhkc =.41 tbhk grtcgr zbtcbrsbh KA ghi KC mb` mgjg dyh dkr pkh mbbrb sgjkp
ecigcmr. ]7 trkstr`` s`i zgig`, M7 mkyemu`u` kcbtkimb hgcig srbsk hgmgrmr. Du
g`mg trkstrb uynucg`g` tbrs hupcgocgig nbrkckik, M7 zbrk`mbhk nbrkcki mi hgmgrmr. ]7
ucgr`mghk nbrkckik` mbkki jz yhsbh ecmuu kk` prgtkhtb du grt M= mkyemu`u` mgjg
brhb` ghi zbrk`b gcigs mbibhtkr, du mg A he`mg`sgtr`` mgjg lgzcg nbrkckicb mecigs
g`cgi`g nbckr. Dycbab dkr se`rghk heitgsye` mgjg hecgy ygpcgdkckr.
B
k]7G
\A
[hkn7G
kA
\]7
kM7
kM=
KC
KC
kn7G
\A
k]7G , kA
k]7
k]7
kM7
kM=
\]7
kcbrk nbrkckimi
s`i zgig`
M'mb kcbrk nbrkckimi
_gig`
m\/mt
KC
kA- KC
KC- kA KC
(g) (d) (a)
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- 7< -
=.2 LETICCBTCB _B]
Du dcimb MA
hgy`gg dgc trkstrcbrk`
s`i kcb kcnkck mbvrbcbr
g`cgtcitr. [h` tkpk`b
nrb mbvrb uynucgigcgr ybr
gcigitr. Mbvrbcbrb T-A
vbyg C-A heidk`gsye`cgr
kbrmkk`mb` mbvrb
mgvrg``g uynu` lericcbr
vbrkcbabhtkr. T-A mbvrbsk`mb
ghi vb nbrkcki zgig`g nrb
mbkibcbrk bhkc =.42 tbhk
nkdkmkr. k9Db-t/] v9B+ Gb-t/]
vb zgig` sgdktk ]9T.A mkr
A
T
k
B
\
(g)
B/T
k
\
(d) t
k
B
\
(a)
\
(m)
t
k
\B
B+\
T
bhkc =.42 TA mbvrbsk`mb mecui heuccgr
A
T
k
B
(g)
C
\
Bk
\
(d)
B
t
\k
B
t
(a) (m)
bhkc =.4< - TCA sbrk mbvrbsk (kch grtcgr slr)
g) Mbvrb d)gz s`ic a)hrktkh m)gr s`ic
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T4 9 =C/A7 ksb
k9b-t(Gt+ D)
v9B + b-t(At+M)
9T/4C ecup t9 6 mg` G,D,A vb M dbckrcb`bdkckr.