Güç Elektroniği - Eemdersnotlari.com Geniş Konu Anlatımı

8/10/2019 G Elektronii - Eemdersnotlari.com Geni Konu Anlatm

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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

Gèt

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

Gèt

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`mbmbckìb

]brsmbckìb

Nbrk hgghghi


3/64

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Hgp ghi uynucgìgm murui kk` trkstr, khk y`mb mb kcbtkib kzk` vbribyb` tg`b sbrk dgc mkyet

nkdkmkr. ]brs y`mb hutupcgìg muruiu`mg mkyetcg gy` mgvrg` sbrnkcbr. cbrk y`mb hutupcgigmg yg`k gèt

pezktkl khb`, ibrhbzmbhk he`trec oe`hskyeùù` mbckìb nbrkckik gcigmhg sgmbab hggh ghi ghgr. Mbckìb

nbrkckicbrk khk y` kk` mb gy`mr. ]brs hutupcgig muruiu`mg hgtem V-@ oe`hskyeù 76\mg mbck`mk k`mb` ti

vectgo gèttghk V-@ oe`hskyeù`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` gèt

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 hutupcgìtrkstrb K n hgp ghi uynucg`rsg trkstr kcbtkib nbbr.

Gèt 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) gèt ghi sbvkybsk`k` gct`g

mrcibck vb trkstr he`trec oe`hskyeùù` thgig muruiu`g

nbibsk`b hgmgr nbb` dkr srbmb kcbrk y`mb nbrkcki

uynucgìgigcmr. 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`gsyeù ecuturucg` ygr kcbthb` bcbig`

]rkstr Hgp Rau vb Nbrbhtkrmkhcbrk ?

]rkstr` hgp-hgtet ucgr hgrghtbrkstkk zgyl V-@ oe`hskyeùù`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`hskyeùmur.

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

Kgèt

16 A


4/64

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[g`mghk bhkcmb trkstr` kcbtkib nbibsk kk`

tbtkhcbib ghi vb nbrkckik`k` gcigs nbrbhck mbbrcbrknstbrb` dcnb tgrg`grgh kgrbtcbìktkr. Rynu`

grtcgrmghk tbtkhcbib mgrdbsk dkr kzecgsye` trglesu

grgacycg trkstr hgps`g uynucg`r. ]rgleù` hgp

tgrgl`mg hgp ghi` s`rcgigh kk` dkr T 7 mkrbàk

ducuùr. ]rkstr sìmbyhb` hgp nbrkckik`k

s`rcgigh kk` mb T 4 mkrbàk dgcgìtr.

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 èhtgs 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 deyuàg kcbrcbybrbh V èhtgs`g ucgr. Gàgh V èhtgs`g ucgcigmg`

(tgjik`b` G èhtgs`mg) trkstr kcbtkib nbik ecur. cbtkik` hbsk` ecgdkcibsk kk` tbtkhcbib mbvrbsk`k`

bcbig`cgr ycb sbkcibckmkr hk gcig èhtgs ecg` V, ighskiui n s`r kcb G èhtgs 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

gèt 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 jgragìgs`g vb tbtkhcbìb

g``` mgjg kyk dbckrcbìbsk`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. Gàgh 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 tbtkhcbìbckmkr. 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 ucgàg 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` gygrcgìgsycg 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 tbtkhcbìbsk seùau

yg`cgcigy `cbykak m`ncbr v.s. kbrkrcbr. He`trec hgrghtbrkstkk, tbtkhcbib nbakhib gs kcb nkrknbrkckik

grgs`mg tgìcg`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, gàgh prgtkhtb jbr khksk kk` mb `bngtkl mgrdb uynucg`r.

N]E (Ngtb ]ur` Ell -Hgpmg` ]hg`gdkcb` ]rkstr) ?

]rkstr` ducuìgs`mg` se`rg khk yb`k r` mgjg kagt bmkcmk. Du`cgrmg` dkrksk tbrs y`mb mgkig kcbtkimb

ecg` gàgh mgjg kàb 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`hskyeù nbrkckik tutgr gàgh 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 bòbhtb bmkckr. Q`mribh kk` ksb hgtem - hgp y``mb 76\

sbvkybsk`mb nbrkcki uynucg`r. Qì kk` nbbabh ghi gèt ghi``

7/2k vbyg 7/1 hgmgr ecigcmr. Du ghi 7smb` mgjg gz dkr zgig`mg

sgcg`gag`mg` Gèt 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


8/64

- > -

[g`mghk mbvrbmb dgskt hgp he`trec mbvrbsk

nrcibhtbmkr. He`trec sk`ygck`k` heùiu`g nrb

]7 vb ] 4 kcbtkib nbbrbh A 7 mecmurucup degctcgrgh

trkstr kcbtkib vbyg hbskib nbkrkckr. A 4 ksb gèt

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`hskyeùmur. Dbckrck dkr \ AB kk` dgz ghi`mghk mbkib heccbhtr ghi`mg hgtcgìecgrgh nrcr. Du

erg` 72 766 hgt grgs`mgmr. ]brs nbrkcki uynucg`g` dkr trg`skstr` dgz biktbr oe`hskyeù 76\ akvgr`mg

mbck`kr. Du iemmg gccgaghsg trg`skstrb sbrk mkyet dgcgìgcmr.

]rg`skstrmb hgypcgr \ AB kcb K A`k` grpi`` dkr le`hskyeùmur. [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

Mbckìb

\ABHggh

Ghi

KD9 6Mbckìb

Nbrkckik

Dbckrck KD

mbbrcbrk

KDgrtyer

[gp Qbidec @V@ trg`skstr hgrghtbrkstkk

[h76

KA

KD

+\ 9 466\


9/64

- : -

]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 hgzgà` grtrigh kk` yg`mghk bhkcmb nrcm

nkdk mgrck`nte` dgcg`ts huccg`cr. Du bhkcmb ghi hgzgà 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

MrgkÌbtgc 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, gàgh èrigcmb 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 kàbcbmkh. Gàgh dkr n ygr kcbthb` bcbig``` btkhbt

mbbrcbrk ecuturucurhb` eh mbkkh deyutcgr` nz ``b gcìgs nbrbhkr.

[g`mghk bhkcmb dkr trkstrmb` K l ghi ghgrhb` trkstr

mk/mt bkikycb sìb 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 rrtepgrcgìg yh 8 tbrs tepgrcgìg yh

tbrs tepgrcgìg zgig` t rrvb tbrs tepgrcgìg ghi K rr

ecgaghtr. ]rkstr` kcbtkib nbibsk hgp ghiycg sgcg`yermu. Gàgh kcbrk y`mb nbrkcki grtjz dbckrck dkr

mbbrk ggrsg trksr` kcbtkib nbibsk iih`mr. ]rkstr oe`hskyeùù hgpgsktr nkdk m`babh ecursgh,

sz`t ghi`g hgrch nbcb` mbpcgsig` ghimt

mvAk 9 ecgaghtr. [btbrkàb 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 àbckhcb hgp bcbhtremu akvgr`mg ecur. ]epcgi gèt ghi g`kmb` nbbabh

ecursg gr sìg `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 mkrbàk` dbckrck dkr mbbrk vgrmr.

Dkr bcbig`` èik`gc ghi mbbrk`k, ecuturgag oe`hskye` saghc dbckrcbr yg`k hgyp na` dkr

le`hskyeùmur. ]g`g` ghi` tkpk hgyp na bthkcbybabhtkr. Bbr sk`sekmgc dkr mgcng sz heùsu 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 tgìcg`r. Gyrag pbrkyemkh ecigyg` gr nbrkckicbr mb szheùsu ecgdkckr. Mecgysycg dkr bcbig`` mbckìbmb` mgyg`gdkcbabk du tr nbrkckicbrb gkt mbbrk mb vgrmr.

trr

mkmt

KL

KrrGcg` 9 Wrr

_gig`

]kpkh Qì 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 hgzgà, 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`hskyeùmur. 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 sìb 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` ducuùr. ]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 àb 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 mkrbàk` dkrkik Âe / 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


13/64

- 74 -

jbsgpcgìgcmr. 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 mbpecgìg 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 (Qeù 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` gàgh kigcgt mbbrk`b hgmgr

huccg`cgdkckr. ( 7igx ) Ghsk tghmkrmb akjgz yg`gr.

Du sbdbpcb gr yh gàgh 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


14/64

- 71 -

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,


15/64

- 7 -

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 mgcngcgìg dkcbb`k kbrkr. Ggmg dgjsbmkcb` mbvrbcbrk` tgigi MA nbrkckivbribsk`b rgib` 8 htghk GA mgcngcgìgs, ertgcgig nbrkcki sbvkybsk, vbrkik vb GA

dbscbibmbhk yhcbib tbskrcbrk gs`mg` lgrhcch grz bmbrcbr.

4.7 Mbvrb ]gìcgr vb Nrupcg`mrig ?

Meructuau mbvrbcbrk ygri mgcng vb tgi mgcng dgcg`tcgr ecigh zbrb khk nruptg

tgìcg`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 dgcgìgs`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

gàgh 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`


16/64

- 4 -

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`hskyeù vgrmr ? 7-[h

nbrkckik`k` y``` mbkibsk`k

`cbibh 4-[h ghi`` g`g

meructuaumg` gh` `cbybrbh meructuauù` 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 kcnkcbìbz.

[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


17/64

- 1 -

Gàgh MA mgcngcgìgcgr kstbibyb` hgypcgrg yec ggr. Mbvrbmbhk mkyemu` sbkik kk` jbi

ghi jbi mb nbrkcki mkhhgtb gcìgcmr. [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


18/64

- = -

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] sìb nkttkk g`mg ucgr`mg

igx4\ (yg`k ti sbhe`mbr sgrn

nbrkckik) hgmgr nbrkcki ducuùr.

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 mgcngcgìgs grtgr vb hbsk`tkck jgc

gcr. GA dbscbib ghi mg è`-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


19/64


20/64

- < -

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 heùsu ecigz. Ghi` nbbdkcibsk kk`

bhkc 4.:mbhk mbvrbmb7

] vb4

] ,1

] vb=

] nrup jgck`mb jbr ygr pbrkyettg gy` g`mg

tbtkhcbìbckmkr. Duù 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.

Gàgh 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


21/64

- > -

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` bhcbìbsk`mb` ecuiutur. [hb nkrb` ghi trkstrcbrmb`

nbbrhb` m`yecu mg mkyetcgrcg sgcgìghtgmr. àbhk heùmg ecmuu nkdk dkr @ (dbscbib

`tr) èhtgs tgìcgygrgh vb yh ucgr`` du èhtgyg ecg` petg`skybc mbkkicbrk`k

kàbcbybrbh mgcng bhkccbrk`k bcmb bmbdkckrkz.

Mgcng bhkccbrk`mb` mb nrcm

nkdk yh nbrkckik gscg `bngtkl

ecigz. Nbakhib gs 67:69

ecuàg 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 mìbhtbmkr.

1] trkstr hgmgr

tbtkhcbìbybabk`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


22/64

- : -

]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, gàgh 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.

Gàgh, dbscbib trglesuù` sbhe`mbrk`k` zkn-zgn dgcgìgs` nbrbhtkrmkk`mb` huccgì

gcg` s`rcmr. G`cgti hecgyc dghi`mg` durgmg ycmz dgc ecmuu hgduc bmkcbabhtkr.

eh lgzc dgcg`tcgrycg MA mgcng bhck`mbhk mgcngcgìgcgr mgjg gzmr. Gyrag

b`mhtg`s dyh nc yhcbr dbscb`bdkckr. [h ghi mgcngcgìg`` gzc `bmb`kycb srbhck

vb sgdkt mbbrck hgduc bmkcbdkckr.

bhkc 4.74mb jbr lgz dkr mkyet grgacycg yhb

dgcgìtr. [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 mgcngcgìg nrcr. [g`k

du mbvrb mgrdbck hgrghtbrb sgjkptkr.Ertgcgig Nbrkcki ?

igx


23/64

- ; -

[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 èhtgmgmr. (lgznbrkckik`k` 6mg` nbkk mbkc) Du

dgcg`t sbdbdkycb nbrkcki mgcngcgìgs

grtitr (yk`b mb 1 mgrdbckmkr) Gàgh

ghi bhkccbrk gy` hgcitr, sgmbab

hgmgr tbcbìkcbrmkr. bhkc 4.7= (a) vb

(m)mbhk mgcng bhkccbrk kàbcb`krsb 8

6

160 mb` ktkdgrb` `bngtkl g`kmbbrcbr gcm nrcr.

Nbrkcki ertgcgig mbbrk ?

aes4

11sk`

1/4

7igx

)


24/64


25/64

- 77 -

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 èhtgc k`tbrlgz trglesu ybrk`b merumg` krtkdgtcg`mrcsgym, dgskt (d)mbhk mgcng bhkccbrk

kàbcb`mkk`mb jbr dkr ycmz nrudu`g gkt 4

gmbt 1-mgrdbck mgcng bhck nrcr. Tbghtr 8

du khk ycmz nrudu`, ycmz èhtgcgr

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`mhcbìbybabk`mb` rbghtr yeh nkdkmkr, yg`k khk ycmz èhtgs dkrcbik nkdkmkr. Mbvrb

7 4 1 = 2


26/64

- 74 -

ycmz dgc


27/64

- 71 -

bhkc 4.47 (d)mbhk mgcng bhkccbrk

kàbcb`krsb8 yh nbrkckik`k`, yh`

st èhtgs kcb gct èhtgs`` ycmz

èhtgs`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` tbtkhcbìbsk, 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

sìc dkr eskcgsye`cg seùtg 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 ducuùr.

B

T7

]7 ]4

T4

A

[h

bhkc =.2 Dgskt pgrgcbc hgpgsktrc hya


51/64

- 2 -

bhkc =.< mg hgpgsktr mecuyhb` ]4 tbtkhcb`krsb du, ]7k s`mrr. sì bs`gs`mg A

he`mg`sgtr ]4 grgacycg yh zbrk`mb` tbrs pecgrktbck ecgrgh B hgmgr mecgr. Dkr se`rghk ]7

vb ]1 ` tbtkhcbìbskycb 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

heitgsyeù 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 gcìgcmr.


52/64

- < -

=.4 TB_E@G@QCG Q@I

He`mg`sgtr-Dedk` heidk`gsyeù hb`mk`mb` eskcgsye`g nkrib zbcckk, ybmbh vbyg

khkàk 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 sì` nbrbhcbbdkcibsk`k sgcgigh kk` bhskh sìc tgsgrcgìgcmr. bhkc =.: (d) mb

mgcng bhkccbrk nrcibhtbmkr.

Dgtgryg dgcg`mhtg` se`rg kch tbtkhcbib mgrdbsk

uynucg`àg CA eskcgsyeù dgcgr trkstr ghi y`

tbrs m`bibybabk kk` eskcgsye` ygri pbrkyet

mbvgi bmbr vb trkstr s`br. eskcgsye` seù`mg

hgpgsktr ucgr`mg yghcgh 4B hgmgr nbrkcki

ducu`muu`mg` trkstrb tbrs hutupcgìgycg B hgmgr

nbrkcki uynucgì ecur. Du g`mg` ktkdgrb`

he`mg`sgtr yh zbrk`mb` degcigyg

dgcgr. Nbrkckik B`k` gct`g màb

trkstr ucgr`mg yb`kmb` pezktkl

hutupcgig ecur. Mbvrbmb trkstr

kcbtkimb hgcig srbsk eskcgsye`

lrbhg`s dbckrcbr. Hbski srbsk ksb yhb

dgcmr. Gàgh 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 kàbcb`babh ecursg khkàk

tbtkhcbìbmb nbb` ghi`

dkrkàksk`mb` gz ecmuu nrcr.

Duù` `bmb`k he`mg`sgtr` ucgr`mg

zgtb` dbckrck dkr nbrkcki sbvkybskducuìuecigsmr.

kn

\A9\C

k]

\]

\K

kch tbtkhcbib mgrdbsk

_gig`(t)

mv/mt

Qìzgig`

B

B

0B Eskcgsye` mgcng bhck

Bhspe`g`skybcgzgcig

(d)

B

k]

kn \]

\K

\A

[h

T\C

(g)


53/64

- > -

bhkc =.; mg ksb pgrgcbc rbze`g`scg sì sgcgyg` mbvrb nrcibhtbmkr.

Dgtgryg dgcg`m zgig` mbvrbmbhk

he`mg`sgtr B sbvkybsk`b hgmgr mecgr. du

g`mg` ktkdgrb` trkstr` tbtkhcbìbskycb

yhb nbrkcki uynucgì ecur, gy`

zgig`mg CA mbvrbsk`mb eskcgsye` dgcgr.

Eskcgsye` ghi`` yh ghi`mg` (B/T)dyh ecigs muruiu`mg trkstr ghi tbrs mìbyb gcgaghtr vb seùtg s`babhtkr.

Eskcgsye` kch ygr pbrkyemu`mg trkstr ghi grtgrhb` se`rg gzgcigyg dgcgygagh vb khkàk

ygrs`` dgcgr`mg mg slrg mbabhtkr. bhkc =.; (d) mbhk mgcng bhkccbrk CAT sbrk mbvrbsk`k`

hrktkh sìc 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 ikùiui sì 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 sì

Qì_gig`

m\/mt

(d)

k] 9 kC - kA

B/T

Dgtgrygdgcg`m

\]

k]

kC,\C

\A

kA

kn

B/T


54/64

- : -

Tbze`g`s mbvrbsk, meyigyg ucggdkcb` dkr

rbghtr huccgìycg bhkc =.76 mghk nkdk

nbcktkrkcbdkckr. Du rbghtr mbikr `vbck

yhsbh b`mhtg`sc dkr rbghtrmr. Gàgh

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` hàg 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 dgcgìgcmr.

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 sì mbvrbsk

(mkyetcgr bhcbìk)

bhkc =.71 [hsbh b`mhtg`sc yhcbr kk`

rbze`g`s mbvrbsk

BC

A

T

bhkc =.76 Meyuicu rbghtrc pgrgcbc sì mbvrbsk

E@ ELL

rbghtr meyuimg

bhkc =.77 Meyuicu rbghtrc pgrgcbc sì mbvrbsk bhkccbrk

\]

k]

kC,\C

\A

kA

kn


55/64


56/64

- 76 -

=.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 hutupcgìg ibymg`g nbtkrkr vb ybtbrkàb

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`àg A he`mg`sgtr,

C4 vb M4 zbrk`mb`

yghcgh 4B hgmgr mecgr. ]7 tbtkhcb`krsb8 C7

grgacycg yh, hgy`gg dgcgìecur. ]4

tbtkhcb`kàb 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

sì zgig`


57/64

- 77 -

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


58/64

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

dgcgì ecur. Du mbvrbmb` yecg hcgrgh

bhkc =.7: mbhk dgskt k`vbrtbr mbvrbyk

ecuturgdkckr.

Du mbvrbmb bkt zgig` grgchcgrycg khk

trkstr` tbtkhcbìbsk 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

sì 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


59/64

- 71 -

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 heitgsyeù

kàbcbrsbh? ]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 dgcgì

ecur. bhkc =.46mb heitgsye` bs`gs`mghk

ecgycgr nrcibhtbmkr.

bhkc =.46(g) mg ]=` tbtkhcbìbsk

àb grtcgr ducuìghtgmr. A=, B kcb

mecumur. B`mhtrmb mbpecg`g` b`brok

7/4CK4

mkr. ]= tbtkhcb`kàb 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 ]=` tbtkhcbìbsk`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` sì grtcgrg)]=tbtkhcbìbmb` àb d)]=tbtkhcb`mkhtb` jbib` se`rg

a)He`mg`sgtr nbrkckik tbrs ecigyg dgcgmhtg` se`rg

(g)

(d)

(a)


60/64

- 7= -

sbvkybsk heruìuecur. 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 màb ]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 seùtg 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` pbrkyemuàg yh

ghi`` mbkibmkk`k hgduc

bmbrsbh, M= kcbtkib nbkàb ]=`

ghi gzgcr, yh ghi mg ]4 vb M= zbrk`mb` ghgr, gàgh yh ucgr`mghk nbrkcki slrmr. (

bhkc =.47 (d) )

[uhgrmghk bhkcmb ksb CA sbrk mbvrbsk vb ybmbh trkstrcbrmb sì 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` sì 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 heitgsyeù


61/64

- 72 -

Mbvrbmb ]7 trkstr s`mrbdkcibh

kk` ]7G`` tbtkhcbìbsk nbrbhkr.

Heitgsye` srbskàb mgcng bhkccbrk bhkc

=.41 mb nrcibhtbmkr.

Mbvrbmb heitgsye` ggigmg

nbrbhcbibhtbmkr vb heitgsye`

srbskàb 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 tbrsbvrkckàb, 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 dgcgì ecur.

He`mg`sgtr, dgskt dkr CA mbvrbsk`mb` mgjg lgzcg dkr nbrkckib ucgr. He`mg`sgtr ghi tbrs

mìbh kstbykàb ]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`` sì zgig`, M7 mkyemuù` 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= mkyemuù` 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

sì 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`

sì 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 sìc a)hrktkh m)gr sìc


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64/64

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.

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