Transferencia Ejercicios .2

 

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BKJXI^KN5 JFHOJFKZ

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N@JHO^H5 FOL AKOOFCKI CSF^@

KZFLOK^XSK5 ^SKOZBHSHOJFK NH JKI@S  JXSZ@5 JXKS^@ ’K‗

^HGK5 ’SHZ@IXJFÚO NH I@Z HEHSJFJF@Z NHI JK]Ç^XI@ > NHI IFCS@ NH @J@O-^@E@‗

 

Hehrjfjf` >-; Ho uok ghzjik nh vkp`r nh t`iuho` y oftrúlho` k 1=µJ y =gg nh Al, ik prhsfúo pkrjfki nhi t`iuho` hs ;8=gg Al. Jkijõihsh ik j`ojhotrkjfúo nh t`iuho`5 ]hs` g`ihjuikr nhi t`iuho`7 63 ]hs` g`ihjuikr nhi oftrúlho`7 31 k) Ho br brkj kjjf jfúo úo g` g`ik ikrr  y 7

;8= =

7=.3=: g`ihst`iuho` / g`ighzjik

c) Ho sskt ktur urkj kjfú fúo o g` g`ik ikrr V g 7

  ;8= = ∓;8=

7

;8= 86=

7=.38> g`ihst`iuho` / g`i O 3

j) Ho skt sktur urkj kjfú fúo o kc kcs` s`iu iutk tk  y 7

63 31

t`iuho` / dloftrúlho` 7=.1:8 dl t`iuho`

Ho hi jks` nh trktkrsh nh uo lks skturkn` j`o vkp`r, sh puhnho hgpihkr iks gfsgks hjukjf`ohs sustftuyhon` ik prhsfúo nh vkp`r p`r ik thosfúo nh vkp`r ` prhsfúo nh vkp`r  j`rrhsp`onfhoth j`rrhsp`onfho th k ik skturkjfúo. I`s nkt`s nh thosf`ohs nh vkp`r sh hojuhotrko ho tkciks ` ho lrëbfjks ho buojfúo nh ik thgphrkturk, nfsp`ofæon`sh nh rhikjf`ohs kokiçtfjks pkrk gujaks sustkojfks

Hehrjfjf` >-3 Xok gksk nh kfrh hstë skturknk j`o æthr nfhtçifj` k 3= ½J y 8 ggAl. Jkijõihsh5 k) c) j) n) h) b)

Ik j`gp` j`gp`sfj sfjfúo fúo ho v`i v`iugh ugho. o. Ik augh aughnk nkn ng g`i `ikr kr.. Ik augh aughnk nkn n kkcs cs`i `iut utk. k. Hi v`i v`iugh ugho o hhsph sphjçb jçbfj` fj`.. Ik au aughnk ghnkn n kcs kcs`iutk `iutk sf sf ik thg thgphrk phrkturk turk n nhsjf hsjfhonh honh a akstk kstk ==½J. ½J. Ik jk jkotfnk otfnkn n nh ææthr thr jj`onh `onhoskn oskn`` sf sh sh hobrçko hobrçko a akstk kstk =½J ;= ;=== == g: nh ghzjik fofjfki.

Iks thosf`ohs nh vkp`r nhi æthr ho buojfúo nh ik thgphrkturk s`o5 ^,µJ ], gg Al Nkt`s5

-;= ;;3,:

= ;18,:

;= 36;,<

3= >>3,3

:= 2>>3 ggAl  7 7=,86>  ] 8 ggAl

 c)  ]v   ]v   >>3 ggAl Vg 7 7 7 7 ;,>2  ]l  ]∓ ]v ( 8∓ >>3 ) ggAl

j) Æthr nfhtçifj` (Gv)7 ,;3 Dl/Dg`i Kfrh (Gl)7 36Dl/Dg`i V 7

 Gv  Vg  Gl

V 7

,;3

;,>2 7 :,<

)(

 

g`i. D  8 ggAl  I g`i

)

)

:

 g   Dl  Dg`i 73,=1 =,=1>1 3>,8:>< :  Dl  Dg`i g

h)  Gv ∜ ]v  Gl V 7  ]∓ ]v ,;3

V 7 36

∜;18,:

8 ∓ ;18,:

 )

∜36: D 

 

V 7 =,1>8

 Dl nhæthr nhæthr  Dl nh kfrh

b) R 7

(

 ))((  )

  V   S^   Gl  Gv  ]  ;

+

(

R 7   ; + =,1>8 36 ,;3

)(

( =,=13 )( 31> g7

  g  Dl nh kfrh

  ( =,1>8 )( ;)   V  .;  .; 7 1=8,66 Dl nh æthr 7 R .R` ( ;,=>1> )( ;=== )

Hehrjfjf` >-: Xok ghzjik kfrh-vkp`r nh kluk j`otfhoh hi 3>% ho v`iugho nh vkp`r nh kluk, k 2∜=.=;3 )7 =.3>88

  Djki  Dl kfrh½ kfrh ½ J 

n. Hi vv`i `iug ugho ho hsp hsphj hjçb çbfj fj`. `.

R hsp

R hsp

(7

 ;

+

  V ;

 G L  G R 

( 7

)∜

 S^ 

 ]

=.=;3   ; ;1

+

36

)∜

=.=13∜:=:

=

:

  g 7=.16<  Dl kfrh

88

)(

 )

 )

 Djki  dl kluk kluk   Djki 7;>.83 ∜:= ½ J  + 86-8 Ho uok ghzjik chojho`-oftrúlho` k >= µJ y .6

;= >8.2

3=

>= ;1:.3

8= 3 36

∓

  38 J   Dlkfrh  Dl kfrh

]`r i` tkot` ik jkotfnkn nh Ji>J j`onhosknk p`r Dfi`lrkg` nh kfrh hs 3,=;2= ∓=,;1=8 7;,1:88 Dl

R`iugho hsphjfbfj` °

(

 ; 36

+

 )

3,=;2 ;8>

:

 g =,13∜:3: 7;,32=3,=;2=  Dl

Jkotfnkn nh kfrh ho dfi`lrkg`s ho i`s ;8== g: nh ghzjik fofjfki 5

 

;8== ;,32=

❛

7;;6= Dl kfrh

Hehrjfjf` >-;= Xok gksk nh kfrh k >=½J tfhoh uok thgphrkturk aõghnk nh 38½J. Hgpihkon` hi nfklrkgk psfjr`gætrfj`, jkijõihsh5 k) c) j) n) h) b) l)

Ik augh aughnk nkn n kc kcs` s`iu iutk tk Ik a aug ughn hnkn kn rhi rhikt ktfv fvkk Ik thg thgph phrk rktu turk rk n nhh r` r`jç jç`` Ik aug aughnkn hnkn n nhh sktu skturkjf rkjfúo úo p`r hobrfkg hobrfkgfhot` fhot` knfkcë knfkcëtfj` tfj` Ik aug aughnkn hnkn n nhh sktu skturkjf rkjfúo úo k ik thgphrkt thgphrkturk urk qu quhh sh hoj hojuhotr uhotrkk Hi jk jki` i`rr hsp hsphj hjçb çbfj fj`` Hi vv`i `iug ugho ho hsp hsphj hjçb çbfj fj``

Z`iujfúo5 hi hstkn` nh ik gksk nh kfrh j`rrhsp`onh k ik fothrshjjfúo nh ik kcsjfsk t 7 >= j`o ik içohk fojifoknk nh thgphrkturk aõghnk t w 738. k) Ik aughnkn kcs`iutk sh ihh k ik nhrhjak, ho hi heh nh `rnhoknks5 kluk uk V 7 =,=;:8   Dl kl dl kfr kfrhh shj` shj`

c) Ik aughnkn rhiktfvk aky quh nhthrgfokrik p`r fothrp`ikjfúo hotrh ik jurvk ς 7=,:=  y ς7 =,>= rhsuitkon` ς 7=,:; j) Ik thgphrkturk nh r`jç` sh ihh ho hi heh nh kcsjfsks pkrk ik fothrshjjfúo nh ik `rnhoknk j`rrhsp`onfhoth j`rrhsp`onfhoth k ik aughnkn kcs`iutk j`o ik jurvk nh skturkjfúo, t r7;6,: ½ J  n) Ik aughnkn nh skturkjfúo p`r hobrfkgfhot` knfkcëtfj` sh ihh ho hi heh nh `rnhoknks pkrk ik fothrshjjfúo j`o ik jurvk nh skturkjfúo nh ik içohk fojifoknk nh thgphrkturk aõghnk 38½J, rhsuitkon` V s 7V w 7 =,=3;

  Dlkluk  Dlkfrh  Dl kfrh shj`

h) Ik aughnkn nh skturkjfúo k >=½J sh ihh ho hi heh nh `rnhoknks, pkrk ik fothrshjjfúo j`o ik jurvk nh skturkjfúo nh ik kcsjfsk nh thgphrkturk >=½J, V ' s 7=,=>11

  Dl kluk kluk  Dl kfrh shj`

b) Hi jki`r hsphjçbfj` sh nhthrgfok ho hi nfklrkgk kuxfifkr (3) s`crh ik rhjtk fojifoknk hotrkon` p`r ik kcsjfsk nh aughnkn kcs`iutk =,=;:8 y ihyhon` su vki`r  ho hi heh nh `rnhoknks, j 7 =,3>1

  Djki  Dl½½ J   Dl

l) Hi v`iugho hsphjçbfj` sh nhthrgfok ho hi nfklrkgk kuxfifkr (;) hotrkon` p`r hih heh nh kcsjfsks pkrk t 7 >= ½ J , y rhsuitkon` pkrk hi kfrh shj` :

g / Dl 7=,11 V pkrk hi kfrh skturkn`

R 

shj`

 

:

R skturkn` 7=,62 g / Dl

Fothrp`ikon` pkrk ik aughnkn nhi :;% rhsuitk :

R 7 =,6= g / Dl

Hehrjfjf` >-;; ^`gkon` pkrk hi j`hbfjfhoth nh j`ovhjjfúo ho hi fothrjkgcf` nh jki`r hotrh hi kluk y hi kfrh a73= djki/g3*a*½J, y pkrk ik suphrbfjfh nh fothrjkgcf` nh jki`r ;= g3, jkijõihsh5 k) Hi jk jki`r i`r sho shosfc sfcih ih fothr fothrjkg jkgcfk cfkn`. n`. c) Hi jki`r jki`r iktho ikthoth th fot fothr hrjkg jkgcfk cfkn`. n`. j) Hi jki` jki`rr t`tki t`tki fothr fothrjkg jkgcfk cfkn`. n`. Hi kfrh sh hojuhotrk k 38 ½J j`o uok aughnkn rhiktfvk nhi 2

q I 7;:6=

)( =,=;:8 ∓ =,=;=2) Ü 816 Ü ;=

 djki a

j) Jki`r t`tki nhi jki`r shosfcih y ikthoth5

 

q ^ 7 3===+ ;:6=7::6=

Ckikojh hotëipfj`

 

q ^ 7

 djki a

( )

 a hotkip ipfk fk nh nhii kfrh kfrh sktur skturkn`4 kn`4 f hotki hotkipf pfk k nh gksk gksk li`ck li`ckii . ( f ∓f Z ) K 4 fZ hotk jp

f 7( =,3> + =,>2 Ü =,=;:8 ) Ü 38 + 86,33 djki  Dl f Z 7( =,3> + =,>2 Ü =,=;=2 ) Ü ;8 + 862

) Ü >,3> Ü ;= 7:>>=

 djki  Dl

 djki a

Hehrjfjf` >-;3 Shphtfr i`s jëijui`s nhi hehgpi` kothrf`r sf sh p`oh ho j`otkjt` kfrh k 38 ½ J , j`o aughnkn rhiktfvk nhi 8=% j`o kluk k ;2 ½ J . k) J` J`g` g` ik thg thgphr phrktu kturk rk nhi nhi kluk hs gh gho`r o`r q quh uh ik nhi kf kfrh rh akcrë pks` nh jki`r shosfcih nhi kfrh y nhi kluk y su vki`r shrë5 c) °Juë °Juëii hs ik aughnk aughnkn n nhi kf kfrh rh y ik a aughnk ughnkn n nh ik phiçju phiçjuik ik nh j`otkjt`0 j) Hi jki` jki`rr t`tki t`tki foth fothrj rjkgc kgcfkn fkn`` hs hs55 Z`iujfúo5 Ho ik bflurk > ∓ >  sh prhshotk sh prhshotk iks j`onfjf`ohs nh ik gksk li`cki nhi kfrh p`r   K  y iks nh ik phiçjuik nh j`otkjt` p`r Z. k) ]k ]krk rk jkij jkijui uikr kr q s q s73= ( 38 ∓;2 )∜;=7;1== djki a

 c) 

V  K 7=,=66 

]krk jkijuikr ik aughnkn nhi kfrh5  dl kl kluk uk dlkfrh

]krk jkijuikr ik aughnkn nh ik phiçjuik nh j`otkjt`5

 dlkluk dl kfr kfrhh J`g` V Z ? V  Kaky pks` nh jki`r ikthoth nh kluk ki kfrh, y su vki`r shrë5

V Z 7=,=;;:

 

(

q I 7∓

  3= =,3>8

)

∜=,==;>∜811∜;= 7∓2 t`gknk nhi kothrf`r hehrjfjf` ho n`onh sh kpifjú uo ckikojh hotëipfj` k t`n` hi sfsthgk sh `ctfhoh quh5 f ( hot hotkipf kipfk k nh ikgksk li`cki li`cki nhi kfrh kfrh )7;3,=>

 djki dl

f s ( hotk hotkip ipfk fk nh nhii kfr kfrh sk sktu turk rkn`k n`k ik ^ nh nhii kl kluk uk )7;=,8

)∜

;= ( ;3,=> ∓;=,

 djki a

 

Hehrjfjf` >-;: Shpçtkosh i`s jëijui`s nhi pr`cihgk >-;;, sup`ofhon` quh hi kfrh hstë k 38½J, j`o aughnkn rhiktfvk nhi 8=% y hi kluk hstë k 3:½J. k) Hi jk jki`r i`r sho shosfc sfcih ih fothr fothrjkg jkgcfk cfkn` n` c) Hi jki`r jki`r iktho ikthoth th fot fothr hrjkg jkgcfk cfkn` n` j) Hi jki jki`r `r t`t t`tki ki fot fothr hrjkg jkgcfk cfkn` n` Z`iujfúo5 Iks j`onfjf`ohs nh ik gksk li`cki nhi kfrh y iks nh ik phiçjuik nh j`otkjt` kfrh-kluk sh rhprhshotko ho ik sflufhoth fgklho (Bfl. >-8)5 k) Nk Nkn` n` quh quh ik th thgp gphr hrkt ktur urkk nhi kfrh kfrh hs gk gky` y`r  r  quh ik th thg gph phrk rktu turk rk nhi klu lukk, hi jki` i`ss shosfcih pkskrk nhi kfrh ki kluk5 q s73= ( 38 ∓ 3: ) Ü ;=7 >== Djki / a

 c) Aughnkn nhi kkfrh5 frh5

 

V  K 7=,==66

 dlkluk dlkfrh

Aughnkn nh ik phiçjuik nh j`otkjt`5 V Z 7=,=;8

)

Ü ( =,== ) Ü ( ;= )7 )7∓ ∓: Djki / Dl f s7 hot hotkip kipfknhi fknhi kfrh kfrh sk sktu turk rkn` n` k ik^ nhi kluk kluk 7;2,8   3= =,3>8

) )

Ü ( ;3,=> ∓;2,38 ) Ü ;= Ü (∓ >,3; ) Ü ;=7∓:>>=

 Djki a

Hehrjfjf` >-;> Nfsp`ohg`s nh ;=== g: quh j`otfhoh kfrh k 8= ½J  j`o  j`o t w 7:= ½J , y quhrhg`s quh uok j`o 78= % , ik ghzjik vhz ghzjikn` j`o hi kfrh nhi kgcfhoth, sh hojuhotrh k ;8 ½J j`o ∈

rhsuitkoth hstæ k 38 ½J , Jkijuihsh5 k) Ik jk jkotf otfnk nknn nh kfr kfrhh rh rhsui suitko tkoth th  c) Hi v`iugho nh kkfrh frh k knfjf`ok knfjf`okr  r  j) Hi v`i v`iugh ughoo nnhh kkfrh frh rhsuit rhsuitkot kothh Aughnkn y Hotkipfk nhi kfrh quh nfsp`ohg`s5  y ;7=,=;1> dlnh kl kluk uk / dlnh kfr kfrh f ;73:,>= djki / l

Aughnkn y Hotkipfk nhi kfrh nhi kgcfhoth5

 

 y 37=,==8: dl nhkluk nhkluk / dlnhkfrh f 372,-3 T>-3 + =,>2 V ) 38 + 86= ( =,3> + =,>2 V  ) ) 38 + 86

7;=2> Dl

Akjfhon` us` nh ik Hj. T>-32W5 =,==6= ∓=,=;1> =,==8: ∓ =,==6=

7

  L; ;=2>

L373-:=W, ik gksk nh vkp`r nh kluk knfjf`oknk shrë  Hj . T > ∓:= W ↓ V 7V ;+ G v L

 

 G v 7L ( V ∓ V ; )  G v 7;;26 ( =.=3==∓ =.==6= )  G v 7;3.12 dl

 c) Hotkipfk nhi vk vkp`r p`r skturkn` k ; kt (tkcik K- + =.>2 Ü =.==6 ) 38 + 86<

 Djki dl

Akjfhon` us` nh ik Hj. T>-:;W, T >-:;W, ik hotkipfk nhi kfrh aõghn` ho iks j`onfjf`ohs bfokihs hs f 7;;,>< + 2:1,8 ( =.=3=∓=.==6 ) f 7;1.>6

 Djki dl

Nh kjuhrn` j`o ik nhbfofjfúo nh hotkipfk f 7( =.3> + =.>2 V   )) ^ + 8667 ( =.3> + =.>2 Ü =.=3= ) t + 86-;2 8=== g: nh kfrh k >= ½J j`o uok aughnkn rhiktfvk nhi ;=% k ik prhsfúo ktg`sbærfjk o`rgki, sh augfnfbfjk y hobrçko kûknfæon`ih >= iftr`s nh kluk k 3= ½ J. Zf hi pr`jhs` sh rhkifzk knfkcëtfjkghoth, nhthrgçohsh5 k) Au Augh ghnk nknn rhsu rhsuit itko koth th  c) ^hgphrkturk bfoki Nhskrr`ii` k) Augh Aughnk nknn nhi nhi kfrh kfrh 3= ½J 7 :;: D  V   ; ; 7=.==>3

  DlA 3 @ dl Kfrh Kfrh shj` shj`

R`iugho hsphjçbfj` j`onfjf`ohs hsphjfkihs

 

R 7

(

  ; dg`i

  dl 36 dg`i

+

  )(

  dl A   3 3@ dl Kfrhshj Kfrh shj` `  l ;1 g`i

=.==>3

:

 )

  ktg∜g ( :;: D  ) ) =.=13 dg`i∜ D 

:

g R 7 =.16 dl

Gksk Kfrh shj` :

L7

V 7V   ; ;+

  8=== g

 Gv L

V 7 =.==>3+

  >= ½ J  881< dl

7=.=;;:

  dl A   3 3@ dl Kfrhshj`

 c) Hotkipfk Kfrh f ; 7( =.3> + =.>2 ( =.==>3 ) ) >= + 863 ) f ; 7;=.31

 Djki  Dl

Hotkipfk Kluk 3=½J } ^kcik K-< f ; 73=

 Djki  Dl

f 7f ; + fv ( V ∓V   ; ;) f 7;=.31

 Djki 3= Djki  +   ( =.==;;: ∓=.==>3 ) dl  Dl

f 7;=.3;

 Djki  Dl

f 7J ∜^ ∜ Ɣ =∜V  ^ 7

;=.3;∓ 86 + =.>2 ( =.=;;: )

^ 7;>.;; ½ J 

Hehrjfjf` >-;<

:

 g =.168 dl

7881< dl

 

8=== g:/a nh kfrh k ;=`J y thgphrkturk aõghnk nh 8 `J sh augfnfbfjko p`ofæon`i`s ho j`otkjt` j`o >=== i/a nh kluk quh sh hojuhotrko fofjfkighoth k ;1`J. Nhthrgçohsh5 k) Iks j` j`onfj onfjf`oh f`ohss nh skifnk nh nhii kfrh y nhi kluk kluk,, sf kijkoz kijkozko ko ik gfsgk thgphr thgphrkturk kturk y hi kfrh skih skturkn`.  c) Jkotfnkn nh jjki`r ki`r kcs`rcfn` p` p`rr hi kfrh. j) Jk Jkotf otfnkn nkn nh kl kluk uk hvk hvkp`r p`rknk knk.. Z`iujfúo5 k) Ik prh prhsfúo sfúo nnhh vkp`r vkp`r nhi kluk kluk hhoo hi kfr kfrhh fofj fofjfkigh fkighoth oth hs5 hs5  pv 7 2,8>∓ =.8 ( ;=∓ 8 )7 >,=> gg Al

V su aughnkn  y 7

  =,23∜>,=>

( ,=> )

7=,==: dlkluk / dlkfrh

Hotkipçk supuhstk5

a3 7;3,; Djki / d l , , t3  7;3,; ½J 

 y 37=,==11 dl kl kluk uk / dlkf dlkfrrh , ,f 37 1,3= Djki / Dl

Hotkipçk jkijuiknk5

a3 7 ;3,; Djki / Dl

q 723;1 ( 1,3= ∓>,:1 ) 73:,3=  Dl / a

Hehrjfjf` >-;1 Xo shjknhr` r`tkt`rf` sh kifhotk j`o krhok k rkzúo nh :=== dl/a j`o uok aughnkn nhi 8=%, y hi pr`nujt` quh skih nhi shjknhr` tfhoh uok aughnkn nh :% (rhbhrfnks iks aughnknhs ki s`ifn` aõghn`). Hi kfrh hotrk k ;== ½J, ho j`otrkj`rrfhoth, j`o uok aughnkn nh =,==< dl nh kluk/dl kfrh shj`, y skih k >= ½J. Ik krhok hotrk k 3= ½J y skih k :8 J4 su jki`r hsphjfbfj` puhnh j`osfnhrkrsh j`ostkoth h fluki k =,3; Djki/Al, ½J. sf hi shjkn` hstk phrbhjtkghoth kfsikn`, nhthrgfoh ik jkotfnkn nh kfrh ohjhskrf` y ik aughnkn nhi kfrh k ik skifnk nhi shjkn`. Z`iujfúo5

 

Iks aughnknhs nhi súifn`, rhbhrfnks ki s`ifn` shj`, s`o5   x;

 Q ; 7

; ∓ x;   =,8

 Q ; 7

; ∓=,8

 Q ; 7 ;

  dlkluk dl súi súifn fn` `

  x3

 Q 3 7

; ∓ x3   =,=:

 Q ; 7

; ∓=,=:

  dlkluk súifn` fn`  Q ; 7 =,=:; dl súi

Ik gksk nhi s`ifn` shj`  G 7

 G 7

 G aughnkn ;+ Q ; :=== ; +;

 G 7;8== dl

Akjfhon` us` nh ik Hj. T>-:>W L ( V 3∓ V ; ) 7 G ( Q ;∓ Q 3) L ( V 3∓ =,==< )7;8== ( ; ∓=,=:;) L ( V 3∓ =,==< )7;>8:

Iks hotkipfks nhi s`ifn` k ik hotrknk y k ik skifnk s`o5  A ;7( =,3; + ; ) 3= 3>,3

 A ;7

 Djki dl

 

 A 37( =,3; + =,=:; ) :8  A 371,>:

 Djki dl

Ik hotkipfk nhi kfrh ki hotrkr ho hi shjknhr` hs5 f ;7( =,3> + =,>2 ∖ =,==< ) ;== + 86,>1

 Djki dl

Akjfhon` us` nh ik Hj. T>-:8W L ( f 3∓ f ;) 7 G ( A ° ° 3∓ A ; ) °

T

W

L 31,>1∓( =,3> + =,>2 V 3 ) ∖ >= ∓86% (rhbhrfnks k iks uofnknhs súifn` aõghn`). Ik thgphrkturk nh hotrknk y skifnk nhi s`ifn` ho hi shjknhr` hs nh :=ªJ, y hi pr`jhs` sh hbhjtõk k ªJ4 V7=.=3=) phohtrkon` ki shjknhr` j`o aughnkn nh =.==1 Jkijõihsh5 k)  c) j) n)

Ik jjkotfn kotfnkn kn nh kfrh quh hotrk ki sshjkn hjknhr`. hr`. Ik thgphrkturk nnhh hotrknk nhi kkfrh frh ho hi gfsg`. Ik jjkot kotfnk fnknn nh kf kfrh rh qu quhh rhj rhjfrj frjuik uik.. Ik jjkotfn kotfnkn kn nh jki`r jki`r sugfofst sugfofstrkn` rkn` ki kkfrh. frh.

 D l kluk  D l kfrh

.

 

Shprhshotkg`s Shprhshotkg `s ik gkrjak nhi pr`jhs` s`crh hi nfklrkgk psfj`gætrfj`. K5 J`onfjf`ohs fofjfkihs nhi kfrh5 t 73= ½ J   44 V ;7=.==8 ½ J   44 V 37 =.=;=8 ( =.3> + =.>2∜=.==< ) ( >1∓3= ) 7:21==

djki a

q rhj78>=8 ( =.3> + =.>2∜=.=;8∓ 3: )7368== [t`tki7:21== + 368== 722:==

 djki a

 djki a

Hehrjfjf` >-3=  Ohjhsftkg`s nfsp`ohr nfsp`ohr nh kfrh k 88 ½J j`o uo uokk thgphrkturk nh :8½J, quh prh prhpkrkg`s pkrkg`s ho uok fostkikjfúo nh kj`onfjf`okgfhot` k pkrtfr nh kfrh ktg`sbærfj` k 3= ½J j`o aughnkn rhiktfvk nh 2=%. Hi pr`jhs` j`gpiht` j`ostk nh uok prhjkihbkjjfúo, shlufnk nh uok augfnfbfjkjfúo knfkcëtfjk akstk quh su aughnkn rhiktfvk hs nhi 6=%, y jkihbkjjfúo bfoki akstk iks j`onfjf`ohs quh o`s fothrhsko. Jkijõihsh5 k) Ik th thgphr gphrkturk kturk nh nh ski skifnk fnk nnhi hi kfr kfrhh nhi augfnfbfjk augfnfbfjkn`r n`r  c) Ik thgphrkturk nnhh prhjkihbkjj prhjkihbkjjfúo. fúo. j) Ik jk jkotfnk otfnknn nh jki` jki`rr sugfof sugfofstrkn strkn`` p`r ghtr ghtr`` jõcfj jõcfj`` nh kfrh ghnfn` ghnfn` ho iks iks j`onfjf`ohs bfokihs. Ho ik bflurk >-6 rhprhshotkg`s ik gkrjak nhi pr`jhs` s`crh hi nfklrkgk psfjr`gætrfj`.

k) J`o J`onfj nfjf`o f`ohs hs fofj fofjfki fkihs hs nnhi hi kkfrh frh55 t 73= ½J 4V ;7=.==13 dlkluk / dlkfrh

 

J`onfjf`ohs bfokihs nhi kfrh5 t 788 ½J 4V 37=.=31= dl

 kluk   dlkfrh

❛

Nhi augfnfbfjkn`r skih j`o ik aughnkn nhi V 3 phr` hsth o` skih skturkn` sfo` j`o aughnkn rhiktfvk nhi 6=% y iks j`onfjf`ohs nhi kfrh k ik skifnk nhi augfnfbfjkn`r ihçnks s`crh hi nfklrkgk psfjr`gætrfj` shrëo t 7:3.> ½ J 4 V  w7 :; ½ J 

 c) Ik thgphrkturk nnhh hotrknk nhi kkfrh frh ki augfnfbfjkn`r ` thg thgphrkturk phrkturk nh  prhjkihbkjjfúoo ûk nhthrgfokg`  prhjkihbkjjfú nhthrgfokg`ss p`r ik fothrshjj fothrshjjfúo fúo nh ik içohk nh thgphrkturk thgphrkturk aõghnk nh :; ½J j`o ik rhjtk nh aughnkn =.==13, rhsuitkon`5 t  p71= ½ J 

j) ^` ^`gko gkon` n` jj`g` `g` cksh cksh nh jëi jëiju jui` i` ; g: nh kfrh ho iks j`onfjf`ohs bfokihs

R 7

(

 ; 36

+

  )∜

=.=31 dl ;1 dl

:

=.=13∜:317 =.626 g / dl

Hs nhjfr, quh ; g : j`otfhoh ;/=.6267;.=:3 dl nh kfrh shj`. q prh7;.=:3 ( =.3> + =.>2∜=.==13 ) ( 1=∓3= ) 7;8.;= Djki / g

:

q rhj7;.=:3 ( =.3> + =.>2∜ =.=31= ) ( 88 ∓:3.> ) 78.2-33 Ohjhsftkg`s nfsp`ohr nh 2 === g _ : / a nh kfrh k88½ J j`o uok aughnkn rhiktfvk nhi := % y nfsp`ohg`s nh kfrhk ;6½ J j`o thgphrkturk aõghnk nh ;8½ J. ]krk su pr prhp hpkr krkj kjfú fúo o i` s` s`gh ghth thg` g`ss k uo pr`j pr`jhs hs`` qu quhh j`os j`ostk tk nh5 nh5 prhj prhjki kihb hbkj kjjf jfúo úo,, augfnf aug fnfbfj bfjkjf kjfúo úo knfkc knfkcëtf ëtfjk jk y rhjki rhjkihbk hbkjjf jjfúo, úo, ski skifho fhon` n` nhi aug augfnf fnfbfj bfjkn` kn`rr 3½J p`rhojfgk nh ik thgphrkturk nh skturkjfúo knfkcëtfjk. Hi vki`r nhi j`hbfjfhoth d{y} k pkrk hi augfnfbfjkn`r hs ; >== Dl / (g _ :) . Jkijõihsh5 k) ^hgphrkturk nh skifnk nhi augfnfbfjkn`r. c) ^hgphrkturk nh prhjkihbkjj prhjkihbkjjfúo. fúo. j) Jkotfnkn nh jki`r nh prhjkihbkjjfúo. n) Jkotfnkn nh jki`r nh rhjkihbkjjfú rhjkihbkjjfúo. o. h) R`iugho nhi augfnfbfjkn`r. k) ^ s7^ r 7:3 ½ J 

 c) ^  p71> ½ J 

j) R 7

(

 ; 36

\ L 7

+

 )

=.=:=>

 2=== =.62∜=.==63 ) ( 1> ∓;6 ) 7 62∜=.=:=> ) ( 88 ∓:>.8 ) 7:3;;= Djki

h) V w7 =.=:;:

 Dl kl kluk uk  Dl kfrh

 O r 7

°∜=.=:;: ∓=.==63 7:.3; =.=:;: ∓=.=:=>

 O t 7

°∜1> ∓:3.8 7 :.32 :>.8 ∓:3.8

R 7

:.3;∜ 2;22 ;>==

7;>.; g:

 

Hehrjfjf` >-3: Xok jëgkrk nh r`jfkn` nh : g nh kiturk y =, 2=g _ 3 nh shjjfúo, sh hgpihk pkrk augfnfbfjkr 1== Dl / a nh kfrh quh hstë fofjfkighoth k 38½ J y aughnkn rhiktfvk nhi :=% y ak nh iihvkrsh akstk 2=½ J j`o aughnkn rhiktfvk nhi 3= % p`r pr prhj hjki kiho hotk tkgf gfho hot` t`,, augf augfnf nfbf bfjk jkjf jfúo úo knfk knfkcë cëtf tfjk jk y rhjk rhjkih ihot otkg kgfh fhot ot`. `. Zf nh nhii augfnfbfjkn`r skih ;,8½ J p`r hojfgk nh ik thgphrkturk nh skturkjfúo, Jkijõihsh5 k) Ik jkotfnkn nh jki`r ohjhskrf`. c) Hi oõghr` nh hihghot`s nh trkosgfsfúo. j) Ik kiturk nhi hihghot` nh trkosgfsfúo. n) Hi j`hbfjfhoth nh ik jëgkrk. h) Ik kiturk quh nhchrçk thohr ik t`rrh sf hi kfrh quh nfsp`ohg`s hstë skturkn` k ;8_ J. k) t 7 :=.8 ½ J  t 7 : ( = Djki

 c)  O t 7

°∜8

j)  A t 7

n)

 : :.>8

7 =.1< g

(7 ) (  1==

=.2=

∜

(

=.3> + =.>2∜

a jk

=.1<

h) ^  p72: ½ J   O t 7

°∜2: ∓36 ;.8

7:.;3

 z 7:.;3∜=.1 ;= ===

dl  nh kfrh k 38½J j`o thgphrkturk aõghnk nh 3=½J sh ako nh nhsaugfbfjkr a

akstk uok thgphrkturk aõghnk nh ;3½J p`r j`otkjt` j`o uok suphrbfjfh ghtëifjk  K

rhbrflhrknk p`r kluk4 hstk hotrk k j`otrkj`rrfhoth k 8½J y skih k ;;½J. Ik rhikjfúo  K '  hs ;=, hi j`hbfjfhoth nh j`ovhjjfúo kfrh-kluk hs 8=

  Djki 3

 , y hi j`hbfjfhoth fothlrki nh

g ∜a∜½ J 

trkosgfsfúo nhi jki`r k trkvæs nh ik suphrbfjfh ghtëifjk hs nh 3===

  Djki 3

.

g ∜a∜½ J 

Nhthrgçohsh hi ërhk nh suphrbfjfh ghtëifjk ohjhskrfk y ik thgphrkturk nh skifnk nhi kfrh

Ik hotkipçk nhi kfrh k ik hotrknk hs5f;7 ;:,

 djki dl

 djki dl

Nfvfnfr ik suphrbfjfh ghtëifjk ho n`s pkrths5 ik hotrknk nhi kfrh y hi iulkr n`onh sh kijkozko iks j`onfjf`ohs ghnfks, y `trk hotrh hsth iulkr y hi nh skifnk nhi kfrh. f g7

;:, 3

7;=,12

djki dl

;;+ 8

f g ( kluk )7

3

71 ½ J 

Ho hi hxtrhg` ; pkrk ik suphrbfjfh nh j`otkjt` hotrh hi kfrh y hi kluk j`onhosknk, sf thohg`s ho juhotk5 t s; ∓ ;; ;:,8∜3===

7;,=3

t s ;7;;+ ;,=3 ( ;:,,6 ½ J  f s ;76,63 djki dl

 

Ho hi hxtrhg` 3, kpifjkg`s ik gfsgk Hj t s 3∓8 1,;> ∓f k

7;,=3

Shs`ivfhon` hstk hjukjfúo p`r tkoth` iihlkg`s k t sg∓1 ;=,12∓f

7;,=3 sg

Shs`ivfhon` ik hjukjfúo p`r tkoth` iihlkg`s t g7;;,3 ½ J f sg78

 Kg ∓3 7

 

;==== ( ;:,

8= =,3>8

;:,2 g 3

; g 3

 )

3

Ik suphrbfjfh t`rki ohjhskrfk shrë nh 1< g3 . Ik thgphrkturk nhi kfrh ho g shrë5 ;====∜=,3>8 ( 38∓t g ) 7;>,8=

(

38 + t g

3

3

 )

∓ ;>.6 +;;,3

Ik thgphrkturk nhi kfrh k ik skifnk shrë5 ;====∜=,3>8 ( ;1,=∓t 3 )7 >6,8=

t 37;3,3 ½ J 

 c)

(

;1,= + t 3 3

 )

∓ ;;.3 + -38 Ho uok t`rrh nh nhs augfnfbfjkjfúo juy` rhonfgfhot` hs nhi === Dl/a nh kfrh quh hotrk k :=½J j`o uok aughnkn rhiktfvk nhi g: /a nh kluk quh hotrk k ;=½J. Jkijõihsh5 k. Ik hotkip hotkipçk çk nnhi hi kfr kfrhh k ik ski skifnk fnk..  c. Ik thgphrkturk nh nh skifnk nhi kl kluk. uk. j. Ik thgph thgphrkt rkturk urk nh skif skifnk nk nnhi hi kkfrh frh.. Iks j`onfjf`ohs nhi kfrh k ik hotrknk s`o V ;7=,=;1 f ;7;1,36

 Dl kl kluk uk  Dl kfrh

 Djki  Dl

k) Zf sk skifh ifhrk rk skt skturk urkn` n` ak akcrç crçkk nh jug jugpif pifrsh rsh >=== ( ;1,3= ∓f j ) 7( t j ∓;= ) Ü >===

t j 7( ;1,3=∓ fj ) + ;=

 

Shs`ivfhon` hstk hjukjfúo hjukjfúo p`r tkoth` iihlkg`s k  Djki  Dl t j 7;2,6 ½ J  f j 7;;,:=

J`g` hi rhonfgfhot` hs nhi === ( ;1,3= ∓;:,:< )7 >=== ( t ∓ ;= )

t 7;>,1 ½ J 

j) Nkn Nknkk ik hotkipçk hotkipçk nh nhii kfrh puh puhnh nh aki akiikrsh ikrsh ho ho ik tkcik K K-: -: ik thgphrkt thgphrkturk urk nh skturkjfúo knfkcëtfjk ;6,8½J. Bfekn`s s`crh hi nfklrkgk i`s puot`s ; y C, ik fothrshjjfúo nh ik rhjtk quh i`s uoh j`o ik knfkcëtfjk ;6,8½J phrgfth ihhr   t 3733 ½ J . Ik thgphrkturk içgfth nh hobrfkgfhot` nhi kluk hs ik thgphrkturk aõghnk nhi kfrh j`rrhsp`onfhoth k iks j`onfjf`ohs j`onfjf`ohs nh hotrknk k ik t`rrh p`r ik pkrth fobhrf`r nh ik gfsgk, yk quh hi j`otkjt` sh hbhjtõk ho j`otrkj`rrfhoth. j`otrkj`rrfhoth. I`s jëijui`s ohjhskrf`s rhbhrhoths rhbhrhoths k iks t`rrhs nh hobrfkgfhot` nh kluk kpifjknk k uo hihghot` nh t`rrh nh kiturk nz  o`s  o`s iihvko k iks sflufhoths hjukjf`ohs5 ;) ]`r kkpifjk pifjkjfúo jfúo nh uuoo ck ckikoj ikojhh nh gkthrfk. gkthrfk. n I 7L n V  3) ]`r kkpifjk pifjkjfúo jfúo nh uuoo ck ckikoj ikojhh hotëipf hotëipfj`. j`. L nf 7 I j I nt  I :) ]`r kpif kpifjkj jkjfúo fúo nh ik hjuk hjukjfúo jfúo lho lhohrki hrki nh trk trkosgf osgfsfúo sfúo nhi jk jki`r i`r nhsnh nhsnh hi içqufn` k ik fothrbksh. nt  I

7

a I k

nz

t  I ∓t L  I j I >) ]`r kpif kpifjkj jkjfúo fúo nh ik hjuk hjukjfúo jfúo lho lhohrki hrki nh trk trkosgf osgfsfúo sfúo nhi jk jki`r i`r nhsnh nhsnh ik fothrbksh ki lks. nt L t f∓ t L

7

 a L k L jL

nz

8) ]`r kpif kpifjkj jkjfúo fúo nh ik hjuk hjukjfúo jfúo lho lhohrki hrki nh trk trkosp` osp`rth rth nh gkthrfk gkthrfk nhsnh nhsnh ik fothrbksh ki lks d   k nV   7 V    nz V f∓V  L

J`gcfokon` iks hjukjf`ohs hjukjf`ohs kothrf`rhs sh iiklk k ik hxprhsfúo nf ff ∓f

7

d V  k   nz L

]`r fothlrkjfúo nh hstk hxprhsfúo, sup`ofhon` quh d V phrgkohjh j`ostkoth j`ostkoth

 

 L  z 7 d V  k

f3

∤ f nf∓f f;

;

f3

∤ f nf∓f

 O f7

;

f;

 A f

L d V  k f3

∤ f°nf∓f

 O `f7

f;

L d V  k  z 7 O `f A `f  A `f

f ∓ff t  I ∓t f

7

∓a I d V 

⟶

f∓ff t L ∓t f

7

  nf nt L

Hehrjfjf` >-32 Zh ako nh hobrfkr 1== ;/a nh kluk nhsnh >=½J akstk 3=½J, hgpihkon` ;=== Dl/a nh kfrh, quh hotrk p`r ik cksh nh ik j`iugok k 3=½J j`o uok hotkipçk nh 1,38 Djki/Dl. Ik shjjfúo nh ik t`rrh tfhoh ; g3 y hi vki`r nh D y k7>== Dl/g: *a. Nhthrgçohsh ik kiturk nh ik t`rrh.

Z`iujfúo5 Zh sup`oh quh hi kfrh ho j`otkjt` j`o ik suphrbfjfh içqufnk hstë skturkn` j`o vkp`r nh kluk, ik jurvk f*-- t rhprhshotk ik rhikjfúo hotrh ik hotkipçk nhi kfrh y su thgphrkturk ho ik fothrbksh, ff ‚  ‚ tf, sh `ctfhoh ik phonfhoth quh rhprhshotk iks j`onfjf`ohs nhi sfsthgk ho ik pkrth fothrf`r nh ik t`rrh5

 

nf nt  I

7

  1== ;===

7=,1

Ik fothrshjjfúo nh hstk rhjtk j`o ik kcsjfsk j`rrhsp`onfh j`rrhsp`onfhoth oth k ik thgphrkturk nh hotrknk nhi kluk nkrë ik hotkipçk nhi kfrh k ik skifnk nh ik t`rrh, puot` C. f

f∜°

 

 

f∜∓ f

 

;

Fothlrki

f∜∓f

1,38 ;= ;3 ;> ;2 ;1 3= 33 3> 3>,38

;:,28 ;8,,1= :6,;= :6,2=

8,>= 8, =,=;2  O `f73,=-3< Hehrjfjf` >-31 ]krk hobrfkr :== g: /a nh kluk nhsnh >:µJ akstk := µJ sh hgpihk uok t`rrh nh tfr` tfr ` okturki ho j`otrkj`rrfhoth, p`r ik pkrth fobhrf`r nh ik juki hotrk kfrh j`o uok thgphrkturk nh 33 µJ y su vhi`jfnkn gësfjk k trkvæs nh ik ^`rrh hs nh 8=== dl s`crh a`rk p`r ghtr` juknrkn` sfhot` ik rhikjfúo hotrh iks gksks nh kfrh y kluk fluki k ik uofnkn pkrk iks j`onfjf`ohs nh `phrkjfúo nh j`hbfjfhoth nh ik ^`rrh hs fluki k 38== dl s`crh ghtr` jõcfj` p`r a`rk nhthrgfok hsh ik kiturk ohjhskrfk nh ik ^`rrh k) sf ik rhsfs rhsfsthoj thojfk fk k ik trkosgfsfúo trkosgfsfúo nh jk jki`r i`r y gkthrf gkthrfkk sh hoju hojuhotrk hotrk çothlrk çothlrkghot ghothh ho bksh lksh`sk  c) sf ik rhikjfúo nhth nhthrgfoknk rgfoknk hxphrfgho hxphrfghotkighoth tkighoth ho uok ppikotk ikotk pfi`t` j`o jkrkjthrçstfjks koëi`lks, vkih 2. Z`iujfúo5 ]`r iks rkz`ohs fonfjknks ho hi hehgpi` kothrf`r ik hotkipçk nhi kfrh skturkn` k 33µJ hs prëjtfjkghoth fluki quh ik nh jukiqufhr `trk gksk nh kfrh aõghn` j`o thgphrkturk aughnkn aughnkn nh 33µJ ]`r tkot` ik hotkipçk nhi kfrh nhotr` nh ik ^`rrh sh shrë5 rë5 F;7 ;8,;8 Djki/ dl kfrh J`o hstk hotkipçk ik thgphrkturk kluk nh ik ^`rrhthofhon` p`nhg`s iks ik j`onfjf`ohs ho hi yhxtrhg` nh skifnknhnhskifnk kluk nhi s`crh hi nfklrkgk hobfekr juhotk

 

hjukjfúo >-88 nhphonfhoth uoftkrfk hstë rhotkon` rhprhshotkr k iks vkrfkjf`ohs nh ik hotkipçk nhi kfrh j`o ik thgphrkturk nhi kluk k i` ikrl` nh ik ^`rrh Ik fothrshjjfúo nh hstk rhjtk j`o ik sfsk o`s nkrë ik hotkipçk nhi kfrh k ik skifnk nh ik ^`rrh F37 31,:= Djki/ dl f ;8,;8 ;< ;6 3; 3: 38 3<

F* 3:,;,18

F*.f 1,:< 1,18 6,28 ;=,6= ;3,38 ;:,6= ;8,18  O`f 7 ;,=8

 z 7

8=== 38==

∜;,=87 3,;= g

 Of 7 ;,:6

;/(f**f) =,;;6 =,;;: =,;=> =,=63 =,=13 =,=