vè;k; 1 os|qr vkos'k rfkk {ks=k · 2019-01-30 · 1.20 dksbz flddk al-mg fejkrq dk cuk gs...

q2

q1

q3

x

y

O

cgq fodYih iz'u I (MCQ I)

1.1 fp=k 1.1 esa y-vk osQ vuqfn'k fLFkr nks oS|qr vkos'k q2 rFkk q

3, x-vk osQ vuqfn'k

fLFkr oS|qr vkos'k q1 ij] + x fn'kk esa dksbZ usV fo|qr cy vkjksfir djrs gSaA ;fn

(x, 0), ij dksbZ /ukos'k Q j[k fn;k tk, rks q1 ij vkjksfir cy

vè;k; 1

oS|qr vkos'k rFkk ks=k

q2

q1

q3

x

y

( 0)x,

Q

O

fp=k 1.1

(a) (b)

23/04/18

iz'u izn£'kdk&HkkSfrdh

2

1.3 uhps fn, x, fp=kksa esa i`"B ls xqtjus okyk fo|qr ÝyDl

(a) /ukRed x-vk osQ vuqfn'k c<+ tk,xkA

(b) /ukRed x-vk osQ vuqfn'k ?kV tk,xkA

(c) Í.kkRed x-vk osQ vuqfn'k laosQr djsxkA

(d) c<+ tk,xk ijUrq q2 ,oa q

3 osQ lkFk Q osQ izfrPNsnu osQ dkj.k fn'kk ifjofrZr gks

tk,xhA

1.2 fdlh fcUnq /ukos'k dks fdlh fo;qDr pkyd xksys osQ fudV yk;k x;k gS (fp=k1.2)Afo|qr ks=k dks n'kkZus okyk loZJs"B fp=k gS]

(a) fp=k (i) (c) fp=k (iii)(b) fp=k (ii) (d) fp=k (iv)

+q +q

+q

(i)(ii)

(iii) (iv)

(ii) (iii) (iv)(i)

+q

S

+q

S

+q

SS

+q

fp=k 1.3

fp=k 1.2

+q

23/04/18


3

(a) fp=k 1.3 (iv) esa lokZf/d gS

(b) fp=k 1.3 (iii) esa U;wure gS

(c) fp=k 1.3 (ii) esa fp=k1.3 (iii) osQ leku gS] ijUrq fp=k 1.3 (iv) ls de gSA

(d) lHkh fp=kksa esa leku gSA

1.4 ik¡p vkos'k q1, q

2, q

3, q

4, rFkk q

5 fp=k 1.4 esa n'kkZ, vuqlkj viuh fLFkfr;ksa ij

fLFkj gSaA S dksbZ xkmlh; i`"B gSA xkml fu;e osQ vuqlkj

qd

0S

.ε

=∫ E s

fuEufyf[kr esa dkSu lk izdFku lgh gS\(a) mijksDr lehdj.k osQ ck;ha vksj E esa q

1, q

5 rFkk q

3 dk ;ksxnku gksxk] tcfd

nk;ha vksj q esa osQoy q2 rFkk q

4 dk gh ;ksxnku gksxkA

(b) mijksDr lehdj.k osQ ck;ha vksj E esa lHkh vkos'kksa dk ;ksxnku gksxk] tcfd nk;havksj q esa osQoy q

2 rFkk q


(c) mijksDr lehdj.k osQ ck;ha vksj E esa lHkh vkos'kksa dk ;ksxnku gksxk] tcfd nk;havksj q esa osQoy q

1, q

3 rFkk q


(d) ck;ha vksj osQ E rFkk nk;ha vksj osQ q nksuksa esa gh osQoy q2 rFkk q

4 dk gh ;ksxnku

gksxkA

1.5 fp=k 1.5 esa fo|qr ks=k js[kk,¡ n'kkZ;h xbZ gSa ftuesa ,d oS|qr f/zqo p fp=kesa n'kkZ, vuqlkj j[kk gSA fuEufyf[kr izdFkuksa esa dkSu lk lgh gS\

(a) f/qzo fdlh cy dk vuqHko ugha djsxkA

(b) f/qzo nk;ha vksj fdlh cy dk vuqHko djsxkA

(c) f/qzo ck;ha vksj fdlh cy dk vuqHko djsxkA

(d) f/qzo mQij dh vksj fdlh cy dk vuqHko djsxkA

1.6 ,d fcUnq vkos'k +q fdlh fo;qDr pkyd ry ls d nwjh ij fLFkr gSA ry osQ nwljh vksjosQ fcUnq P ij ks=k dh fn'kk

(a) ry osQ yEcor rFkk ry ls nwj dh vksj gSA

(b) ry osQ yEcor ijUrq ry dh vksj gSA

(c) fcUnq vkos'k ls nwj dh vksj fn"V gSA

(d) vjh;r% fcUnq vkos'k dh vksj gSA

1.7 dksbZ v/Zxksyk ,dleku /ukosf'kr gSA xksys osQ osQUnz ls ijs blosQ fdlh O;kl ij fLFkrfcUnq ij tks osQUnz ls nwj gS] fo|qr ks=k dh fn'kk

(a) bl O;kl osQ yEcor gSA

(b) bl O;kl osQ lekUrj gSA

q1

q5

q4

q2

q3

S

– q + qp

fp=k 1.4

fp=k 1.5

xkmlh; i`"B

23/04/18


4

(c) bl O;kl dh vksj fdlh dks.k ij >qdh gSA

(d) bl O;kl ls nwj fdlh dks.k ij >qdh gSA

cgqfodYih iz'u II (MCQ II)

1.8 ;fn fdlh i`"B ij s

.d 0=∫ E S gS] rc

(a) ml i`"B ij rFkk mlosQ Hkhrj fo|qr ks=k 'kwU; gSA

(b) ml i`"B osQ Hkhrj vko';d :i ls fo|qr ks=k ,dleku gSA

(c) ml i`"B esa izos'k djus okyh ÝyDl js[kkvksa dh la[;k mlls fudyus okyhÝyDl js[kkvksa dh la[;k osQ cjkcj gksuh pkfg,A

(d) lkjk vkos'k vko';d :i ls ml i`"B osQ ckgj gksuk pkfg,A

1.9 fdlh fcUnq ij fo|qr ks=k

(a) lnSo larr gksrk gSA

(b) larr gksrk gS ;fn ml fcUnq ij dksbZ vkos'k u gksA

(c) osQoy rc larr ugha gksrk tc ml fcUnq ij dksbZ Í.kkos'k gksA

(d) larr ugha gksxk] ;fn ml fcUnq ij dksbZ vkos'k gksA

1.10 ;fn fo'o esa osQoy ,d gh izdkj dk vkos'k gks rks

(a) rc fdlh Hkh i`"B ij s

.d 0≠∫ E S

(b) vkSj vkos'k i`"B osQ ckgj gks] rks s

.d 0=∫ E S

(c) rc s

.d∫ E S dks ifjHkkf"kr ugha fd;k tk losQxkA

(d) rc s

0

.dq

ε=∫ E S , ;fn q ifjek.k dk vkos'k i`"B osQ Hkhrj gSA

1.11 fdlh ,sls ks+=k ij fopkj dhft, ftlesa fofHkUu izdkj osQ vkos'k gSa ijUrq oqQy vkos'k'kwU; gSA bl ks=k ls ckgj osQ fcUnqvksa ij(a) fo|qr ks=k vko';d :i ls 'kwU; gksrk gSA

(b) fo|qr ks=k osQoy vkos'k forj.k osQ f/zqo vk?kw.kZ osQ dkj.k gksrk gSA

(c) izHkkoh fo|qr ks=k 3

1

r osQ vuqozQekuqikrh gksrk gS tgk¡ r bl ks=k esa fdlh ewy fcUnq

ls nwjh gS vkSj bldk eku cgqr vfèkd gSA

(d) bl ks=k ls nwj] fdlh lao`r (cUn) iFk osQ vuqfn'k] fdlh vkos'k dks xfr djkusesa fd;k x;k dk;Z 'kwU; gksxkA

23/04/18


5

1.12 fp=k 1.6 esa vkos'kksa dh O;oLFkk rFkk R f=kT;k osQ xkmlh; i`"B] ftlosQ osQUnz ij dksbZvkos'k Q gS] ij fopkj dhft,] rc

(a) xksys osQ i`"B ls xqtjus okyk oqQy ÝyDl 0

–Q

ε gSA

(b) xksys osQ i`"B ij fo|qr ks=k 20

–

4

Q

Rπε gSA

(c) 5Q osQ dkj.k xksys osQ i`"B ls xqtjus okyk ÝyDl 'kwU; gSA

(d) –2Q osQ dkj.k xksys osQ i`"B ij ks=k gj LFkku ij leku gSA

1.13 dksbZ /ukos'k Q fdlh R f=kT;k osQ o`Ùkkdkj ywi osQ vuqfn'k ,dleku :i lsforfjr gSA ywi osQ osQUnz ij dksbZ NksVk ijhk.k vkos'k q fLFkr gS (fp=k 1.7)Arc

(a) ;fn q > 0 rFkk bls ywi osQ ry esa osQUnz ls nwj foLFkkfir djsa rks ;g okilosQUnz dh vksj /osQy fn;k tk,xkA

(b) ;fn q < 0 rFkk bls ywi osQ ry esa osQUnz ls nwj foLFkkfir djsa rks ;g dHkhHkh osQUnz ij okil ugha vk,xk rFkk ywi ls Vdjkus rd lrr xfr djsxkA

(c) ;fn q < 0, rc ;g vk osQ vuqfn'k NksVs foLFkkiuksa osQ fy, SHM djsxkA(d) q > 0 osQ fy,] ywi osQ ry osQ Hkhrj] ywi dk osQUnz ,d vLFkk;h larqyu

esa gSA

vfr y?kqmÙkjh; (VSA)

1.14 fdlh ;kn`fPNd i`"B esa dksbZ f/zqo ifjc¼ gSA bl i`"B ls xqtjus okyk fo|qr ÝyDlfdruk gS\

1.15 fdlh /krq osQ xksyh; [kksy dh Hkhrjh f=kT;k R1 rFkk ckgjh f=kT;k R

2 gSA bl [kksy

dh xksyh; xqfgdk osQ osQUnz ij dksbZ vkos'k Q j[kk gSA [kksy osQ (i) Hkhrjh i`"B rFkk(ii) ckgjh i`"B ij] i`"Bh; vkos'k&?kuÙo D;k gksxk\

1.16 fdlh ijek.kq dh foek,¡ ,d ,sXalVªe osQ dksfV dh gksrh gSaA vr% izksVkWuksa ,oa bysDVªkWuksaosQ chp mPp fo|qr ks=k gksuk pkfg,A rc fdlh pkyd osQ Hkhrj fLFkj&fo|qr ks=k'kwU; D;ksa gksrk gS\

1.17 ;fn fdlh i`"B kjk ifjc¼ oqQy vkos'k 'kwU; gS] rks D;k bldk ;g rkRi;Z gS fd bli`"B osQ gj LFkku ij fo|qr ks=k 'kwU; gS\ foykser% ;fn fdlh i`"B osQ gj LFkku ijfo|qr ks=k 'kwU; gS rks D;k blls ;g rkRi;Z fudyrk gS fd bl i"B osQ Hkhrj usV vkos'k'kwU; gSA

R/2

Q R

–2Q

R

5Q

Rz

q

++ Q

fp=k 1.6

fp=k 1.7

xkmlh; i`"B

23/04/18


6

1.18 fdlh ,dleku vkosf'kr [kks[kys flfy.Mj (fp=k 1.8) osQ fy, fo|qr ks=k js[kk,¡[khafp,A

++

++

++

++

++

++

++

++

++++

++++

A

B

C

D

fp=k 1.8

fp=k 1.9

1.19 fdlh a yEckbZ osQ ?ku (fp=k 1.9) osQ iQydksa ls xqtjus okyk ÝyDl fdruk gksxk;fn vkos'k q fLFkr gks

(a) A ij tks ?ku dk ,d dksuk gSA

(b) B ij tks fdlh dksj dk eè; fcUnq gSA

(c) C ij tks ?ku osQ fdlh iQyd dk osQUnz gSA

(d) D ij tks B rFkk C dk eè; fcUnq gSA

y?kqmÙkjh; (SA)

1.20 dksbZ flDdk Al-Mg feJkrq dk cuk gS vkSj bldk Hkkj 0.75g gSA ;g oxkZdkj gS rFkkblosQ fod.kksZa dh eki 17 mm gSA ;g oS|qr mnklhu gS rFkk blesa /u vkSj Í.kvkos'k leku ek=kk esa gSaA

;g ekurs gq, fd iSls osQ flDosQ osQoy Al osQ cus gSa] /u rFkk Í.k vkos'kksa dh lekula[;kvksa osQ ifjek.k Kkr dhft,A bl ifjek.k ls vki D;k fu"d"kZ fudkyrs gSa\

1.21 iz'u 1.20 esa o£.kr ,d flDosQ ij fopkj fdft,A ;g oS|qr mnklhu gS rFkk blesaleku ifjek.k] 34.8 kc osQ èku rFkk Í.k vkos'k gSaA ;fn ;s vkos'k nks fcUnq vkos'kksa

esa lkafnzr gSa] ftudk i`Fkdu (i) 1 cm 1

~2

×

ilS s osQ flDoQs dk fod.kZ ,

(ii) 100 m (~ fdlh cMs+ Hkou dh yEckbZ)] rFkk (iii) 106 m (i`Foh dh f=kT;k)gks rks] rhuksa izdj.kksa esa izR;sd osQ fy, bl izdkj osQ fcUnq vkos'k ij cy Kkr dhft,Abu ifj.kkeksa ls vki D;k fu"d"kZ fudkyrs gSa\

1.22 fp=k 1.10 lht+h;e DyksjkbM] (CsCl) dh fozQLVy bdkbZ dks fu:fir djrk gSA [kqysoÙkksa kjk fu:fir lht+h;e ijek.kq 0.40 nm Hkqtk osQ ?ku osQ dksuksa ij fLFkr gS tcfd

23/04/18


7

Cl ijek.kq ?ku osQ osQUnz ij fLFkr gSaA Cs ijek.kqvksa esa ,d bysDVªkWu de gS tcfd Cl

ijek.kq esa ,d bysDVªkWu dk vkf/D; gSA

(i) vkB Cs ijek.kqvksa osQ dkj.k Cl ijek.kq ij usV fo|qr ks=k fdruk gS\

(ii) eku yhft, dksus A ij Cs ijek.kq yqIr gks tkrk gS] rc ckdh cps lkr Cs

ijek.kqvksa osQ dkj.k vc Cl ijek.kq ij usV cy fdruk gS\

1.23 nks vkos'kksa q rFkk –3q dks x-vk ij ‘d’ nwjh osQ i`Fkdu osQ lkFk j[kk x;k gSA rhljsvkos'k 2q dks dgk¡ j[kk tk; rkfd ;g dksbZ cy vuqHko u djs\

1.24 fp=k 1.11 esa rhu fcUnq vkos'kksa A, B rFkk C osQ pkjksa vksj fo|qr ks=k js[kk,a n'kkZ;hxbZ gSa

0.40 nm

A

fp=k 1.10

A

C

B

fp=k 1.11

(a) dkSu ls vkos'k /ukRed gSa\

(b) fdl vkos'k dk ifjek.k vf/dre gS\ D;ksa\

(c) fp=k osQ fdl ks=k@ks=kksa esa fo|qr ks=k 'kwU; gS\ vius mÙkj dh iqf"V dhft,A

(i) A osQ fudV (ii) B osQ fudV (iii) C osQ fudV (iv) dgha ugha

1.25 ik¡p vkos'k] ftuesa izR;sd q gS] ‘a’ Hkqtk osQ fdlh fu;fer iapHkqt osQ dksuksa ij j[ksx, gSa (fp=k 1.12)A

(a) (i) bl iapHkqt osQ osQUnz O ij fo|qr ks=k fdruk gksxk\

(ii) ;fn fdlh ,d dksus (tSls A) ls vkos'k dks gVk fn;k tk, rks O ij fo|qrks=k fdruk gksxk\

(iii) ;fn A ij vkos'k dks –q kjk izfrLFkkfir dj fn;k tk, rks O ij fo|qrks=k fdruk gksxk\

(b) vkiosQ (a) osQ mÙkj ij D;k izHkko iM+sxk ;fn iapHkqt dks n-Hkqtk osQ ,sls fu;fercgqHkqt ls izfrLFkkfir dj fn;k tk, ftlosQ izR;sd dksus ij q vkos'k gks\

A

B

CD

E

q

q

qq

q

O

r

a

fp=k 1.12

Cs+

Cl–

23/04/18


8

nh?kZmÙkjh; (LA)

1.26 lu~ 1959 esa ykbV~ysVu ,oa ckW.Mh us lq>k;k fd ;fn nzO; ij dksbZ usV vkos'k gks rksfo'o (;wfuolZ)] osQ izlj.k dh O;k[;k dh tk ldrh gSA eku yhft, fo'o gkbMªkstuijek.kqvksa ls feydj cuk gSA ftudk la[;k ?kuRo N gS vkSj ftls fu;r j[kk tkrk gS]eku yhft, izksVkWu ij vkos'k e

p =

– (1 + y)e gS] ;gk¡ e bysDVªkWfud vkos'k gSA

(a) y dk og ozQakfrd eku Kkr dhft,] ftl ij izlj.k vkjEHk gks losQA(b) ;g n'kkZb, fd izlj.k dk osx osQUnz ls nwjh osQ oxZ osQ vuqozQekuqikrh gSA

1.27 R f=kT;k osQ fdlh ,sls xksys ij fopkj dhft, ftl ij vkos'k ?kuRo ,r R≤ osQ fy,( ) krrρ = rFkk r R> osQ fy, ( ) 0rρ = gSA

(a) r osQ lHkh ekuksa osQ fy, fo|qr ks=k Kkr dhft,A(b) eku yhft, xksys ij oqQy vkos'k 2e gS] tgk¡ e bysDVªkWu dk vkos'k gSA nks izksVkWuksa

dks dgk¡ ij vUr% LFkkfir fd;k tk, fd buesa izR;sd ij vkjksfir cy 'kwU; gksA;g ekfu, fd izksVkWuksa osQ j[kus ij Í.kkos'k forj.k ifjofrZr ugha gksrkA

1.28 nks fLFkj] loZle IysV ( ) ,α βvkjS ftuesa izR;sd dk i`"Bh; ks=kiQy S gS] ozQe'k–

Q rFkk q, kjk vkosf'kr gSa tgk¡ Q > q > 0A xfr djus osQ fy, Lora=k dksbZ rhljhloZle IysV q vkos'k okyh IysV osQ nwljh vksj blls d nwjh ij j[kh tkrh gS(fp=k 1.13)A rhljh IysV dks eqDr NksM+us ij ;g β IysV ls Vdjkrh gSA eku yhft,fd VDdj izR;kLFk gS rFkk VDdj esa yxk le; IysVksa β rFkk γ esa vkos'k osQ iqu%forj.k osQ fy, i;kZIr gSA

(a) VDdj ls iwoZ IysV γ ij vkjksfir fo|qr cy Kkr dhft,A

(b) VDdj osQ i'pkr β rFkk γ vkos'k Kkr dhft,A

(c) VDdj osQ i'pkr IysV β ls nwjh d ij IysV γ dk osx Kkr dhft,A

1.29 SI/MKSA ek=kd iz.kkfy;ksa osQ vfrfjDr ek=kdksa dh ,d vU; mi;ksxh ek=kdiz.kkyh gS ftls cgs (lsUVhehVj&xzke&lsd.M) iz.kkyh dgrs gSaA bl iz.kkyh osQvuqlkj owQykWe&fu;e bl izdkj O;Dr fd;k tkrk gS%

2

Qqˆ

r=F r

;gk¡ nwjh r dks cm (= 10–2 m), F dks Mkbu (=10–5 N) rFkk vkos'kksa dks fLFkj oS|qr

ek=kdksa (es ek=kdksa), ;gk¡ vkos'k dk 1es ek=kd –9110 C

[3]= × gSA lehdj.k esa

la[;k [3] okLro esa izdk'k dh pky] osQ dkj.k ftldk ;FkkFkZ eku vcC = 2.99792458 × 108 m/s fy;k tkrk gS] vkbZ gSA

a b g

-Q q Qd

fp=k 1.13

x

y

23/04/18


9

(i) ;g n'kkZb, fd cgs esa owQykWe&fu;e osQ vuqlkj

1 esu vkos'k = 1 (Mkbu)1/2 lsUVhehVj

nzO;eku M, yEckbZ L rFkk le; T osQ inksa esa vkos'k dh foek,¡ izkIr dhft,A ;gn'kkZb, fd bls M rFkk L dh fHkUukRed ?kkrksa osQ inksa es O;Dr fd;k tkrk gSA

(ii) 1 esu vkos'k = x C fyf[k,] ;gk¡ x dksbZ foekghu la[;k gSA ;g n'kkZb, fdblls ;g izkIr gksrk gS fd

–9 2

2 20

1 10 N.m

4 Cx=

π ∈

ftlesa –91

10[3]

x = ×

vFkok 2

2 9

20

1 Nm[3] 10

4 C= ×

π ∈

22 9

20

1 Nm(2.99792458) 10

4 C= ×

π ∈(;FkkFkZ)

1.30 nks vkos'k ftuesa izR;sd dk ifjek.k –q gS] 2d nwjh ij fLFkj j[ks x, gaSA fp=k 1.14

esa n'kkZ, vuqlkj m nzO;eku osQ fdlh rhljs vkos'k q dks] tks buosQ eè; fcUnq ijfLFkr gS] bu nks fu;r vkos'kksa dks feykus okyh js[kk osQ yEcor~] oqQN nwjh x (x<<d)

kjk foLFkkfir fd;k tkrk gSA n'kkZb, fd q ljy vkorZ xfr djsxk ftldk vkorZdky

1/23 30

2

8 mdT

q

π ε =

gksxkA

1.31 R f=kT;k osQ fdlh NYys dh yEckbZ osQ vuqfn'k oqQy vkos'k –Q dks ,d leku :ils iSQyk;k x;k gSA nzO;eku m osQ NksVs ijhk.k vkos'k +q dks NYys osQ osQUnz ijj[kdj NYys osQ vk osQ vuqfn'k /hjs ls /osQyk tkrk gSA

(a) n'kkZb, fd d.k ljy vkoZr nksyu djrk gSA

(b) bldk vkorZdky Kkr dhft,A

q

q x

d– q d – q

fp=k 1.14

23/04/18

10



2.1 fp=k 2.1 n'kkZ, vuqlkj ifjiFk esa 4 µ F dk la/kfj=k la;ksftr gSA cSVjh dk vkUrfjdizfrjks/ 0.5 Ω gSA la/kfj=k dh IysVksa ij vkos'k dh ek=kk gksxh&

(a) 0

(b) 4 µ C

(c) 16 µ C

(d) 8 µ C

2.2 fdlh ,dleku fo|qr ks=k esa fdlh èkukosf'kr d.k dks eqDr fd;k tkrk gSA vkos'k dhoS|qr fLFkfrt mQtkZ

(a) fu;r jgrh gS D;ksafd fo|qr ks=k ,dleku gSA

(b) c<+ tkrh gS D;ksafd vkos'k fo|qr ks=k osQ vuqfn'k xfr djrk gSA

(c) ?kV tkrh gS D;ksafd vkos'k fo|qr ks=k osQ vuqfn'k xfr djrk gSA

(d) ?kV tkrh gS D;ksafd vkos'k fo|qr ks=k osQ foijhr xfr djrk gSA

vè;k; 2

fLFkj oS|qr foHko rFkkèkkfjrk

4 Fm

10W

2.5V

2W

fp=k 2.1

23/04/18

11

fLFkj oS|qr foHko rFkk /kfjrk

A B

30V

10V 20V 40V 50V

A B

10V 20V 40V30V 50V 10V

A

30V 40V

20V 50V

B

2.3 fp=k 2.2 esa fnDdky esa forfjr oqQN lefoHko js[kk,¡ n'kkZ;h xbZ gSaA dksbZ vkosf'kr fi.MfcUnq A ls fcUnq B rd xfr djrk gS

(a) fp=k (i) esa fd;k x;k dk;Z vf/dre gSA

(b) fp=k (ii) esa fd;k x;k dk;Z U;wure gSA(c) fp=k (i), fp=k (ii), fp=k (iii) esa fd;k x;k dk;Z leku gSA(d) fp=k (iii) esa fd;k x;k dk;Z fp=k (ii) ls vf/d gS ijUrq fp=k (i) osQ leku gSA

2.4 fdlh vkosf'kr pkyd xksys osQ i`"B ij fLFkr oS|qr foHko 100 V gSA blosQ lanHkZ esanks izdFku fn, x, gS%S

1 : xksys osQ Hkhrj fdlh fcUnq ij fo|qr rhozrk 'kwU; gSA

S2 : xksys osQ Hkhrj fdlh fcUnq ij fLFkj oS|qr foHko 100 V gSA

uhps fn, x, izdFkuksa esa dkSu lk lgh gS\

(a) S1 lR; gS ijUrq S

2 vlR; gSA

(b) S1 rFkk S

2 vlR; gSA

(c) S1 lR; gS] S

2 Hkh lR; gS rFkk izdFku S

2 dk dkj.k izdFku S

1 gSA

(d) S1 lR; gS] S

2 Hkh lR; gS ijUrq nksuksa izdFku ,d nwljs ls Lora=k gSaA

2.5 oqQN vkos'kksa osQ ,d lewg dk oqQy ;ksx 'kwU; ugha gSA blls vfèkd nwjh ij cuus okyslefoHko i`"B gksaxs(a) xksys(b) lery(c) ijoy;t(d) nh?kZoÙkt

fp=k 2.2

(i) (ii) (iii)

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12


2.6 dksbZ lekUrj ifêðdk la/kfj=k nks Js.khc¼ ijkoS|qr xqVdksa ls cuk gSA buesa fp=k 2.3 esan'kkZ, vuqlkj ,d xqVosQ dh eksVkbZ d

1 rFkk ijkoS|qrkad k

1 rFkk nwljs xqVosQ

dh eksVkbZ d2 rFkk ijkoS|qrkaoQ k

2 gSA bl O;oLFkk dks ,d ,slk ijkoS|qr

xqVdk ekuk tk ldrk gS ftldh eksVkbZ d (= d1+d

2) rFkk izHkkoh ijkoS|qrkad

k gSA rc k dk eku gS

(a) 1 1 2 2

1 2

k d k d

d d

(b) 1 1 2 2

1 2

k d k d

k k

(c) 1 2 1 2

1 2 2 1

( )

( )

k k d d

k d k d

(d) 1 2

1 2

2k k

k k

cgq fodYih iz'u II (MCQ II)

2.7 z fn'kk esa fdlh ,dleku fo|qr ks=k ij fopkj dhft,A bl fLFkfr esa foHko fu;rgksxkA

(a) leLr fnDdky esaA

(b) fn, x, z osQ fy, fdlh Hkh x osQ fy,A

(c) fn, x, z osQ fy, fdlh Hkh y osQ fy,A

(d) fn, x, z osQ fy, xy ry ijA

2.8 lefoHko i`"B

(a) fuEu fo|qr ks=kksa osQ izns'kksa dh rqyuk esa mPp fo|qr ks=k osQ izns'kksa esa vf/d iklgksrs gSaA

(b) pkyd osQ rh.k fdukjksa osQ fudV vf/d laoqQy gksaxsA

(c) mPp vkos'k ?kuRoksa osQ izns'kksa osQ fudV laoqQy gksaxsA

(d) lnSo leku nwjh ij gksaxsA

2.9 fdlh lefoHko i"B osQ vuqfn'k fdlh vkos'k dks A ls B rd xfr djkus esa fd;k x;k dk;Z

(a)

B

A

– .d∫ lE osQ :i esa ifjHkkf"kr ugha fd;k tk ldrkA

d1

d1

k1

k2

fp=k 2.3

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13


(b)

B

A

– .d∫ lE osQ :i esa ifjHkkf"kr fd;k tkuk pkfg,A

(c) 'kwU; gksrk gSA(d) 'kwU;srj gks ldrk gSA

2.10 fu;r foHko osQ fdlh izns'k esa

(a) fo|qr ks=k ,dleku gksrk gSA

(b) fo|qr ks=k 'kwU; gksrk gSA

(c) izns'k osQ Hkhrj dksbZ vkos'k ugha gks ldrkA

(d) ;fn vkos'k izns'k osQ ckgj fLFkr gS rks vo'; ifjofrZr gksxkA

2.11 fp=k 2.4 esa n'kkZ, x, ifjiFk esa vkjEHk esa oqQUth K1 cUn rFkk oqQUth

K2 [kqyh gSA rRi'pkr K

1 [kksyh tkrh gS rFkk K

2 cUn dh tkrh gS

(ozQe egRoiw.kZ gS)A (C1 rFkk C

2 ij ozQe'k% vkos'k Q

1′ rFkk Q

2′ vkSj

oksYVrk V1 rFkk V

2 yhft,) rc

(a) C1 ij vkos'k bl izdkj iqu% forfjr gks tkrk gS fd V

1 = V

2 gksA

(b) C1 ij vkos'k bl izdkj iqu% forfjr gks tkrk gS fd Q

1′ = Q

2′

gksA

(c) C1 ij vkos'k bl izdkj iqu% forfjr gks tkrk gS fd C

1V

1 +

C2V

2 = C

1E

(d) C1 ij vkos'k bl izdkj iqu% forfjr gks tkrk gS fd Q

1′ + Q

2′ = Q

2.12 ;fn fdlh pkyd dk foHko 0V ≠ gS rFkk mlosQ i`"B ls ijs dgha Hkh dksbZ vkos'kugha gS] rc

(a) pkyd osQ i`"B vFkok blosQ Hkhrj vkos'k gksus pkfg,A(b) pkyd esa dgha Hkh dksbZ vkos'k ugha gks ldrkA

(c) osQoy pkyd osQ i`"B ij gh vkos'k gksus pkfg,A

(d) pkyd osQ i`"B osQ Hkhrj vkos'k vo'; gksus pkfg,A

2.13 fp=k 2.5 esa n'kkZ, vuqlkj dksbZ lekUrj ifêðdk la/kfj=k fdlh cSVjh ls la;ksftr gSAnks fLFkfr;ksa ij fopkj dhft,A

A: oqaQth K cUn j[kh tkrh gS rFkk la/kfj=k dh ifêðdkvksa osQ eè; nwjh fo|qrjksèkh gRFksdh lgk;rk ls c<+kbZ tkrh gSA

B: oqaQth K [kqyh gS rFkk fo|qrjks/h gRFkh kjk la/kfj=k dh ifêðdkvksa osQ chp dhnwjh c<+kbZ tkrh gSA

lgh fodYi (fodYiksa) dk p;u dhft, %

fp=k 2.4

fp=k 2.5

C

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14


Q

b a

q

fp=k 2.6

(a) A esa – Q leku jgrk gS ijUrq C ifjofrZr gksrk gSA

(b) B esa – V leku jgrk gS ijUrq C ifjofrZr gksrk gSA

(c) A esa – V leku jgrk gS blfy, Q ifjofrZr gksrk gSA

(d) B esa – Q leku jgrk gS blfy, V ifjofrZr gksrk gSA


2.14 R1 rFkk R

2 f=kT;kvksa (R

1 > R

2) osQ nks pkyd xksyksa ij fopkj dhft,A ;fn nksuksa xksys

leku foHko ij gSa rks NksVs xksys dh viskk cMs+ xksys ij vf/d vkos'k gksrk gSA mYys[kdhft,] NksVs xksys dk vkos'k ?kuRo cM+s xksys dh rqyuk esa vf/d gksxk vFkok de\

2.15 eqDr bysDVªkWu mPp foHko osQ ks=k dh vksj xeu djrs gSa vFkok fuEu foHko osQ ks=kdh vksj\

2.16 leku vkos'k okys nks fudVorhZ pkydksa osQ chp D;k dksbZ foHkokUrj gks ldrk gS\

2.17 D;k eqDr vkdk'k esa foHko iQyu vf/dre vFkok U;wure gks ldrk gS\

2.18 dksbZ ijhk.k vkos'k q fdlh fcUnq vkos'k Q osQ fo|qr ks=k esa nks fHkUu cUn iFkksa ijxeu djrk gS (fp=k 2.6)A igyk iFk fo|qr ks=k dh js[kkvksa osQ vuqfn'k rFkk yEcordksbZ Hkkx gSA nwljk iFk ,d vk;rkdkj ik'k gS ftldk ks=kiQy igys ik'k osQ cjkcjgSA bu nksuksa izdj.kksa esa fd, x, dk;Z dh rqyuk dhft,A

y?kqmÙkjh; (SA)

2.19 fl¼ dhft, fd fdlh ,sls cUn lefoHko i`"B] ftlosQ Hkhrj dksbZ vkos'k ugha gS]esa dksbZ lefoHko vk;ru ifjc¼ gksuk pkfg,A

2.20 fdlh la/kfj=k dh ifêðdkvksa osQ chp dksbZ ijkoS|qr gS rFkk ;g la/kfj=k fdlh fn"Vlzksr ls la;ksftr gSA vc cSVjh dks gVk;k tkrk gS vkSj fiQj ijkoS|qr dks gVk fn;k tkrkgSA ;g mYys[k dhft, fd ,slk djus ij la/kfj=k dh /kfjrk mlesa lafpr mQtkZ] fo|qrks=k] lafpr vkos'k] rFkk oksYVrk esa o`f¼ gksxh] deh gksxh vFkok fu;r jgsxh\

2.21 fl¼ dhft, fd] ;fn dksbZ fo|qr jksf/r] vukosf'kr pkyd fdlh vkosf'kr pkydosQ lehi j[kk gS] rFkk dksbZ vU; pkyd ogk¡ ugha gS] rks vukosf'kr fi.M dk foHkovkosf'kr oLrq rFkk vuUr osQ foHko osQ eè;LFk gksuk pkfg,A

2.22 R f=kT;k osQ NYys osQ vuqfn'k ,dleku forfjr vkos'k +Q dh vk ij fdlh fcUnqvkos'k –q dh fLFkfrt mQtkZ ifjdfyr dhft,A NYys osQ osQUnz ls vkh; nwjh z osQ

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15


iQyu osQ :i esa fLFkfrt mQtkZ (P.E.) dk xzkiQ [khafp,A xzkiQ dks ns[kdj D;k vki;g crk ldrs gSa fd ;fn vkos'k –q dks NYys osQ osQUnz (vk osQ vuqfn'k) ls FkksM+kfoLFkkfir dj nsa rks D;k gksxk\

2.23 R f=kT;k osQ NYys osQ vuqfn'k ,dleku :i ls forfjr vkos'k Q osQ dkj.k] NYysosQ vk ij foHko ifjdfyr dhft,A

nh?kZmÙkjh; (LA)

2.24 fdlh r0 f=kT;k osQ vuUr flfy.Mj (csyu) ij vkos'k dk jSf[kd ?kuRo λ gSA blosQ

lefoHko osQ fy, lehdj.k izkIr dhft,A

2.25 +q rFkk -q ifjek.k osQ nks fcUnq vkos'k ozQe'k% (-d/2, 0,0) rFkk (d/2, 0,0) ijfLFkr gSaA ml lefoHko i`"B osQ fy, lehdj.k izkIr dhft, tgk¡ foHko 'kwU; gSA

2.26 fdlh lekUrj ifêðdk la/kfj=k esa dksbZ ,slk ijkoS|qr Hkjk gS ftldk vkisfkdijkoS|qrkad] vuqiz;qDr oksYVrk (U ) osQ lkFk ε = αU osQ :i esa ifjofrZr gksrk gS] ;gk¡α = 2V–1 gSA blh izdkj osQ ,d vU; la/kfj=k] ftlesa dksbZ ijkoS|qr ugha gS] dksU

0 = 78 V rd vkosf'kr fd;k tkrk gSA bls fiQj ijkoS|qr okys la/kfj=k ls la;ksftr

fd;k tkrk gSA la/kfj=kksa ij vfUre oksYVrk Kkr dhft,A

2.27 dksbZ la/kfj=k R f=kT;k dh nks o`Ùkkdkj ifêðdkvksa ls cuk gS vkSj bu ifêðdkvksa osQ chpi`Fkdu d<<R rFkk ,d nwljs osQ mQij gSA bl la/kfj=k dks fu;r oksYVrk ls la;ksftrfd;k tkrk gSA fupyh ifêðdk osQ osQUnz ij f=kT;k r<<R rFkk eksVkbZ t<<r dh dksbZpkyd pfozQdk j[kh tkrh gSA ;fn pfozQdk dk nzO;eku m gS rks bls mBkus osQ fy,vko';d fuEure oksYVrk Kkr dhft,A

2.28 (a) ewy d.kksa osQ DokoZQ ekWMy osQ vuqlkj U;wVªkWu ,d viDokoZQ [vkos'k (2/3 e)]

rFkk nks MkmuDokdksZa [vkos'k (–1/3 e)] ls feydj cuk gSA eku yhft, budkf=kdks.k foU;kl gS ftldh Hkqtkvksa dh dksfV 10–15 m gSA U;wVªkWu dh fLFkj oS|qrfLFkfrt mQtkZ ifjdfyr djosQ bldh rqyuk blosQ nzO;eku 939 MeV lsdhft,A

(b) mijksDr vH;kl dks nks vi rFkk ,d Mkmu DokoZQ ls cus izksVkWu osQ fy, nksgjkb,A

2.29 R rFkk 2R f=kT;kvksa osQ nks /krq osQ xksyksa osQ i`"Bh; vkos'k ?kuRo leku gSaA bUgsalEioZQ esa ykdj i`Fkd dj fn;k tkrk gSA bu nksuksa ij u, i`"Bh; vkos'k ?kuRo D;kgksaxs\

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16


2.30 fp=k 2.7 esa n'kkZ, x, ifjiFk esa vkjEHk esa K1 dks cUn rFkk K

2 dks [kqyk j[kk x;k

gSA izR;sd la/kfj=k ij fdruk vkos'k gS\blosQ i'pkr~ K

1 dks [kksyk x;k rFkk K

2 dks cUn fd;k x;k (ozQe egÙoiw.kZ gS)A vc

izR;sd la/kfj=k ij fdruk&fdruk vkos'k gksxk\ [C = 1 µF]

K2K

1

C =3C2

C =6C1

C =3C3

C2E = 9V

fp=k 2.7

2.31 R f=kT;k dh pfozQdk osQ i`"B ij vkos'k Q ,dleku :i ls forfjr gSA bl vkos'kosQ dkj.k pfozQdk dh vk ij foHko ifjdfyr dhft,A

2.32 nks vkos'k q1 rFkk q

2 ozQe'k% (0, 0, d) rFkk (0, 0, – d) ij fLFkr gSaA buosQ dkj.k 'kwU;

foHko osQ fcUnqvksa dk fcUnqiFk Kkr dhft,A

2.33 nks vkos'kksa ftuesa izR;sd –q gS osQ chp 2d dk i`Fkdu gSA rhljk vkos'k +q buosQeè;fcUnq O ij fLFkr gSA –q vkos'kksa osQ dkj.k O ls y?kq nwjh osQ iQyu osQ :i esa+q dh fLFkfrt mQtkZ (P.E.) Kkr dhft,A fLFkfrt mQtkZ (P.E.) rFkk nwjh x osQ chpxzkiQ [khafp, vkSj ;g lqfuf'pr dhft, fd O ij +q vLFkk;h lkE;koLFkk esa gSA

23/04/18

fo|qr /kjk

17


3.1 o`r dh vko`Qfr osQ fdlh /kjkokgh rkj (/kjk I) ij fopkj dhft,A è;ku nhft,tSls&tSls rkj osQ vuqfn'k /kjk fodflr gksrh gS] j (/kjk ?kuRo) dh fn'kk ;FkkFkZ <axls ifjofrZr gksrh gS] tcfd /kjk I vizHkkfor jgrh gSA blosQ fy, vfuok;Z :i lsmÙkjnk;h ,stsUV gS&

(a) lzksr dk fo|qrokgd cy (emf)

(b) rkj osQ i`"B ij lafpr vkos'kksa kjk mRiUu fo|qr ks=k

(c) rkj osQ fn, x, [k.M osQ Bhd ihNs osQ vkos'k tks izfrd"kZ.k kjkvkos'kksa dks ek=k lgh <ax ls /osQyrs gSaA

(d) vkxs osQ vkos'k

3.2 nks cSVfj;k¡ ftuosQ emf ε1 rFkk ε

2 [ε

2 > ε

1] rFkk vkUrfjd izfrjks/ ozQe'k%

r1 rFkk r

2 gSa] fp=k 3.1 esa n'kkZ, vuqlkj ik'oZ ozQe esa la;ksftr gSaA

(a) nksuks a lsyksa dk rqY; emf εrqY;] ε

1 rFkk ε

2 osQ chp vFkkZr~] ε

1<

εrqY; <

ε

2 gSA

vè;k; 3

fo|qr /kjk

fp=k 3.1

23/04/18

iz'u izn£'kdk – HkkSfrdh

18

(b) rqY; emf εrqY;] ε

1 ls de gSA

(c) lnSo εrqY; = ε

1 +

ε

2 gksrk gSA

(d) εrqY;

vkUrfjd izfrjks/ksa r1 rFkk r

2 ij fuHkZj ugha gSA

3.3 ehVj lsrq osQ mi;ksx kjk izfrjks/ R ekik tkuk gSA ,d Nk=k ekud izfrjks/ S dk p;u100Ω djrk gSA og 'kwU; foksi fcUnq l

1 = 2.9 cm ij ikrk gSA mls ifj'kq¼rk esa

lqèkkj osQ fy, iz;Ru djus dks dgk tkrk gSA blosQ fy, fuEufyf[kr esa dkSu mi;ksxh<ax gS\

(a) mls l1 dks vkSj vf/d ifj'kq¼rk ls ekiuk pkfg,A

(b) mls S dks 1000Ω ysdj iz;ksx nksgjkuk pkfg,A(c) mls S dks 3Ω ysdj iz;ksx nksgjkuk pkfg,A(d) mls ehVj lsrq osQ mi;ksx kjk vf/d ifj'kq¼ eki dh vk'kk NksM+ nsuh pkfg,A

3.4 5V rFkk 10V lfUudV emf osQ nks lsyksa dh rqyuk ifj'kq¼ :i ls 400 cm yEckbZosQ foHkoekih kjk dh tkuh gSA

(a) foHkoekih esa mi;ksx gksus okyh cSVjh dh oksYVrk 8V gksuh pkfg,A

(b) foHkoekih dh oksYVrk 15V gks ldrh gS rFkk R dks bl izdkj lek;ksftr djldrs gSa fd rkj osQ fljksa ij foHkoikr 10V ls FkksM+k vf/d gksA

(c) Lo;a rkj osQ igys 50 cm Hkkx ij foHkoikr 10V gksuk pkfg,A

(d) foHkoekih dk mi;ksx izk;% izfrjks/ksa dh rqyuk osQ fy, fd;k tkrk gS] foHkoksa osQfy, ughaA

3.5 vk;rkdkj vuqizLFkdkV 1cm × 1

2 cm rFkk 10 cm yEckbZ dh dksbZ èkkrq dh NM+

foijhr iQydksa ij fdlh cSVjh ls la;ksftr gSA bldk izfrjks/

(a) rc vf/dre gksxk tc cSVjh 1 cm × 1

2 cm iQydksa osQ chp la;ksftr gSA

(b) rc vf/dre gksxk tc cSVjh 10 cm × 1 cm iQydksa osQ chp la;ksftr gSA

(c) rc vf/dre gksxk tc cSVjh 10 cm × 1

2 cm iQydksa osQ chp la;ksftr gSA

(d) leku jgsxk pkgs rhuksa iQydksa esa ls fdlh osQ chp Hkh cSVjh dks la;ksftr djsaA

3.6 bysDVªkWuksa dk dkSu lk vfHkyk.k pkyd esa /kjk osQ izokg dks fu/kZfjr djrk gS\

(a) osQoy viokg osx(b) osQoy rkih; osx(c) viokg osx rFkk rkih; osx nksuksa(d) u rks viokg vkSj u rkih; osx

23/04/18

fo|qr /kjk

19


3.7 fdj[kksiQ laf/ fu;e vuqfpUru gS

(a) /kjk ?kuRo lfn'k osQ lajk.k dkA

(b) vkos'k osQ lajk.k dkA

(c) bl rqY; dk fd vkosf'kr d.k ftl laosx ls fdlh lafèk osQ lehi igq¡prk gS]ml lafèk dks NksM+rs le; ;g laosx vifjofrZr (lfn'k dh Hkk¡fr) jgrk gSA

(d) fdlh laf/ ij vkos'k dk lap; ugha gksus dkA

3.8 fp=k 3.2. esa n'kkZ, ljy ifjiFk ij fopkj dhft,A vo;o ifjorhZ izfrjks/

R′ dks n'kkZrk gSA R′ dks R0 ls vuUr rd ifjofrZr fd;k tk ldrk gSA r cSVjh dk

vkUrfjd izfrjks/ gS (r<<R<<R0)A

(a) tSls R′ esa ifjorZu gksrk gS AB osQ fljksa ij foHkoikr yxHkx fu;r jgrk gSA

(b) tSls R′ esa ifjorZu gksrk gS] R′ ls izokfgr /kjk yxHkx fu;r jgrh gSA

(c) /kjk I lqxzkgh :i ls R′ ij fuHkZj djrh gSA

(d) lnSo gh VI

r R≥

+

3.9 v/Zpkydksa] fo|qrjksf/;ksa rFkk /krqvksa dh izfrjks/drk ρ(T) dh rki&fuHkZjrk uhps fn,x, dkjdksas ij lkFkZd :i ls fuHkZj djrh gS%

(a) vkos'k okgdksa dh la[;k rki T osQ lkFk ifjofrZr gks ldrh gSA

(b) nks ozQekxr la?kêðksa osQ chp dky&vUrjky T ij fuHkZj dj ldrk gSA

(c) inkFkZ dh yEckbZ] T dk iQyu gks ldrh gSA

(d) vkos'k okgdksa dk nzO;eku] T dk iQyu gSA

3.10 OghVLVksu lsrq osQ kjk fdlh vKkr izfrjks/ R dh eki dh tkuh gS (,u-lh-bZ-vkj-Vh-dh iqLrd dk fp=k 3-25 ns[ksa)A nks Nk=k iz;ksx dks nks fofHkUu <axksa ls djrs gSaA igykNk=k ‘R

2’ = 10Ω rFkk ‘R

1’ = 5Ω ysrk gSA nwljk Nk=k R

2 = 1000Ω rFkk R

1 =

500Ω ysrk gSA ekud Hkqtk esa nksuksa R3 = 5Ω ysrs gSaA nksuksa Nk=k =kqfV;ksa dh lhekvksa

esa] 23

1

10R

R RR

= = Ω ikrs gSaA

(a) nksuksa Nk=kksa dh eki esa =kqfV;k¡ leku gSaA

(b) eki esa =kqfV;k¡ ml ifj'kq¼rk ij Hkh fuHkZj djrh gSa ftlls R2 rFkk R

1 dks ekik

tk ldrk gSA(c) ;fn Nk=k vf/d ekuksa osQ R

2 rFkk R

1 dk mi;ksx djrk gS rks Hkqtkvksa ls izokfgr

/kjk kh.k gksxh ftlosQ dkj.k ;FkkFkZ 'kwU; foksi fLFkfr fu/kZfjr djuk vf/ddfBu gks tk,xkA

(d) OghVLVksu lsrq vR;ar ;FkkFkZ midj.k gS rFkk bldh eki esa =kqfV;k¡ ugha gksrhaA

V

R¢

I

A

R

B

r

fp=k 3.2

23/04/18


20

( )

G

E

J

R

BA

3.11 fdlh ehVj lsrq esa fcUnq D 'kwU; foksi fcUnq gS (fp=k 3.3)AR S

( )

A C

D

G

B

l1 100 – l1


3.12 D;k fdlh fo|qr usVooZQ esa fdlh lafèk osQ ikj xfr esa] vkos'k dk laosx lajfkr jgrk gS\

3.13 foJkafr dky τ vuqiz;qDr ks=k E ij yxHkx fuHkZj ugha djrk tcfd rki osQ lkFk blesalkFkZd :i ls ifjorZu gks tkrk gSA igyk rF; (va'k esa) vkse&fu;e osQ fy, mÙkjnk;hgS tcfd nwljk rF; rki osQ lkFk ρ esa ifjorZu dh vksj ys tkrk gSA ,slk D;ksa gS\lfoLrkj izfrikfnr dhft,A

3.14 OghVLVksu lsrq esa 'kwU; foksi fof/ osQ D;k ykHk gSa\ vU; fdlh fof/ kjk RvKkr

ifjdfyr djus osQ fy, fdl vfrfjDr eki dh vko';drk gksxh\

3.15 foHkoekih esa rkjksa dks la;ksftr djus osQ fy, /krq dh eksVh ifêð;ksa dks mi;ksx djusdk D;k ykHk gS\

3.16 ?kjksa esa fo|qr osQ fy, rkacs (Cu) vFkok ,syqfefu;e (Al) osQ rkjksa dk mi;ksx fd;ktkrk gSA ,slk djus osQ ihNs fdu&fdu fopkjksa dks è;ku esa j[kk tkrk gS\

3.17 ekud izfrjks/ oqQ.Mfy;ksa dks cukus esa feJkrqvksa dk mi;ksx D;ksa fd;k tkrk gS\

3.18 RC izfrjks/ dh lapkj osQfcyksa ls gksdj fdlh ;qfDr dks 'kfDr P iznku dh tkuh gSA

;fn R osQ fljksa ij oksYVrk V rFkk blls izokfgr /kjk I gS rks 'kfDr&k; Kkr dhft,Abls fdl izdkj de fd;k tk ldrk gS\

3.19 AB dksbZ foHkoekih&rkj gS (fp=k 3.4)A ;fn R osQ eku esa o`f¼ dj nsa] rks foksifcUnq (J) fdl fn'kk esa LFkkukUrfjr gks tk,xk\

fp=k 3.3

(a) ehVj lsrq esa izfrjks/ksa osQ bl leqPp; osQ fy, dksbZ vU; 'kwU; foksifcUnq ugha gks ldrkA

(b) tc tkWdh fcUnq D osQ ck;ha vksj ehVj lsrq osQ rkj osQ fdlh fcUnq lslEioZQ djrh gS rks rkj ls B esas /kjk izokfgr gksrh gSA

(c) tc tkWdh fcUnq D osQ nk;ha vksj ehVj lsrq osQ rkj osQ fdlh fcUnq lslEioZQ djrh gS rks rkj esa xSYosuksehVj ls gksrs gq, B ls /kjk izokfgrgksrh gSA

(d) tc R c<+rk gS rks] 'kwU; foksi fcUnq] ck;ha vksj foLFkkfir gks tkrk gSA

fp=k 3.4

23/04/18

fo|qr /kjk

21

( )

G

E

BAE

1

X y

fp=k 3.5

E1 E2

A B

fp=k 3.6

fp=k 3.7

E EB

R

3.20 foHkoekih ls dksbZ iz;ksx djrs le; ;g ik;k x;k fd] foksi ,d gh fn'kkesa gksrk gS (fp=k 3.5) rFkk (i) rkj osQ fljs A ls fljs B dh vksj tkus ijfoksi de gks tkrk gS] (ii) tcfd tkWdh dks fljs B dh vksj ys tkus ijfoksi c<+ tkrk gSA

(a) lsy E1 dk dkSu lk VfeZuy] èkukRed ;k ½.kkRed] izdj.k

(i) esa X ls la;ksftr gsS\

(b) izdj.k (ii) esa lsy E1 dk dkSu lk VfeZuy X ls la;ksftr gS\

3.21 dksbZ lsy ftldk emf E rFkk vkUrfjd izfrjks/ r gS fdlh ckg~; izfrjks/ R osQ fljksals la;ksftr gSA R osQ fljksa osQ chp foHkokUrj esa ifjorZu rFkk R osQ chp xzkiQ[khafp,A

y?kqmÙkjh; (SA)

3.22 igys R izfrjks/ osQ n leku izfrjks/dksa osQ leqPp; dks Js.khozQe esa emf E rFkkvkUrfjd izfrjks/ R dh cSVjh ls la;ksftr fd;k x;kA ifjiFk esa /kjk I izokfgr gksrhgSA rRi'pkr~ n izfrjks/dksa dks blh cSVjh ls ik'oZozQe esa la;ksftr fd;k x;kA ;g ik;kx;k fd /kjk 10 xquk c<+ xbZA ‘n’ dk D;k eku gS\

3.23 eku yhft, n izfrjks/d R1 ............R

n ftuesa R

vf/dre = vf/dre R

1......... R

n

rFkk RU;wure

= U;wure R1 ..... R

nA ;g n'kkZb, fd tc bUgsa ik'oZozQe esa la;ksftr djrs

gSa rks ifj.kkeh izfrjks/ RP< R

U;wure rFkk tc bUgsa Js.khozQe esa la;ksftr djrs gSa rks

ifj.kkeh izfrjks/ RS > R

vfèkdre gksrk gSA bldh HkkSfrd O;k[;k dhft,A

3.24 fp=k 3.6 esa n'kkZ, ifjiFk esa nks lsy ,d nwljs osQ lkFk izfrowQyrk lsla;ksftr gSaA lsy E

1 dk emf 6V rFkk vkUrfjd izfrjks/ 2Ω, vkSj lsy

E2 dk emf 4V rFkk vkUrfjd izfrjks/ 8Ω gSA fcUnq A rFkk B osQ chp

foHkokUrj Kkr dhft,A

3.25 leku fo|qr okgd cy E, ijUrq vkUrfjd izfrjks/ r1 rFkk r

2 osQ nks

lsy Js.khozQe eas fdlh ckg~; izfrjks/ R ls la;ksftr gSa (fp=k 3.7)AR dk D;k eku gksuk pkfg, rkfd igys lsy osQ VfeZuyksa osQ chpfoHkokUrj 'kwU; gks tk,A

3.26 nks pkyd leku inkFkZ osQ cus gSa rFkk budh yEckbZ Hkh leku gSaA

23/04/18


22

pkyd 1mm O;kl dk Bksl rkj gSA pkyd B 2mm ckg~; O;kl rFkk 1mm

vkarfjd O;kl dh [kks[kyh ufydk gSA izfrjks/ksa RA rFkk R

B dk vuqikr Kkr dhft,A

3.27 eku yhft, dksbZ ,slk ifjiFk gS ftlesa osQoy izfrjks/ ,oa cSVfj;k¡ gSaA eku yhft, gesalHkh oksYVrkvksa rFkk lHkh izfrjks/ksa dks nks xquk (vFkok n xquk) djuk gS ;g n'kkZb,fd /kjk,¡ vifjo£rr jgrh gSaA bls dkk 12 dh ,u-lh-bZ-vkj-Vh- dh ikB~;iqLrd osQvH;kl 3.7 osQ fy, ifjdfyr dhft,A

nh?kZmÙkjh; (LA)

3.28 nks lsy ftudh oksYVrk 10V rFkk 2V ,oa vkUrfjd izfrjks/ ozQe'k% 10Ω rFkk 5Ω

gSa] ik'oZozQe esa bl izdkj la;ksftr gSa fd 10V cSVjh dk èkukRed VfeZuy 2V cSVjhosQ Í.kkRed VfeZuy ls la;ksftr gS (fp=k 3.8)A la;kstu dh izHkkoh oksYVrk rFkkizHkkoh izfrjks/ Kkr dhft,A

3.29 fdlh dejs esa 220V dh oksYVrk ij dksbZ ,;j dUMh'kuj izfrfnu 5 ?kUVs pyrk gSAdejs esa fcNs fo|qr rkj rk¡cs osQ cus gSa ftudh f=kT;k 1 mm rFkk yEckbZ 10m gSAizfrfnu mQtkZ dh [kir 10 O;kikfjd ek=kd gSA bldk fdruk Hkkx rkjksa esatwy&rkiu esa u"V gks tkrk gSA ;fn rkj blh yEckbZ vkSj O;kl osQ gksa ijUrq ,syqfefu;eosQ cus gksa rks D;k gksxk\

[ρcu

= 1.7 × –810 mΩ , ρ

Al = 2.7 × 10–8 Ωm]

3.30 foHkoekih osQ fdlh iz;ksx esa] VB = 10V gSA R dks 50Ω ij lek;ksftr fd;k x;k

gS (fp=k 3.9)A dksbZ Nk=k tks fdlh cSVjh dh oksYVrk E1 (yxHkx 8V) ekiuk pkgrk

gS ;g ikrk gS fd dksbZ 'kwU; foksi fcUnq laHko ugha gSA fiQj og R dks ?kVkdj 10Ω

dj nsrk gS vkSj foHkoekih osQ vafre (pkSFks) [k.M esa 'kwU; foksi fcUnq izkIr dj ysrkgSA nwljs izdj.k esa foHkoekih osQ rkj dk izfrjks/ rFkk rkj osQ fljksa ij foHkoikr izfr,dkad yEckbZ Kkr dhft,A

3.31 (i) fp=k 3.10 osQ ifjiFk ij fopkj dhft,A 'kwU; /kjk dh vkjfEHkd voLFkk lsviokg osx dh fLFkfr rd (rkih; xfr dh miskk djrs gq,) bysDVªkWuksa kjkfdruh mQtkZ vo'kksf"kr dh tkrh gS\

(ii) bysDVªkWu] rkih; mQtkZ dks izfr lsd.M RI2 dh nj ls mQtkZ iznku djrs gSaA iz'u(i) esa mQtkZ osQ lkFk vki D;k le; LosQy lac¼ djsaxs\ n = izfr vk;rubysDVªkWuksa dh la[;k = 1029/m3, ifjiFk dh yEckbZ = 10 cm, vuqizLFk dkVdk ks=kiQy = A = (1mm)2

fp=k 3.8

B

( )

AG

N1

CK1

R

E1E2

1

2

3

fp=k 3.9

2V

I2

I

R

10W

10VI

1

5W

R= 6W

I

V = 6V

I

fp=k 3.10

23/04/18


4.1 nks vkosf'kr d.k fdlh ,dleku pqEcdh; ks=k B = B0k esa iw.kZr% loZle lfiZy iFkksa

ij foijhr fn'kkvksa esa xeu djrs gSa rks buosQ

(a) laosxksa osQ z-vo;o leku gksus pkfg,A

(b) vkos'k leku gksus pkfg,A

(c) vkos'k vo'; gh d.k&izfrd.k ;qxy dks fu:fir djrs gksaxsA

(d) vkos'k ,oa nzO;eku dk vuqikr lacaèk% 1 2

0e e

m m

+ =

dh iqf"V djsxkA

4.2 ck;ks lkoVZ fu;e bafxr djrk gS fd v osx ls xfreku bysDVªkWuksa kjk pqEcdh; ks=k Bbl izdkj dk gksrk gS fd

(a) B ⊥ v

(b) B ||v

vè;k; 4

xfreku vkos'k vkSjpqEcdRo

23/04/18


24

(c) ;g O;qRozQe ?ku fu;e dk ikyu djrk gSA

(d) ;g izsk.k fcUnq vkSj bysDVªkWu dks feykus okyh js[kk osQ vuqfn'k gksrk gSA

4.3 R f=kT;k dk dksbZ /kjkokgh o`Ùkkdkj ywi x-y ry esa bl izdkj j[kk gS fd mldk osQUnzewy fcUnq ij gksA bldk og v¼ZHkkx ftlosQ fy, x > 0 gS] vc bl izdkj eksM+ fn;kx;k gS fd ;g y-z ry esa jgssA

(a) vc pqEcdh; vk?kw.kZ dk ifjek.k ?kV tkrk gSA

(b) pqEcdh; vk?kw.kZ ifjofrZr ugha gksrkA

(c) (0,0,z), z >>R ij B dk ifjek.k c<+ tkrk gSA

(d) (0,0,z), z >>R ij B dk ifjek.k vifjofrZr jgrk gSA

4.4 ,d bysDVªkWu dks fdlh yEch /kjkokgh ifjukfydk osQ vk osQ vuqfn'k ,dleku osxls izksfir fd;k tkrk gSA fuEufyf[kr esa dkSu lk izdFku lR; gS\

(a) bysDVªkWu vk osQ vuqfn'k Rofjr gksxkA

(b) vk osQ ifjr% bysDVªkWu dk iFk o`Ùkkdkj gksxkA

(c) bysDVªkWu vk ls 45° ij cy vuqHko djsxk vkSj bl izdkj oqaQMfyuh iFk ij xeudjsxkA

(d) bysDVªkWu ifjukfydk osQ vk osQ vuqfn'k ,dleku osx ls xfr djrk jgsxkA

4.5 lkbDyksVªkWu esa dksbZ vkosf'kr d.k

(a) lnSo Rofjr gksrk gSA

(b) pqEcdh; ks=k osQ dkj.k nksuksa ^Mh* osQ chp osQ varjky esa Rofjr gksrk gSA

(c) dh pky ^Mh* esa c<+ tkrh gSA

(d) dh pky ^Mh* esa eUn gks tkrh gS rFkk nksuksa ^Mh* osQ chp c<+ tkrh gSA

4.6 pqEcdh; vk?kw.kZ M dk dksbZ fo|qrokgh o`Ùkkdkj ywi] fdlh ;kn`fPNd fnfXoU;kl esa]fdlh ckg~; pqEcdh; ks=k B esa fLFkr gSA ywi dks blosQ ry osQ yEcor~ vk osQ ifjr%30° ij ?kw.kZu djkus esa fd;k x;k dk;Z gS%

(a) MB

(b) 32

MB

(c)2

MB

(d) 'kwU;

23/04/18

xfreku vkos'k vkSj pqEcdRo

25


4.7 cksgj ekWMy osQ vuqlkj H-ijek.kq esa fdlh bysDVªkWu dk ?kw.kZ pqEcdh; vuqikr

(a) bl ij fuHkZj ugha djrk gS fd og fdl dkk esa gSA

(b) ½.kkRed gksrk gSA

(c) /ukRed gksrk gSA(d) DokUVe la[;k n osQ lkFk c<+ tkrk gSA

4.8 fdlh ,sls rkj ij fopkj dhft, ftlls vifjorhZ /kjk I izokfgr gks jgh gS vkSj tksviuh yEckbZ osQ yEcor~ fdlh ,dleku pqEcdh; ks=k B esa fLFkr gSA rkj osQ Hkhrjvkos'kksa ij fopkj dhft,A ;g Kkr gS fd pqEcdh; cy izHkkoh :i esa dksbZ dk;Z ughadjrsA blls ;g èofur gksrk gS fd

(a) pkyd osQ Hkhrj vkos'kksa dh xfr B kjk izHkkfor ugha gksrh D;ksafd ;s mQtkZvo'kksf"kr ugha djrsA

(b) B osQ ifj.kkeLo:i rkj osQ Hkhrj osQ oqQN vkos'k i`"B ij igq¡p tkrs gSaA

(c) ;fn rkj B osQ izHkko esa xfr djrk gS] rks cy kjk dksbZ dk;Z ugha fd;k tkrkA

(d) ;fn rkj B osQ izHkko esa xfr djrk gS] rks pqEcdh; cy kjk vk;uksa ij] ftUgsa rkjosQ Hkhrj fLFkj ekuk tkrk gS] dksbZ dk;Z ugha fd;k tkrkA

4.9 nks loZle /kjkokgh lekkh ywiksa esa] foijhr fn'kkvksa esa /kjk I izokfgr gks jgh gSA ,d ljy,sfEi;jh ywi bu nksuksa ywiksa ls ,d ckj xqtjrk gSA ;fn bl rhljs ywi dks C dgsa rks&

(a) 02c

Iµ=∫ B.dl ∓

(b)c

∫ B.dl dk eku C dh fn'kk ij fuHkZj ugha djrkA

(c) C ij dksbZ ,slk fcUnq gks ldrk gS] tgk¡ B rFkk dl yEcor~ gksaxsA(d) C osQ izR;sd fcUnq ij B yqIr gks tkrk gSA

4.10 vkdk'k osQ fdlh ?kukdkj ks=k esa dksbZ ,dleku fo|qr ,oa pqEcdh; ks=k fo|eku gSaAbl ?ku osQ fdlh iQyd osQ yEcor~ dksbZ bysDVªkWu v osx ls izos'k djrk gS rFkk bliQyd osQ foijhr iQyd ls dksbZ ikWftVªkWu – v osx ls izos'k djrk gSA bl k.k ij

(a) fo|qr cyksa kjk nksuksa d.kksa esa loZle Roj.k mRiUu gksrs gSaA

(b) pqEcdh; cyksa kjk nksuksa d.kksa esa leku Roj.k mRiUu gksrs gSaA

(c) nksuksa d.k leku nj ij mQtkZ yfC/ vFkok mQtkZ&ßkl djrs gSaA

(d) nzO;eku osQUnz dh xfr osQoy B kjk fu/kZfjr gksrh gSA

23/04/18


26

O1

O2

z

I2

y

d

I1

x

4.11 fuEufyf[kr esa fdl n'kk esa] dksbZ vkosf'kr d.k ml ks=k esa fLFkj osx ls xfr djrkjgsxk ftlesa

(a) E = 0, 0≠B

(b) 0, 0≠ ≠E B

(c) 0, 0≠ =E B

(d) E = 0, B = 0


4.12 ;g lR;kfir dhft, fd lkbDyksVªkWu vko`fÙk ω = eB/m dh lgh foek,¡ (T)–1 gSaA

4.13 ;g n'kkZb, fd ,slk cy tks dksbZ izHkkoh dk;Z ugha djrk osx&fuHkZj cy gksuk pkfg,A

4.14 pqEcdh; cy v ij fuHkZj djrk gS tks Lo;a tM+Roh; funsZ'k izsQe ij fuHkZj djrk gSArc D;k pqEcdh; cy dk eku funsZ'k&vk osQ cnyus ls cnysxk\ fiQj D;k ;groZQlaxr gS fd fofHkUu funsZ'k izsQeksa esa usV Roj.k dk eku fHkUu&fHkUu gks\

4.15 lkbDYkksVªkWu esa ;fn jsfM;ks vko`fÙk (rf) fo|qr ks=k dh vko`fÙk dh nks xquh gks tk,] rksmlesa fdlh vkosf'kr d.k dh xfr dk o.kZu dhft,A

4.16 nks yEcs rkjksa dks] ftuesa /kjk,¡ I1 rFkk I

2 izokfgr gks jgh gSa] fp=k 4.1 esa n'kkZ, vuqlkj

O;ofLFkr fd;k x;k gSA ftl rkj ls /kjk I1 izokfgr gksrh gS og x-vk osQ vuqfn'k

gSA vU; ftlls /kjk I2 izokfgr gksrh gS og y-vk osQ lekUrj fdlh js[kk osQ vuqfn'k

gS ftls x = 0 rFkk z = d kjk n'kkZ;k tkrk gSA x-vk osQ vuqfn'k rkj osQ dkj.k fcUnqO

2 ij vkjksfir cy Kkr dhft,A

y?kqmÙkjh; (SA)

4.17 dksbZ /kjkokgh ywi R f=kT;k osQ o`Ùk osQ rhu loZle prqFkk±'kksa ls feydj cuk gS] tksx-y, y-z vkSj z-x ryksa osQ /ukRed prqFkk±'kksa esa fLFkr gS rFkk ftuosQ osQUnz ewy fcUnqij gSaA ewy fcUnq ij B dk ifj.kke ,oa fn'kk Kkr dhft,A

4.18 vkos'k e rFkk nzO;eku m dk dksbZ vkosf'kr d.k fdlh fo|qr ks=k E ,oa pqEcdh;ks=k B esa xfr dj jgk gSA bl d.k dh xfr ls lacafèkr foekghu jkf'k;ksa rFkk (T )–1

foek;qDr jkf'k;ksa dh jpuk dhft,A

fp=k 4.1

23/04/18

xfreku vkos'k vkSj pqEcdRo

27

GR1 R2 R3

2V 20V 200V

4.19 ,sls ?kukdkj ks=k esa ftlosQ iQyd funsZ'kkad ryksa osQ lekUrj gSa rFkk ftlesa ,dleku

fo|qr ,oa pqEcdh; ks=k fo|eku gSa] dksbZ bysDVªkWu v = 0ˆv i osx ls izos'k djrk gSA

;fn bl bysDVªkWu dh dkk ?ku osQ vanj x-y ry osQ lekUrj ry esa uhps dh vksjlfiZy gks rksA ks=k E rFkk ks=k B dk og foU;kl crkb, ftldk izHkko bysDVªkWu dks,slk djus osQ fy, izsfjr dj ldrk gSA

4.20 D;k pqEcdh; cy U;wVu osQ rhljs fu;e dk ikyu djrs gSa\ ewyfcUnq ij fLFkr èkkjk

?kVd (d l1 = ˆdl i ) rFkk (0, R, 0) ij fLFkr /kjk ?kVd (d l

2 = ˆdl j ) osQ fy,

bls lR;kfir dhft,A nksuksa ?kVdksa ls /kjk I izokfgr gksrh gSA

4.21 fp=k 4.2. esa n'kkZ, x, xSYosuksehVj ifjiFk dk mi;ksx djosQ cgqifjljh; oksYVehVjdh jpuk dh tk ldrh gSA ge ,d ,sls oksYVehVj dh jpuk djuk pkgrs gSa] tks 2V,

20V rFkk 200V eki losQ rFkk 10Ω izfrjks/ osQ ,sls xSYosuksehVj ls cuk gks ftlesa1 mA /kjk ls vfèkdre foksi mRiUu gksrk gSA blosQ fy, mi;ksx fd, tkus okysR

1, R

2 rFkk R

3 osQ eku Kkr dhft,A

4.22 dksbZ yEck lh/k rkj ftlls 25A /kjk izokfgr gks jgh gS fp=k 4.3 esa n'kkZ, vuqlkjfdlh est ij j[kk gSA 1m yEck 2.5 g nzO;eku dk dksbZ vU; rkj PQ gS ftllsfoijhr fn'kk esa bruh gh /kjk izokfgr gks jgh gSA rkj PQ mQij vFkok uhps ljoQusosQ fy, Loar=k gSA rkj PQ fdl mQ¡pkbZ rd mQij mBsxk\

nh?kZmÙkjh; (LA)

4.23 100 isQjksa dh dksbZ vk;rkdkj oqQ.Myh ABCD ( XY ry esa) rqyk dh ,d Hkqtkls yVdh gS (fp=k 4.4)A oqQ.Myh dk Hkkj larqfyr djus osQ fy, nwljh Hkqtk ij500 g ckV j[kk x;k gSA vc oqQ.Myh ls 4.9 A /kjk izokfgr dh tkrh gS rFkk Hkhrjdh vksj (XZ ry esa) dk;Zjr 0.2 T dk fu;r pqEcdh; ks=k bl izdkj yxk;k tkrkgS fd osQoy CD Hkqtk ftldh yEckbZ 1 cm gS] oqQ.Myh ks=k esa jgsA rqyk ij fdrukvfrfjDr nzO;eku ‘m’ j[ksa fd iqu% larqyu izkIr gks tk,\

4.24 fdlh vk;rkdkj pkyd ywi* esa l yEckbZ osQ nks rkj bldh nks foijhr Hkqtkvksa esa yxsgSa ftUgsa yEckbZ d dh NM+kas ls vkil esa tksM+k x;k gSA ;s rkj leku inkFkZ ls cus gSaijUrq budh vuqizLFk dkV esa 1:2 dk vuqikr gSA eksVs rkj dk izfrjks/ R gSA NM+sa fuEuizfrjks/ dh gSa vkSj ;s fu;r oksYVrk lzksr V

0 ls tqM+h gSaA ;g ywi fdlh ,dleku

pqEcdh; ks=k B esa bl izdkj j[kk gS fd mldk ry ks=k ls 45° dk dks.k cukrkgSA ywi ij NM+ksa osQ osQUnzksa ls xqtjus okys vk osQ ifjr% pqEcdh; ks=k kjk vkjksfircy vk?kw.kZ τ Kkr dhft,A

fp=k 4.2

fp=k 4.3

X X X

X X X

BA

D CX

X

X

XX

fp=k 4.4

P Q

h

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28

A

B

C

E

D

O

R

4.25 ,d bysDVªkWu rFkk ,d ikWftVªkWu dks leku ifjek.k osQ laosx p = e BR ls fdlh,dleku pqEcdh; ks=k B = 0

ˆB i esa ozQe'k% (0, 0, 0) rFkk (0, 0, 1.5R ) fLFkfr;ksaij eqDr fd;k x;k gSA laosx dh fn'kkvksa dh fdu voLFkkvksa esa dkk,¡ vizfrPNsnho`Ùk gksaxh\

4.26 12a yEckbZ rFkk izfrjksèk R dk dksbZ ,dleku pkyd rkj ,d /kjkokgh oqQ.Myh osQ:i esa (i) Hkqtk a osQ leckgq f=kHkqt (ii) Hkqtk a osQ oxZ (iii) Hkqtk a osQ fu;fer "kVHkqtdh vko`Qfr esa yisVk x;k gSA oqQ.Myh foHkolzksr V

0 ls lEc¼ gSA izR;sd izdj.k esa

oqQ.Mfy;ksa dk pqEcdh; vk?kw.kZ Kkr dhft,A

4.27 R f=kT;k osQ fdlh o`Ùkkdkj /kjkokgh ywi ij fopkj dhft,] tks x-y ry esa gS rFkkftldk osQUnz ewy fcUnq ij gSA eku yhft, z-vk osQ vuqfn'k js[kk lekdyu

( )–

.L

L

Lℑ = ∫ B dl fd;k x;k gSA

(a) ;g n'kkZb, fd ℑ (L) esa L lkFk ,dfn"Vr% o`f¼ gksrh gSA

(b) ;g n'kkZus osQ fy, fd ( ) 0Iτ µ=∞ (;gk¡ I rkj es izokfgr /kjk gS) fdlh mfpr

,sfEi;jh; ywi dk mi;ksx dhft,A

(c) mijksDr fu"d"kZ dh izR;kr% iqf"V dhft,A

(d) eku yhft, ge o`Ùkkdkj oqQ.Myh dks R Hkqtk dh oxkZdkj oqQ.Myh ls izfrLFkkfirdjrs gSa ftlesa leku èkkjk I izokfgr gks jgh gS rc vki ( )Lℑ rFkk ( )ℑ ∞ osQ

fo"k; esa D;k dg ldrs gSa\

4.28 fp=k 4.5 esa n'kkZ, x, xSYosuksehVj ifjiFk dk mi;ksx djosQ cgqifjljh; /kjkekfi;ksadh jpuk dh tk ldrh gSA ge 10 mA, 100 mA rFkk 1A dh /kjk eki ldus okys,sls /kjkekih dh jpuk djuk pkgrs gSa tks 10Ω izfrjks/ osQ ,sls xSYosuksehVj ls cukgks ftlesa 1mA /kjk izokfgr gksus ij vf/dre foksi gksrk gSA blosQ fy, mi;ksxfd, tkus okys izfrjksèkksa S

1, S

2 rFkk S

3 osQ eku Kkr dhft,A

4.29 ik¡p yEcs rkjksa A, B, C, D rFkk E ftuesa izR;sd ls /kjk I izokfgr gks jgh gS bl izdkjO;ofLFkr gSa fd ;s fp=k 4.6 esa n'kkZ, vuqlkj fdlh iapHkqth; fizT+e osQ fdukjs cukrsgSaA izR;sd ls /kjk dkxt osQ ry ls ckgj dh vksj izokfgr gksrh gSA

(a) dkxt osQ yEcor~ vk O osQ fdlh fcUnq ij pqEcdh; izsj.k D;k gksxk\ ;g vkizR;sd rkj ls leku nwjh R ij gSA

(b) ;fn fdlh rkj (tSls A) ls /kjk lekIr dj nh tk,] rks pqEcdh; ks=k D;k gksxk\

(c) D;k gksxk ;fn fdlh rkj (tSls A) esa /kjk izokg dh fn'kk mRozQfer dj nh tk,\

G

S3

S1 S2

10mA 100mA 1A

fp=k 4.5

fp=k 4.6

23/04/18

pqEcRo ,oa nzO;


5.1 n isQjksa] ekè; f=kT;k R rFkk vuqizLFk dkV f=kT;k a osQ fdlh VksjkW;M ls I /kjk izokfgrgks jgh gSA ;g fdlh kSfrt est ij] ftls x – y ry ekuk x;k gS] j[kk gSA bldkpqEcdh; vk?kw.kZ m

(a) 'kwU;srj gS rFkk lefefr kjk z-fn'kk esa gS

(b) VksjkW;M ( ˆm=m φφφφ ) osQ vk osQ vuqfn'k gSA

(c) 'kwU; gS] vU;Fkk ;gk¡ ,d ks=k gksxk tks VksjkW;M osQ ckgj vfèkd nwfj;ksa ij 3

1

r osQ

vuqlkj de gksrk gSA

(d) f=kT;r% ckgj dh vksj fn"V gSA

5.2 i`Foh osQ pqEcdh; ks=k dks i`Foh osQ osQUnz ij fLFkr fcUnq f/zqo osQ ks=k dk izfr:iekuk tk ldrk gSA bl f/zqo dk vk i`Foh osQ vk ls 11.3° dk dks.k cukrk gSA eqEcbZesa fnDikr yxHkx 'kwU; gSA rc

vè;k; 5

pqEcdRo ,oa nzO;

23/04/18


30

(a) i`Foh ij fnDikr dk eku 11.3°W ls 11.3°E osQ chp ifjofrZr gksrk gSA

(b) fuEure fnDikr 'kwU; va'k (0°) gSA

(c) f/zqo vk rFkk i`Foh osQ vk dks èkkj.k djus okyk ry xzhufop ls xqtjrk gSA

(d) leLr i`Foh ij fnDikr lnSo ½.kkRed gksuk pkfg,A

5.3 dejs osQ rki ij fdlh LFkk;h pqEcd esa

(a) izR;sd v.kq dk pqEcdh; vk?kw.kZ 'kwU; gksrk gSA

(b) lHkh vyx&vyx v.kqvksa osQ 'kwU;srj pqEcdh; vk?kw.kZ gksrs gSa tks iw.kZr% Lakjsf[krgksrs gSaA

(c) oqQN Mksesu va'kr% lajsf[kr gksrs gSaA

(d) lHkh Mksesu iw.kZr% Lakjsf[kr gksrs gSaA

5.4 nks vkn'kZ fudk;ksa ij fopkj dhft,% (i) fo'kky ifêðdkvksa rFkk y?kq i`Fkdu okyk dksbZlekUrj ifêðdk laèkkfj=k rFkk (ii) dksbZ yEch ifjukfydk ftldh yEckbZ L >> R

(vuqizLFk dkV&f=kT;k) gSA (i) esa E dks vkn'kZ :i ls ifêðdkvksa osQ chp vpj ysrs gSarFkk ckgj 'kwU; ysrs gSaA (ii) esa ifjukfydk osQ Hkhrj pqEcdh; ks=k vpj ysrs gSa rFkkckgj 'kwU; ysrs gSaA rFkkfi ;s vkn'kZ ekU;rk,¡ ewy fu;eksa dk uhps fn, vuqlkj [akMu;k leFkZu djrh gSa]

(a) izdj.k (i) ls fLFkj oS|qr ks=k osQ fy, xkml&fu;e dk [akMu gksrk gSA

(b) izdj.k (ii) ls pqEcdh; ks=k osQ fy, xkml&fu;e dk [akMu gksrk gSA

(c) izdj.k (i) . 0d =∫ E l osQ vuqowQy gSA

(d) izdj.k (ii) . end I=∫ H l dk [akMu djrk gSA

5.5 dksbZ vuqpqEcdh; uewuk 4K rki ij 0.6T osQ ckg~; pqEcdh; ks=k esa j[ks tkus ij8Am–1 dk usV pqEcdu n'kkZrk gSA tc blh uewus dks 16K rki ij 0.2T osQ ckg~;pqEcdh; ks=k esa j[krs gSa rks pqEcdu gksxk

(a)–132

Am3

(b)–12

Am3

(c) –16 Am

(d) –12.4 Am

23/04/18

pqEcdRo ,oa nzO;

31


5.6 pqEcdh; inkFkZ osQ fdlh fiaM dk i`"B S gSA

(a) S ls xqtjus okyh B dh js[kk,¡ vko';d :i ls vfofNUu gSaA

(b) S ls xqtjus okyh B dh oqQN js[kk,¡ fofNUu gksuh pkfg,A

(c) S ls xqtjus okyh H dh lHkh js[kk,¡ vko';d :i ls vfofNUu gSaA

(d) S ls xqtjus okyh H dh lHkh js[kk,¡ vfofNUu ugha gks ldrhaA

5.7 pqEcdRo dk ewy mn~Hko lzksr gS

(a) ijekf.od /kjk,¡(b) ikmyh&viotZu fl¼kar(c) v.kq dh /zqoh; izo`Qfr(d) bysDVªkWu dk uSt pozQ.k

5.8 fdlh yEch ifjukfydk esa izfrehVj 1000 isQjs gSa rFkk blls 1 A /kjk izokfgr gks jghgSA blosQ Hkhrj 1000rµ = dk ueZ ykSg ozQksM gSA bl ozQksM dks D;wjh rki] T

c ls vfèkd

rki rd xje fd;k tkrk gSA(a) ifjukfydk osQ Hkhrj H &ks=k (yxHkx) vifjofrZr jgrk gS] ijUrq B &ks=k izcy

:i ls ?kV tkrk gSA

(b) H rFkk B &ks=k ifjukfydk osQ Hkhrj (yxHkx) vifjofrZr jgrs gSaA

(c) ozQksM esa pqEcdu dh fn'kk mRozQfer gks tkrh gSA

(d) ozQksM esa pqEcdu yxHkx 108 xquk de gks tkrh gSA5.9 fdlh pkyd [kksy kjk fLFkj oS|qr ifjjk.k rFkk fLFkj pqEcdh; ifjjk.k esa ewyHkwr

vUrj dk dkj.k gS(a) fLFkj oS|qr ks=k js[kk,¡ vkos'kksa ij lekIr gks ldrh gSa rFkk pkydksa esa eqDr vkos'k

gksrs gSaA

(b) B dh js[kk,¡ lekIr rks gks ldrh gSa] ijUrq pkyd mUgsa lekIr ugha dj ldrsA

(c) B dh js[kk,¡ fdlh Hkh inkFkZ ij lekIr ugha gks ldrha rFkk vkn'kZ ifjjk.k laHkougha gSA

(d) mPp pqEcd'khyrk osQ inkFkksZa osQ [kksyksa dk mi;ksx] Hkhrjh ks=k ls B dh js[kkvksadks foifFkr djus osQ fy, fd;k tk ldrk gSA

5.10 eku yhft, fd i`Foh ij pqEcdh; ks=k i`Foh osQ osQUnz ij fLFkr pqEcdh; f/zqo osQdkj.k gksrk gSA HkkSxksfyd fo"kqor o`Ùk osQ fdlh fcUnq ij ufr dks.k(a) lnSo 'kwU; gksxkA

(b) fof'k"V fcUnqvksa ij 'kwU; gks ldrk gSA

23/04/18


32

(c) /ukRed vFkok ½.kkRed gks ldrk gSA

(d) ifjc¼ gksrk gSA


5.11 bysDVªkWu dh Hkk¡fr izksVkWu esa Hkh pozQ.k rFkk pqEcdh; vk?kw.kZ gksrk gSA rc inkFkksZa osQpqEcdRo esa blosQ izHkko dh miskk D;ksa dh tkrh gS\

5.12 10 cm yEckbZ ossQ irys flfy.Mj dh vko`Qfr osQ fdlh LFkk;h pqEcd dk M = 106

A/m gSA pqEcd /kjk IM ifjdfyr dhft,A

5.13 (STP ij) N2 (~5 × 10–9) rFkk Cu (~10–5) dh izfr pqEcdh; izo`fÙk osQ chp ifjek.k

dh dksfV;ksa esa ek=kkRed vUrj Li"V dhft,A

5.14 vk.kfod n`f"Vdks.k ls izfr pqEcdRo] vuqpqEcdRo rFkk yksg pqEcdRo dh pqEcdh;izo`fÙk;ksa dh rki fuHkZjrk dh foospuk dhft,A

5.15 vfrpkyd inkFkZ dh ,d xsan dks nzo ukbVªkstu esa Mqcksdj fdlh pqEcd osQ fudV j[kktkrk gSA (i) ;g fdl fn'kk esa xfr djsxh\ (ii) blosQ pqEcdh; vk?kw.kZ dh D;k fn'kkgksxh\

y?kqmÙkjh; (SA)

5.16 R f=kT;k osQ xksykdkj osQ i`"B osQ fy, ewy fcUnq ij fLFkr m f/zqo vk?kw.kZ osQ fdlhfcUnq f/zqo osQ pqEcdh; ks=k osQ fy, xkml&fu;e lR;kfir dhft,A

5.17 fp=k 5.1 esa n'kkZ, vuqlkj rhu loZle NM+ pqEcdksa dks leku ry esa osQUnz ij fjoV kjktM+ fn;k x;k gSA bl fudk; dks fojke voLFkk esa fdlh /hjs&/hjs ifjofrZr gksus okyspqEcdh; ks=k esa j[kk x;k gSA ;g ik;k x;k gS fd pqEcdksa osQ fudk; esa dksbZ xfr ughagqbZA ,d pqEcd osQ mÙkj&nfk.k /zqoksa dks fp=k esa n'kkZ;k x;k gSA vU; nks pqEcdksa osQ/zqo fu/kZfjr dhft,A

5.18 eku yhft, ge ,d lqLi"V iz;ksx kjk fLFkj oS|qr rFkk fLFkj pqEcdRo osQ chpvuq:irk lR;kfir djuk pkgrs gSaA (1) fdlh fLFkj oS|qr ks=k E esa oS|qr f/zqo p rFkk(ii) fdlh pqEcdh; ks=k B esa pqEcdh; f/zqo m dh xfr ij fopkj dhft,A E, B, p,

m ij izfrcaèkksa dk ,d leqPp; fyf[k, rkfd nksuksa xfr;k¡ loZle lR;kfir dh tk losaQA(vkjfEHkd voLFkkvksa dks loZle ekfu,A)

60°

60°

? ?

??

N

S

fp=k 5.1

23/04/18

pqEcdRo ,oa nzO;

33

5.19 pqEcdh; vk?kw.kZ m rFkk tM+Ro vk?kw.kZ I (osQUnz osQ ifjr% yEckbZ osQ yEcor) osQ fdlhNM+ pqEcd dks yEckbZ osQ yEcor nks cjkcj Hkkxksa esa dkVk x;k gSA eku yhft, ewypqEcd dk] pqEcdh; ks=k B esa] eè; fcUnq ls xqtjus okys yEckbZ osQ yEcor vk osQifjr% nksyu dky T gSA izR;sd VqdMs+ osQ fy, blh izdkj dk nksyu dky T′ D;k gksxk\

5.20 (i) H osQ fy, ,sfEi;j fu;e rFkk (ii) B dh js[kkvksa dh vfofNUurk dk mi;ksx djosQ;g fu"d"kZ fudkfy, fd fdlh NM+ pqEcd osQ Hkhrj (a) H dh js[kk,¡ N /zqo ls S èkzqodh vksj tcfd (b) B dh js[kk,¡ S /zqo ls N /zqo dh vksj fn"V gksrh gSaA

nh?kZmÙkjh; (LA)

5.21 f/zqo vk?kw.kZ m ˆ=m k osQ fdlh fcUnq f/zqo osQ pqEcdh; ks=k osQ fy, ,sfEi;j dk

fu;e lR;kfir dhft,A C dks ,slk cUn oozQ ekfu, tks nfk.kkoÙkZ xeu djrk gS (i) z-

vk osQ vuqfn'k z = a > 0 ls z = R, (ii) x-y ry osQ izFke prqFkk±'k esa] osQUnz ewy fcUnqij R osQ pkSFkkbZ o`Ùk osQ vuqfn'k (iii) x-vk osQ vuqfn'k x = R ls x = a rdA (iv) x-

z ry osQ izFke prqFkk±'k esa] osQUnz ewy fcUnq ij] a f=kT;k osQ pkSFkkbZ o`Ùk osQ vuqfn'kA

5.22 pqEcdh; izo`fÙk χ dh foek,¡ D;k gSa\ fdlh H-ijek.kq ij fopkj dhft,A ijek.kq osQizkpyksa e, m, v, R rFkk 0µ osQ mi;ksx kjk χ dh foekvksa dh fdlh jkf'k dh jpukkjk fdlh fu;rkad rd χ osQ O;atd dk dksbZ vuqeku yxkb,A ;gk¡ m bysDVªkWfudnzO;eku] v bysDVªkWuh; osx rFkk R cksgj f=kT;k gSA bl izdkj izfr la[;k dk vuqekuyxkb, rFkk bldh rqyuk cgqr ls Bksl inkFkksZ osQ fy, –5

~10χ osQ eku ls dhft,A

5.23 ;g ekfu, fd i`Foh osQ pqEcdh; ks=k dk f/zqo ekWMy gS ftlosQ vuqlkj ml ks=k dk

mQèokZ/j vo;o BV = =

0

3

2 cos

4

m

r

µ θ

π, rFkk kSfrt vo;o B

H =

0

34

sin m

r

µ θ

π

rFkk θ = 90° – pqEcdh; fo"kqor o`Ùk ls ekius ij vkka'k gSA mu fcUnqvksa dk fcUnq iFkKkr dhft, ftuosQ fy,(i) B U;wure gS] (ii) ufrdks.k 'kwU; gS] (iii) ufrdks.k ± 45° gSA

5.24 ry S ij fopkj dhft, ftlesa f/zqo vk rFkk i`Foh dk vk vofLFkr gksrs gSaA ekuyhft, P dksbZ ,slk fcUnq gS tks pqEcdh; fujk ij ,oa S esa gSA eku yhft, Q og fcUnqgS ftl ij HkkSxksfyd fo"kqoÙk o`Ùk RkFkk pqEcdh; fujk izfrPNsnu djrs gSaA P rFkk Q ijufrdks.k rFkk fnDikr dks.k Kkr dhft,A

5.25 yEckbZ L osQ loZle rkjksa dh cuh nks leryh; /kjkokgh oqQ.Mfy;k¡ gSa ftuesa C1 o`Ùkkdkj

(f=kT;k R) rFkk C2 oxkZdkj (Hkqtk a) gSA budh jpuk bl izdkj dh xbZ gS fd ,d

tSls ,d leku B esa j[kus ij rFkk leku /kjk izokfgr djus ij ;s nksuksa leku vko`fÙkls oaQiu djrs gSA R osQ inksa esa a dk eku Kkr dhft,A

23/04/18


34


6.1 x – y ry osQ fdlh izns'k esa] tgk¡ pqEcdh; ks=k Boˆ ˆ ˆ(2 3 4 )T= + +B i j k gS] (;gk¡

Bo dksbZ fu;rkad gS)] L ehVj Hkqtk dk dksbZ oxZ j[kk gSA bl oxZ ls xqtjus okys ÝyDl

dk ifjek.k gS%

(a) 2 Bo L2 Wb

(b) 3 Bo L2 Wb

(c) 4 Bo L2 Wb

(d)oB L229 Wb

6.2 lh/s fdukjksa ls cus fdlh ywi esa N% dksus A(0,0,0), B(L,O,0) C(L,L,0), D(0,L,0)

E(0,L,L) rFkk F(0,0,d) ij gSaA bl izns'k esa mifLFkr pqEcdh; ks=k B ˆ ˆ( ) T= +oB i k

fo|eku gSA ywi ABCDEFA (bl ozQe esa) ls xqtjus okyk ÝyDl gS%

(a) Bo L2 Wb

(b) 2 Bo L2 Wb

(c) 2 Bo L2 Wb

(d) 4 Bo L2 Wb

vè;k; 6

oS|qrpqEcdh; izsj.k

23/04/18

oS|qrpqEcdh; izsj.k

35

6.3 fdlh csyukdkj NM+ pqEcd dks mlosQ vk osQ ifjr% (fp=k 6.1) ?kw.kZu djk;k tkrkgSA fdlh rkj dks blosQ vk ls la;ksftr djosQ blosQ csyukdkj i`"B ls fdlh lEioZQkjk Li'kZ djk;k x;k gS rc

(a) ,sehVj A ls fn"V /kjk izokfgr gksrh gSA

(b) ,sehVj A ls dksbZ /kjk izokfgr ugha gksrh gSA

(c) ,sehVj A ls vkorZdky T = 2π/ω dh izR;korhZ T;koozQh; /kjk izokfgr gksrh gSA

(d) ,sehVj A ls dky ifjofrZr /kjk izokfgr gksrh gS tks T;koozQh; ugha gksrhA

6.4 fp=k 6.2 esa n'kkZ, vuqlkj A rFkk B nks oqQ.Mfy;k¡ gSaA tc A dks B dh vksj xfr djkrsgSa rks B esa fp=k esa n'kkZ, vuqlkj /kjk izokfgr gksus yxrh gS rFkk A osQ #dus ij èkkjkizokfgr gksuk cUn gks tkrh gSA B esa /kjk okeorhZ gSA tc A xfr djrk gS rks B dks fLFkjj[kk tkrk gSA ge ;g fu"d"kZ fudky ldrs gSa fd

(a) A esa nfk.kkorhZ fn'kk esa fu;r /kjk gSA

(b) A esa ifjorhZ /kjk gSA

(c) A esa dksbZ /kjk ugha gSA

(d) A esa okeorhZ fn'kk esa fu;r /kjk gSA

6.5 bl iz'u esa Hkh fLFkfr iz'u 6.4 dh Hkk¡fr gSA vUrj osQoy ;g gS fd vc oqQ.Myh Adks mQèokZ/j vk osQ ifjr% ?kw.kZu djk;k x;k gS (fp=k 6.3)A ;fn A fojke esa gS rksB es dksbZ /kjk izokfgr ugha gksrhA tc B esa (t = 0 ij) /kjk okeorhZ fn'kk esa gS rFkkbl k.k] t = 0, ij oqQ.Myh A n'kkZ, vuqlkj gS rc oqQ.Myh A esa izokfgr gksrh gS\

(a) nfk.kkorZ fu;r /kjk

(b) nfk.kkorZ ifjorhZ /kjk

(c) okekorZ ifjorhZ /kjk

(d) okekorZ fu;r /kjk

6.6 fdlh vuqizLFk dkV osQ ks=kiQy A rFkk fu;r isQjksa dh la[;k N okyh l yEckbZ dhifjukfydk dk LoizsjdRo L c<+ tkrk gS%

(a) l rFkk A esa o`f¼ osQ lkFk

(b) l esa deh rFkk A esa o`f¼ osQ lkFk

(c) l esa o`f¼ rFkk A esa deh osQ lkFk

(d) l rFkk A esa deh osQ lkFk

AB

w

fp=k 6.3

s

A

A B

v

fp=k 6.2

fp=k 6.1

vk

n.MpqEcd

23/04/18


36


6.7 dksbZ /krq dh IysV rIr gks jgh gSA bldk dkj.k ;g gks ldrk gS fd

(a) IysV ls dksbZ fn"V (ijUrq izR;korhZ ugha) /kjk izokfgr gks jgh gSA(b) ;g fdlh dky ifjorhZ pqEcdh; ks=k esa j[kh gSA(c) IysV LFkkukorhZ pqEcdh; ks=k esa j[kh gS tks dky ifjorhZ ugha gSA(d) IysV ls dksbZ /kjk (;k rks fn"V vFkok izR;korhZ) izokfgr gks jgh gSA

6.8 fdlh oqQ.Myh esa] tks fdlh oksYVrk lzksr ls la;ksftr ugha gS] dksbZ fo|qr okgd cymRiUu gksrk gSA bldk dkj.k ;g gks ldrk gS fd

(a) ;g oqQ.Myh fdlh dky ifjorhZ pqEcdh; ks=k esa j[kh gSA

(b) ;g oqQ.Myh fdlh dky ifjorhZ pqEcdh; ks=k esa xfr dj jgh gSA

(c) ;g oqQ.Myh fdlh fu;r pqEcdh; ks=k esa xfr dj jgh gSA

(d) ;g oqQ.Myh fdlh ,sls cká LFkkukorhZ pqEcdh; ks=k esa fLFkj j[kh gS tks dkyosQ lkFk ifjofrZr ugha gksrkA

6.9 oqQ.Myh 1 dk oqQ.Myh 2 osQ lkisk vU;ksU; izsjdRo M12

(a) oqQ.Mfy;ksa dks ikl ykus ij c<+ tkrk gSA(b) oqQ.Mfy;ksa esa izokfgr /kjk ij fuHkZj djrk gSA(c) fdlh ,d oqQ.Myh osQ vius vk ij ?kw.kZu djus ij c<+ tkrk gSA(d) oqQ.Myh 2 osQ oqQ.Myh 1 osQ lkisk vU;ksU; izsjdRo M

21 osQ leku gksrk gSA

6.10 dksbZ o`Ùkkdkj oqQ.Myh fdlh pqEcdh; ks=k esa f=kT;r% iSQy jgh gS vkSj oqQ.Myh esadksbZ fo|qr okgd cy mRiUu ugha gksrkA bldk dkj.k ;g gks ldrk gS fd

(a) pqEcdh; ks=k fu;r gSA

(b) pqEcdh; ks=k dk ry ,oa oqQ.Myh dk ry leku gS vkSj pqEcdh; ks=k ifjofrZrgks ldrk gS vkSj ugha Hkh gks ldrkA

(c) pqEcdh; ks=k dk dksbZ yEcor~ (oqQ.Myh osQ ry osQ) vo;o gS ftldk ifjek.kmi;qDr :i ls ?kV jgk gSA

(d) ;gk¡ yEcor~ (oqQ.Myh osQ ry osQ) fn'kk esa dksbZ fu;r pqEcdh; ks=k gSA


6.11 fdlh ,sls pqEcd ij fopkj dhft, tks ,d vkWu@vkWiQ fLop yxs rkj osQ ywi ls f?kjkgS (fp=k 6.4)A ;fn fLop dks vkWiQ fLFkfr ([kqys ifjiFk) ls vkWu fLFkfr (cUnifjiFk) ij yk;k tk, rks D;k ifjiFk esa dksbZ /kjk izokfgr gksxh\

23/04/18

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37

NN

fp=k 6.4

fp=k 6.5

6.12 dldj fyiVh ifjukfydk osQ :i esa dksbZ rkj fdlh fn"V/kjk lzksr ls la;ksftr gS vkSjblesa fo|qr èkkjk izokfgr gks jgh gSA ;fn oqQ.Myh dks bl izdkj ls [khapk tk, fdlfiZykdkj oqQ.Myh osQ ozQekxr yisVksa osQ chp vUrjky gks tk,] rks D;k fo|qr /kjkc<+sxh vFkok ?kVsxh] Li"V dhft,A

6.13 dksbZ ifjukfydk fdlh cSVjh ls la;ksftr gS ftlosQ dkj.k mles vifjorhZ /kjk izokfgrgks jgh gSA ;fn bl ifjukfydk osQ Hkhrj dksbZ yksg ozQksM j[k fn;k tk, rks fo|qr èkkjk?kVsxh vFkok c<+sxh\ Li"V dhft,A

6.14 /krq osQ fdlh ,sls NYys ij fopkj dhft, tks fdlh ÅèokZèkjr% j[kh fLFkj ifjukfydk(tSls dkMZ cksMZ esa tM+h) osQ 'kh"kZ ij j[kk gS (fp=k 6.5)A NYys dk osQUnz ifjukfydkosQ vk osQ laikrh gSA ;fn vpkud fLop vkWu djosQ ifjukfydk esa /kjk izokfgr djk,¡rks /krq dk NYYkk mQij mNyrk gSA Li"V dhft,A

6.15 /krq osQ fdlh ,sls NYys ij fopkj dhft, tks dkMZ cksMZ osQ mQij j[kk gS tks fdlh,slh n`<+ ifjukfydk osQ 'kh"kZ ij j[kk gS ftlls I fo|qr /kjk izokfgr gks jgh gS(fp=k 6.5)A NYys dk osQUnz ifjukfydk osQ vk osQ laikrh gSA ;fn ifjukfydk ls/kjk izokfgr djuk cUn dj nsa] rks /krq osQ NYys dk D;k gksxk\

6.16 1 cm vkUrfjd f=kT;k osQ fdlh /krq osQ ikbi ij fopkj dhft,A ;fn 0.8 cm f=kT;kdk dksbZ csyukdkj NM+ pqEcd bl ikbi esa fxjk;k tk, rks og uhps fxjus esa fdlhizdkj dh vpqEcfdr csyukdkj yksg NM+ dh rqyuk esa vf/d le; ysrk gSA Li"Vdhft,A

y?kqmÙkjh; (SA)

6.17 fdlh fuf'pr LFkku ij fo|eku pqEcdh; ks=k dks ( ) ˆcosoB tω=B k kjk O;Dr

fd;k x;k gS rFkk bl pqEcdh; ks=k esa x – y ry esa izfrjks/ R rFkk f=kT;k a dh dksbZoqQ.Myh j[kh gS ftldk osQUnz ewy fcUnq ij gS (fp=k 6.6) A fcUnq (a, 0, 0) ij

fp=k 6.6

n.M pqEcd

[kqyk ifjiFk cUn ifjiFk

n.M pqEcd

( ,0,0)ax

(0,0,0)

y

k

23/04/18


38

2A

1A

0

–1A

–2A

5 10 15 20 25 30 35 40

C

B

A

èkkjk(A

)

le; (s)

2t

π=

ω, t

π=

ω rFkk

3

2t

π=

ω. le;ksa ij /kjk dk ifjek.k ,oa fn'kk Kkr dhft,A

6.18 pqEcdh; ks=k esa fdlh cUn ywi C ij fopkj dhft, (fp=k 6.7)A bl ywi ls xqtjusokys ÝyDl dh ifjHkk"kk fdlh ,sls i`"B dk p;u djosQ ftlosQ fdukjs bl ywi osQlaikrh gSa rFkk lw=k 1 1 2 2. . ...φ = + +B A Ad B d . osQ kjk dh tkrh gSA vc ;fn ge

nks vU; i`"Bksaa S1 rFkk S

2 dk p;u djas ftuosQ fdukjs C gksa rks D;k gesa ÝyDl osQ

fy, leku mÙkj izkIr gksxk\ vius mÙkj dh iqf"V dhft,A

6.19 fp=k 6.8 esa n'kkZ, x, foU;kl osQ fy, rkj esa /kjk Kkr dhft,A rkj PQ dk izfrjks/ misk.kh;gS rFkk pqEcdh; ks=k B i"B ls ckgj vk jgk gSA θ ,d fu;r dks.k gS tks rkj PQ nks ,slslekUrj pkyd rkjksa ls cukrs gq, fuckZèk xfr djrk gS ftuosQ chp iFkdu d gS]A

6.20 fdlh ifjukfydk ls izokfgr /kjk dk (/kjk ,oa le; osQ chp) xzkiQ fp=k 6.9 esan'kkZ;k x;k gSA fdl le; ij i'p fo|qr okgd cy (u) vf/dre gS\ ;fn t = 3s

ij i'p fo|qr okgd cy l gS] rks t = 7 s, 15 s ,oa 40 s ij i'p fo|qr okgdcy Kkr dhft,A OA, AB rFkk BC ljy js[kk[k.M gSaA

fp=k 6.9

S1

S2

B D B

BC

q

B

B

P

Q B

Rv

fp=k 6.8

fp=k 6.7

fu;r

6.21 nks oqQ.Mfy;ksa P rFkk Q osQ chp oqQN i`Fkdu gSA ;fn P ls 2A /kjk izokfgr gksrh gSrks Q ls 10-2 Wb dk pqEcdh; ÝyDl (B esa dksbZ /kjk ugha) xqtjrk gSA ;fn P lsdksbZ /kjk izokfgr ugha gksrh rFkk Q ls 1A /kjk izokfgr gksrh gS] rks P ls fdruk ÝyDlxqtjrk gS\

nh?kZmÙkjh; (LA)

6.22 dksbZ pqEcdh; ks=k ( ) ˆsinoB tω=B k fdlh fo'kky izns'k ij vkPNkfnr gS ftlesarkj AB ,sls nks lekUrj pkydksa ij fuckZ/ ljdrk gS tks ,d nwljs ls d nwjh kjkiFkDoQr gSa (fp=k 6.10)A ;s rkj x-y ry esa gSaA rkj AB (yEckbZ d dh) dk izfrjks/R gS rFkk lekUrj pkydksa (rkjksa) dk izfrjks/ misk.kh; gSA ;fn AB v osx ls xeu

y

xB

C A

O

v

fp=k 6.10

23/04/18

oS|qrpqEcdh; izsj.k

39

A

D

B

I t( )

xo

C

l

r

drx

X

B

x t( )

Bl

Y

B

Dx

C

A

R

y

A

C

B

D

B

l

w

P¢O

l l

P

B B

2l

djrk gS rks ifjiFk esa fdruh /kjk gS\ rkj dks fu;r osx ls xeu djus osQ fy, fdruscy dh vko';drk gS\

6.23 dksbZ pkyd rkj XY ftldk nzO;eku m gS rFkk izfrjks/ misk.kh; gS] fp=k 6.11 esan'kkZ, vuqlkj nks lekUrj pkyd rkjksa ij fuckZèk :i ls ljdrk gSA AC osQ dkj.kifjiFk dk izfrjks/ R gSA AB rFkk CD vkn'kZ pkyd gSaA bl ks=k esa pqEcdh;ks=k ˆ( )B t=B k gSA

(a) rkj XY osQ Roj.k osQ fy, lehdj.k fyf[k,A

(b) ;fn B dky ij fuHkZj ugha djrk rks] v (0) = u ekudj v(t) Kkrdhft,A

(c) (b) osQ fy, ;g n'kkZb, fd XY dh xfrt mQtkZ esa deh R esa gq,mQ"ek&ßkl osQ cjkcj gSA

6.24 ODBAC dksbZ misk.kh; izfrjks/ dk vpy vk;rkdkj pkyd(CO la;ksftr ugha gS) gS rFkk OP ,d ,slk pkyd gS tks dks.kh; osx lsnfk.kkorZ ?kw.kZu djrk gS (fp=k 6.12)A leLr fudk; fdlh ,dlekupqEcdh; ks=k B esa gS ftldh fn'kk vk;rkdkj pkyd ABCD osQ i`"B osQvfHkyEcor~ gSA pkyd OP, ABCD osQ oS|qr lEioZQ esa gSA ?kw.khZ pkyd dkizfr ,dkad yEckbZ izfrjks/ λ gSA 180° ?kw.kZu djus ij ?kw.khZ pkyd esaizokfgr /kjk Kkr dhft,A (0 < t < π/4ω osQ fy,] OP Hkqtk BD dks Li'kZdjrk gS)

6.25 fp=k 6.13 esa n'kkZ;s vuUr yEckbZ osQ rkj ftlesa /kjk I (t ) dI

dt

= λ =

vpj

izokfgr gks jgh gS] ij fopkj dhft,A vk;rkdkj ywi ABCD ftldk izfrjks/R gS] esa mRiUu èkkjk Kkr dhft,A

6.26 rkj ABCD dk dksbZ vk;rkdkj ywi fdlh vuUr yEckbZ osQ èkkjkokgh rkj osQ lehij[kk gS] ftlesa 0 t T≤ ≤ osQ fy, /kjk ( ) ( )1 – /oI I t Tt = rFkk t > T osQ fy,/kjk I (0) = 0 izokfgr gksrh gS (fp=k 6.14)A le; T esa ywi osQ fdlh fn, x,fcUnq ls xqtjus okyk oqQy vkos'k Kkr dhft,A ywi dk izfrjks/ R gSA

fp=k 6.11

fp=k 6.12

fp=k 6.13

A

D

B

I t( )

x C

L1

L + x2

fp=k 6.14

23/04/18


40

6.27 dksbZ pqEcdh; ks=k B fdlh izns'k r a≤ rd lhfer gS rFkk bldh fn'kk dkxt+ osQyacor~ ckgj dh vksj (z-vk) gS] r = 0 bl orh; izns'k dk osQUnz gSA m nzO;eku rFkkf=kT;k b, (b > a) dk dksbZ vkosf'kr NYyk (vkos'k Q) ftldk osQUnz ewy fcUnq ijgS x – y ry esa gSA ;g NYyk ?kw.kZu djus osQ fy, Lora=k gS rFkk fojke voLFkk esa gSApqEcdh; ks=k dk ifj.kke ∆t le; esa 'kwU; dj fn;k tkrk gSA pqEcdh; ks=k lekIrgksus ij NYys dk dks.kh; osx ω Kkr dhft,A

6.28 nzO;eku m rFkk izfrjks/ R dh dksbZ NM+ kSfrt ls θ dks.k cukrs gq, j[ks nks lekUrjvkn'kZ pkyd rkjksa ij fuckZ/ ljdrh gS (fp=k 6.15) A ifjiFk dks 'kh"kZ ij vkn'kZpkyd kjk cUn fd;k x;k gSA mQèokZ/j fn'kk osQ vuqfn'k dksbZ fu;r pqEcdh; ks=kB mifLFkr gSA ;fn NM+ vkjEHk esa fojke esa gS] rks le; osQ iQyu osQ :i esa NM+ dkosx Kkr dhft,A

6.29 fp=k 6.16 esa n'kkZ;h xbZ O;oLFkk esa ljdrh gqbZ NM+ AB (izfrjks/ = R) esa èkkjk Kkrdhft,A B fu;r gS vkSj ;g mQèokZèkjr% dkxt+ ls ckgj dh vksj gSA lekUrj rkjksa dkdksbZ izfrjks/ ugha gSA v fu;r gSA le; t = 0 ij fLop S cUn gSA

B

BC

B

dv

A

X

Y

S

fp=k 6.16

6.30 fp=k 6.17 esa n'kkZ;h xbZ O;oLFkk esa ljdrh gqbZ NM+ AB (izfrjks/ = R) esa èkkjk Kkrdhft,A B fu;r gS vkSj ;g dkxt+ ls ckgj dh vksj gSA lekUrj rkjksa dk dksbZ izfrjks/ugha gSA v fu;r gSA le; t = 0 ij fLop S cUn gSA

v

B

qd

fp=k 6.15

d

B

B B

B

L

B

v

AXS

B B

fp=k 6.17

23/04/18

oS|qrpqEcdh; izsj.k

41

6.31 nzO;eku m rFkk f=kT;k l dk dksbZ NYyk (NYyk kSfrt gS) pqEcdh; ks=k osQ fdlhizns'k esa xq#Ro osQ v/hu eqDr :i ls fxj jgk gSA ;fn ÅèokZ/j fn'kk z gS] rks pqEcdh;ks=k dk z-vo;o B

z = B

o (1+λz) gSA ;fn NYys dk izfrjks/ R gS rFkk ;g v osx

ls fxjrk gS] rks izfrjks/ esa u"V gqbZ mQtkZ Kkr dhft,A ;fn NYys us fu;r osx izkIrdj fy;k gS] rks mQtkZ lajk.k dk mi;ksx djosQ m, B, λ rFkk xq#Roh; Roj.k g osQ inksaesa v dk eku ifjdfyr dhft,A

6.32 O;kl 'a' fdlh yEch ifjukfydk ‘S’ esa izfr ehVj ‘n’ yisVsa gSaA bl ifjukfydk osQosQUnz ij geus ‘N’ yisVksa dh ‘b’ O;kl dh (;gk¡ b < a) dksbZ NksVh oqQ.Myh j[kh gSA;fn ifjukfydk esa le; osQ lkFk /kjk esa o`f¼ jSf[kdr% gksrh gS] rks NksVh oqQ.Myhesa izdV gksus okyh izsfjr èkkjk fdruh gS\ ;fn èkkjk dks le; osQ iQyu osQ :i esaI = mt 2 + c kjk O;Dr fd;k tk ldrk gks rks le; osQ lkFk fo|qr okgd cyesa ifjorZu dh izo`Qfr dks n'kkZus okyk xzkiQ [khafp,A

23/04/18



7.1 ;fn 50 gV~Z”k ac ifjiFk esa 5 A dh rms /kjk izokfgr gks jgh gks] rks /kjkifjek.k 'kwU; gksus osQ 1/300 s i'pkr bldk eku gksxk %(a) (5 2 ) A

(b) (5 3 / 2 ) A

(c) ( 5/6 ) A

(d) (5 / 2 ) A

7.2 fdlh izR;korhZ /kjk tfu=k dk vkarfjd izfrjks/ Rg rFkk vkarfjd izfr?kkr X

g gSA bls R

g

izfrjks/ rFkk XL izfr?kkr osQ fdlh fuf"ozQ; ykssM dks 'kfDr iznku djus osQ fy, mi;ksx

esa yk;k x;k gSA tfu=k ls yksM dks vf/dre 'kfDr iznku djus osQ fy, XL dk eku

gksuk pkfg, %(a) 'kwU;(b) X

g

(c) – Xg

(d) Rg

vè;k; 7

izR;korhZ /kjk

23/04/18

izR;korhZ /kjk

43

7.3 fdlh oksYVrk ekid ;qfDr dks ac esal ls tksM+us ij ;g ;qfDr 220V fLFkj fuos'koksYVrk n'kkZrh gSA bldk vFkZ ;g gS fd %

(a) fuos'k oksYVrk ac oksYVrk ugha gks ldrh] ijUrq ;g dc oksYVrk gSA

(b) vf/dre fuos'k oksYVrk 220V gSA

(c) ekid ;qfDr v dk ikB~;kad ugha nsrh vfirq <v2> dk ikB~;kad nsrh gS vkSj bldkva'kkadu 2v< > dk ikB~;kad ysus osQ fy, fd;k x;k gSA

(d) fdlh ;kaf=kd nks"k osQ dkj.k ekid ;qfDr dk laosQrd vVd tkrk gSA

7.4 fdlh tfu=k ls Js.khozQe esa tqM+s LCR ifjiFk dh vuquknh vkofÙk de djus osQ fy, %

(a) tfu=k dh vko`fÙk de djuh pkfg,A

(b) ifjiFk esa yxs la/kfj=k osQ ik'oZozQe esa ,d vU; la/kfj=k tksM+uk pkfg,A

(c) izsjd osQ yksg&ozQksM dks gVk nsuk pkfg,A

(d) la/kfj=k osQ ijkoS|qr dks gVk nsuk pkfg,A

7.5 lapkj esa iz;qDr LCR ifjiFk osQ vf/d vPNs leLoj.k osQ fy, fuEufyf[kr esa fdlla;kstu dk p;u djuk pkfg,\

(a) R = 20 Ω, L = 1.5 H, C = 35µF

(b) R = 25 Ω, L = 2.5 H, C = 45µF

(c) R = 15 Ω, L = 3.5 H, C = 30µσF

(d) R = 25 Ω, L = 1.5 H, C = 45µF

7.6 1 Ω izfrck/k osQ fdlh izsjd rFkk 2 Ω izfrjks/ osQ fdlh izfrjks/d dks 6 V (rms)

osQ ac lzksr ls Js.khozQe esa tksM+k x;k gSA ifjiFk esa kf;r 'kfDr dk eku gS %

(a) 8 W

(b) 12 W

(c) 14.4 W

(d) 18 W

7.7 fdlh vipk;h Vªk¡liQkeZj dk fuxZe 12 W osQ izdk'k cYc dks la;ksftr djus ij24 V ekik tkrk gSA f'k[kj /kjk dk eku gS %

(a) 1/ 2 A

(b) 2 A

(c) 2 A

(d) 2 2 A

23/04/18

iz'u&iznf'kZdk&HkkSfrdh

44


7.8 tc fdlh ac ifjiFk dh vko`fÙk esa o`f¼ gksrh gS] rks blesa izokfgr èkkjk igys c<+rhgS vkSj fiQj de gks tkrh gSA bl ifjiFk esa ifjiFk vo;oksa osQ fdl la;kstu dhlokZfèkd laHkkouk gS\

(a) izsjd ,oa la/kfj=kA

(b) izfrjks/d ,oa izsjdA

(c) izfrjks/d ,oa la/kfj=kA

(d) izfrjks/d] izsjd ,oa la/kfj=kA

7.9 fdlh ac ifjiFk esa vo;o Js.khozQe esa tqM+s gSaA blesa yxs vkiwfrZ lzksr dh vko`fÙk c<+kusls /kjk c<+rh gSA ifjiFk esa fdu vo;oksa osQ tqM+s gksus dh laHkkouk gS\

(a) osQoy izfrjks/dA

(b) izfrjks/d ,oa izsjdA

(c) izfrjks/d ,oa la/kfj=kA

(d) osQoy la/kfj=kA

7.10 fo|qr mQtkZ dk fo'kky nwfj;ksa rd izs"k.k mPp izR;korhZ oksYVrkvksa ij fd;k tkrk gSAbl laca/ esa fuEufyf[kr esa ls dkSu&lk (ls) izdFku lR; gS (gSa)\

(a) fdlh fn, x, 'kfDr Lrj osQ laxr izokfgr /kjk fuEu gksrh gSA

(b) /kjk fuEu gksus dk vFkZ 'kfDr k; de gksuk gSA

(c) izs"k.k osQ fy, irys rkjksa dk mi;ksx fd;k tk ldrk gSA

(d) xzkgh osQUnz ij vipk;h VªkUliQkWeZj dk mi;ksx djosQ oksYVrk de djuk vklkugksrk gSA

7.11 fdlh LCR ifjiFk esa ifjpkyd lzksr ls ifjpkfyr nkssfy=k dks LFkkukUrfjr 'kfDrP = I2Z cos φ gSA

(a) ;gk¡] 'kfDr xq.kkad cos 0. 0Pφ ≥ ≥

(b) oqQN izdj.kksa esa ifjpkyd cy nksfy=k dks dksbZ 'kfDr iznku ugha dj ldrk(P = 0)A

(c) ifjpkyd cy nksfy=k ls mQtkZ dks ckgj ugha fudky (P < 0) ldrkA

(d) ifjpkyd cy nksfy=k ls mQtkZ ckgj ys tk ldrk gSA

7.12 tc 220 V dh ac oksYVrk la/kfj=k C ij yxkbZ tkrh gS] rks

(a) bldh IysVksa osQ chp vf/dre oksYVrk 220 V gksrh gSA

(b) /kjk rFkk vuqiz;qDr oksYVrk leku dyk esa gksrh gSaA

23/04/18

izR;korhZ /kjk

45

(c) IysVksa ij vkos'k oksYVrk leku dyk esa gksrh gSA

(d) la/kfj=k dks iznku dh xbZ 'kfDr 'kwU; gksrh gSA

7.13 lM+d osQ [kEcs ls vkiosQ ?kj rd fo|qr 'kfDr ys tkus okys rkj

(a) esa izokfgr vkSlr /kjk 'kwU; gksrh gSA(b) dh vkSlr oksYVrk 220 V gksrh gSA(c) dh oksYVrk vkSj /kjk dh dyk esa 90° dk vUrj gksrk gSA

(d) dh oksYVrk vkSj /kjk esa laHkkfor dyk&vUrj φ bl izdkj gksrk gS fd <2

πφ


7.14 ;fn fdlh LC ifjiFk dks vkorhZ nksyudkjh fLaizx&CykWd iz.kkyh osQ rqY; le>k tkrkgS rc bl LC ifjiFk dh dkSu lh mQtkZ fLFkfrt mQtkZ osQ vkSj dkSu lh xfrt mQtkZosQ rqY; gksxh\

7.15 vR;qPp vko`fÙk ij fp=k 7.1 esa n'kkZ, x, ifjiFk dk izHkkoh rqY; ifjiFk cukb, vkSjbldh izHkkoh izfrck/k Kkr dhft,A

fp=k 7.2

~

R1

C1

L1

L2

R2

C2

R3

~

R

~

R C L

(a) (b)

7.16 fp=k 7.2 (a) ,oa (b) esa n'kkZ, x, ifjiFkksa dk vè;;u dhft, vkSj fuEufyf[kr iz'uksaosQ mÙkj nhft, %

(a) fdu n'kkvksa esa nksuksa ifjiFkksa esa rms /kjk leku gksxh\

(b) D;k ifjiFk (a) ls ifjiFk (b) esa rms /kjk vf/d gks ldrh gS\

fp=k 7.1

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46

7.17 D;k dHkh fdlh ac lzksr dk rkRkf.kd 'kfDr fuxZe ½.kkRed gks ldrk gS\ D;kvkSlr 'kfDr fuxZe ½.kkRed gks ldrk gS\

7.18 fp=k 7.3 esa LCR Js.kh ifjiFk osQ fy, ω vkSj Imax

osQ chp xzkiQ n'kkZ;k x;k gSA fp=kls cSaM pkSM+kbZ Kkr dhft, vkSj xzkiQ ij bls vafdr dhft,A

fp=k 7.4

–3

1

0

2

–1

–2

3

T 2T

t

IA(

)

v,

i, P

A

B

Ct

fp=k 7.5

.5 1.0 1.5 2.0

0.5

1.0

0

w(rad/s)

I (A)m

fp=k 7.3

7.19 fdlh ifjiFk dh ac /kjk dks fp=k 7.4 esa n'kkZ, xzkiQ kjk fu:fir fd;k tkrk gSAbl xzkiQ ij rms /kjk n'kkZb,A

7.20 iznk;h lzksr dh vko`fÙk vR;Yi ls èkhjs&èkhjs vR;fèkd eku rd c<+k, tkus ij mldyk dks.k φ osQ fpg~u esa D;k ifjorZu gksxk tks LCR Js.kh ifjiFk esa iznk;h oksYVrkèkkjk ls vxz gS\

y?kqmÙkjh; (SA)

7.21 dksbZ ;qfDr ‘X’ fdlh ac lzksr ls tqM+h gSA,d iw.kZ pozQ esa oksYVrk] /kjk ,oa 'kfDrosQ ifjorZu fp=k 7.5 esa n'kkZ, x, gSa%

(a) dkSu lk oozQ ,d iw.kZ pozQ esa'kfDr&k; n'kkZrk gS\

(b) ,d iw.kZ pozQ esa vkSlr mieqDr'kfDr fdruh gS\

(c) ;qfDr ‘X’ dh igpku dhft,A

7.22 izR;korhZ /kjk rFkk fn"V/kjk nksuksa dks gh ,fEi;j esa ekik tkrk gSA ijUrq] izR;korhZ èkkjkosQ fy, ,fEi;j dh ifjHkk"kk dSls dh tkrh gS\

7.23 0.01 gsujh izsjdRo rFkk 1 vkse izfrjks/ dh dksbZ oqQaMyh 200 oksYV] 50 gV~Z”k osQac 'kfDr iznk; ls tksM+h xbZ gSA ifjiFk dh izfrck/k rFkk vf/dre izR;korhZ oksYVrk,oa /kjk osQ chp dky&i'prk ifjdfyr dhft,A

23/04/18

izR;korhZ /kjk

47

7.24 60 okV dk dksbZ yksM fdlh ,sls VªkUliQkWeZj dh frh;d oqaQMyh ls tksM+k x;k gSftldh izkFkfed oqQaMyh ykbu oksYVrk ls tqM+h gSA ;fn yksM esa 0.54A èkkjk izokfgrgks jgh gks] rks izkFkfed oqaQMyh esa fdruh /kjk izokfgr gks jgh gSA ;gk¡ iz;qDrVªkUliQkWeZj osQ izdkj ij fVIi.kh dhft,A

7.25 Li"V dhft, fd laèkkfj=k kjk iznÙk izfr?kkr izR;korhZ /kjk dh vko`fÙk esa o`f¼ djusij de D;ksa gks tkrk gS\

7.26 Li"V dhft, fd fdlh izsjd kjk iznÙk izfr?kkr izR;korhZ oksYVrk dh vko`fÙk esa o`f¼djus ij D;ksa c<+rk gS\

nh?kZmÙkjh; (LA)

7.27 dksbZ oS|qr ;qfDr rms oksYVrk 223V = 50,000 v dh ac esUl ls 2kW 'kfDr

ysrh gSA /kjk] oksYVrk dh rqyuk esa dyk –3tan

4

φ φ =

dk vUrj (i'prk)

n'kkZrh gSA (i) R, (ii) XC – X

L, rFkk (iii) I

M. Kkr dhft,A fdlh vU; ;qfDr osQ fy,

R, XC ,oa X

L osQ eku blosQ nks xqus gSaA bl ;qfDr osQ fy, mÙkj fdl izdkj izHkkfor

gksaxs\

7.28 fdlh 'kfDr osQUnz ls 1MW 'kfDr 10 km nwj fLFkr fdlh 'kgj dks iznku dh tkuhgSA dksbZ O;fDr bl mn~ns'; osQ fy, 0.5 cm f=kT;k osQ rk¡cs osQ rkjksa osQ tksM+s dkmi;ksx djrk gSA lapfjr 'kfDr dh vkseh; kfr osQ va'k dk ifjdyu dhft, tcfd

(i) 'kfDr izs"k.k 220V ij fd;k tkrk gSA bl fLFkfr dh O;ogk;Zrk ij fVIi.khdhft,A

(ii) fdlh mPpk;h VªkUliQkWeZj kjk oksYVrk 11000 oksYV rd c<+k dj 'kfDr lapj.kfd;k tkrk gS vkSj fiQj vipk;h VªkUliQkWeZj kjk oksYVrk dks 220 V fd;k tkrkgSA ρ = × –8

( 1.7 10 )Cu SI

7.29 fp=k 7.6 esa n'kkZ, x, LCR ifjiFk ij fopkj dhft,A usV /kjk i rFkk i dh dyk dk

ifjdyu dhft,A n'kkZb, fd v

iZ

= A bl ifjiFk dh izfrck/k Z Kkr dhft,A

7.30 ω vkofÙk ij izpkfyr fdlh LCR ifjiFk dks fuEu lehdj.k kjk O;Dr fd;k x;k gS%

sini m

di qL Ri v v t

dt C+ + = = ω

23/04/18


48

1. lehdj.k dks i ls xq.kk dhft, vkSj tgk¡ laHko gks] ljy dhft,A

2. izR;sd in dh HkkSfrd O;k[;k dhft,A

3. mQtkZ lajk.k osQ izdFkuksa osQ :i esa lehdj.k dks O;Dr dhft,A

4. ,d pozQ osQ fy, lehdj.k dks lekdfyr dhft, ftlls ;g Li"V gks fd v,oa i osQ chp dyk&vUrj U;wu dks.k gksuk pkfg,A

7.31 fp=k 7.7 esa n'kkZ, x, LCR ifjiFk esa ifjpkyd ac oksYVrk v = vm sin ωt gSA

(i) q(t ) osQ fy, xfr dk lehdj.k fyf[k,A

(ii) t = t0 ij oksYVrk lzksr dk;Z djuk cUn dj nsrk gS vkSj R y?kqifFkr gks tkrk gSA

Kkr dhft, fd L vkSj C esa izR;sd esa fdruh fdruh mQtkZ laxzfgr gksrh gSA

(iii) vkos'kksa dh blosQ ckn dh xfr dk o.kZu dhft,A

C

R L

fp=k 7.7

R

LC

i2

i1

i

v sin tm

w

C

fp=k 7.6

23/04/18

fo|qr pqEcdh; rjaxsa


8.1 dkcZu eksuksDlkbM osQ ,d v.kq dks dkcZu ,oa vkWDlhtu ijek.kqvksa esa fo?kfVr djus osQfy, 11eV mQtkZ dh vko';drk gksrh gSA bl fo?kVu osQ fy, mi;qDr oS|qrpqEcdh;fofdj.k dh U;wure vko`fÙk gksrh gS %

(a) n`'; ks=k esa

(b) vojDr ks=k esa

(c) ijkcSaxuh ks=k esa

(d) ekbozQksrjax ks=k esa

8.2 ,d jSf[kdr% /zqfor oS|qrpqEcdh; rjax tks ( )ˆcos – tkz= ωEo

E i kjk fu:fir dh

tk ldrh gS] fdlh vuUr foLrkj dh iw.kZ ijkorZd nhokj ij vkifrr gS tks –z=a ijfLFkr gSA ;g ekurs gq, fd nhokj izdk'kdh; :i ls vfozQ; gS ijkofrZr rjax dks fy[kldrs gSa %

vè;k; 8


23/04/18


50

(a) ( )ω= ˆ– cos – toE kzrE i

(b) ( )ω= +ˆ cos toE kzrE i

(c) ( )ω= +ˆ– cos toE kzrE i

(d) ( )ω= ˆ sin – toE kzrE i

8.3 mQtkZ ÝyDl 20 W/cm2 dk izdk'k ,d vijkorhZ i`"B ij vfHkyEcor~ vkifrr gksrkgSA ;fn i`"B dk ks=kiQy 30 cm2 gks rks 30 feuV esa (iw.kZ vo'kks"k.k osQ fy,) iznÙkoqQy laosx gksxk %

(a) 36 × 10–5 kg m/s

(b) 36 × 10–4 kg m/s

(c) 108 × 104 kg m/s

(d) 1.08 × 107 kg m/s

8.4 100 W osQ cYc ls 3 m dh nwjh ij igq¡pus okys fofdj.kksa ls mRiUu fo|qr ks=k dhrhozrk E gSA mruh gh nwjh ij 50 W osQ cYc ls vkus okys izdk'k osQ fofdj.kksa osQdkj.k mRiUu fo|qr ks=k dh rhozrk gksxh %

(a)2

E

(b) 2E

(c)2

E

(d) 2E

8.5 ;fn E ,oa B ozQe'k% oS|qrpqEcdh; rjaxksa osQ fo|qr ,oa pqEcdh; ks=k (lfn'k) gksa rksoS|qrpqEcdh; rjaxksa dh lapj.k fn'kk gS %

(a) E osQ vuqfn'k

(b) B osQ vuqfn'k

(c) B × E osQ vuqfn'k

(d) E × B osQ vuqfn'k

8.6 oS|qrpqEcdh; rjax dh rhozrk esa fo|qr ,oa pqacdh; ks=k ?kVdksa osQ ;ksxnkuksa dk vuqikrgksrk gS %

(a) c : 1

(b) c2 : 1

(c) 1 : 1

23/04/18


51

(d) :1c

8.7 ,d f/zqo ,s.Vsuk ls EM rjaxsa ckgj dh vksj fofdfjr gksrh gSa ftuosQ fo|qr ks=k lfn'kdk vk;ke E

0 gSA fo|qr ks=k E

0, tks mQtkZ lapkj dk izeq[k okgd gS] lzksr ls nwjh osQ

lkFk bldk ifjek.k

(a) 3

1

r osQ vuqlkj ?kVrk gS

(b) 2

1


(c)1


(d) vpj cuk jgrk gS


8.8 dksbZ oS|qrpqEcdh; rjax ( ) ( )cos t1 2E + E kz= − ωE fuokZr esa z fn'kk osQvuqfn'k xfreku gSA fuEu esa ls lgh fodYi pqfu, %

(a) lEc¼ pqEcdh; ks=k dks fy[k ldrs gSa% ( )1 ˆ ˆc 1 2E – E=B i j cos (kz-ωt)

(b) lEc¼ pqEcdh; ks=k dks fy[k ldrs gaS% ( )ˆ ˆ1 2

1E – E

c=B i j cos (kz-ωt)

(c) fn;k x;k oS|qrpqEcdh; ks=k o`Ùkr% /zqfor gS

(d) nh xbZ oS|qrpqEcdh; rjax lery esa /zqfor gS

8.9 z-vk osQ vuqfn'k xeu djrh gqbZ ,d oS|qrpqEcdh; rjax dks =0

E E cos (kz -

ωt.) ls fu:fir djrs gSaA fuEufyf[kr esa lgh fodYi dk p;u dhft, %

(a) lEc¼ pqEcdh; ks=k dks fy[k ldrs gSa% 1 1ˆ ˆ= × = ( × )c ω

B k E k E

(b) lEc¼ pqEcdh; ks=k osQ inksa esa oS|qrpqEcdh; ks=k dks fy[k ldrs gSa %

E = c ˆ( )×B k

(c) ˆ ˆ. 0, 0= =k E k B.

(d) ˆ ˆ0, 0× = × =k E k B

8.10 x fn'kk osQ vuqfn'k lapfjr gksrh gqbZ fdlh lery oS|qrpqEcdh; rjax osQ E ,oa BosQ fuEufyf[kr ?kVd ;qxy laHko gSa %

(a) Ex, B

y

(b) Ey, B

z

23/04/18


52

(c) Bx, E

y

(d) Ez, B

y

8.11 dksbZ vkosf'kr d.k viuh ekè; larqyu fLFkfr osQ nksuksa vksj 109 Hz vko`fÙk osQ nksyudjrk gSA blls mRiUu oS|qrpqEcdh; rjaxksa

(a) dh vko`fÙk 109 Hz gksxh

(b) dh vko`fÙk 2 × 109 Hz gksxh

(c) dh rjaxnS?;Z 0.3 m gksxh

(d) osQ fofdj.k jsfM;ks rjaxksa osQ ks=k esa gksaxs

8.12 oS|qrpqEcdh; rjaxksa dk lzksr gks ldrk gS dksbZ vkos'k

(a) tks fu;r osx ls py jgk gksA

(b) tks o`Ùkh; dkk esa py jgk gksA

(c) tks fojkekoLFkk esa gksA

(d) tks fo|qr ks=k esa fxj jgk gksA

8.13 I rhozrk dh dksbZ oS|qrpqEcdh; rjax fuokZr esa j[ks ,d i`"B ij Vdjkrh gS vkSj blij fofdj.k nkc p vkjksfir djrh gSA fuEufyf[kr esa dkSu ls dFku lR; gSa\

(a) ;fn rjax iw.kZr% vo'kksf"kr gks tk, rks fofdj.k nkc gS I/c

(b) ;fn rjax iw.kZr% ijkofrZr gks tk, rks fofdj.k nkc gS I/c

(c) ;fn rjax iw.kZr% ijkofrZr gks tk, rks fofdj.k nkc gS 2I/c

(b) okLrfod i`"Bksa osQ fy, fofdj.k nkc dk ijkl gS I/c < p < 2I/c


8.14 fdlh lqokg~; jsfM;ks dk izlkjd LVs'ku osQ lkisk vfHkfoU;kl egRoiw.kZ D;ksa gksrk gS\

8.15 ekbozQksoso vksou ty v.kq ;qDr [kk| inkFkZ dk mQ"eu lokZf/d izHkkoh <ax ls D;ksadjrk gS\

8.16 fdlh lekUrj IysV la/kfj=k ij vkos'k q = q0 cos 2πνt osQ vuqlkj ifjofrZr gksrk gSA

bldh IysVsa cgqr fo'kky (ks=kiQy = A) gSa vkSj ,d nwljs osQ cgqr ikl&ikl j[khgSa (iFkdu = d)A dksj izHkkoksa dks ux.; ekurs gq, la/kfj=k esa foLFkkiu /kjk dh x.kukdhft,A

8.17 ifjorZuh; vko`fÙk dk ,d a.c. lzksr ,d la/kfj=k ls tqM+k gSA vko`fÙk esa deh djusij foLFkkiu /kjk fdl izdkj izHkkfor gksxh\

23/04/18


53

8.18 fdlh iwjiznhfIr (ÝyM ykbV) dh vksj vfHkeq[k ,d fiQYVj ls fuxZfer gksus okys fdj.kiqat dk pqEcdh; ks=k B

y = 12 × 10–8 sin (1.20 × 107 z – 3.60 × 1015 t ) T gSA

bl fdj.k iqat dh vkSlr rhozrk fdruh gS\

8.19 ikW;fUaVx osDVj S ,d ,slk osDVj gksrk gS ftldk ifjek.k rjax dh rhozrk osQ cjkcjgksrk gS rFkk ftldh fn'kk rjax dh xeu fn'kk osQ vuqfn'k gksrh gSA xf.krh; :i lsbldks O;Dr djrs gSa]

0

1

µ= ×S E B A S vkSj t esa [khaps x, xzkiQ dh izo`Qfr n'kkZb,A

8.20 izksisQlj lh- oh- je.k us ,d ikjn'khZ fuokZfrr izdks"B esa ,d NksVh gydh xsan dks ystjiaqt ls izdkf'kr dj Lora=krkiwoZd fcuk vk/kj osQ Bgjk dj fn[kk;k vkSj viusfo|kfFkZ;ksa dks vk'p;Zpfdr dj fn;kA os oS|qrpqEcdh; rjaxksa osQ fdl xq.k dks iznf'kZrdj jgs Fks\ bl xq.k dk ,d vkSj mnkgj.k nhft,A

y?kqmÙkjh; (SA)

8.21 n'kkZb, fd fdlh lekUrj IysV la/kfj=k dks vkosf'kr djrs le; mldh IysVksa osQ chp

fdlh fcUnq ij pqEcdh; ks=k B dk eku gksxk 0 r d

2 d

E

t

ε µ (tgk¡ laosQr vius lkekU;

vFkZ esa mi;ksx esa yk, x, gSaA)

8.22 oS|qrpqEcdh; rjaxsa ftudh rjaxnS?;Z

(i) λ1 gS] mixzg lapkj esa iz;qDr gksrh gSaA

(ii) λ2 gS] ty 'kksf/=kksa esa thok.kquk'k osQ fy, iz;qDr gksrh gSaA

(iii) λ3 gS] Hkwfexr ikbi ykbuksa esa rsy osQ fjlko osQ lalwpu osQ fy, mi;ksx esa ykbZ

tkrh gSaA

(iv) λ4 gS] /qa/ vkSj dksgjs dh fLFkfr esa ok;q;ku mM+ku iFk ij n`';rk esa lq/kj ykus

osQ fy, mi;ksx esa ykbZ tkrh gSaA

(a) bu oS|qrpqEcdh; fofdj.kksa dks igpkfu, vkSj crkb, fd ;s oS|qrpqEcdh; LisDVªeosQ fdl Hkkx ls lacaf/r gSaA

(b) bu rjaxnS?;ks± dks ifjek.k osQ c<+rs ozQe esa O;ofLFkr dhft,A

(c) izR;sd dh ,d vU; mi;ksfxrk fyf[k,A

8.23 n'kkZb, fd fofdj.k ÝyDl ?kuRo ‘S’ dk ,d iw.kZ pozQ dky ‘T’ esa vkSlr eku

23/04/18


54

xV

y

L

a

x

20

0

1S

2cE=

µ kjk O;Dr gksrk gSA

8.24 vkidks ,d 2µF dk lekUrj IysV la/kfj=k fn;k x;k gSA vki bldh IysVksa osQ chposQ vUrjky esa 1mA dh rkRkf.kd foLFkkiu /kjk oSQls LFkkfir djsaxs\

8.25 n'kkZb, fd I rhozrk dh EM rjax osQ kjk fuokZr esa j[ks fdlh i`"B ij yxk;k x;kfofdj.k nkc I/c gksrk gSA

8.26 fdlh cYc ls mRl£tr izdk'k dks nksxquh nwjh ij izkIr fd;k tk, rks bldh rhozrk fdlizdkj izHkkfor gksxhA dksbZ ystj iqat tc dejs dh yEckbZ osQ ,d fljs ls nwljs fljsij tkrk gS rc bldh rhozrk rRor% vpj jgrh gSA ystj fdj.k iqat dk og dkSu lkT;kferh; vfHkyk.k gS tks bldh rhozrk vpj cuk, j[kus osQ fy, mÙkjnk;h gS vkSjtks cYc ls vkus okys izdk'k esa ugha gksrkA

8.27 ;|fi fo|qr ks=k E vkosf'kr d.k ij cy q E vkjksfir djrk gS rFkkfi fdlh

oS|qrpqEcdh; rjax dk fo|qr ks=k fofdj.k nkc esa ;ksxnku ugha djrk ij mQtkZLFkkukUrfjr djrk gSA le>kb, fd ,slk D;ksa gksrk gS\

nh?kZmÙkjh; (LA)

8.28 ,d vuUr yEckbZ dk iryk rkj] ftldk ,dleku jSf[kd fLFkj vkos'k ?kuÙo λ gS]z-vk osQ vuqfn'k j[kk gS (fp=k 8.1)A bl rkj dks bldh yEckbZ osQ vuqfn'k

,dleku osx ˆ=v ezv ls xfr nh tkrh gSA ikW;fUVax osDVj o

1( )= ×

µS E B dk

ifjdyu dhft,A

8.29 vko`fÙk ν = 4 × 108 Hz osQ fy, leqnz ty dh oS|qr ikjxE;rk ε ≈ 80 εo,

pqEcd'khyrk µ ≈ µo rFkk izfrjks/drk ρ = 0.25 Ω–m gSA ,d lekUrj iV~fVdk

laèkkfj=k osQ laca/ esa fopkj dhft, ftldks leqnz ty essa Mqck dj j[kk gqvk gS vkSjizR;korhZ oksYVrk lzksr V(t ) = V

o sin (2π νt) kjk izpkfyr fd;k x;k gSA foLFkkiu

èkkjk ?kuRo] pkyu /kjk ?kuRo dk dkSu lk Hkkx gS\

8.30 l yEckbZ dh ,d yEch lh/h osQfcy lefer :i ls z-vk osQ vuqfn'k j[kh gS vkSjbldh f=kT;k a(<<l) gSA osQfcy esa ,d iryk rkj gS rFkk ,d lg&vkh; pkydufydk gSA ,d izR;korhZ /kjk I(t) = I

o sin (2πνt) osQUnzh; irys rkj ls izokfgr gksdj

lgvkh; pkyd ufydk osQ vuqfn'k okfil vkrh gS osQfcy osQ Hkhrj] rkj ls s nwjh

fp=k 8.1

23/04/18


55

ij izsfjr fo|qr ks=k s

s t I vta

o oˆ( , ) cos(2 ) In

= µ ν π

E k gSA

(i) osQfcy osQ vUnj foLFkkiu /kjk ?kuRo dk ifjdyu dhft,A

(ii) osQfcy osQ ifjPNsn ij foLFkkiu /kjk ?kuRo dks lekdfyr dhft, vkSj oqQyfoLFkkiu /kjk Id ls rqyuk dhft,A

(iii) pkyu /kjk Io dh foLFkkiu /kjk d

oI ls rqyuk dhft,A

8.31 fuokZr esa z fn'kk osQ vuqfn'k xeu'khy ,d lery oS|qrpqacdh; rjax dks

0ˆsin( – )E kz tω=E i rFkk ˆsin( – )0B kz tω=B j kjk iznf'kZr fd;k

x;k gS (fp=k 8.2)A

(i) fp=k esa n'kkZ, x, vk;rkdkj ywi 1234 ij .∫ E dl dk eku Kkr

dhft,A

(ii) ywi 1234 kjk f?kjs i`"B osQ fy, .∫B ds dk eku Kkr dhft,A

(iii) lehdj.k B–d.

dt=∫ E dl

φ dk mi;ksx djosQ fl¼ dhft,

0

0

cE

B=

(iv) blh izdkj dh izfozQ;k rFkk lehdj.k E0 0

d.

dI

t= +

φµ εB dl dk mi;ksx

djosQ fl¼ dhft, fd 0 0

1c =

µ ε

8.32 z fn'kk osQ vuqfn'k xfreku ,d lery oS|qrpqacdh; rjax dks 0

ˆsin( – )E kz tω=E i

rFkk 0

ˆsin( – )B kz t=B jω kjk of.kZr fd;k x;k gSA n'kkZb, fd%

(i) rjax dk vkSlr mQtkZ ?kuRo gS%

22 0

av 0 0

0

B1 1

4 4u E= +ε

µ

(ii) rjax dh dky&vkSlr rhozrk gS%

2

av 0 0

1c

2I E= ε

fp=k 8.2

23/04/18


9.1 fdlh fiz”e osQ ,d viorZd iQyd ij dks.k θ cukrs gq, vkifrr gksus okyh ,d izdk'kfdj.k nwljs iQyd ls vfHkyEcr% fuxZr gksrh gSA ;fn fiz”e dk dks.k 5° gS rFkk fiz”e1.5 viorZukad osQ inkFkZ dk cuk gS] rks vkiru dks.k gS

(a) 7.5°

(b) 5°

(c) 15°

(d) 2.5°

9.2 'osr izdk'k dk ,d y?kq Lian ok;q ls dk¡p osQ ,d LySc ij yEcor vkifrr gksrk gSALySc ls xq”kjus osQ i'pkr~ lcls igys fuxZr gksus okyk o.kZ gksxk

(a) uhyk

(b) gjk

(c) cSaxuh

(d) yky

vè;k; 9

fdj.k izdkf'kdh ,oaizdkf'kd ;a=k

23/04/18

fdj.k izdkf'kdh ,oa izdkf'kd ;a=k

57

9.3 ,d fcac fdlh vfHklkjh ysal osQ ckbZa vksj ls 5 m/s dh ,dleku pky ls mixeudjrk gS vkSj iQksdl ij tkdj #d tkrk gSA izfrfcac

(a) 5 m/s dh ,dleku pky ls ysal ls nwj xfr djrk gSA

(b) ,dleku Roj.k ls ysal ls nwj xfr djrk gSA

(c) vleku Roj.k ls ysal ls nwj xfr djrk gSA

(d) vleku Roj.k ls ysal dh vksj xfr djrk gSA

9.4 ok;q;ku esa dksbZ ;k=kh

(a) dHkh Hkh bUnz/uq"k ugha ns[k ikrk gSA

(b) izkFkfed rFkk frh;d bUnz/uq"k dks laosQUnzh o`Ùkksa osQ :i esa ns[k ikrk gSA

(c) izkFkfed rFkk frh;d bUnz/uq"k dks laosQUnzh vkoZQ osQ :i esa ns[k ikrk gSA

(d) dHkh Hkh frh;d bUnz/uq"k ugha ns[k ikrk gSA

9.5 vkidks izdk'k osQ pkj lzksr fn, x, gSa] ftuesa ls izR;sd ls ,dy o.kZ&yky] uhyk] gjkrFkk ihyk izdk'k feyrk gSA eku yhft, ihys izdk'k osQ ,d fdj.k iaqt osQ fy, nksekè;eksa osQ varjki`"B ij fdlh fo'ks"k vkiru dks.k osQ fy, laxr viorZu dks.k 90°

gSA ;fn vkiru dks.k dks ifjofrZr fd, cxSj ihys izdk'k lzksr dks nwljs izdk'k lzksrksa lscny fn;k tk, rks fuEufyf[kr dFkuksa esa ls dkSu lk dFku lgh gS\

(a) yky izdk'k osQ fdj.k iaqt esa iw.kZ vkUrfjd ijkorZu gksxkA

(b) nwljs ekè;e esa viofrZr gksus ij yky izdk'k dk fdj.k iaqt vfHkyac dh vksj eqM+tk,xkA

(c) uhys izdk'k osQ fdj.k iqat esa iw.kZ vkUrfjd ijkorZu gksxkA

(d) nwljs ekè;e esa viofrZr gksus ij gjs izdk'k dk fdj.k iqat vfHkyac ls nwj dh vksjeqM+ tk,xkA

9.6 fdlh lery mÙky ysal osQ oozQ i`"B dh oozQrk f=kT;k 20 cm gSA ;fn ysal osQ inkFkZdk viorZukad 1.5 gks] rks ;g

(a) mu fcacksa osQ fy, gh mÙky ysal dh Hkk¡fr dk;Z djsxk tks blosQ ofozQr Hkkx dhvksj fLFkr gSaA

(b) ofozQr Hkkx dh vksj fLFkr fcacksa osQ fy, vory ysal dh Hkk¡fr dk;Z djsxkA

(c) bl ckr dk è;ku fd, fcuk fd fcac blosQ fdl Hkkx dh vksj fLFkr gS] mÙkyysal dh Hkk¡fr dk;Z djsxkA

(d) bl ckr dk è;ku fd, fcuk fd fcac blosQ fdl Hkkx dh vksj fLFkr gS] voryysal dh Hkk¡fr dk;Z djsxkA

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58

1

2

C

P3

F

Q 4

9.7 vk;u eaMy (vk;uksfLi+Q;j) kjk jsfM;ks rjaxksa osQ ijkorZu esa lfEefyr ifj?kVuk

(a) lery niZ.k kjk izdk'k osQ ijkorZu osQ leku gSA

(b) ejhfpdk osQ le; ok;q esa gksus okys izdk'k osQ iw.kZ vkarfjd ijkorZu osQ leku gSA

(c) bUnz/uq"k osQ curs le; ty osQ v.kqvksa kjk izdk'k osQ ifjksi.k (o.kZ&foksi.k)osQ leku gSA

(d) ok;q osQ d.kksa kjk izdk'k osQ izdh.kZu osQ leku gSA

9.8 fdlh vory niZ.k ij vkifrr izdk'k fdj.k dh fn'kk PQ kjk n'kkbZ xbZ gS tcfdijkorZu osQ i'pkr~ ftu fn'kkvksa esa ;g fdj.k xeu dj ldrh gS og 1, 2, 3 rFkk4 kjk fpfÉr pkj fdj.kksa (fp=k 9.1) kjk n'kkZbZ xbZ gSA pkjksa fdj.kksa esa ls dkSu lhfdj.k ijkofrZr fdj.k dh fn'kk dks lgh n'kkZrh gS\

(a) 1

(b) 2

(c) 3

(d) 4

9.9 rkjihu dk izdkf'kd ?kuRo ty ls vf/d gS tcfd bldk nzO;eku ?kuRo ty lsde gSA fp=k 9.2 esa ,d crZu esa ty osQ mQij rkjihu dh ,d irZ rSjrh n'kkZbZ xbZgSA fp=k 9.2 esa rkjihu osQ mQij vkifrr pkj fdj.kksa esa ls fdldk iFk lgh n'kkZ;kx;k gS\

(a) 1

(b) 2

(c) 3

(d) 4

9.10 ,d lh/h lM+d ij dksbZ dkj 60 km h–1 dh ,dleku pky ls xfreku gSA i'pn`'; niZ.k ls ns[kus ij pkyd ikrk gS fd mldk ihNk dj jgh ,d dkj 100 m

nwjh ij gS rFkk 5 km h –1 dh pky ls mldh vksj vk jgh gSA ihNs vkrh gqbZ dkjij n`f"V j[kus osQ fy, pkyd izR;sd 2s osQ i'pkr~ viuh dkj osQ i'p n`'; rFkkik'oZ n`'; niZ.k esa ckjh&ckjh ls ns[kuk izkjEHk djrk gS] tc rd fd nwljh dkj vkxsugha fudy tkrhA ;fn nksuksa dkjsa viuh pkyksa dks cuk, j[krh gSa] rks fuEu dFku(dFkuksa) esa ls dkSu lk@ls dFku lgh gS\

fp=k 9.1

fp=k 9.2

1 2 3 4

ok;q

rkjihu

ty

23/04/18


59

(a) ihNs vkrh gqbZ dkj dh pky 65 km h–1 gSA

(b) vkxs py jgh dkj osQ pkyd dks ik'oZ n`'; niZ.k esa ihNs dh dkj5 km h–1 dh pky ls vkrh gqbZ izrhr gksxhA

(c) tSls&tSls dkjksa osQ chp nwjh ?kVrh tkrh gS i'p n`'; niZ.k esa] mldh vksj vkrhgqbZ dkj dh pky ?kVrh gqbZ izrhr gksrh gSA

(d) tSls&tSls dkjksa osQ chp nwjh ?kVrh tkrh gS ik'oZ n`'; niZ.k esa ikl vkrh gqbZ dkjdh pky c<+rh gqbZ izrhr gksrh gSA

9.11 iz;ksx'kkyk esa oqQN ,sls inkFkZ fodflr fd, x, gSa ftudk viorZukad Í.kkRed gksrkgS (fp=k 9.3)A ,sls ekè;e (ekè;e 2) esa ok;q (ekè;e 1) ls vkifrr ,d fdj.kfuEu esa ls fdl iFk dk vuqxeu djsxh\

i

r

1

2

i

r

1

2

1

2

(a) (b)

(d)(c)

i r 1

2


9.12 fdlh lery nzks.kh esa fy, x, ty esa Mwcs ,d foLrfjr fcac ij fopkj dhft,A tcnzks.kh dh dksj osQ lehi ls ns[kk tkrk gS rks fcac foo`Qr fn[kkbZ nsrk gS] D;ksafd

(a) dksj osQ fudVLFk fcUnqvksa dh vkHkklh xgjkbZ dksj ls nwjLFk fcUnqvksa dh rqyukesa de gSA

(b) vk¡[k ij fcac osQ izfrfcac kjk varfjr dks.k fcac kjk ok;q esa varfjr okLrfoddks.k ls NksVk gSA

(c) dksj ls cgqr nwjLFk fcac osQ oqQN fcanq iw.kZ vkarfjd ijkorZu osQ dkj.k fn[kkbZ ughansrsA

(d) nzks.kh esa ty ,d ysal dh Hkk¡fr dk;Z djrk gS vkSj fcac dks vkof/Zr djrk gSA

9.13 dk¡p osQ ,d vk;rkdkj xqVosQ ABCD dk viorZukad 1.6 gSA iQyd AB

(fp=k 9.4) osQ eè; esa ,d fiu j[kk x;k gSA iQyd AD ls izsfkr djus ij ;gfiu

A B

D C

fp=k 9.3

fp=k 9.4

23/04/18


60

(a) A osQ fudV izrhr gksxk

(b) D osQ fudV izrhr gksxk

(c) AD osQ eè; esa izrhr gksxk

(d) fcyoqQy fn[kkbZ ugha nsxk

9.14 izkFkfed rFkk frh;d bUnz/uq"k osQ chp ,d vnhIr iêðh gksrh gS ftls vySDtsUMjdh vnhIr iêðh dgrs gSaA ,slk blfy, gS fd

(a) bl ks=k esa izdhf.kZr izdk'k esa fouk'kh O;frdj.k gksrk gSA(b) bl ks=k esa izdk'k izdhf.kZr ugha gksrkA(c) bl ks=k esa izdk'k vo'kksf"kr gks tkrk gSA

(d) lw;Z osQ vkifrr izdk'k osQ lkisk izdhf.kZr fdj.kksa kjk vk¡[k ij cuk;k x;k dks.kyxHkx 42° vkSj 50° osQ chp gksrk gSA

9.15 ,d vko/Zd yssal dk iz;ksx blfy, fd;k tkrk gS ftlls fd ns[ks tkus okys fcac dkslkekU; fudV fcanq dh viskk us=k osQ vf/d lehi yk;k tk losQA blosQ iQyLo:i

(a) fcac kjk us=k ij varfjr dks.k cM+k gksrk gS vkSj bl izdkj bls vf/d foLrkj lsns[kk tkrk gSA

(b) vkHkklh lh/k izfrfcac curk gSA

(c) n`f"V ks=k esa o`f¼ gksrh gSA

(d) fudV fcUnq ij vuUr vko/Zu gksrk gSA

9.16 ,d [kxksyh; viorhZ nwjn'kZd osQ vfHkn`';d dh iQksdl nwjh 20 m rFkk usf=kdk dhiQksdl nwjh 2 cm gSA

(a) nwjn'kZd dh V~;wc dh yEckbZ 20.02 m gSA(b) vko/Zu kerk 1000 gSA(c) cuk gqvk izfrfcac myVk gSA(d) cM+s kjd dk vfHkn`';d izfrfcac dh |qfr dks c<+k,xk rFkk o.kZ foiFku dks de

djsxkA


9.17 D;k fdlh ysal dh yky izdk'k osQ fy, iQksdl nwjh uhys izdk'k osQ fy, mldhiQksdl nwjh ls vf/d gksxh] leku gksxh ;k de gksxh\

9.18 lkekU; O;fDr dh fudV n`f"V 25 cm gSA fdlh fcac dk dks.kh; vko/Zu 10 izkIrdjus osQ fy, lwen'khZ dh kerk fdruh gksuh pkfg,\

9.19 ,d vlefer iryk mHk;ksÙky ysal fdlh fcanq fcac dk izfrfcac vius vk ij cukrk

23/04/18


61

gSA ;fn ysal dk ik'oZ ifjorZu dj j[kk tk, rks D;k izfrfcac dh fLFkfr esa ifjorZu gksxk\

9.20 d1 > d

2 > d

3 ?kuRoksa rFkk µ

1 > µ

2 > µ

3 viorZukadksa osQ rhu vfeJ.kh; nzoksa dks ,d

chdj esa j[kk x;k gSA izR;sd nzo osQ LraHk dh mQ¡pkbZ 3

h gSA chdj dh iSanh ij ,d

fcUnq cuk;k x;k gSA lkekU; fudV n`f"V osQ fy, fcanq dh vkHkklh xgjkbZ Kkr dhft,A

9.21 fdlh dk¡p osQ fizT+e (µ = 3 ) osQ fy, U;wure fopyu dks.k fizT+e&dks.k osQ cjkcj

gSA fizT+e&dks.k dk eku Kkr dhft,A

y?kqmÙkjh; (SA)

9.22 fdlh vory niZ.k osQ eq[; vk osQ vuqfn'k iQksdl ls nwj] L yEckbZ dk ,d NksVkfcac j[kk x;k gSA fcac dh nwjh v gSA ;fn niZ.k dh iQksdl nwjh f gS rks izfrfcac dhyEckbZ fdruh gksxh\ vki L <<|v – f|eku ldrs gSaA

9.23 ‘R’ f=kT;k dh ,d o`rkdkj fMLd ‘a’ f=kT;k osQ ,d vikjn'khZ v/Zxksyh; dVksjs(ckmy) osQ vUnj lekkr% rFkk kSfrtr% j[kh gS (fp=k 9.5)A dVksj osQ dksj lsns[kus ij fMLd dk nwjLFk Nksj ek=k fn[kkbZ nsrk gSA dVksjs dks µ viorZukad osQ ikjn'khZnzo ls Hkjus ij fMLd osQ lehi dk Nksj Hkh n`f"Vlhek esa vk tkrk gSA fMLd dks dVksjsosQ mQijh fdukjs ls fdruk uhps j[kk x;k gS\

9.24 25 cm iQksdl nwjh osQ ,d irys mÙky ysal dks eq[; vk ls 0.5 cm mQij nks Hkkxksaesa dkVk tkrk gSA mQijh Hkkx dks (0,0) ij j[kk x;k gS rFkk ,d fcac dks(–50 cm, 0) ij j[kk x;k gSA izfrfcac osQ funsZ'kkad Kkr dhft,A

9.25 vusd izk;ksfxd O;oLFkkiuksa (lsV vi) esa lzksr rFkk ijns dks oqQN nwjh] (ekuk D)ij vkc¼ dj nsrs gSa rFkk ysal dks pyk;eku j[krs gSaA n'kkZb, fd ysal dhnks fLFkfr;ksa osQ fy, ijns ij izfrfcac cuk;k tk ldrk gSA bu fcUnqvksa(fLFkfr;ksa) osQ chp dh nwjh rFkk bu nks fcanqvksa osQ fy, izfrfcac osQ lkbtksadk vuqikr Kkr dhft,A

9.26 h mQ¡pkbZ osQ ,d tkj dks µ viorZukad osQ ,d ikjn'khZ nzo ls Hkjk x;k gS(fp=k 9.6)A tkj osQ osQUnz esa bldh iSanh ij ,d fcUnq cuk;k x;k gSA mlfMLd dk U;wure O;kl Kkr dhft, ftls tkj osQ osQUnz osQ b/j&m/j 'kh"kZi`"B ij leferr% j[kus ij fcUnq vn`'; gks tk,A

9.27 ,d fudV n`f"V nks"k;qDr o;Ld dk nwj fcanq 0.1 m ij gSA mldh leatukerk 4 MkbvkWIVj gSA (i) nwjLFk oLrqvksa dks ns[kus osQ fy, fdruh kerk osQ

O

90 - aa

a

a

A BC

id

Ma a

a

R R

fp=k 9.5

fp=k 9.6

d

O

hi i

23/04/18


62

y

x

qi

R

x

o

qi

qr

fp=k 9.7

ysalksa dh vko';drk gS\ (ii) cxSj p'es osQ lkFk mldk fudV fcanq fdruk gS\(iii) p'es osQ lkFk mldk fudV fcUnq fdruk gS\ (us=k osQ ysal ls n`f"ViVy (jsfVuk)rd izfrfcac nwjh 2 cm yhft,A)

nh?kZmÙkjh; (LA)

9.28 n'kkZb, fd viorZukad µ ≥ 2 osQ inkFkZ osQ fy,] fdlh Hkh dks.k ij vkifrr izdk'kvkiru iQyd ij yEc osQ vuqfn'k funsZf'kr gksaxsA

9.29 ,d yEcs mQèokZ/j LrEHk (vFkkZr] kSfrt foek,¡ << mQèokZ/j foek,¡) esa 'kq¼ nzorFkk ,d foy;u dk feJ.k foys; d.kksa dk folj.k mRiUu djrk gS vkSj bl izdkjmQèokZèkj foekvksa osQ vuqfn'k viorZukad izo.krk mRiUu gksrh gSA bl LrEHk esamQèokZèkj osQ yEcor izos'k djus okyh izdk'k fdj.k vius ewy iFk ls fopfyr gkstkrh gSA kSfrt nwjh d << h pyus esa gq, fopyu dks Kkr dhft,A ;gk¡ h LraHkdh mQ¡ pkbZ gSA

9.30 ;fn izdk'k fdlh LFkwy fiaM osQ ikl ls xqt+jrk gS rks xq#Roh; vU;ksU; fozQ;k osQ dkj.kfdj.k esa cadu gksrk gSA ,slk gksus dk dkj.k ekè;e osQ izHkkoh viorZukad esa ifjorZudks ekuk tk ldrk gSA ;g ifjorZu gksxk%

n(r) = 1 + 2 GM/rc2

tgk¡ r fopkjk/hu fcUnq dh LFkwy fiaM osQ nzO;eku osQUnz ls nwjh gS] G lkoZf=kdxq#Roh; fLFkjkad gS] M oLrq dk nzO;eku rFkk c fuokZr esa izdk'k dh pky gSA fiaMdks xksykdkj ekurs gq, fdj.k osQ vius ewy iFk ls fopyu dks Kkr dhft, tc ;gfiaM ls laLi'kZ djrh gqbZ fudyrh gSA

9.31 f=kT;k R dk ,d vR;f/d yEck csyu (flfyUMj) ,d vlk/kj.k vlkekU; inkFkZdk cuk gS ftldk viorZukad –1 gS (fp=k 9.7)A csyu dks nks ryksa osQ chp j[kkx;k gS ftuosQ vfHkyEc y fn'kk osQ vuqfn'k gSaA csyu dk osaQnz O, y&vk osQ vuqfn'kgSA fupys ry ls y fn'kk osQ vuqfn'k ,d ladh.kZ ys”kj fdj.k iaqt funZsf'kr dh tkrhgSA ys”kj lzksr y fn'kk esa O;kl ls kSfrt nwjh x ij gSA x dk ijkl Kkr dhft, ftllsfd fupys ry ls fudyus okyk izdk'k mQij osQ ry rd u igq¡p ik,A

9.32 (i) ,d lzksr (S) rFkk ,d izskd (O) osQ chp j[ks ,d ysal ij fopkj dhft,

(fp=k 9.8)A eku yhft, ysal dh eksVkbZ b

w b w2

0( ) –α

= osQ vuqlkj cnyrh

gS] tgk¡ b izdkf'kd osQUnz ls mQèokZ/j nwjh gS] 0w ,d fu;rkad gSaA iQjeSV osQ

23/04/18


63

fl¼kUr (vFkkZr fdlh fdj.k osQ fy, lzksr rFkk izskd osQ chpikjxeu dk le; pjeeku gksrk gS) dk mi;ksx djosQ 'krZ Kkrdhft, fd lzksr ls izkjEHk gksus okyh lHkh mikkh; fdj.ksa vk osQfcUnq O ij vfHklfjr gksaxhA ysal dh iQksdl nwjh Hkh Kkr dhft,A

(ii) xq#Roh; ysal dks fuEufyf[kr lw=kkuqlkj cnyrh gqbZ eksVkbZ dk ekuk tk ldrk gS%

21( )

kw b k ln

b

=

b

min < b < b

max

2

1

min

kk ln

b

=

b < b

min

n'kkZb, fd dksbZ izskd fcanq&fcac osQ izfrfcac dks ysal osQ osQUnz osQ fxnZ ,d oy;osQ :i esa ns[ksxk ftldh dks.kh; f=kT;k gksxh&

( ) 1– 1u

knv

u vβ =

+

P1

S u v O

b

fp=k 9.8

23/04/18

Exemplar Problems–Physics

P


10.1 fp=k 10.1 esa n'kkZ, ,d izdk'k fdj.k iqat ij fopkj djsa tks ok;q ls dk¡p dh flYyhij czwLVj dks.k ij vkifrr gksrh gS

fuxZr fdj.k osQ ekxZ esa fcanq P ij ,d iksysjkWbM j[kk x;k gS vkSj bls blosQ ry osQyEcor~ rFkk blosQ osaQnz ls xqtjus okyh vk osQ ifjr% ?kqek;k tkrk gSA

(a) ,d fof'k"V vfHkfoU;kl osQ fy, iksysjkWbM ls ns[kus ij va/sjk fn[kkbZ nsxkA

(b) iksysjkWbM ls ns[ks tkus okys izdk'k dh rhozrk ?kw.kZu ij fuHkZj ugha gksrhA

(c) iksyssjkWbM ls ns[ks tkus okyh izdk'k dh rhozrk iksysjkWbM osQ nks vfHkfoU;klksa osQfy, U;wure gksxh ysfdu 'kwU; ugha gksxhA

(d) iksysjkWbM ls ns[kus ij izdk'k dh rhozrk iksyssjkWbM osQ pkj vfHkfoU;klksa osQ fy,U;wure gksxhA

10.2 104 A pkSM+kbZ dh ,d f>jh ij vkifrr gksus okys lw;Z osQ izdk'k ij fopkj djsaA fNnzls ns[kus ij

(a) osQUnz ij 'osr o.kZ dh ,d iryh rh.k f>jh fn[kkbZ nsxhA

vè;k; 10

rjax&izdkf'kdh

fp=k 10.1

23/04/18

rjax izdkf'kdh

65

(b) osQUnz ij nhIr 'osr f>jh tSlk gksxk tks dksjksa ij 'kwU; rhozrk esa folfjr gks tk,xhA

(c) osQUnz ij nhIr 'osr f>jh tSlk gksxk tks fofHkUu o.kksZa osQ ks=kksa esa folfjr gks tk,xhA

(d) osQoy 'osr o.kZ dh folfjr f>jh fn[kkbZ nsxhA

10.3 ok;q ls dk¡p dh flYyh (viorZukad n] eksVkbZ d) ij θθθθθ. dks.k ij vkifrr gksusokyh ,d izdk'k fdj.k ij fopkj dhft,A dk¡p osQ 'kh"kZ i`"B rFkk ryh osQ i`"B lsijkofrZr gksus okyh fdj.kksa osQ chp dykUrj gS

(a)1/2

22

4 11 – sin θ

π + π

λ

d

n

(b)1/2

22

4 11 – sin

d

nθ

π

λ

(c)1/2

22

4 11 – sin

2d

nθ

π π +

λ

(d)1/2

22

4 121 – sin

d

nθ

π + π

λ

10.4 ;ax osQ ff>jh iz;ksx esa lzksr 'osr izdk'k dk gSA ,d fNnz dks yky fiQYVj ls <dfn;k x;k gSA bl voLFkk esa

(a) yky rFkk uhys jax osQ ,dkUrj O;frdj.k iSVuZ gksaxsA

(b) yky rFkk uhys jax osQ i`Fkd&i`Fkd lqLi"V O;frdj.k iSVuZ gksaxsA

(c) dksbZ Hkh O;frdj.k fizQtsa ugha gksaxhA

(d) yky jax ls cuk O;frdj.k iSVuZ uhys jax ls cus iSVuZ ls fefJr gksxkA

10.5 fp=k (10.2) esa S1, S

2 f>fj;ksa osQ lkFk ,d ekud ff>jh O;oLFkk dks n'kkZ;k x;k

gSA P1 rFkk P2, P osQ nksuksa vksj nks fufEu"B fcanq gSaA

ijns ij P2 ,d fNnz gS vkSj P

2 osQ ihNs ,d nwljh ff>jh O;oLFkk

S3 rFkk S

4 f>fj;ksa osQ lkFk gS vkSj muosQ ihNs ,d nwljk ijnk gSA

(a) nwljs ijns ij dksbZ O;frdj.k iSVuZ ugha gksxk fdUrq ogizdkf'kr gksxkA

(b) nwljk ijnk iw.kZ :i ls vnhIr gksxkA(c) nwljs ijns ij ,d ,dy nhIr fcUnq gksxkA(d) nwljs ijns ij ,d fu;fer ff>jh iSVuZ gksxkA

igyk inkZ

P1

P2

S3

S4

S1

S2

SP

nwljk inkZ

fp=k 10.2

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10.6 I1 rFkk I

2 rhozrk osQ nks lzksr S

1 rFkk S

2 ,d ijns osQ lkeus j[ks x, gSa

[fp=k 10.3 (a)]A osQUnzh; Hkkx esa ns[kk x;k rhozrk forj.k iSVuZ fp=k 10.3 (b) esafn;k x;k gSA

bl fLFkfr esa dkSu lk izdFku lR; gS\

(a) S1 rFkk S

2 dh rhsozrk,¡ leku gSaA

(b) S1 rFkk S2 esa ,d fu;r dykUrj gSA

(c) S1 rFkk S

2 leku dyk esa gSA

(d) S1 rFkk S

2 dh rjaxnS?;Z leku gSA

10.7 103 A

pkSM+kbZ osQ ,d lwphfNnz ij vkifrr lw;Z osQ izdk'k ij fopkj djsaA ijns ij

ns[kk tkus okyk lwphfNnz dk izfrfcac gksxk&

(a) ,d rh.k 'osr oy;

(b) T;kferh; izfrfcac ls fHkUu

(c) 'osr o.kZ dk folfjr osQUnzh; fcanq

(d) rh.k osQUnzh; 'osr fcanq osQ pkjksa vksj folfjr jaxhu ks=k

10.8 ,d y?kq lwphfNnz osQ foorZu iSVuZ ij fopkj dhft,A tc fNnz dk lkbt+ c<+k fn;ktkrk gS rks

(a) lkb”k ?kVrk gS

(b) rhozrk c<+rh gS

(c) lkb”k c<+rk gS

(d) rhozrk ?kVrh gS

10.9 ,d fcanq lzksr ls vilkfjr gksrs izdk'k osQ fy,

(a) rjaxkxz xksyh; gSA

(b) rhozrk] nwjh osQ oxZ osQ vuqikr esa ?kVrh gSA

(c) rjaxkxz ifjofy;d (iSjkcksyh;) gSA

(d) rajxkxz ij rhozrk nwjh ij fuHkZj ugha djrhA


10.10 D;k gkbxsal dk fl¼kar vuqnS?;Z èofu rajxksa osQ fy, oSèk gS\

10.11 fdlh vfHklkjh ysal osQ iQksdl fcanq ij fLFkr ,d fcanq ij fopkj dhft,A de

xx = 0

fp=k 10.3 (b)

x

S1

S2

fp=k 10.3 (a)

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iQksdl nwjh dk ,d nwljk vfHklkjh ysal blosQ nwljh vksj j[kk gSA vafre izfrfcac lsfudyus okys rjaxkxz dh izo`Qfr D;k gS\

10.12 lw;Z osQ izdk'k osQ fy, i`Foh ij rjaxkxz dh vko`Qfr oSQlh gksrh gS\

10.13 nSfud vuqHko esa izdk'k rjaxksa dh viskk èofu rjaxksa dk foorZu D;ksa vf/d izR;kgksrk gSA

10.14 ekuo us=k dk dks.kh; foHksnu yxHkx φ = × –45.8 10 rad gS rFkk ,d fof'k"V

iQksVksfizUVj U;wure 300 dpi (MkV~l izfr bap] 1 inch = 2.54 cm) Nkirk gSA,d Nis gq, i`"B dks fdl U;wure nwjh ij j[kk tk, fd mlesa i`Fkd fcanq u fn[kkbZnsaA

10.15 ,d iksysjkWbM (I) dks fdlh ,do.khZ lzksr osQ lkeus j[kk x;k gSA nwljk iksysjkWbMj (II)bl iksysjkWbM (I) osQ lkeus j[kk x;k gS rFkk bls ?kqek;k tkrk gS tc rd fd bllsdksbZ izdk'k ugha xqt+jrkA vc ,d rhljk iksysjkWbM (III), (I) rFkk (II) osQ chp j[kktkrk gSA D;k bl fLFkfr esa iksysjkWbM (II) ls izdk'k ckgj fudysxk\ O;k[;k dhft,A

y?kqmÙkjh; (SA)

10.16 D;k ijkorZu ls lery /zqfor izdk'k izkIr gksuk lEHko gS] ;fn izdk'k varjki`"B ijmPp viorZukad dh vksj ls vkifrr gksrk gS\

10.17 fdlh lwen'khZ kjk mlh vfHkn`';d osQ fy, nks fcUnqvksa esa Hksn djus osQ fy,]muosQ chp U;wure i`Fkduksa osQ vuqikr dks Kkr dhft, tcfd inkFkZ dks iznhIr

djus osQ fy, 5000 A

osQ izdk'k dk rFkk 100V ls Rofjr bysDVªkWuksa dk mi;ksx

fd;k x;k gks\

10.18 ,d ff>jh O;frdj.k O;oLFkk ij fopkj dhft, (fp=k 10.4) ftlesa f>fj;ksals ijns dh nwjh] f>fj;ksa osQ chp dh nwjh dh vk/h gksA ;fn ijns ij igykfufEu"B osQUnz O ls D nwjh ij gks rks D osQ eku dks λ inksa esa Kkr dhft,A

S1 T1

P

O

T2

S C

S2

inkZ

lzksr

fp=k 10.4

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68

R1 A B C

D

l/2

l/2 l/2

R2

nh?kZmÙkjh; (LA)

10.19 fp=k 10.5 esa ,d lzksr tks v/zqfor izdk'k mRl£tr djrk gS] ff>jh izcU/ n'kkZ;kx;k gSA P ,d iksysjkb”kj ftlosQ vk dh fn'kk ugha nh xbZ gSA iksysjkb”kj fo|ekugksus ij gS ;fn eqq[; mfPp"B dh rhozrk I

0 gS rc orZeku n'kk esa eq[; mfPp"B rFkklkFk gh izFke fufEu"B dh rhozrk Kkr dhft,A

10.20

P1

S1

S2

AC

q O

Ld

=/4 inkZ

AC = CO = D, S1C = S2C = d << D

1.5µ = osQ inkFkZ ls cuh ,d NksVh ikjn'khZ flYyh (Lysc) AS2 osQ vuqfn'k j[kh

gS (fp=k 10.6)A O ls vc izkIr eq[; mfPp"B rFkk eq[; ifV~Vdk dh vuqifLFkfresa izkIr mfPp"B osQ fdlh Hkh vksj izFke fufEu"B dh nwjh D;k gksxhA

10.21 fp=k esa n'kkZ, vuqlkj pkj le:i ,do.khZ lzksr A,B,C,D leku rjaxnS?;Z λ dh rjaxsamRiUu djrs gSa rFkk dyk lac¼ gSa (fp=k 10.7)A B ls leku nwjh ij nks vfHkxzkghR

1 rFkk R

2 gSa vkSj ;g nwjh cgqr vfèkd gSA

(i) nksuksa esa ls dkSu lk vfHkxzkgh c`gÙkj flXuy xzg.k djrk gS\(ii) tc B dks cUn dj fn;k tkrk gS rks nksuksa esa ls dkSu lk vfHkxzkgh cgrj flXuy

xzg.k djrk gS\(iii) tc D dks cUn dj fn;k tkrk gS rks nksuksa esa ls dkSu lk vfHkxzkgh cgÙkj flXuy

xzg.k djrk gS\(iv) nksuksa esa ls dkSu lk vfHkxzkgh Hksn dj ldrk gS fd B ;k D esa ls dkSu lk lzksr

cUn dj fn;k x;k gS\

10.22 fdlh ekè;e osQ izdkf'kd xq.k vkisfkd ijkoS|qrkad ε( )r

rFkk vkisfkd pqEcd'khyrk

(µr ) ls fu;af=kr gksrs gSaA viorZukad dks εµ =

r rn ls ifjHkkf"kr fd;k tkrk gSA

lkekU; inkFkZ osQ fy, rε > 0 rFkk µ

r > 0 vkSj oxZewy osQ fy, èkukRed fpg~u fy;k

fp=k 10.6

fp=k 10.7

S1

P

S

S2

1

2

fp=k 10.5

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69

tkrk gSA 1964 esa :lh oSKkfud oh- oslsykxks us ,sls inkFkZ osQ vfLrRo dh vfHk/kj.kk

dh ftuosQ fy, εr < 0 rFkk µ

r < 0A rc ls iz;ksx'kkyk esa ,sls inkFkZ mRiUu fd,

x, rFkk muosQ izdkf'kd xq.kksa dk vè;;u fd;k x;kA ,sls inkFkksZa osQ fy,

ε= µ–r r

n tc izdk'k bl izdkj osQ viorZukad osQ ekè;e essa izos'k djrk gS rks

;g lapj.k dh fn'kk ls nwj xeu djrk gSA

(i) mijksDr o.kZu osQ vk/kj ij n'kkZb, fd] ;fn ,sls ekè;e esa] ok;q (viorZukad=1) ls izdk'k dh fdj.ksa nwljs prqFkk±'k esa θ dks.k ij izos'k djrh gSa rks] viofrZrfdj.k iqat rhljs prqFkk±'k esa gksrh gSA

(ii) fl¼ dhft, fd ,sls ekè;e osQ fy, Lusy dk fu;e ykxw gksrk gSA

10.23 yxHkx 100% ikjxE;rkad lqfuf'pr djus osQ fy, iQksVks ysal izk;% ijkoS|qr inkFkZdh iryh ijr ls foysfir fd, tkrs gSaA bl inkFkZ dk viorZukad ok;q rFkk dk¡p (tksysal osQ izdkf'kd vo;o dks cukrk gS) osQ chp gksrk gSA mi;ksx dh tkus okyh ,dfof'k"V ijkoS|qr ijr MgF2 (n = 1.38) gSA n`'; LiSDVªe osQ osQUnz (5500 Å ) ijvfèkdre lapj.k osQ fy, ijr dh eksVkbZ D;k gksuh pkfg,A

23/04/18



11.1 fdlh d.k dks H mQ¡ pkbZ ls fxjk;k tkrk gSA mQ¡ pkbZ osQ iQyu osQ :i esa d.k dhns&czkWXyh rjaxnS?;Z fuEu esa ls fdlosQ vuqozQekuqikrh gksrh gS\

(a) H

(b) H1/2

(c) H0

(b) H–1/2

11.2 ukfHkd ls 1 MeV mQtkZ kjk cfU/r izksVkWu dks ukfHkd ls ckgj fudkyus osQ fy,vko';d iQksVkWu dh rjaxnS?;Z yxHkx fdruh gksrh gS\

(a) 1.2 nm

(b) 1.2 × 10–3nm

(c) 1.2 × 10–6nm

(d) 1.2 × 101nm

vè;k; 11

fofdj.k rFkk nzO; dh Srizo`Qfr

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71

11.3 fuokZfrr izdks"B esa j[ks èkkrq osQ i`"B ij vkifrr bysDVªkWuksa dks fdlh iqat (ftlesaizR;sd bysDVªkWu dh mQtkZ E

0 gS) ij fopkj dhft,A bl i`"B ls&

(a) dksbZ bysDVªkWu mRlftZr ugha gksxk D;ksafd osQoy iQksVkWu gh bysDVªkWu mRlftZr djldrs gSaA

(b) bysDVªkWu mRlftZr gks ldrs gSa ijUrq izR;sd dh mQtkZ E0 gksxhA

(c) vf/dre mQtkZ E0 – φ lfgr] (φ /krq dk dk;ZiQyu gS) fdlh Hkh mQtkZ osQ

bysDVªkWu mRlftZr gks ldrs gSaA

(d) vf/dre mQtkZ E0 lfgr fdlh Hkh mQtkZ osQ bysDVªkWu mRlftZr gks ldrs gSaA

11.4 ,u-lh-bZ-vkj-Vh- dh HkkSfrdh dh dkk 12 dh ikB~;iqLrd esa fn, x, fp=k 11.7 ijfopkj dhft,A eku yhft, A ij yxkbZ xbZ oksYVrk dks c<+k;k tkrk gSA foo£rr fdj.kiqat esa mfPp"B θ osQ ftl eku osQ fy, gksxk og&

(a) iwoZorhZ eku ls vf/d gksxk

(b) iwoZorhZ eku osQ cjkcj gksxk

(c) iwoZorhZ eku ls de gksxk

(d) y; ij fuHkZj djsxk

11.5 ,d izksVkWu] ,d U;wVªkWu] ,d bysDVªkWu rFkk ,d α-d.k dh mQtkZ ijLij cjkcj gS rksmudh ns&czkWXyh rajxnS?;ksZa esa rqyuk bl izdkj dh tk ldrh gS&

(a) λp = λ

n > λ

e > λ

α

(b) λα < λ

p = λ

n > λ

e

(c) λe < λ

p = λ

n > λ

α

(d) λe = λ

p = λ

n = λ

α

11.6 dksbZ bysDVªkWu ftldk izkjafHkd osx 0ˆv v= i gS fdlh pqEcdh; ks=k

0ˆB=B j esa

xfreku gSA bl bysDVªkWu dh ns&czkWXyh rajxnS?;Z&

(a) vpj jgrh gS

(b) le; osQ lkFk c<+rh gS

(c) le; osQ lkFk ?kVrh gS

(d) vkorhZ :i ls c<+rh vkSj ?kVrh gS

11.7 dksbZ bysDVªkWu (nzO;eku m) ftldk izkjafHkd osx 0 0ˆ( 0)v v= >v i gS fdlh fo|qr

ks=k 0 0ˆ– ( 0)E E= = >E i vpj esa xfreku gSA t k.k ij bl bysDVªkWu dh ns&czkWXyh

rjaxnS?;Z gS&

(a)

0

0

0

1eE t

m v

+

λ

23/04/18


72

(b)0

0

1eE t

mV0

+λ

(c) λ0

(d) λ0t.

11.8 dksbZ bysDVªkWu (nzO;eku m) ftldk izkjafHkd osx 0ˆv=v i gS] fdlh fo|qr ks=k

0ˆE=E j esa xfreku gSA 0

0

h

mvλ = gS] rks bl bysDVªkWu dh t k.k ij ns&czkWXyh

rjaxnS?;Z gS

(a) λ0

(b)

2 2 20

0 2 20

1e E t

m vλ +

(c)0

2 2 20

2 20

1e E t

m v

λ

+

(d)0

2 2 20

2 20

1e E t

m v

λ

+


11.9 tc xfrt mQtkZ 21

2mv jkf'k mc2 osQ rqyuh; gksus yxrh gS] tgk¡ m d.k dk

nzO;eku gS] rks lkisfkdrk la'kks/u vfuok;Z gks tkrs gSaA bysDVªkWu dh ns&czkWXyhrjaxnS?;Z osQ fdl eku osQ fy, lkisfkdrk la'kks/u egÙoiw.kZ gksaxs\

(a) λ =10 nm

(b) λ =10–1 nm

(c) λ =10–4 nm

(d) λ =10–6 nm

11.10 m1 rFkk m

2 (m

1 > m

2) nzO;eku osQ nks d.kksa A

1 rFkk A

2 dh ns&czkWXyh rjaxnS?;Z leku

gSaA rc&

(a) muosQ laosx leku gSa

(b) mudh mQtkZ leku gSa

(c) A1 dh mQtkZ A

2 ls de gS

(d) A1 dh mQtkZ A

2 ls vf/d gSA

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11.11 fdlh iQksVkWu dh ns&czkWXyh rjaxnS?;Z ,d bysDVªkWu dh ns&czkWXyh rjaxnS?;Z dh nksxquh

gSA ;fn bysDVªkWu dh pky 100

e

cv = gS] rc

(a) –410eE

Eγ

=

(b) –210eE

Eγ

=

(c) –210e

e

p

m c=

(d) –410e

e

p

m c=

11.12 nzO; esa vo'kksf"kr iQksVkWu mQ"ek esa ifjo£rr gks tkrs gSaA ν vko`fÙk osQ n izfr lsd.MiQksVkWu mRl£tr djus okys fdlh lzksr dks 0°C dh 1 kg ciZQ dks 0°C osQ tyesa ifjo£rr djus osQ fy, mi;ksx fd;k tkrk gSA rc bl ifjorZu esa yxk le; T

(a) fu;r ν osQ fy,] n esa o`f¼ osQ lkFk de gksrk gSA

(b) fu;r n osQ fy,] ν esa o`f¼ osQ lkFk de gksrk gSA

(c) vifjofrZr jgrk gS ;fn n vkSj ν esa bl izdkj ifjorZu gks fd nν = vpj jgsA

(d) xq.kuiQy nν esa o`f¼ gksus ij c<+rk gSA

11.13 dksbZ d.k ewy fcUnq dh vksj yxus okys fdlh cy osQ dkj.k ewy fcUnq osQ ifjr%fdlh cUn dkk esa xeu djrk gSA bl d.k dh ns&czkWXyh rjaxnS?;Z pozQh; ozQe esanks ekuksa λ

1 ,oa λ

2 (λ

1>λ

2) osQ chp ifjofrZr gksrh gSA uhps fn, x, izdFkuksa esa dkSu

ls lR; gSa\

(a) d.k ewy fcUnq dks osQUnz cukdj o`Ùkh; dkk esa xfr djsxkA

(b) d.k ewy fcUnq dks viuk iQksdl j[krs gq, nh?kZo`Ùkh; dkk esa xfr djsxkA

(c) tc ns&czkWXyh rjaxnS?;Z λ1 gS] rks d.k ml fLFkfr dh viskk ewy fcUnq osQ

fudVrj gksrk gS tc bldk eku λ2 gSA

(d) tc nss&czkWXyh rjaxnS?;Z λ2 gS rks d.k ml fLFkfr dh viskk ewy fcUnq osQ fudVrj

gksrk gS tc bldk eku λ1 gSA

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74

bysDVªkWu

izdk'k

èkkrq


11.14 fdlh izksVkWu vkSj fdlh α-d.k dks leku foHkokUrj kjk Rofjr fd;k x;k gSAns&czkWXyh rjaxnS?;Z λ

p ,oa λ

a ijLij fdl izdkj lacaf/r gSa\

11.15 (i) izdk'k fo|qr izHkko dh O;k[;k djrs le; geus ;g ekuk Fkk fd ν vko`fÙk dkiQksVkWu fdlh bysDVªkWu ls la?kV~V djrk gS vkSj viuh mQtkZ mldks gLrkarfjr djnsrk gSA blls gesa mRlftZr bysDVªkWu dh vf/dre mQtkZ] E

vfèkdre] osQ fy, fuEu

izdkj dk lehdj.k izkIr gksrk gS&

Evfèkdre

= hν – φ0

tgk¡ φ0 /krq dk dk;ZiQyu gSA ;fn dksbZ bysDVªkWu nks iQksVkWu (izR;sd dh vko`fÙk

ν gS) vo'kksf"kr djrk gS] rks mRlftZr bysDVªkWu dh vf/dre mQtkZ D;k gksxh\

(ii) fujks/h foHko laca/h gekjh foospuk esa nks iQksVkWu vo'kks"k.k osQ bl izdj.k ijfopkj D;ksa ugha fd;k x;k\

11.16 oqQN inkFkZ ,sls gksrs gSa tks y?kq rjaxnS?;Z osQ iQksVkWu dks vo'kksf"kr djrs gSa vkSj nh?kZrjaxnS?;Z osQ iQksVkWu mRlftZr djrs gSaA D;k ,sls LFkk;h inkFkZ Hkh gks ldrs gSa tks nh?kZrjaxnS?;Z osQ iQksVkWu vo'kksf"kr djosQ y?kq rjaxnS?;ksZa dk izdk'k mRlftZr djsaA

11.17 D;k iQkssVkWu vo'kksf"kr djus okys lHkh bysDVªkWu iQksVksbysDVªkWuksa osQ :i essa fu"ozQfergksrs gSa\

11.18 nks izdk'k lzksr gSa ftuesa izR;sd 100 W 'kfDr mRl£tr djrk gSA buesa ls ,d1nm rjaxnS?;Z dh X&fdj.ksa vkSj nwljk 500 nm dk n`'; izdk'k mRlftZr djrkgSA nh xbZ rjaxnSè;ksZa osQ fy, X–fdj.kksa osQ iQksVkWuksa dh la[;k rFkk n`'; izdk'k osQiQksVkWuksa dh la[;k dk vuqikr Kkr dhft,A

y?kqmÙkjh; (SA)

11.19 izdk'k fo|qr mRltZu laca/h fp=k 11.1 ij fopkj dhft,A bl izdj.k osQ fy, vki;gk¡ laosx lajk.k ls lkeatL; oSQls LFkkfir djsaxs\ è;ku nhft,] bl fLFkfr esa izdk'k(iQksVkWu) dk laosx mRl£tr bysDVªkWuksa osQ laosx ls fHkUu fn'kk esa gSA

11.20 600 nm dh rjaxnS?;Z osQ izdk'k ls mn~Hkkflr fdlh èkkrq dh lrg ls mRl£trbysDVªkWuksa dh vfèkdre mQtkZ ekih xbZA ;g ik;k x;k fd 400 nm rjaxnS?;Z osQizdk'k dk mi;ksx djus ij blls mRl£tr gksus okys bysDVªkWuksa dh vfèkdre mQtkZnksxquh gks xbZA /krq dk dk;Z iQyu (eV esa) Kkr dhft,Afp=k 11.1

23/04/18


75

11.21 eku yhft, dksbZ bysDVªkWu 1nm pkSM+s ks=k esa ifjlhfer gSA gkbts+ucxZ vfuf'prrkosQ fl¼kUr dk mi;ksx djosQ laosx esa vfuf'prrk ifjdfyr dhft, (lanHkZ%HkkSfrdh] dkk&12] ,u-lh-bZ-vkj-Vh-] lehdj.k 11.12)A vki ;g eku ldrs gSa fdfLFkfr esa vfuf'prrk ∆x gS ftldk eku 1nm gSA ;g ekurs gq, fd p p∆

bysDVªkWu dh mQtkZ bysDVªkWu oksYV (eV) esa ifjdfyr dhft,A

11.22 leku rhozrk I osQ nks ,do.khZ fdj.k iqat A ,oa B fdlh insZ ls Vdjkrs gSaA iqat A

osQ insZ ij Vdjkus okys iQksVkWuksa dh la[;k iqat B dh nksxquh gSA mudh vko`fÙk;ksa osQfo"k; esa vki D;k fu"d"kZ fudky ldrs gSa\

11.23 λ1 ,oa λ

2 ns&czkWXyh rjaxnS?;Z osQ nks d.k A ,oa B feydj dksbZ d.k C cukrs gSaA bl

izfozQ;k esa laosx lajk.k gksrk gSA d.k C osQ ns&czkWXyh rjaxnS?;Z dk ifjdyu dhft,(xfr ,dfoeh; gS)A

11.24 E mQtkZ dk U;wVªkWu iqat fdlh ,sls i`"B osQ ijek.kqvksa ls izdhf.kZr gksrk gS ftlesaijek.kqvksa osQ chp nwjh d = 0.1nm gSA ijkofrZr iqat dh rhozrk dk izFke mfPp"Bθ = 30° ij izkIr gksrk gSA iqat dh mQtkZ (eV esa) E dk eku D;k gS\

nh?kZmÙkjh; (LA)

11.25 lksfM;e osQ fdlh ruq y; (10–2m2 ks=kiQy, 10–3m eksVkbZ) ij fopkj dhft,ftl ij tc 100W/m2 rhozrk dk izdk'k (λ = 660 nm) Mkyk tkrk gS rks blls100µA dh izdk'k fo|qr /kjk mRiUu gksrh gSA tc dksbZ bysDVªkWu fdlh lksfM;eijek.kq (Na dk ?kuRo 0.97kg/m3) ls Vdjkrk gS rks iQksVksbysDVªkWu mRiUu gksus dhizkFkfedrk ifjdfyr dhft,A

11.26 fdlh /kfRod i`"B (ftls vuUr foLrkj dk lery i`"B eku ldrs gSa) osQ lkeusd nwjh ij fLFkr bysDVªkWu ij fopkj dhft,A eku yhft, fd IysV osQ kjk bl ij

yxus okyk vkd"kZ.k cy 2

20

1

4 4

q

dεπgSA vkos'k dks IysV ls vuUr nwjh ij ys tkus

esa fd;k tkus okyk dk;Z ifjdfyr dhft,A d = 0.1nm ysdj dk;Z (eV esa)ifjdfyr dhft,A [d < 0.1nm osQ fy, ;g cy fu;e ykxw ugha gksrk]

11.27 dksbZ fo|kFkhZ nks inkFkZ A ,oa B ysdj izdk'k fo|qr izHkko laca/h iz;ksx djrk gSAV

fujks/h rFkk ν dk xzkiQ fp=k 11.2 esa n'kkZ;k x;k gSA

(i) A ,oa B esa fdl inkFkZ dk dk;ZiQyu vf/d gS\

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(ii) bysDVªkWu dk fo|qr vkos'k = 1.6 × 10–19C ysdj iz;ksx ls izkIr vkadM+ksa osQvk/kj ij A ,oa B nksuksa osQ fy, h dk eku Kkr dhft,A

fVIi.kh dhft, fd D;k ;g vkbUlVkbu osQ fl¼kUr osQ vuq:i gSA

11.28 mA nzO;eku dk dksbZ d.k A v osx ls xfr'khy gksdj m

B nzO;eku osQ fojkekoLFkk

esa j[ks d.k B ls Vdjkrk gS (xfr ,dfoeh; gS)A d.k A dh ns&czkWXyh rjaxnS?;Z esagksus okyk ifjorZu ifjdfyr dhft,A la?kV~V dks izR;kLFk ekfu,A

11.29 20 W dk dksbZ cYc 5000 A

rjaxnS?;Z dk izdk'k mRlftZr dj jgk gS tks 2m

nwjh ij j[ks fdlh /kfRod i`"B dks izdkf'kr dj jgk gSA ;g ekudj fd /kfRod

i`"B dk dk;ZiQyu 2 eV gS vkSj blosQ izR;sd ijek.kq dks 1.5 A

f=kT;k dh o`Ùkh;

pdrh ekuk tk ldrk gS&

(i) cYc ls izfr lsoaQM mRlftZr gksus okys iQksVkWuksa dh la[;k dk vkdyu dhft,(dksbZ Hkh vU; k; ifjdyu esa u ykb,)A

(ii) D;k /kfRod i`"B ls izdk'k fo|qr mRltZu gksxk\

(iii) ijekf.od pdrh dks dk;ZiQyu (2 eV) osQ cjkcj mQtkZ izkIr djus esa fdrukle; yxsxk\

(iv) mQij (iii) esa ifjdfyr le; vUrjky esa ijekf.od pdrh fdrus iQksVkWu xzg.kdjsxh\

(v) D;k vki Li"V dj ldrs gSa fd izdk'k fo|qr izHkko dk rkRkf.kd izsk.k fdlizdkj fd;k x;k\

[laosQr% Hkkx (iii) esa ifjdfyr le; fpj izfrf"Br fopkjksa osQ vk/kj ij izkIr fd;kx;k gS] bl fopkj dks vkxs c<+krs gq, vki 1cm2 i`"Bks=k osQ y; dks ysdj ;gvkdyu dhft, fd D;k gksxkA]

fp=k 11.2

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12.1 cksj f=kT;k dks a0 = 53pm ysrs gq,] cksj ekWMy osQ vk/kj ij Li++ vk;u dh] blosQ

fuEure voLFkk esa] f=kT;k gksxh yxHkx&

(a) 53 pm(b) 27 pm(c) 18 pm(d) 13 pm

12.2 ,d bysDVªkWu dks] ,d fLFkj ukfHkd (izksVkWu) osQ pkjksa vksj ifjozQe.k djrk gqvk ekursgq,] ,d gkbMªkstu&ijek.kq dh cU/u mQtkZ gS&

4

2 2 20

–8

meB

n hε= (m = bysDVªkWu dk nzO;eku)

;fn dksbZ O;fDr ,d ,sls funsZ'k izsQe dks mi;ksx esa yk, ftlesa bysDVªkWu fojke esa gksrks izksVkWu blosQ pkjksa vksj ifjozQe.k djsxkA lerqY; rdksZa ls vc cUèku mQtkZ gksxh&

vè;k; 12

ijek.kq

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78

4

2 2 20

–8

MeB

n h=

ε (M = izksVkWu nzO;eku)

;g vfUre O;atd lgh ugha gS D;ksafd(a) n iw.kk±d ugha gksxkA(b) cksj Dok.Vehdj.k osQoy bysDVªkWuksa osQ fy, iz;qDr gksrk gSA(c) og funsZ'k izsQe ftlesa bysDVªkWu fojke esa jgrk gS tM+Roh; ugha gSA(d) izksVkWu dh xfr lfUudV :i ls Hkh o`Ùkh; dkk esa ugha gksxhA

12.3 ,d lkekU; cksj ekWMy dks dbZ bysDVªkWuksa okys ,d ijek.kq osQ mQtkZ Lrjksa dh x.kukosQ fy, izR;kr% iz;qDr ugha fd;k tk ldrkA ,slk blfy, gS D;ksafd&

(a) bysDVªkWu osaQnzh; cy osQ vk/hu ugha gSaA

(b) bysDVªkWu ,d nwljs ls Vdjkrs jgrs gSaA

(c) LozQhu izHkko chp es vkrs gSaA

(d) ukfHkd rFkk bysDVªkWu osQ chp cy] vc owQykWe osQ fu;e ls fuèkkZfjr ugh gksrsA

12.4 lkekU; cksj ekWMy osQ vuqlkj] fuEure voLFkk esa] gkbMªkstu ijek.kq osQ bysDVªkWu dkdks.kh; laosx osQ rqY; gSA dks.kh; laosx ,d lfn'k gS vr% dkkvksa dh la[;kvuUr gksxh] ftuesa dks.kh; laosx lfn'k izR;sd lEHko fn'kk dh vksj bafxr dj jgkgksxkA okLro esa ;g lgh ugha gS&

(a) D;ksafd cksj ekWMy dks.kh; laosx dk xyr eku nsrk gSA(b) D;ksafd buesa ls osQoy ,d dh mQtkZ U;wure gksxhA(c) dks.kh; laosx bysDVªkWu osQ pozQ.k dh fn'kk esa gksuk pkfg,A(d) D;ksafd bysDVªkWu osQoy kSfrt dkkvksa esa pDdj yxkrs gSaA

12.5 O2 v.kq esa vkWDlhtu osQ nks ijek.kq gksrs gSaA v.kq esa] nks ijek.kq&ukfHkdksa osQ eè;ukfHkdh; cy&

(a) egÙoiw.kZ ugha gS D;ksafd ukfHkdh; cyksa dk ifjlj U;wu gksrk gSA(b) nks ijek.kqvksa dks ck¡/us osQ fy, vko';d fLFkj oS|qr cyksa ftrus gh egÙoiw.kZ

gSaA(c) ukfHkdksa osQ eè; izfrd"kZ.kkRed fLFkj oS|qr cykas dks fujLr dj nsrs gSaA(d) egÙoiw.kZ ugha gS D;ksafd vkDlhtu ukfHkd esa U;wVªkWuksa vkSj izksVWkuksa dh la[;k cjkcj

gksrh gSA

12.6 nks H & ijek.kqvksa dk buosQ fuEure voLFkk esa vizR;kLFk la?kêð gksrk gSA nksuksa dhla;qDr xfrt mQtkZ esa gksus okyh vf/dre deh gS&

(a) 10.20 eV(b) 20.40 eV(c) 13.6 eV(d) 27.2 eV

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12.7 mÙksftr voLFkk esa ijek.kqvksa dk ,d lewg fo?kfVr gksrk gS&

(a) lkekU;r% fuEurj mQtkZ dh fdlh Hkh voLFkk rd(b) ,d fuEurj voLFkk rd osQoy rHkh tc ,d ckg~; fo|qr ks=k kjk mÙksftr

fd;k x;k gksA

(c) ftuesa lHkh ,d lkFk ,d fuEurj voLFkk esa vkrs gSaA

(d) rks buls iQksVkWu osQoy rHkh mRlftZr gksrs gSa tc muesa la?kV~V gksrk gSA

cgqfodYih iz'u II (MCQ II)

12.8 ,d vk;fur H-v.kq eas ,d bysDVªkWu rFkk nks izksVkWu gksrs gSaA izksVkWuksa osQ eè; nwjhvkWXLVªkWe dh dksfV dh gksrh gSA fuEure voLFkk esa&

(a) bysDVªkWu o`Ùkh; dkkvksa esa xfr ugha djsaxsA

(b) mQtkZ] gkbMªkstu&ijek.kq dh (2)4 xquk gksxhA

(c) bysDVªkWu dh dkk izksVkWuksa osQ pkjksa vksj gksxhA

(d) v.kq 'kh?kz gh ,d izksVkWu vkSj ,d gkbMªkstu ijek.kq esa fo?kfVr gks tk,xkA

12.9 eqDr bysDVªkWuksa osQ ,d fdj.k iqat dks eqDr izksVkWuksa dh vksj fn"V ekusaaA tc osizdh£.kr gksrs gSa rks] ,d bysDVªkWu o ,d izksVkWu feydj ,d gkbMªkstu&ijek.kq ughacuk ldrs&

(a) mQtkZ&lajk.k osQ dkj.k

(b) fofdj.k osQ :i esa lekf.kd mQtkZ&ekspu osQ fcuk

(c) laosx lajk.k osQ dkj.k

(d) dks.kh;&laosx lajk.k osQ dkj.k

12.10 gkbMªkstu ijek.kq osQ LisDVªe osQ fy, cksj ekWMy&

(a) gkbMªkstu dh vkf.od voLFkk esa ykxw ugha gksxkA

(b) He- ijek.kq dh Hkk¡fr ykxw ugh gksxkA

(c) osQoy dejs osQ rki ij oS/ gSA

(d) vfojr rFkk fofoDr nksuksa izdkj dh LisDVªeh js[kkvksa dh izkxqfDr djrk gSA

12.11 H- ijek.kq osQ fy, ckWej Js.kh izsfkr dh tk ldrh gS&

(a) ;fn ge mRl£tr izdk'k dh vko`fÙk ml k.k ekisa tc ijek.kq mÙksftr voLFkkls fuEure voLFkk eas vkrk gSA

(b) ;fn ge mRl£tr izdk'k dh vko`fÙk] mÙksftr voLFkkvksa ls izFke mÙksftrvoLFkk rd laozQe.k esa ekisaA

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(c) gkbMªkstu&ijek.kq osQ fdlh Hkh laozQe.k esaA

(d) vko`fÙk;ksa osQ vuqozQe dh Hkk¡fr] ftlesa mPprj vko`fÙk;k¡ lqLakoqQfyr gks jgh gksaA

12.12 ekuk fd 4

2 2 20

1

8n

meE

n hε

−= gkbMªkstu ijek.kq osQ n osa Lrj dh mQtkZ gSA ;fn lHkh

gkbMªkstu ijek.kq fuEure voLFkk es gksa rFkk (E2–E1)/h vko`fÙk dk fofdj.k blij vkifrr gks rks&

(a) ;g fcyoqQy Hkh vo'kksf"kr ugha gksxkA(b) oqQN ijek.kq izFke mÙksftr voLFkk dh vksj xfr djsaxsA

(c) lHkh ijek.kq n = 2 voLFkk rd mÙksftr gksaxsA

(d) dksbZ Hkh ijek.kq n = 3 voLFkk rd laozQe.k ugha djsxkA

12.13 lkekU; cksj ekWMy 4He ijek.kq ij ykxw ugha gksrk gS&

(a) D;ksafd 4He ,d vfozQ;&xSl gSA

(b) D;ksafd 4He osQ ukfHkd esa U;wVªkWu gSaA

(c) D;ksafd 4He osQ ikl ,d bysDVªkWu vf/d gSA

(d) D;ksafd bysDVªkWu osQUnzh; cyksa osQ v/hu ugha gSaA


12.14 ,d gkbMªkstu ijek.kq dk nzO;eku] ,d izksVku o bysDVªkWu osQ nzO;ekuksa osQ ;ksx lsde gSA ,slk D;ksa gS\

12.15 4He rFkk 3He ls ,d bysDVªkWu osQ fu"dklu dh dYiuk djsaA cksj ekWMy osQ vkèkkjij ifjdfyr] buosQ mQtkZ Lrj cgqr vf/d fudV gksaxsA ,slk D;ksa_ O;k[;k djsaA

12.16 tc ,d bysDVªkWu mPprj mQtkZ ls fuEu mQtkZ Lrj esa vkrk gS rks mQtkZ dk vUrjfo|qr pqEcdh; fofdj.k osQ :i esa izdV gksrk gSA ;g mQtkZ osQ vU; :iksa esa mRl£trD;ksa ugha gks ldrk\

12.17 ;fn izksVkWu ij vkos'k (+4/3)e vkSj bysDVªkWu ij vkos'k ( )3/4 e− gks rks D;k

H-ijek.kq dk cksj lw=k vifjofrZr jgsxk A ;gk¡ e = 1.6 × 10–19C gSA vius mÙkjosQ leFkZu esa roZQ nsaA

12.18 nks fHkUu gkbMªkstu ijek.kq ysaA izR;sd ijek.kq esa bysDVªkWu mÙksftr voLFkk esa gSA cksjekWMy osQ vuqlkj D;k ;g lEHko gS fd bysDVªkWuksa dh mQtkZ rks fHkUu gks ijUrq dkh;dks.kh; laosx leku gks\

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81

y?kqmÙkjh; (SA)

12.19 ikWftVªksfu;e] H-ijek.kq dh Hkk¡fr gh gS ftlesa izksVkWu] bysDVªkWu osQ /ukosf'kr izfrd.k (bls ikWftVªkWu dgrs gSa] tks bysDVªkWu osQ cjkcj gh Hkkjh gS) kjk izfrLFkkfir gksrkgSA iksftVªksfu;e dh fuEure voLFkk esa mQtkZ D;k gksxh\

12.20 dYiuk djsa fd ,d ijek.kq osQ bysDVªkWuksa osQ eè; dksbZ izfrd"kZ.k cy ugha gS ysfdu/ukos'k rFkk ½.kkos'k osQ eè; cy iwokZuqlkj owQykWe osQ fu;e ls fn;k tkrk gSA buifjfLFkfr;ksa esa He-ijek.kq dh fuEure voLFkk esa mQtkZ ifjdfyr dhft,A

12.21 cksj ekWMy dk mi;ksx djosQ] gkbMªkstu ijek.kq dh fuEure voLFkk esa bysDVªkWu kjkfufeZr fo|qr&/kjk dk ifjdyu dhft,A

12.22 n'kkZb, fd tc bysDVªkWu fdlh mPprj Lrj ls n osa Lrj esa vkrk gS (n >>1)] rksmRlftZr izdk'k dh igyh oqQN vko`fÙk;k¡ yxHkx lauknh (vFkkZr~ 1 : 2: 3... osQvuqikr esa) gksrh gSaA

12.23 ckWej Js.kh dh Hγ js[kk dks mRl£tr dj ldus gsrq] gkbMªkstu ijek.kq dks fuEure

voLFkk esa nh tkus okyh U;wure mQtkZ fdruh gksxh\ ;fn fudk; dk dks.kh; laosx

lajfkr jgrk gks] rks bl Hγ iQksVkWu dk dks.kh; laosx D;k gksxk\

nh?kZmÙkjh; (LA)

12.24 gkbMªkstu ijek.kq dh ykbeu Js.kh dh izFke pkj LisDVªeh js[kk,¡ gSa&λ = 1218 Å, 1028Å, 974.3 Å vkSj 951.4ÅA ;fn gkbMªkstu osQ LFkku ijM~;wVhfj;e dks ysa rks bu js[kkvksa osQ rjaxnS?;Z eas fopyu dh x.kuk djsaA

12.25 M~;wVhfj;e dh [kkst] 1932 esa gkjksYM mjs kjk] 1H rFkk 2H eas ,d fo'ks"k laozQe.kosQ fy, rjaxnS?;Z osQ vYi ifjorZu dks uki dj dh xbZA ,slk blfy, gqvk] D;ksafdfdlh laozQe.k osQ laxr rjaxnS?;Z fdlh lhek rd ukfHkd osQ nzO;eku ij fuHkZj djrhgSA ;fn ukfHkdh; xfr dks è;ku esa j[kk tk, rks bysDVªkWu o ukfHkd vius mHk;fu"BnzO;eku osaQnz dh ifjozQek djrs gSaA ;g fudk; ,d ,sls d.k osQ lerqY; gS ftldklekuhr nzO;eku µ gS, vkSj tks ukfHkd osQ pkjksa vksj bysDVªkWu&ukfHkd osQ chp dhnwjh osQ cjkcj nwjh ij ifjozQe.k djrk gSA ;gk¡ µ = m

eM/(m

e + M) tgk¡ M ukfHkd

dk nzO;eku rFkk me bysDVªkWu dk nzO;eku gSA 1H rFkk 2H esa ykbeu Js.kh dh izFke

js[kk dh rjaxnS?;Z es gksus okys vUrj osQ izfr'kr dk ifjdyu djsaA(1H ukfHkd dk nzO;eku =1.6725 × 10–27 kg] 2H ukfHkd dk nzO;eku=3.3374 × 10–27 kg] bysDVªkWu dk nzO;eku = 9.109 × 10–31 kg)

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12.26 ;fn izksVkWu dh f=kT;k 'R' rFkk vkos'k ,dleku :i ls forfjr gksa] rks cksj fl¼kUrdk mi;ksx djosQ gkbMªkstu ijek.kq dh fuEure Lrj dh mQtkZ dh x.kuk djsa tc(i) R = 0.1Å, (ii) R = 10 ÅA

12.27 vks”ks izde esa ,d ijek.kq fcuk iQksVkWu mRl£tr fd,] fuEu voLFkk esa laozQe.k djrkgSA vfrfjDr mQtkZ ,d ckg~; bysDVªkWu dks LFkkukUrfjr dh tkrh gS ftlosQ ijek.kqls mRlftZr gks tkus dh laHkkouk gSA (bls vks”ks bysDVªkWu dgrs gSa)A ukfHkd dks Hkkjhekurs gq, ozQksfe;e esa n = 2 ls n = 1 esa laozQe.k osQ iQyLo:i mRl£tr iQksVkWuosQ laxr vkWxj bysDVªku dh xfrt mQtkZ dk ifjdyu dhft,A

12.28 bysDVªkWu o izksVkWu osQ eè; cy gsrq fLFkj oS|qfrdh dk O;qRozQe oxZ fu;e gS&

( )

2

20

| |4 .

e

rε=

πF | |F dh

1r

fuHkZjrk dks Dok.Ve fl¼kUr esa bl izdkj

le>k tk ldrk gS& fd izdk'k dk ^d.k* (iQksVku) nzO;eku jfgr gSA ;fn izksVkudk nzO;eku m

p gks rks cy dk la'kksf/r :i gksxkA

( )( )

2

2 20

1| | . –

4

ee p r

rr r

λλ

ε

= ×+ π

F tg k ¡ pm c /λ = rF k k 2h

=π

gkbMªkstu ijek.kq dh U;wure voLFkk dh mQtkZ esa ifjorZu dk vkdyu djsa ;fn mp

bysDVªkWu osQ nzO;eku dk 10–6 xquk gSA

12.29 gkbMªkstu ijek.kq dk cksj ekWMy fLFkj fo|qr osQ owQykWe&fu;e ij fuHkZj djrk gSAowQykWe dk fu;e izR;kr% cgqr vYi nwfj;kas (Å osQ ledk) osQ fy, ijhfkr ughagSA ekuk owQykWe dk fu;e nks foijhr vkos'kksa + q

1, –q

2 osQ fy, ifj"o`Qr fd;k x;k

gS&

( )1 2

020

1| | ,

4q q

r Rrε

= ≥π

F

1 2 002

0 0

1,

4q q R

r RR r

ε

ε

= ≤

π

bl fLFkfr esa H-ijek.kq dh U;wure mQtkZ voLFkk dk ifjdyu dhft,] ;fnε = 0.1, R

0 = 1ÅA

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ukfHkd


13.1 eku yhft, ge ,sls cgqr ls ik=kksa ij fopkj djrs gSa ftuesa izR;sd esa izkjEHk esa 1 o"kZvèkkZ;q okys jsfM;ks,fDVo inkFkZ osQ 10000 ijek.kq gSaA 1 o"kZ osQ i'pkr~

(a) lHkh ik=kksa esa bl inkFkZ osQ 5000 ijek.kq gksaxsA

(b) lHkh ik=kksa esa bl inkFkZ osQ ijek.kqvksa dh la[;k leku gksxh] ijUrq ;g yxHkx5000 gksxhA

(c) lkekU; rkSj ij bu ik=kksa esa bl inkFkZ osQ ijek.kqvksa dh la[;k fHkUu gksxh] ijUrqbudk vkSlr 5000 osQ fudV gksxkA

(d) fdlh Hkh ik=k esa bl inkFkZ osQ 5000 ijek.kqvksa ls vf/d ugha gksaxsA

13.2 fdlh gkbMªkstu ijek.kq rFkk m nzO;eku osQ fdlh vU; d.k osQ eè; xq#Roh; cy dksU;wVu osQ fu;e kjk fu:fir fd;k tk,xk&

2

.M mF G

r= ;gk¡ r fdyksehVj esa gS rFkk

(a) M = mizksVkWu

+ m bysDVªkWu

vè;k; 13

ukfHkd

23/04/18


84

(b) M = mizksVkWu

+ m bysDVªkWu 2

B

c− (B = 13.6 eV)

(c) M gkbMªkstu ijek.kq osQ nzO;eku ls lacaf/r ugha gSA

(d) M = mizksVkWu

+ m bysDVªkWu

2

| |V

c− (V = H-ijek.kq esa bysDVªkWu dh fLFkfrt mQtkZ dk

ifjek.k)A

13.3 tc fdlh ijek.kq osQ ukfHkd dk jsfM;ks,fDVo fo?kVu gksrk gS rks ijek.kq osQ bysDVªkWfudmQtkZ Lrjksa esa

(a) fdlh Hkh izdkj dh jsfM;ks,fDVork osQ fy, dksbZ ifjorZu ugha gksrkA

(b) α ,oa β jsfM;ks,fDVork osQ fy, ifjorZu gksrs gSa ijUrq γ jsfM;ks ,fDVork osQ fy,dksbZ ifjorZu ugha gksrsA

(c) α jsfM;ks,fDVork osQ fy, ifjorZu gksrs gSa] ijUrq vU; osQ fy, ughaA

(d) α jsfM;ks,fDVork osQ fy, ifjorZu gksrs gSa] ijUrq vU; osQ fy, ughaA

13.4 Mx rFkk M

y fdlh jsfM;ks,fDVo fo?kVu esa ewy vkSj fo?kVut ukfHkdksa osQ ijek.kq

nzO;ekuksa dks fu:fir djrs gSaA β fo?kVu dk Q-eku Q1 vkSj β + fo?kVu dk Q

eku

Q2 gSA ;fn m

e ,d bysDVªkWu osQ nzO;eku dks fu:fir djrk gS rks buesa ls dkSu lk

izdFku lgh gS\

(a) Q1 = (M

x – M

y) c2 rFkk Q

2 = (M

x – M

y – 2m

e)c2

(b) Q1 = (M

x – M

y) c2 rFkk Q

2 = (M

x – M

y )c2

(c) Q1 = (M

x – M

y – 2m

e) c2 rFkk Q

2 = (M

x – M

y +2 m

e)c2

(d) Q1 = (M

x – M

y + 2m

e) c2 rFkk Q

2 = (M

x – M

y +2 m

e)c2

13.5 VªkbfV;e gkbMªkstu dk ,d leLFkkfud gS ftlosQ ukfHkd VªkbVkWu esa nks U;wVªkWu vkSj ,dizksVkWu gSA eqDr U;wVªkWu ep v+ + esa fo?kfVr gks tkrs gSaA ;fn VªkbVkWu osQ nks U;wVªkWuksa esals fdlh ,d U;wVªkWu dk fo?kVu gksrk] rks ;g He

3 ukfHkd esa :ikUrfjr gks tkrk] ijUrq

,slk ugha gksrk D;ksafd

(a) VªkbVkWu dh mQtkZ He3 ukfHkd dh mQtkZ ls de gksrh gSA

(b) β – fo?kVu izfd;k esa mRiUu bysDVªkWu ukfHkd osQ Hkhrj ugha jg ldrkA(c) VªkbVkWu esa nksuksa U;wVªkWu LkkFk&lkFk fo?kfVr gksrs gSa] ftlosQ iQyLo:i rhu izksVkWuksa

dk ,d ukfHkd curk gS tks He3 ukfHkd ugha gksrkA(d) D;ksafd eqDr U;wVªkWu ckg~; kksHk osQ dkj.k fo?kfVr gksrs gSa vkSj VªkbVkWu ukfHkd esa

eqDr U;wVªkWu ugha gksrsA

13.6. LFkk;h Hkkjh ukfHkdksa esa U;wVªkWuksa dh la[;k izksVkWuksa ls vfèkd gksrh gSA bldk dkj.k ;ggS fd

(a) U;wVªkWu izksVkWu ls vf/d Hkkjh gksrs gSaA

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ukfHkd

85

(b) izksVkWuksa osQ chp fLFkj fo|qr cy izfrd"kZ.kkRed gksrk gSA

(c) β fo?kVu kjk U;wVªkWu izksVkWuksa esa fo?kfVr gks tkrs gSaA

(d) U;wVªkWuksa osQ chp ukfHkdh; cy izksVkWu osQ chp ukfHkdh; cy dh viskk nqcZy gksrkgSA

13.7 fdlh ukfHkdh; fj,DVj esa voeand fo[kaMu izfozQ;k esa eqDr U;wVªkWuksa dh xfr dksean dj nsrs gSaA voeand osQ :i esa gyosQ ukfHkdksa dk iz;ksx fd;k tkrk gSA HkkjhukfHkd ;g mís'; iwjk ugha dj ldrs] D;ksafd

(a) os VwV tk,¡xsA

(b) Hkkjh ukfHkdksa osQ lkFk U;wVªkWuksa dk izR;kLFk la?kêð mUgsa /hek ugha djsxkA

(c) fj,DVj dk usV Hkkj vR;fèkd gks tk,xkA

(d) Hkkjh ukfHkdksa okys inkFkZ dk&rki ij nzo vFkok xSlh; voLFkk esa ugha ik, tkrsA


13.8 lay;u izfozQ;k,¡ tSls nks M~;wVjkWu osQ lay;u kjk ,d He ukfHkd cukuk] lkekU; rki,oa nkc ij vlaHko gSA blosQ dkj.kksa dks fuEufyf[kr rF;ksa ls le>k tk ldrk gS%

(a) ukfHkdh; cy y?kq ijklh; gksrs gSaA

(b) ukfHkd /u&vkosf'kr gksrs gSaA

(c) ewy ukfHkd dks lay;u ls iwoZ iw.kZr% vk;fur gks tkuk pkfg,A

(d) lay;u ls iwoZ ewy ukfHkd dks igys VwVuk pkfg,A

13.9 nks jsfM;ks,fDVo ukfHkdksa A vkSj B osQ uewus fy, x,A λA vkSj λ

B ozQe'k% A vkSj B

osQ fo?kVu fu;rkad gSaA buesa ls fdu fLFkfr;ksa esa nksuksa uewuksa osQ fo?kVu dh lekf.kdnj leku gksxhA

(a) A osQ izkjfEHkd fo?kVu dh nj B osQ izkjfEHkd fo?kVu dh nj dh nqxquh rFkkλ

A = λ

B gksA

(b) A osQ izkjfEHkd fo?kVu dh nj B osQ izkjfEHkd fo?kVu dh nj dh nqxquh rFkkλ

A > λ

B gksA

(c) B osQ izkjfEHkd fo?kVu dh nj A osQ izkjfEHkd fo?kVu dh nj dhnqxquh rFkk λ

A > λ

B gksA

(d) t = 2h ij B osQ izkjfEHkd fo?kVu dh nj A osQ izkjfEHkd fo?kVu dhnj osQ leku rFkk λ

B < λ

A gksA

13.10 nks jsfM;ks,fDVo uewuksa A vkSj B osQ fo?kVu dh nj dk le; osQ lkFkifjorZu fp=k 13.1 esa n'kkZ;k x;k gSA buesa ls dkSu ls izdFku lgh gSaA

(a) A dk fo?kVu fu;rkad B osQ fo?kVu fu;arkd ls vf/d gS] vr% AlnSo B dh viskk rhoz xfr ls fo?kfVr gksrk gSA

A

B

t

d N

d t

fp=k 13.1

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(b) B dk fo?kVu fu;rkad A osQ fo?kVu fu;rkad ls vf/d gS] ijUrq B osQ fo?kVudh nj lnSo A osQ fo?kVu dh nj ls de gSA

(c) A dk fo?kVu fu;rkad B osQ fo?kVu fu;rkad ls vf/d gS ijUrq A lnSo B lsigys fo?kfVr ugha gksrkA

(d) B dk fo?kVu fu;rkad A osQ fo?kVu fu;rkad ls de gS fiQj Hkh blosQ fo?kVudh nj] oqQN k.kksa i'pkr] A osQ cjkcj gks tkrh gSA

VSA (vfr y?kqmÙkjh;)

13.11 32He rFkk 3

1 He ukfHkdksa dh nzO;eku la[;k,¡ leku gSaA D;k budh cU/u mQtkZ,¡

Hkh leku gSa\

13.12 lfozQ; ukfHkdksa dh la[;k esa ifjorZu osQ lkFk fo?kVu dh nj esa ifjorZu n'kkZus okykxzkiQ [khafp,A

13.13 fp=k 13.2 esa n'kkZ, nks uewuksa A vFkok B esa fdldh vkSlr vk;q de gS\

13.14 fuEu esa ls dkSu fofdj.k mRl£tr ugha dj ldrk vkSj D;ksa\

mÙksftr ukfHkd] mÙksftr bysDVªkWu

13.15 ;qXe foyksiu esa ,d bysDVªkWu rFkk ,d ikWftVªkWu ,d nwljs dk vfLrRo lekIr djxkek fofdj.k mRiUu djrs gSaA blesa laosx lajk.k oSQls gksrk gS\

y?kqmÙkjh; (SA)

13.16 LFkk;h ukfHkdksa esa izksVkWuksa dh la[;k U;wVªkWuksa dh la[;k ls dnkfi vfèkd ugha gksldrh] D;ksa\

13.17 fdlh jsfM;ks,fDVo ukfHkd A ij fopkj dhft, ftlosQ fdlh LFkk;h ukfHkd C rdfo?kVu dk ozQe bl izdkj gS

A → B → C

;gk¡ B dksbZ eè;orhZ ukfHkd gS tks jsfM;ks,fDVo Hkh gSA ;g ekurs gq, fd izfozQ;k osQizkajHk esa A esa ijek.kqvksa dh la[;k N

0 gSA A vkSj B osQ ijek.kqvksa dh la[;k esa le;

osQ lkFk ifjorZu dks n'kkZus okyk xzkiQ [khafp,A

13.18 fdlh izkphu bekjr osQ [kaMgj ls izkIr ydM+h osQ ,d VqdM+s esa 14C dh lfozQ;rkblosQ dkcZu va'k dh 12 fo?kVu izfr feuV izfr xzke ikbZ tkrh gSA fdlh ltho

A

B

t

d N

d t

fp=k 13.2

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87

ydM+h dh 14C dh lfozQ;rk 16 fo?kVu izfr feuV izfr xzke gksrh gSA fdrus le;iwoZ og o`k ftldh ydM+h dk ;g izkIr uewuk gS] dkVk x;k Fkk\ 14C dh vèkkZ;q5760 o"kZ gSA

13.19 D;k U;wfDy;kWu ewy d.k gSa vFkok muosQ vkSj NksVs Hkkx Hkh gksrs gSaA blosQ vUos"k.kdh ,d fofèk ;g Hkh gks ldrh gS fd U;wfDy;kWu dk mlh izdkj vUos"k.k fd;k tk,tSlk jnjiQksMZ us ,d ijek.kq ls fd;k FkkA fdlh U;wfDy;kWu osQ vUos"k.k osQ fy,bysDVªkWu dh xfrt mQtkZ fdruh gksuh pkfg,\ U;wfDy;kWu dk O;kl yxHkx 10–15 m

yhft,A

13.20 ;fn Z1 =N

2 rFkk Z

2 = N

1 gks rks fdlh ukfHkd1 dks fdlh nwljs ukfHkd2 dk niZ.k

leHkkfjd dgk tkrk gSA (a) 2311 Na dk niZ.k leHkkfjd ukfHkd D;k gS\ (b) nks niZ.k

laHkkfjdksa esa ls fdl ukfHkd dh ca/u mQtkZ vf/d gS vkSj D;ksa\

nh?kZmÙkjh; (LA)

13.21 dHkh&dHkh dksbZ jsfM;ks,fDVo ukfHkd fo?kfVr gksdj ,d ,slk ukfHkd cukrk gS tksLo;a Hkh jsfM;ks,fDVo gksrk gS] mnkgj.kkFkZ&

38 38 38

=2.48h =0.62h S Cl Ar→ →

vèkkZ;q vèkkZ;q. (LFkk;h)

eku yhft, ge t = 0 ij 1000 S38 ukfHkdksa ls izkjEHk djrs gSaA t = 0 ij 38Cl

dh la[;k 'kwU; gS rFkk t = ∞ ij iqu% 'kwU; gSA t osQ fdl eku ij ukfHkdksa dh la[;kvf/dre gksxh vkSj ml le; ;g la[;k D;k gksxh\

13.22 M~;wVjkWu ,d U;wVªkWu rFkk ,d izksVkWu dh og ifjc¼ voLFkk gS ftldh ca/u mQtkZB = 2.2 MeV gSA mQtkZ E dh ,d γ -fdj.k] M~;wVjkWu ukfHkd dh vksj bls U;wVªkWu+ izksVkWu esa bl izdkj fo[kf.Mr djus osQ fy, y;Hkwr dh tkrh gS fd U;wVªkWu ,oaizksVkWu vkifrr γ -fdj.k dh fn'kk esa xfr djsaA ;fn E = B gS] rks n'kkZb, fd ,slkdjuk laHko ugha gSA bl izdkj] ;g ifjdfyr dhft, fd ,slh izfozQ;k osQ fy, Bdh viskk E fdruk vfèkd gksuk pkfg,A

13.23 M;wVjkWu ukfHkdh; cyksa kjk mlh izdkj ca/k gksrk gS ftl izdkj izksVkWu rFkk bysDVªkWukjk cus gkbMªkstu ijek.kq esa p rFkk e fLFkj oS|qr cy kjk caèks gksrs gSaA ;fn ge ;gekusa fd M~;wVjkWu esa U;wVªkWu ,oa izksVkWu osQ eè; cy owQykWe foHko osQ :i esa fn;k

tk ldrk gS ftlesa izHkkoh vkos'k e ′ gSA2

0

1

4

eF

rε

′=

π

(e’/e) dk eku vkdfyr dhft, fn;k gS fd M~;wVjkWu dh ca/u mQtkZ 2.2 MeV gSA

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13.24 U;wfVªuks ifjdYiuk ls iwoZ β– fo?kVu izfd;k dks n→p + e laozQe.k le>k tkrk Fkk] ;fn ;g lR; gS rks ;g n'kkZb, fd ;fn U;wVªkWu fojke eas gks] rks izksVkWu vkSj bysDVªkWufu;r mQtkZvksa ls fudyasxsA bu mQtkZvksa dk ifjdyu dhft,A izk;ksfxd :i ls]bysDVkWu dh mQtkZ dk nh?kZ ijkl gksrk gSA

13.25 fdlh vKkr jsfM;ks lfozQ; U;wDykbM dh lfozQ;rk R ,d&,d ?kaVs osQ varjkyksa ijekih xbZ vkSj izkIr ifj.kkeksa dks bl izdkj lkj.kh&c¼ fd;k x;k%

t (h) 0 1 2 3 4

R (MBq) 100 35.36 12.51 4.42 1.56

(i) R rFkk t osQ chp xzkiQ [khafp, rFkk blls v/kZ;q ifjdfyr dhft,A

(ii)0

R

R

rFkk t osQ chp xzkiQ [khafp, vkSj blls v/kZ;q dk eku Kkr dhft,A

13.26 ,sls ukfHkd ftuesa izksVkWu dh LFkkf;Ro (magic) la[;k Z = 2, 8, 20, 28, 50, 52

rFkk U;wVªkWu dh LFkkf;Ro la[;k N = 2, 8, 20, 28, 50, 82 vkSj 126 gS vR;fèkdLFkk;h ik, tkrs gSaA

(i) 120Sn (Z = 50) rFkk 121Sb = (Z = 51) osQ fy, izksVkWu dh mQtkZ Sp

ifjdfyr djosQ bl rF; dks lR;kfir dhft,A

fdlh U;wDykbM osQ fy, izksVkWu i`Fkdu mQtkZ og U;wure mQtkZ gksrh gS tks mlU;wDykbM osQ fdlh ukfHkd ls U;wure n`<+rk ls ca/s izksVkWu dks i`Fkd djus osQfy, vko';d gksrh gSA ;g bl izdkj O;Dr dh tkrh gSA

Sp = (M

Z–1,

N + M

H – M

Z,N) c2

;gk¡ fn;k gS fd119In = 118.9058u,

120Sn = 119.902199u,

121Sb = 120.903824u,

1H = 1.0078252u

(ii) LFkkf;Ro la[;k dk vfLrRo D;k bafxr djrk gS\

23/04/18

vèkZpkyd bysDVªkWfudh& inkFkZ] ;qfDr;k¡ rFkkljy ifjiFk


14.1 rki esa o`f¼ ls fdlh vèkZpkyd dh pkydrk esa o`f¼ dk dkj.k ;g gS fd eqDrèkkjkokgdksa dk&

(a) la[;k ?kuRo c<+ tkrk gS

(b) foJkafr dky c<+ tkrk gS

(c) la[;k ?kuRo rFkk foJkafr dky nksuksa c<+ tkrs gSa

(d) la[;k ?kuRo c<+ tkrk gS vkSj foJkafr dky ?kV tkrk gS

14.2 fp=k 14.1 esa fdlh lafèk Mk;ksM osQ fy, lafèk osQUnz ls nwj tkus ij nwjhosQ lkFk lafèk osQ fljksa ij foHko izkphj esa vUrj dks n'kkZ;k x;k gSA blesaV

o lafèk osQ fljksa ij og foHko izkphj gS tks rc izHkkoh gksrh gS tc lafèk

osQ fljksa osQ chp dksbZ cSVjh u tqM+h gksA

(a) 1 ,oa 3 nksuksa vxzck;flr laf/ osQ laxr gSaA

(b) 3 vxzck;flr lafèk osQ laxr vkSj 1 i'pck;flr laf/ osQ laxr gSA

V0

1

2

3

vè;k; 14

vèkZpkyd bysDVªkWfudh&inkFkZ] ;qfDr;k¡ rFkk ljyifjiFk

fp=k 14.1

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(c) 1 vxzck;flr lafèk osQ laxr vkSj 3 i'pck;flr lafèk osQ laxr gSA

(d) 3 ,oa 1 nksuksa i'pck;flr laf/ osQ laxr gSaA

14.3 fp=k 14.2 esa Mk;ksMksa dks vkn'kZ ekusa rks&

(a) D1 vxzck;flr gS vkSj D

2 i'pck;flr gS] vr% /kjk A ls B dh vksj izokfgr

gksrh gSA

(b) D2 vxzck;flr vkSj D

1

i'pck;flr gS vr% B lsA dh vksj vFkok A ls Bdh vksj dksbZ èkkjk izokfgrugha gksrhA

(c) D1,oa D2 nksuksa vxzck;flr gSa] vr% èkkjk A ls B dh vksj vFkok B ls A dh vksjizokfgr gksrh gSA

(d) D1 ,oa D

2 nksuksa i'pck;flr gSa] vr% A ls B dh vksj vFkok B ls A dh vksj

dksbZ èkkjk izokfgr ugha gksrhA

14.4 220 V ac fo|qr iznk; fcUnqvksa A ,oa B osQ chp tqM+k gS (fp=k 14.3)A la/kfj=kosQ fljksa ij foHkokUrj V fdruk gksxk\

(a) 220V(b) 110V

(c) 'kwU;

(d) 220 2 V

14.5 gksy gksrk gS&

(a) bysDVªkWu dk izfrd.kA

(b) lgla;ksth vkcaèk ls ,d bysDVªkWu nwj fNVd tkus ij mRiUu fjfDrA

(c) eqDr bysDVªkWuksa dh vuqifLFkfr

(d) o`Qf=ke :i ls l`ftr dksbZ d.kA

14.6 fp=k 14.4 esa fn, x, ifjiFk dk fuxZe gksxk&

B

AR D1

D2

–10V

fp=k 14.2

fp=k 14.3

~vm sin wt

fp=k 14.4

(a) gj le; 'kwU;A

(b) fdlh vèkZ rjax fn"Vdkjh dh Hkk¡fr fuxZe esa /ukRedvèkZ pozQ gksaxsA

(c) fdlh vèkZ rjax fn"Vdkjh dh Hkk¡fr fuxZe esa ½.kkRedvèkZpozQ gksaxsA

(d) fdlh iw.kZ rjax fn"Vdkjh osQ fuxZe tSlkA

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14.7 fp=k 14.5 esa n'kkZ, ifjiFk esa ;fn Mk;ksM dk vxzfn'k oksYVrk ikr 0.3 V gS] rksA ,oa B osQ chp foHkokUrj gS&

(a) 1.3 V(b) 2.3 V

(c) 'kwU;(d) 0.5 V

14.8 fn, x, ifjiFk (fp=k 14.6) osQ fy, lR;kiu lkj.kh gS&

(a) A B E0 0 10 1 01 0 11 1 0

(b) A B E0 0 10 1 01 0 01 1 1

(c) A B E0 0 00 1 11 0 01 1 1

(d) A B E0 0 00 1 11 0 11 1 0


14.9 fdlh vèkZpkyd ij dksbZ fo|qr ks=k vuqiz;qDr fd, tkus ij&

(a) pkyu cSaM esa bysDVªkWu fuEurj mQtkZ Lrjksa ls mPprj mQtkZ Lrjksa dh vksj xfrdjrs gSaA

(b) pkyu cSaM esa bysDVªkWu mPprj mQtkZ Lrjksa ls fuEurj mQtkZ Lrjksa dh vksj xfrdjrs gSaA

(c) la;kstdrk cSaM esa gksy mPprj mQtkZ Lrjksa ls fuEurj mQtkZ Lrjksa dh vksj xfrdjrs gSaA

A

0.2 mA

5 K

5 K

B

E

A

B

C

D

fp=k 14.5

fp=k 14.6

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(d) la;kstdrk cSaM esa gksy fuEurj mQtkZ Lrjksa ls mPprj mQtkZ Lrjksa dh vksj xfrdjrs gSaA

14.10 eku yhft, fdlh ,d n-p-n VªakftLVj vk/kj&mRltZd laf/ dks vxzck;l rFkklaxzkgd vk/kj laf/ dks i'pck;l fn;k x;k gSA fuEufyf[kr esa dkSu lk@ls izdFkulR; gS@gSa\

(a) bysDVªkWu mRltZd ls laxzkgd dh vksj laozQe.k djrs gSaA

(b) gksy vk/kj ls laxzkgd dh vksj xfr djrs gSaA

(c) bysDVªkWu mRltZd ls vk/kj dh vksj xfr djrs gSaA

(d) bysDVªkWu mRltZd ls laxzkgd esa tk, fcuk vkèkkj ls ckgj fudy tkrs gSaA

14.11 fp=k 14.7 esa vk/kj ck;flr CE VªakftLVj osQ vUrj.k vfHkyk.k n'kkZ, x, gSaAfuEufyf[kr esa dkSu ls izdFku lR; gSa\

(a) V1 = 0.4V ij VªakftLVj lfozQ; voLFkk esa gSA

(b) V1 = 1V ij ;g izo/Zd dh Hkk¡fr mi;ksx fd;k tk ldrk gSA

(c) V1 = 0.5V ij bls ^vkWu* fLop osQ :i esa mi;ksx fd;k tk ldrk gSA

(d) V1 = 2.5V ij bls ^vkWiQ* fLop osQ :i esa mi;ksx fd;k tk ldrk gSA

14.12 fdlh n-p-n VªakftLVj ifjiFk esa laxzkgd /kjk 10 mA gSA ;fn 95% mRlftZrbysDVªkWu laxzkgd ij igq¡prs gksa] rks fuEufyf[kr esa dkSu lk@ls izdFku lR; gS@gSa\

(a) mRltZd /kjk 8 mA gksxhA

(b) mRltZd /kjk 10.53 mA gksxhA

(c) vk/kj /kjk 0.53 mA gksxhA

(d) vk/kj /kjk 2 mA gksxhA

14.13 fdlh Mk;ksM osQ ßklh ks=k esa&

(a) dksbZ xfr'khy vkos'k ugha gksrsA

(b) leku la[;k esa bysDVªkWu ,oa gksy gksrs gSa ftlls ks=k mnklhu gks tkrk gSA

(c) gksyksa vkSj bysDVªkWuksa dk iqul±;kstu gks tkrk gSA

(d) vkos'k;qDr fu'py vk;u fo|eku gksrs gSaA

14.14 tsuj Mk;ksM dh fu;ked fozQ;k osQ le; D;k gksrk gS\

(a) tsuj Mk;ksM esa izokfgr /kjk vkSj blosQ fljksa ij oksYVrk fLFkj jgrh gSA

(b) Js.khozQe esa yxs izfrjks/ (Rs) ls izokfgr /kjk ifjofrZr gksrh gSA

(c) tsuj izfrjks/ fu;r jgrk gSA

(d) tsuj Mk;ksM izfrjks/ esa ifjorZu gksrk gSA

fp=k 14.7

Vo

0 0.6V 2V Vi

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93

14.15 fdlh fn"Vdkjh ifjiFk esa la/kfj=k fiQYVj kjk rjafxdkvksa osQ vk;ke dks ?kVkusosQ fy,&

(a) RL dks c<+kuk pkfg,A

(b) fuos'k vko`fÙk ?kVkuh pkfg,A

(c) fuos'k vko`fÙk c<+kuh pkfg,A

(d) vf/d /kfjrk osQ la/kfj=kksa dk mi;ksx djuk pkfg,A

14.16 i'p ck;flr p-n laf/ Mk;ksM esa Hkatu dh laHkkouk fdlosQ dkj.k vf/d gksrh gS\

(a) ;fn eknu lkanzrk de gS rks vYika'k vkos'k okgdksa osQ mPp osx osQ dkj.kA

(b) ;fn eknu lkanzrk vf/d gS rks vYika'k vkos'k okgdksa osQ mPp osx osQ dkj.kA

(c) ;fn eknu lkanzrk de gS rks ßklh ks=k esa izcy fo|qr ks=k osQ dkj.kA

(d) ;fn eknu lkanzrk vf/d gS rks ßklh ks=k esa izcy fo|qr ks=k osQ dkj.kA


14.17 flfydu ;k tesZfu;e osQ eknu osQ fy, rkfRod ekndksa dk p;u izk;% ;k rks lewgXIII vFkok lewg XV osQ rRoksa esa ls gh D;ksa fd;k tkrk gS\

14.18 Sn, C, rFkk Ge, Si lHkh lewg XIV osQ rRo gSaA fiQj Hkh Sn pkyd gS] C

fo|qrjks/h gS tcfd Si ,oa Ge vèkZpkyd gSaA ,slk D;ksa gS\

14.19 D;k p-n laf/ osQ fljksa ij foHko izkphj dh eki osQoy laf/ ij oksYVrkekih tksM+dj dh tk ldrh gS\

14.20 izfrjks/d osQ fljksa osQ chp fuxZe rjax:i cukb, (fp=k 14.8)A

fp=k 14.8

–1V

0

+1V

A

V0

p

14.21 izo/Zdksa X, Y ,oa Z dks Js.khozQe esa tksM+k x;k gSA ;fn X, Y ,oa Z dh oksYVrkyfC/ ozQe'k% 10, 20 ,oa 30 vkSj fuos'k flXuy dk f'k[kj eku 1 mV gS] rksfuxZr flXuy oksYVrk dk f'k[kj eku D;k gksxk] tcfd

(i) dc iznk; oksYVrk 10V gS\

(ii) dc iznk; oksYVrk 5V gS\

A ij fuos'kh rjax:i

23/04/18


94

fp=k 14.9

P

I

( A)m

(volt)V

P

I

Q

V

14.22 fdlh CE VªkaftLVj izo/Zd ifjiFk ls dksbZ /kjk vkSj oksYVrk yfC/ lac¼ gSA nwljs'kCnksa esa] dksbZ 'kfDr&yfC/ gksrh gS\ 'kfDr dks mQtkZ dh eki ekurs gq, D;k blifjiFk esa mQtkZ lajk.k dk mYya?ku gksrk gS\

y?kqmÙkjh; (SA)

14.23

fp=k 14.10

(i) ml Mk;ksM osQ izdkj dk uke fyf[k, ftlosQ vfHkykf.kd fp=k 14.9 (a) ,oa(b) esa n'kkZ, x, gSaA

(ii) fp=k 14.9 (a) esa fcUnq P D;k fu:fir djrk gS\

(iii) fp=k 14.9 (b) esa fcUnq P ,oa Q D;k fu:fir djrs gSa\

14.24 rhu iQksVks Mk;ksM D1, D2 ,oa D3 ,sls vèkZpkydksa ls cuk, x, gSa ftuosQ cSaM varjkyozQe'k% 2.5 eV, 2 eV ,oa 3 eV gSaA buesa ls dkSu lk Mk;ksM 6000Å rjaxnS?;Z osQizdk'k dk lalwpu djus ;ksX; gksxk\

14.25 ;fn izfrjks/ R1 c<+k;k tkrk gS (fp=k 14.10) rks ,ehVj rFkk oksYVehVj osQ

ikB~;kadksa esa D;k ifjorZu gksaxs\

(a) (b)

23/04/18


95

fp=k 14.11

D1

D2

A

B

V0

+5V

R

14.26 nks dkj xSjktksa dk ,d mHk;fu"B Lopkfyr izos'k kj gS tks fdlh Hkh ,d xSjkt esafdlh dkj osQ izos'k djus ij ;k nksuksa xSjktksa esa dkjksa osQ izos'k djus ij vius vkils [kqy tkrk gSA Mk;ksMksa dk mi;ksx djosQ bl izdkj dh fLFkfr osQ fy, ifjiFkcukb,A

14.27 fdlh VaªkftLVj dk mi;ksx djosQ NOT kj izkIr djus osQ fy, vki ifjiFk oSQlsLFkkfir djsaxs\

14.28 Li"V dhft, fd rkfRod vèkZpkydksa dk mi;ksx n`"; LEDs cukus esaD;ksa ugha fd;k tk ldrkA

14.29 fp=k 14.11 esa fn, x, ifjiFk dh lR;eku lkj.kh cukb,A ifjiFk osQrqY; roZQ kj dk uke fyf[k,A

14.30 1 W 'kfDr lhekad osQ fdlh tsuj Mk;ksM dks oksYVrk fu;ked osQ:i esa mi;ksx fd;k tkuk gSA ;fn tsuj dh Hkatu oksYVrk 5V gS vkSjbls 3V vkSj 7V osQ chp mPpkopu dh oksYVrk dk fu;eu djuk gSrks blosQ fujkin izpkyu osQ fy, fdl eku osQ Rs dk mi;ksx fd;ktkuk pkfg, (fp=k 14.12)\

nh?kZmÙkjh; (LA)

14.31 ;fn fp=k 14.13 esa n'kkZ, x, izR;sd Mk;ksM dk vxzck;l izfrjks/ 25Ω rFkk i'pck;l izfrjks/ vuUr gks] rks /kjk I

1, I

2, I

3 ,oa I

4 osQ eku D;k gksaxs\

fp=k 14.12

AI4

I3

I2

5VG

I4

E

C

B

D

F

H

25W

125W

125W

125WI4

fp=k 14.13

Rp

400

kW

RC

10V

3kW

Vi

fp=k 14.14

14.32 fp=k 14.14 esa n'kkZ, x, ifjiFk esa tc vk/kj izfrjks/ ij fuos'k oksYVrk 10V gS]rks Vbe 'kwU; gS rFkk Vce Hkh 'kwU; gSA Ib, Ic rFkk β osQ eku Kkr dhft,A

23/04/18


96

14.33 fp=k 14.15 esa kjksa osQ fn, x, la;kstuksa osQ fuxZe flXuyksa C1 ,oa C2 dks vkjsf[krdhft,A

A

B

0

0

1

1

2

2

3

3

4

4

5

5

t (s)

t (s)

A

B

C1

A

BC2

14.34 CE foU;kl esa n-p-n VªkaftLVj osQ fuos'k vkSj fuxZe vfHkykf.kdksa dk vè;;udjus osQ fy, fp=k 14.16 (a) esa fn, x, ifjiFk ij fopkj dhft,A;fn fdlh VªakftLVj osQ fy, V

BE = 0.7 V gS] rks R

B vkSj R

C osQ ,sls ekuksa dk

p;u dhft, ftuosQ fy, VªkaftLVj fp=k 14.16 (b) esa n'kkZ, vfHkykf.kd fcUnqQ ij izpkfyr gksAfn;k gS fd VªkaftLVj dk fuos'k izfrckèkk cgqr de gS rFkk V

CC = V

BB = 16 V

gSA mi;qDr iwoZ/kj.kkvksa dk mYys[k djrs gq, ifjiFk dh oksYVrk yfC/ rFkk 'kfDryfC/ Hkh Kkr dhft,A

VBE

VCE

VBB

BC

E

RC

VCCRB

ICC

fp=k 14.16 (a)

IC

(mA)

IB = 30 Am

8V VCE (Volts)

4mAQ

fp=k 14.15

fp=k 14.17

14.35 ;g ekurs gq, fd Mk;ksM ,dvkn'kZ Mk;ksM gS fp=k 14.17

esa fn, x, ifjiFk dk fuxZerjax:i cukb,A bl rjax :idh O;k[;k dhft,A

~ 5V

fp=k 14.16 (b)

20 sin ω t

23/04/18


97

mA

VDC

V+

–

14.36 eku yhft, fdlh Si fozQLVy] ftlesa 5 × 1028 ijek.kq izfr ?ku ehVj gSa] dks As

dh 1ppm laknzrk kjk ekfnr djosQ n-izdkj osQ vèkZpkyd dh dksbZ ijr cukbZ xbZgSA blosQ i`"B ij cksjkWu dh 200 ppm laknzrk ls ekfnr ‘P’ ks=k fufeZr fd;k x;kgSA ;g ekurs gq, fd ni = 1.5 × 1016 m–3, (i) n rFkk p ks=kksa esa vkos'k okgdksa dkla[;k ?kuRo ifjdfyr dhft,A (ii) fVIi.kh dhft, fd Mk;ksM dks i'pck;flrdjus ij dkSu ls vkos'k&okgd O;qRozQe lar`fIr /kjk osQ fuekZ.k esa vfèkdak'k ;ksxnkudjsaxs\

14.37 fdlh X-OR kj dh lR;eku lkj.kh uhps nh xbZ gS%

A B Y

0 0 0

0 1 1

1 0 1

1 1 0

bls fuEufyf[kr roZQ laca/ kjk fu:fir fd;k x;k gS

Y =A.B+ A.B

bl kj dh jpuk AND, OR ,oa NOT kjksa dk mi;ksx djosQ dhft,A

14.38 fdlh ckWDl ftlosQ 'kh"kZ Hkkx ij] fp=k 14.18 (a) esa n'kkZ, vuqlkj rhu VfeZuyyxs gSa] ij fopkj dhft,%

A

BC

fdlh O;oLFkk esa bu VfeZuyksa osQ fljksa ij rhu vo;o ls nkstesZfu;e Mk;ksM vkSj ,d izfrjks/d la;ksftr fd, x, gSaAdksbZ fo|kFkhZ iz;ksx djrs le; bu rhu VfeZuyksa esa ls fdUghanks dks tksM+dj fp=k 14.18 (b) esa n'kkZ, vuqlkj ifjiFkcukrk gSAog fo|kFkhZ ifjiFk esa bu nks VfeZuyksa osQ chp tqM+s vo;oksa osQvKkr la;kstu osQ fy, /kjk&oksYVrk vfHkykf.kd izkIr djrk gSA

fp=k 14.18 (a)

fp=k 14.18 (b)

ckWDlVfeZuy

23/04/18


98

;s xzkiQ bl izdkj gSa

(i) tc A /ukRed ,oa B ½.kkRed gS%

I

V

(ii) tc A ½.kkRed ,oa B /ukRed gS%

I

V0.7V

(iii) tc B ½.kkRed ,oa C èkukRed gS%

I

V

0.7V

(iv) tc B /ukRed ,oa C ½.kkRed gS%

I

V

10001

ioz .krk

fp=k 14.18 (c)

fp=k 14.18 (d)

fp=k 14.18 (e)

fp=k 14.18 (f)

23/04/18


99

(v) tc A /ukRed ,oa C ½.kkRed gS%

I

V

(vi) tc A ½.kkRed ,oa C /ukRed gS%

I

V1.4V

fp=k 14.18 (c) ls (h) rd esa n'kkZ, /kjk&oksYVrk vfHkykf.kdksa osQ xzkiQksa osQvk/kj ij A, B ,oa C osQ chp yxs vo;oksa dh O;oLFkk dk fuèkkZj.k dhft,A

14.39 fp=k 14.19 esa n'kkZ, x, VªkaftLVj ifjiFk osQ fy, VE, R

B, ,oa R

E dk

ifjdyu dhft,A fn;k gS% IC = 1 mA, V

CE = 3V, V

BE = 0.5 V rFkk

VCC

= 12 Vβ = 100

fp=k 14.18 (g)

fp=k 14.19

fp=k 14.18 (h)

A

VC

R = 7.8KC

RE

V = 12VCC

RB

20K

23/04/18


100

fp=k 14.20

ARC100K

12V

20K

C

E

14.40 fp=k 14.20 esa n'kkZ, ifjiFk esa RC dk eku Kkr dhft,A

23/04/18

101

lapkj O;oLFkk

101


15.1 rhu rjaxsa A, B vkSj C ftudh vko`fÙk;k¡ ozQe'k% 1600 kHz, 5 MHz vkSj 60

MHz gSa] ,d LFkku ls nwljs LFkku ij Hksth tkuh gSaA fuEu esa ls dkSu lk lapkj dkloksZi;qDr <ax gSA

(a) A dks vkdk'k rjax osQ :i esa rFkk B vkSj C dks O;kse rjaxksa osQ :i esa Hkstk tk,A

(b) A dks Hkw rjax] B dks O;kse rjax rFkk C dks vkdk'k rjax osQ :i esa Hkstk tk,A

(c) B vkSj C dks Hkw rjax] rFkk A dks O;kse rjax osQ :i esa Hkstk tk,A

(d) B dks Hkw rjax rFkk A vkSj C dks vkdk'k rjax osQ :i esa Hkstk tk,A

15.2 ,d 100 m yack ,UVsuk 500 m mQ¡ph bekjr ij yxk gSA ;g la;kstu λ rjaxnS?;Z dhrjaxksa osQ fy, ,d lapj.k Vkoj (transmission tower) cu tk,xk tgk¡ λ gS&

(a) ~ 400 m

(b) ~ 25 m

(c) ~ 150 m

(d) ~ 2400 m

vè;k; 15

lapkj O;oLFkk

23/04/18

102


102

15.3 ,d 1 kW flXuy dks ,d lapkj pSuy dk mi;ksx djosQ izsf"kr fd;k tkrk gSA blpSuy esa flXuyksa dk 2dB izfr fdyksehVj dh nj ls kh.ku gks tkrk gSA ;fn lapkjpSuy dh oqQy yEckbZ 5 km gks rks] izkIr flXuy dh 'kfDr gksxh [dB esa O;Dr yfCèk

= 10 log 0

i

P

P

]

(a) 900 W

(b) 100 W

(c) 990 W

(d) 1010 W

15.4 3 kHz vko`fÙk dk ,d oko~Q flXuy] 1 MHz vko`fÙk osQ ,d okgd flXuy dksvk;ke ekMqyhdj.k kjk ekMqfyr djus osQ fy, iz;qDr fd;k x;k gSA ik'oZ cS.Mksa dhvko`fÙk;k¡ gksaxh&

(a) 1.003 MHz o 0.997 MHz

(b) 3001 kHz o 2997 kHz

(c) 1003 kHz o 1000 kHz

(d) 1 MHz o 0.997 MHz

15.5 ωm vko`fÙk osQ ,d lans'k flXuy dks] vk;ke ekMqfyr (AM) rjax izkIr djus osQ fy,]

ωc vko`fÙk dh ,d okgd rjax ij vkjksfir (superposed) fd;k x;k gSA

AM rjax dh vko`fÙk gksxh&

(a) ωm

(b) ωC

(c)2

c mω ω+

(d)–

2c mω ω

15.6 pkj ;qfDr;ksa osQ I-V vfHkykkf.kd oozQ fp=k 15.1 esa fn[kk, x, gSaA

I

V

I

V

I

V

I

V

(a) (b) (c) (d)

fp=k 15.1

23/04/18

103

lapkj O;oLFkk

103

ekMqyhdj.k osQ fy, mi;ksx esa yh tk ldus okyh ;qfDr gS&

(a) ‘a’ o ‘c’ osQ laxr

(b) osQoy ‘c’ osQ laxr

(c) ‘b’ rFkk ‘d’ osQ oqQN Hkkx osQ laxr

(d) lHkh pkjksa ;qfDr;k¡

15.7 ,d iq#"k dh ok.kh] ekMqyhdj.k o izs"k.k osQ i'pkr] xzkgh dks efgyk dh ok.kh dhHkk¡fr lqukbZ nsrh (izrhr gksrh) gSA bldk dkj.k gS&

(a) vuqi;qDr ekMqyu lwpdakd dk pquko (0 < m < 1 pquk x;k)

(b) vko/Zdksa osQ fy, vuqi;qDr cS.M pkSM+kbZ dk pquko

(c) okgd rjaxksa dh vko`fÙk dk vuqi;qDr pquko

(d) lapj.k esa mQtkZ&ßklA

15.8 ,d ewy&lapkj izozQe esa gksrk gS&

(A) izs"kd

(B) lwpuk L=kksr

(C) lwpuk dk mi;ksx djus okyk

(D) pSuy

(E) xzkgh

fuEufyf[kr esa dkSu og lgh ozQe iznku djrk gS ftlesa ;s ,d ewy lapkj izozQeesa O;ofLFkr gksrs gSa&

(a) ABCDE

(b) BADEC

(c) BDACE

(d) BEADC

15.9 vk;ke ekMqfyr rjaxksa osQ xf.krh; O;atd dh igpku dhft,&

(a) Ac sin [ω

c + k

1v

m(t)t + φ ]

(b) Ac sin ω

ct + φ + k

2 v

m(t)

(c) Ac + k

2 v

m(t) sin (ω

ct

+ φ )

(d) Ac v

m(t) sin (ω

ct

+ φ )


15.1015kHz vko`fÙk dk ,d èofu flXuy] fcuk ekMqfyr gq, vf/d nwjh rd izsf"kr ughafd;k tk ldrk gS D;ksafd&

23/04/18

104


104fp=k 15.2

ωc – ω

m

ωc – ω

m ωc + ω

m ω ωc – ω

mω

c + ω

mω

(i) (ii)

(iii) (iv)

yfCèk

ωc + ω

mω

yfCèk

yfCèk yfCèk

(a) ,UVsuk dk visfkr lkbt+ de ls de 5 km gksxk] tks lqfo/ktud ugha gSA

(b) èofu flXuy O;kse rjax osQ :i esa iszf"kr ugha fd, tk ldrsA

(c) vko';d ,UVsuk dk lkbt de ls de 20 km gksxk] tks lqfo/ktud ugha gSA(d) izHkkoh iszf"kr 'kfDr cgqr de gksxh] ;fn ,UVsuk dk lkbt 5 km ls de gSA

15.11 3 kHz vko`fÙk dh èofu T;k&rjaxsa] 1.5 MHz osQ okgd flXuyksa dks ekMqfyr djusosQ fy, mi;ksx esa ykbZ tk jgh gSaA fuEufyf[kr esa ls dkSu lk dFku lgh gS&

(a) ik'oZ cS.M vko`fÙk;k¡ 1506 kHz rFkk 1494 kHz gSaA(b) vk;ke ekMqyu osQ fy, vko';d cS.M dh pkSM+kbZ 6kHz gSA(c) vk;ke ekMqyu osQ fy, vko';d cS.M dh pkSM+kbZ 3MHz gSA(d) ik'oZ cS.M vko`fÙk;k¡ 1503 kHz rFkk 1497 kHz gSaA

15.12 ,d Vh- oh- lapj.k Vkoj dh mQ¡pkbZ 240 m gSA blls izlkfjr fd, tkus okysflXuy] n`f"V js[kk lapj.k (LOS) kjk ftl nwjh rd izkIr fd, tk ldrs gSa og gSa&(i`Foh dh f=kT;k 6.4 × 106 m eku fyft,)

(a) 100 km(b) 24 km

(c) 55 km(d) 50 km

15.13 vk;ke&ekMqfyr rjaxksa osQ mRiknu esa mi;ksx gksus okys fdlh fiQYVj ifjiFk dkvko`fÙk vuqfozQ;k oozQ (fp=k 15.2) gS&

ω

23/04/18

105

lapkj O;oLFkk

105

(a) (i) mlosQ ckn (ii)

(b) (ii) mlosQ ckn (i)(c) (iii)

(d) (iv)

15.14 vk;ke ekMqyu esa] ekMqyu&lwpdakd m dks 1 osQ cjkcj ;k 1 ls de j[kk tkrkgS] D;ksafd&

(a) m > 1 ij] okgd vko`fÙk;ksa rFkk lans'k vko`fÙk;ksa esa O;frdj.k gksxk iQyLo:ifoo`Qfr gksxhA

(b) m > 1 ij nksuksa ik'oZ cS.Mksa dk vfrO;kiu gksxk iQyLo:i lwpuk dk ßklgksxkA

(c) m > 1 ij okgd rjaxksa rFkk lans'k flXuy osQ eè; dyk esa ifjorZu gksxkA(d) m > 1 ij lans'k flXuy osQ vk;ke dk okgd rjaxksa osQ vk;ke ls vf/d gksuk

bafxr djrk gS fd blosQ iQyLo:i foo`Qfr gksrh gSA


15.15 fuEufyf[kr esa fdlesa vuq:i (analog) flXuy rFkk fdlesa vadh; (digital)

flXuy mRiUu gksrs gSa\

(i) ,d dfEir Lofj=k fHkqt

(ii) flrkj osQ dfEir rkj dh lqLoj èofu

(iii) izdk'k LiUn

(iv) NAND xsV (kj) dk fuxZr

15.16 D;k O;kse rjaxsa] 60 MHz vko`fÙk osQ (Vh-oh-) flXuyksa dks izsf"kr djus osQ fy,mi;qDr gksaxh\

15.17 nks rjaxsa A rFkk B ftudh vko`fÙk;k¡ 2 MHz vkSj 3 MHz gSa] ,d gh fn'kk esa] O;kserjax osQ kjk lapfjr djus osQ fy, fodhf.kZr dh tkrh gSaA buesa ls dkSu lh vk;ue.My ls iw.kZ&vkUrfjd ijkorZu osQ iwoZ vf/d nwjh r; dj ldrh gS\

15.18 ,d vk;ke ekMqfyr (AM) rjax dk vf/dre vk;ke 15 V izkIr gksrk gS tcfdbldk U;wure vk;ke 3 V izkIr gksrk gSA ekMqyu lwpdakd Kkr djsaA

15.19 vk;ke ekMqyu gsrq] 1 MHz vko`fÙk dh okgd rjaxksa dk mRiknu djus osQ fy,vko';d] ,d leLofjr vko/Zd ifjiFk osQ LC xq.kuiQy dh x.kuk dhft,A

23/04/18

106


106

15.20 fdlh pSuy ls lapj.k ij] vk;ke ekMqfyr (AM) flXuy esa] vko`fÙk ekMqfyrflXuy (FM) ls vf/d jo D;ksa gksrk gS\

y?kqmÙkjh; (SA)

fp=k 15.3

15.21 fp=k 15.3 esa ,d lapkj iz.kkyh iznf'kZr gSA ;fn fuos'k laosQr (flXuy) 1.01mW

dk gks rks fuxZe 'kfDr fdruh gksxh\ [dB esa O;Dr yfC/ = 10 log10

(Po/P

i )]A

15.22 ,d nwjn'kZu lapj.k Vkoj ,UVsuk 20m dh mQ¡pkbZ ij gSA blls fdrus ks=k esa laosQrizkIr gks losaQxs& ;fn xzkgh ,UVsuk (i) Hkwry ij gks (ii) Hkwry ls 25 m mQ¡pkbZ ijgks (iii) izFke fLFkfr osQ lkisk frh; fLFkfr esa blesa gksus okyh izfr'kr o`f¼ dkifjdyu dhft,A

15.23 ;fn vkdk'k rjaxksa dk iz;ksx djosQ LOS (n`f"V js[kk) lapj.k osQ kjk laiw.kZ i`Fohdks tksM+uk gks (,UVsuk osQ vkdkj vFkok Vkoj dh mQ¡pkbZ ij dksbZ izfrca/ ugha gSA)rks vko';d ,UVsukvksa dh U;wure la[;k fdruh gksuh pkfg,\ bu ,UVsukvksa osQ VkWojksadh mQ¡pkbZ i`Foh dh f=kT;k osQ inksa esa ifjdfyr dhft,A

15.24 vk;ueaMy dh ,d fo'ks"k ijr ls ifjofrZr gksus okyh O;kse rjaxksa dh vf/drevko`fÙk f

max = 9(N

max)1/2 ikbZ tkrh gS] tgk¡ N

max ml vk;ueaMy dh ijr esa

vfèkdre bysDVªkWu ?kuRo gSA fdlh fnu ;g izsk.k fd;k x;k fd 5MHz ls vfèkdvkofÙk osQ flXuy vk;ueaMy dh F

1 ijr ls ijko£rr gksdj izkIr ugha gksrs gSa tcfd

8MHz ls vf/d vko`fÙk osQ flXuy vk;ueaMy dh F2 ijr ls ijkorZu osQ kjk

izkIr ugha gksrs gSaA ml fnu F1 rFkk F

2 ijrksa osQ vf/dre bysDVªkWu ?kuRo dh x.kuk

dhft,A

15.25 ,d vk;ke ekMqfyr flXuy (laosQr) dks fofdfjr djus ij (Hkstus ij) oqQyfofdfjr 'kfDr ω

c, ω

c – ω

m vkSj ω

c + ω

m dh mQtkZ osQ dkj.k gksrh gSA lwpuk dh

xq.koÙkk le>kSrk u djrs gq,] fofdj.k dh ykxr U;wure djus osQ <ax lq>kb,A

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lapkj O;oLFkk

107

nh?kZmÙkjh; (LA)

15.26 (i) fdlh lapkj pSuy osQ vuqfn'k xfr'khy izdk'k LiUn dh rhozrk] nwjh osQ lkFkpj?kkrkadh :i ls] fuEu laca/ osQ vuqlkj ?kVrh gS] I = I

oe–αx, tgk¡ I

o, x = 0

ij rhozrk gS rFkk α khj.k fu;rkad gSA fn[kkb;s fd ln4

α

nwjh r; djus

osQ i'pkr~ rhozrk esa 75% dh deh vk tkrh gSA

(ii) fdlh laosQr (flXuy) osQ khj.k dks (dB) esa laca/ 10 log10

o

I

I

osQ

vuqlkj O;Dr dj ldrs gSaA ,d vkWfIVdy iQkbcj osQ fy, dB/km esa khj.kD;k gksxk ftlesa 50 km nwjh r; djus ij rhozrk 50 izfr'kr fxj tkrh gSA

15.27 50 MHz dh ,d O;kse rjax i`Foh dh lrg ls 600 km mQij fLFkr ,d mixzgls iqu% iszf"kr gksdj ,d xzkgh rd igq¡pus esa 4.04 ms ysrh gSA ;fn mixzg kjkiqu% izs"k.k osQ le; dks ux.; ekusa rks] L=kksr vkSj xzkgh osQ chp dh nwjh Kkr dhft,A;fn bu nksuksa osQ chp LOC (n`f"V js[kk i¼fr) ls lapkj.k gks rks xzkgh rFkk izs"kd,UVsuk dk lkbt rFkk fLFkfr D;k gksxh\

15.28 ,d vk;ke ekMqfyr rjax fp=k 15.4 esa fn[kkbZ xbZ gSA ifjdyu dhft,&(i) ekMqyu izfr'kr (ii) f'k[kj okgd foHko (iii) lwpuk foHko dk f'k[kj eku

fp=k 15.4

(100V)

(20V)

V

t

15.29 (i) ,d vk;ke ekMqfyr rjax osQ fy,] ftldh okgd rjax (ωc) esa] nks ekMqyd

laosQr (flXuy) ω1 rFkk ω

2 (ω

2 > ω

1) gSa] osQ fy, vk;ke vkSj ω osQ chp

xzkiQ [khafp,A [laosQr% ,u-lh-bZ-vkj-Vh- dh dkk 12 dh ikB~;iqLrd osQlehdj.k 15.6 dh O;qRifÙk dk vuqlj.k dhft,]

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108

(ii) D;k oozQ ωc osQ lkisk lefer gS\ oozQ esa ω < ω

c osQ ks=k osQ fy, fo'ks"k fVIi.kh

dhft,\(iii) mRiUu gksus okyh mu leL;kvksa dk vuqeku yxkb, rFkk cfgosZ'ku dhft, ;fn

vf/d rjaxksa dk ekMqyu fd;k tkuk gksA(iv) mijksDr leL;kvksa dk gy lq>kb;sA bl izfozQ;k esa cSaM dh pkSM+kbZ osQ lUnHkZ esa

D;k vU; ykHk Hkh gks ldrs gSa\

15.30 ,d èofu flXuy (laosQr) 20MHz dh okgd rjax kjk bl izdkj ekMqfyr fd;kx;k gS fd ekMqyu osQ fy, vko';d cSaM dh pkSM+kbZ 3kHz gSA D;k bl rjax dk,d Mk;ksM (diode) lalwpd kjk foekMqyu (demodulation) fd;k tk ldrkgS ftlosQ fy, R vkSj C osQ eku gSa\(i) R = 1 kΩ, C = 0.01µ F(ii) R = 10 kΩ, C = 0.01µ F(iii) R = 10 kΩ, C = pF

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203

izfrn'kZ iz'u i=k

HkkSfrdhdkk XII

le; : 3 ?kaVs vf/dre vad : 70

iz'u i=k osQ fofHkUu vk;keksa ij vadksa dk forj.k fuEuor gksxkµ

A. fo"k; oLrq@ikB&bdkb;ksa osQ vuqlkj vad forj.k

Ø- la- bdkbZ vad

1. fLFkjoS|qfrdh 08

2. fo|qr /kjk 07

3. /kjk dk pqEcdh; izHkko vkSj pqEcdRo 08

4. oS|qr pqEcdh; izsj.k vkSj izR;korhZ /kjk 08

5. fo|qr pqEcdh; rjaxsa 03

6. izdkf'kdh 14

7. fofdj.k rFkk nzO; dh Sr izÑfr 04

8. ijek.kq vkSj ukfHkd 06

9. v/Zpkyd bysDVªkWfudh 07

10. lapkj O;oLFkk 05

;ksx 70

B. iz'uksa osQ izdkj osQ vuqlkj vad forj.k

Ø- la- iz'u dk izdkj izR;sd iz'u esa vad iz'uksa dh la[;k oqQy vad

1. nh?kZ mÙkjh; iz'u (LA) 5 3 15

2. y?kq mÙkjh; iz'u (I) SA (I) 3 09 27

3. y?kq mÙkjh; iz'u (II) SA (II) 2 10 20

4. vfr y?kq mÙkjh; iz'u (VSA) 1 08 08

cgq&fodYih; iz'u (MCQ)

;ksx – 30 70

iz'u i=k dk fM”kkbu

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1 vad osQ iz'u vfr y?kq mÙkjh; (VSA) izdkj osQ gks ldrs gSa ;k fiQj ,sls cgq&fodYih iz'u (MCQ) gks ldrs gSa ftuesa

osQoy ,d gh fodYi lgh gksA

C. oSdfYid iz'uksa dh ;kstuk

1. iz'u&i=k esa lexz ij dksbZ fodYi (vksoj vky p;u) ugha gSA

2. oqQN iz'uksa esa vR;ar p;ukRed vk/kj ij vkarfjd p;u (;g ;k fiQj ;g izdkj) dh lqfo/k nh xbZ gSA

D. iz'uksa osQ dfBukbZ Lrj osQ vuqlkj vad forj.k

Ø-la- vuqekfur dfBukbZ Lrj vad forj.k (izfr'kr)

1. vlku 15

2. eè;e 70

3. dfBu 15

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izfrn'kZ iz'u i=k

izfrn'kZ iz'u i=k ICyw fiazV (:ijs[kk)

fo"k; VSA (1 vad) SA II (2 vad) SA I (3 vad) LA (5 vad) ;ksx

I fLFkjoS|qfrdh 1(1) 4 (2) 3 (1) — 8 (4)

II fo|qr /kjk 1 (1) — 6 (2) — 7 (3)

III /kjk dk pqEcdh; izHkko 1 (1) 2 (1) — 5 (1) 8 (3)

vkSj pqEcdRo

IV fo|qr pqEcdh; izsj.k vkSj 1(1) 2 (1) — 5 (1) 8 (3)

izR;korhZ /kjk

V fo|qr pqEcdh; rjaxsa 1 (1) 2 (1) — — 3 (2)

VI izdkf'kdh — — 9 (3) 5 (1) 14 (4)

VII fofdj.k rFkk nzO; dh — 4 (2) — — 4 (2)

Sr izÑfr

VIII ijek.kq vkSj ukfHkd 1(1) 2 (1) 3 (1) — 6 (3)

IX v/Zpkyd bysDVªkWfudh 2 (2) 2 (1) 3 (1) — 7 (4)

X lapkj O;oLFkk — 2 (1) 3 (1) — 5 (2)

;ksx 8 (8) 20 (10) 27 (9) 15 (3) 70 (30)

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206

izfrn'kZ iz'u i=k IHkkSfrdhdkk 12


lkekU; funsZ'k %

(i) lHkh iz'u vfuok;Z gSaA

(ii) bl iz'u i=k esa 30 iz'u gSaA iz'u 1 ls 8 rd osQ iz'u ,d vad osQ gSa] iz'u 9 ls 18 rd osQ izR;sd iz'u nks vadksa osQ]iz'u 19 ls 27 rd osQ izR;sd iz'u rhu vadksa osQ rFkk iz'u 28 ls 30 rd osQ izR;sd iz'u ik¡p vadksa osQ gSaA

(iii) iz'u i=k esa lexz ij dksbZ fodYi ugha gSA rFkkfi] ik¡p vad osQ rhuksa iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA ,sls iz'uksa esa lsvkidks osQoy ,d fodYi dk mÙkj nsuk gSA

(vi) oSQyoqQysVj osQ mi;ksx dh vuqefr ugha gSA

(v) tgk¡ vko';d gks vki fuEufyf[kr fu;rkadksa osQ ekuksa dk mi;ksx dj ldrs gSaµ

c = 3 × 108 m s-1

h = 6.6 × 10-34 J s

e = 1.6 × 10-19 C

µo = 4π × 10-7 T m A-1

29

20

1 Am9 10

4 Cπε= ×

cksYV~”keku fu;rkad] k = 1.38 × 1023 JK–1

,oksxknzks la[;k NA = 6.023 × 1023/mole

U;wVªkWu dk nzO;eku mn = 1.6 × 10–27 kg

1. fp=k 1.1 esa y-vk osQ vuqfn'k fLFkr nks oS|qr vkos'k q2 rFkk q

3, x-vk osQ vuqfn'k fLFkr oS|qr vkos'k q

1 ij]

+ x fn'kk esa dksbZ usV fo|qr cy vkjksfir djrs gSaA ;fn (x, 0), ij dksbZ /ukos'k Q j[k fn;k tk, rks q1 ij vkjksfir

cyq2

q1

q3

x

y

( 0)x,

Q

O

q2

q1

q3

x

y

O

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izfrn'kZ iz'u i=k

(a) /ukRed x-vk osQ vuqfn'k c<+ tk,xkA

(b) /ukRed x-vk osQ vuqfn'k ?kV tk,xkA

(c) Í.kkRed x-vk osQ vuqfn'k laosQr djsxkA

(d) c<+ tk,xk ijUrq q2 ,oa q

3 osQ lkFk Q osQ izfrPNsnu osQ dkj.k fn'kk ifjofrZr gks tk,xhA

2. nks cSVfj;k¡ ftuosQ emf ε1 rFkk ε

2 [ε

2 > ε

1] rFkk vkUrfjd izfrjks/

ozQe'k% r1 rFkk r

2 gSa] fp=k esa n'kkZ, vuqlkj ik'oZ ozQe esa la;ksftr

gSaA

(a) nksuks a lsyksa dk rqY; fo|qr okgd cy εrqY;] ε

1 rFkk ε

2 osQ

chp vFkkZr~] ε1<

εrqY; <

ε

2 gSA

(b) rqY; fo|qr okgd cy εrqY;] ε

1 ls de gSA

(c) lnSo εrqY; = ε

1 +

ε

2 gksrk gSA

(d) εrqY;

vkUrfjd izfrjks/ksa r1 rFkk r

2 ij fuHkZj ugha gSA

3. bysDVªkWu dh Hkkafr izksVkWu esa Hkh pozQ.k rFkk pqEcdh; vk?kw.kZ gksrk gSA rc inkFkksZa osQ pqEcdRo esa blosQ izHkko dh miskkD;ksa dh tkrh gS\

4. ;fn fdlh LC ifjiFk dks vkorhZ nksyudkjh fLaizx&CykWd iz.kkyh osQ rqY; le>k tkrk gS rc bl LC ifjiFk dhdkSu&lh mQtkZ fLFkfrt mQtkZ osQ vkSj dkSu&lh xfrt mQtkZ osQ rqY; gksxh\

5. ifjorZuh; vko`fÙk dk ,d a.c. lzksr ,d la/kfj=k ls tqM+k gSA vko`fÙk esa deh djus ij foLFkkiu /kjk fdl izdkjizHkkfor gksxh\

6. ;qXe foyksiu esa ,d bysDVªkWu rFkk ,d ikWftVªkWu ,d nwljs dk vfLrRo lekIr dj xkek fofdj.k mRiUu djrs gSaA blesalaosx lajk.k oSQls gksrk gS\

7. D;k p-n laf/ osQ fljksa ij foHko izkphj dh eki osQoy laf/ ij oksYVrkekih tksM+ dj dh tk ldrh gS\

8. rki esa o`f¼ ls fdlh vèkZpkyd dh pkydrk esa o`f¼ dk dkj.k ;g gS fd eqDr èkkjk okgdksa dkµ

(a) la[;k ?kuRo c<+ tkrk gSA

(b) foJkafr dky c<+ tkrk gSA

(c) la[;k ?kuRo rFkk foJkafr dky nksuksa c<+ tkrs gSaA

(d) la[;k ?kuRo c<+ tkrk gS vkSj foJkafr dky ?kV tkrk gSA

9. nks vkos'kksa q rFkk –3q dks x-vk ij ‘d’ nwjh osQ i`Fkdu osQ lkFk j[kk x;k gSA rhljs vkos'k 2q dks dgk¡ j[kk tk,rkfd ;g dksbZ cy vuqHko u djs\

10. fdlh lekarj ifêðdk la/kfj=k dh ifêð;ksa osQ chp ,d ijkoS|qr ifêðdk j[kh tkrh gSA la/kfj=k cSVjh ls la;ksftr jgrhgSA la/kfj=k osQ (i) foHkokUrj] (ii) /kfjrk] (iii) oS|qr ks=k] rFkk (iv) lapfjr ÅtkZ esa bldk D;k izHkko iM+sxk\

B

r2

r1

A

e1

e2

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11. cksj ekWMy esa ifjØeh bysDVªkWu dks pqEcdh; f/zqo vk?kw.kZ osQ fy, O;atu izkIr dhft,A

12. dldj fyiVh ifjukfydk osQ :i esa dksbZ rkj fdlh fn"V/kjk lzksr ls la;ksftr gS vkSj blesa fo|qr èkkjk izokfgr gksjgh gSA ;fn oqQ.Myh dks bl izdkj ls [khapk tk, fd lfiZykdkj oqQ.Myh osQ ozQekxr yisVksa osQ chp vUrjky gks tk,]rks D;k fo|qr /kjk c<+sxh vFkok ?kVsxh] Li"V dhft,A

13. vkidks ,d 2 µF dk lekUrj IysV la/kfj=k fn;k x;k gSA vki bldh IysVksa osQ chp osQ vUrjky esa 1mA dhrkRkf.kd foLFkkiu /kjk oSQls LFkkfir djsaxs\

14. nks izdk'k lzksr gSa ftuesa izR;sd 100 W 'kfDr mRltZu djrk gSA buesa ls ,d 1nm rjaxnS?;Z dh X&fdj.ksa vkSj nwljk500 nm dk n`'; izdk'k mRlftZr djrk gSA nh xbZ rjaxnS?;ks± osQ fy, X–fdj.kksa osQ iQksVkWuksa dh la[;k rFkk n`';izdk'k osQ iQksVkWuksa dh la[;k dk vuqikr Kkr dhft,A

15. ,d d.k bysDVªkWu dh viskk rhu xquk vf/d pky ls xfr dj jgk gSA bl d.k dh ns&czkWXyh rjaxnS?;Z rFkk bysDVªkWuosQ ns&czkWXyh rjaxnS?;Z dk vuqikr 1.813 × 10–4 gSA d.k osQ nzO;eku dk ifjdyu dhft, rFkk d.k dks igpkfu,A

16. nks fHkUu gkbMªkstu ijek.kq ysaA izR;sd ijek.kq esa bysDVªkWu mÙksftr voLFkk esa gSaA cksj ekWMy osQ vuqlkj D;k ;g laHkogS fd bysDVªkWuksa dh mQtkZ rks fHkUu gks ijUrq dkh; dks.kh; laosx leku gks\

17. fdlh p-n laf/ osQ fy, ^àklh ks=k* rFkk ^jksf/dk foHko* inksa dk rkRi;Z D;k gS\

18. ;fn vkdk'k rjaxksa dk iz;ksx djosQ LOS (n`f"V js[kk) lapj.k osQ kjk laiw.kZ i`Foh dks tksM+uk gks (,UVsuk osQ vkdkjvFkok Vkoj dh mQ¡pkbZ ij dksbZ izfrca/ ugha gS) rks vko';d ,UVsukvksa dh U;wure la[;k fdruh gksuh pkfg,\ bu,UVsukvksa osQ Vkojksa dh mQ¡pkbZ i`Foh dh f=kT;k osQ inksa esa ifjdfyr dhft,A

19. fdlh oS|qr f/zqo osQ dkj.k fo"kqorh; ry ij fLFkr fcUnqvksa osQ fy, oS|qr ks=k dk O;atu lafn'k :i esa izkIr dhft,Avf/d nwfj;ksa ij ks=k oSQls cnyrk gS\

20. ^foJkafr dky* D;k gS\ foJkafr dky* rFkk bysDVªkWuksa dh la[;k ?kuRo osQ inksa esa fdlh pkyd dh izfrjks/drk dkO;atu izkIr dhft,A

21. igys R izfrjks/ osQ n leku izfrjks/dksa osQ leqPp; dks Js.khozQe esa emf E rFkk vkUrfjd izfrjks/ R dh cSVjh lsla;ksftr fd;k x;kA ifjiFk esa /kjk I izokfgr gksrh gSA rRi'pkr~ n izfrjks/dksa dks blh cSVjh ls ik'oZozQe esa la;ksftrfd;k x;kA ;g ik;k x;k fd /kjk 10 xquk c<+ x;hA ‘n’ dk D;k eku gS\

22. dksbZ lery ysal (viorZukad 1.50) fdlh lery niZ.k osQ iQyd ij fdlh nzodh ijr osQ laioZQ esa j[kk x;k gS tSlk fp=k esa n'kkZ;k gSA dksbZ NksVh lqbZ ftldh uksadeq[; vk ij gS] vk osQ vuqfn'k Åij&uhps xfr djkdj bl izdkj lek;ksftr dh tkrhgS fd lqbZ dh ukssad dk myVk izfr¯cc lqbZ dh fLFkfr ij gh cusA bl fLFkr esa lqbZ dhysal ls nwjh 45.0 cm gSA nzo dks gVkdj iz;ksx dks nksgjk;k tkrk gSA u;h nwjh 30.0 cm

ekih tkrh gSA nzo dk viorZukad D;k gS\

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izfrn'kZ iz'u i=k

23. laioZQ esa j[ks irys ysalks osQ la;kstu osQ iQksdl nwjh osQ fy, O;atu izkIr dhft,A

24. d1 > d

2 > d

3 ?kuRoksa rFkk µ

1 > µ

2 > µ

3 viorZukadksa osQ rhu vfeJ.kh; nzoksa dks ,d chdj esa j[kk x;k gSA izR;sd

nzo osQ LraHk dh mQ¡pkbZ 3

h gSA chdj dh iSanh ij ,d fcUnq cuk;k x;k gSA lkekU; fudV n`f"V osQ fy, fcanq dh

vkHkklh xgjkbZ Kkr dhft,A

25. fdlh jsfM;ks,fDVo inkFkZ osQ fy, ^v/Z&vk;q* rFkk ^vkSlr&vk;q* dks ifjHkkf"kr dhft,A nksuksa esa D;k laca/ gS\

26. NOR xsV] OR xsV rFkk NOT xsV osQ mfpr la;kstu ls fuEu lR;eku lkj.kh izkIr djus osQ fy, ifjiFk cukb;sA

27. vk;ke ekMqfyr rjax osQ fy, êkMqyu lwpdkad* dks ifjHkkf"kr dhft,A fdlh vk;ke ekMqfyr rjax dk vf/drevk;ke ‘a’ gS rFkk Û;wure vk;ke* ‘b’ gSA bldk êkMqyu lwpdkad* D;k gksxk\

28. (i) fdlh fo|qr /kjkokgh o`Ùkkdkj ik'k osQ vk ij pqEcdh; ks=k osQ fy, O;atu dh mRifÙk dhft,A

(ii) 10 cm f=kT;k dks 100 dldj yisVs x, isQjksa dh fdlh ,slh oqaQMyh ij fopkj dhft, ftlesa 1A fo|qr/kjk izokfgr gks jgh gSA oqaQMyh osQ osaQnz ij pqEcdh; ks=k dk ifjek.k D;k gS\

vFkok

,sfEi;j osQ ifjiFkh; fu;e dk dFku nhft,A ,d yacs lh/s o`Ùkkdkj vuqizLFk dkV osQ rkj (ftldh f=kT;k a gS)ij fopkj dfj, ftlesa LFkk;h fo|qr /kjk I izokfgr gks jgh gksA fo|qr /kjk bl vuqizLFk dkV ij ,dleku :i lsforfjr gSA ,sfEi;j osQ ifjiFkh; fu;e dk mi;ksx dj ks=kksa r < a rFkk r > a esa pqEcdh; ks=k ifjdfyr dhft,A

29. ,d ac cksYVrk v = vm sinωt fdlh Js.khc¼ LCR ifjiFk ij iz;qDr gSA ifjiFk esa /kjk rFkk /kjk ,oa cksYVrk osQ

eè; dykdks.k osQ fy, O;atu izkIr dhft,A vuqukn vko`fÙk D;k gS\

vFkok

,d ac cksYVrk v = vm sinωt fdlh 'kq¼ izsjd ij iz;qDr gSA ifjiFk esa /kjk dk O;atu izkIr dhft,A fl¼ dhft,

fd ,d iwjs pØ esa fdlh izsjd dks vkiwrZ ekè; 'kfDr 'kwU; gksrh gSA

30. (i) gkbxsal fl¼kar dk dFku vkSj O;k[;k dhft,A bldk mi;ksx djrs gq, LuSy dk viorZu laca/h fu;e izkIrdhft,A

A B Y

0 0 0

0 1 0

1 0 1

1 1 0

A B Y

0 0 1

0 1 1

1 0 0

1 1 1

(i) (ii)

23/04/18


210

(ii) tc izdk'k fojy ls l?ku ekè;e esa xfr djrk gS rks mldh pky esa deh vkrh gSA D;k pky esa vkbZ deh izdk'krjaxksa kjk lapkfjr ÅtkZ dh deh dks n'kkZrh gS\

vFkok

fpfÉr fdj.k vkjs[k dh lgk;rk ls la;qDr lwen'khZ kjk izfr¯cc cuuk n'kkZb,A blosQ vko/Zu osQ fy, O;atuO;qRifÙk dfj,A vko/Zu dks oSQls c<+k;k tk ldrk gS\

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211

izfrn'kZ iz'u i=k

izfrn'kZ iz'u i=k Igy ,oa vadu ;kstuk

1. (a) (1)

2. (a) (1)

3. 2p

p

e

mµ ≈

vkSj ,2 2

e

e

e h

mµ

π≈ = (1/2)

e pµ µ>> D;ksafd mp >> m

e. (1/2)

4. pqEcdh; mQtkZ xfrt mQtkZ osQ ln`'k rFkk oS|qr mQtkZ fLFkfrt mQtkZ osQ ln`'kA (1/2), (1/2)

5. vko`fÙk ?kVkus ij izfr?kkr 1cX

Cω= c<+sxk tks pkyu /kjk dks ?kVk,xkA bl fLFkfr esa i

D = i

C; vr% foLFkkiu /kjk de gks

tk,xhA (1/2, 1/2)

6. nks iQksVkWu mRiUu gksrs gSa] tks ÅtkZ&lajk.k gsrq foijhr fn'kkvksa esa xfr djrs gSaA (1)

7. th ugha] D;ksafd lafèk&izfrjksèk dh rqyuk esa oksYVehVj dk izfrjksèk vR;qPp gksuk gh pkfg,] tcfd lafèk izfrjksèk yxHkxvuUr gSA (1/2, 1/2)

8. (d) (1)

9. fcUnq P ij fLFkr vkos'k 2q ij q osQ dkj.k cy ck;ha vksj rFkk –3q osQ dkj.k nk;ha vksj gSA

∴ q q

x d x

2 2

2 20 0

2 6

4 4 ( )πε πε=

+(1/2)

∴ (d + x)2 = 3x2

∴ 2x2 – 2dx – d2 = 0

d dx

3

2 2= ± (1/2)

(½.kkRed fpg~u ysus ij x dk eku q rFkk –3q osQ chp gksxk] vr% ;g ekU; ugha gSA)

d d dx

3(1 3)

2 2 2= + = + q osQ ck;ha vksjA (1)

10. tc cSVjh la;ksftr jgrh gS]

(i) foHkokUrj V vpj jgrk gSA (1/2)

(ii) /kfjrk C c<+rk gSA (1/2)

P q

– q32q x

d

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(iii) fo|qr ks=k ?kVrk gSA (1/2)

(iv) lapkfjr ÅtkZ c<+rh gS D;ksafd C c<+rk gSA (1/2)

11. /I e T= (1/2)

2 /T r vπ= (1/2)

2 /2l IA I r evrµ π= = = (1/2)

2l

e

el

mµ = (1/2)

12. èkkjk c<+ tk,xhA tSls gh rkjksa dks ,d nwljs ls nwj [khapk tkrk gS fjDr LFkkuksa ls ÝyDl dk kj.k gksrk gSA ysat+ osQ fu;e osQvuqlkj izsfjr fo|qr okgd cy bl deh dk fojksèk djrk gS ftls fo|qr èkkjk esa o`f¼ kjk iwjk fd;k tkrk gSA (1,1)

13.D

dVi C

dt= (1/2)

–3 –61 10 2 10dV

dt× = ×

3 2110 5 10 /

2

dVV s

dt= × = × (1/2)

vr% 5 × 102 V/s dk ifjorhZ foHkokUrj yxk dj yfkr eku dh foLFkkiu èkkjk mRiUu dh tk ldrh gSA (1)

14. oqQy E fu;r gSA (1/2)

eku yhft, n1 rFkk n

2 X-fdj.kksa rFkk n`'; ks=k osQ iQksVkWu dh la[;k gSA

n1E

1 = n

2E

2(1/2)

1 2

1 2

hc hcn n

λ λ=

1 1

2 2

.n

n

λ

λ= (1/2)

1

2

1

500

n

n= (1/2)

15. xfr djrs gq, d.k (nzO;eku m rFkk osx v) dh ns&czkWXyh rjaxnS?;Z :

λ =h/p=h/mv

nzO;eku m=h/λv 1/2)

bysDVªkWu dk nzO;eku me = h/λ

e v

e

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izfrn'kZ iz'u i=k

gesa Kkr gS fd v/ve = 3 rFkk λ/λ

e = 1.813 × 10−4

d.k dk nzO;eku] m= me (λ

e/λ) (v

e/v) (1/2)

m = (9.11 × 10-31 kg) × (1/3)× (1/1.813 ×10-4)

m =1 × 1.675 × 10-27 kg. (1/2)

bl nzO;eku dk d.k izksVkWu ;k U;wVªkWu gks ldrk gSA (1/2)

16. ugha] D;ksafd cksgj izfr:i osQ vuqlkj 2

13.6–=nE

n, (1)

vkSj fHkUu&fHkUu mQtkZ osQ bysDVªkWu fofHkUu n& eku okys Lrjksa ls lEc¼ gksrs gSa% vr% muosQ dks.kh;&laosx fHkUu gksaxs] D;ksafd

.2π

=nh

mvr (1)

17. ifjHkk"kk % àklh ks=k (1)

ifjHkk"kk % jksf/dk foHko (1)

18. 2 22( )m Td R h= + (1/2)

8RhT = 2(R+h

T)2 ( 2 2 )m Td Rh=∵

2 24 2T T TRh R h Rh= + +

(R – hT)2 = 0

R = hT

(1/2)

D;ksafd osQoy vkdk'k rjax vko`fÙk iz;qDr gqbZ gS] λ << hT vr% osQoy ehukj dh mQ¡pkbZ dk fopkj djsaA f=kfoeh; vkdk'k

esa] hT = R, osQ 6 ,sUVhuk&ehukj iz;qDr gksaxsA (1)

19. mRifÙk (2)

vf/d nwjh osQ fy,] E ∝ 1/r3 (1)

20. ifjHkk"kk (1)

mRifÙk (2)

21. I = E/(R+nR) (1)

10I = E/(R+R/n) (1)

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(1+n)/(1+1/n) = 10 = (1+n)/(n+1)n = n, n = 10. (1)

22. mÙky ysal rFkk lery&mÙky nzo ysal osQ la;kstu dh iQksdl nwjh 45 cm gSA tc nzO; fudky ysrs gSa rks f 1= 30 cm mÙky

ysal dh iQksdl nwjh gksrh gSA ;fn f2 lery&mÙky nzo ysal dh iQksdl nwjh gks rks

1 2

1 1 1

f f f+ = (1/2)

2

2 1

1 1 1 1 1 1, 90cm

45 30 90f

f f f

−= − = − = = − (1/2)

ysal&esdj lw=k dk iz;ksx djus ls ( R1=R, R

2=–R )

( )2 1 2

1 1 1 1 1 1( 1) 1.5 1 30 cm

30R

f R R R Rµ

= − − ⇒ = − + ⇒ =

(1/2,1/2)

lery&mÙky ysal osQ fy,

2 1 2

1 1 1( 1)

f R Rµ

= − −

(1/2)

1 1 1 1( 1)

90 30 30

µµ

− − = − − =

∞ −

µ = 1.33 (1/2)

23. mRifÙk] 1 2

1 1 1...

f f f= + + (3)

24. ekuk fd µ2 ls oLrq dks ns[kus ij vkHkklh xgjkbZ O

1 gS %

21

1

O3

hµ

µ= (1)

µ3 ls ns[kus ij] vkHkklh xgjkbZ O

2 gS %

2 3 33 32 1

1 2 12 2

O O3 3 33

h h hh µ µ µµ µ

µ µ µµ µ

+ += = =+

(1)

ckgj ls ns[kus ij] vkHkklh Å¡pkbZ gS %

O

m3

m2

m1

h/3

h/3

h/3

O3

O2

O1

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izfrn'kZ iz'u i=k

3 23

1 hO +O

3µ

=

= 3 3

2 13

1++

3 3

h h

µ µ

µ µµ

1 2 3

1 1 1+ +

3

h =

µ µ µ (1)

25. ifjHkk"kk ,oa O;atu (1/2,1/2)

ifjHkk"kk ,oa O;atu (1/2,1/2)

nksuksa esa laca/ (1)

26. A, B = (0,1) rFkk (1,0) osQ fy, fuxZr lefer ugha gSA ,d fuos'k ij NOT xsVA (1)

(i) esa rhu 'kqU; gSA NOR xsV %

vr% (1)

(ii) esa rhu ,dkad gSA OR xsV %

vr% (1)

27. ifjHkk"kk] µ = Am/A

c(1)

a = Ac + A

m

b = Ac - A

m(1/2)

Ac = (a + b)/2, A

m = (a–b)/2 (1/2)

µ = (a - b)/(a+b) (1)

28. (i) mRifÙk (3)

(ii) pw¡fd oqaQMyh dldj yisVh xbZ gS vr% ge izR;sd o`Ùkkdj vo;o dh f=kT;k R = 10 cm = 0.1m eku ldrs gSaA isQjksadh la[;k N=100 gS] vr% pqEcdh; ks=k dk ifj.kke

B = µ0N I/(2 R) = 4π×107×10–2× 1/(2 ×10−1) = 2π×10–4 = 6.28 × 10–4 T. (2)

vFkok

,sfEi;j fu;e dk dFku (1)

mRifÙk B = µ0 I/2πr, for r > a (2)

mRifÙk B = (µ0 I/2πa2) r, for r < a (2)

A

BY

A

BY

23/04/18


216

29. mRifÙk (4)

vuqukn vko`fÙk (1)

vFkok

mRifÙk (3)

iwziQ (2)

30. (i) dFku ,oa O;k[;k (1)

LuSy fu;e dh mRifÙk (3)

(ii) ughaA rjax kjk ys tkus okyh ÅtkZ rjax osQ vk;ke ij fuHkZj djrh gS] ;g rjax lapj.k dh pky ij fuHkZj ughadjrhA (1)

vFkok

la;qDr lwen'khZ kjk izfr¯cc cuus dk vafdr fdj.k vkjs[k (2)

vko/Zu osQ fy, O;atu O;qRifÙk 1o e

L Dm

f f

= +

(2)

vf/d vko/Zu izkIr djus osQ fy, vfHkn`';d rFkk usf=kdk dh iQksdl nwjh de gksuh pkfg,A O;ogkj esa]1cm ls de iQksdl nwjh dk ysal cukuk vR;ar dfBu dk;Z gSA blh osQ lkFk L dks cM+k djus osQ fy, cM+sysalksa dh vko';drk gksrh gSA (1)

23/04/18

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izfrn'kZ iz'u i=k

izfrn'kZ iz'u i=k IICyw ¯izV (:ijs[kk)

fo"k; VSA (1 vad) SA II (2 vad) SA I (3 vad) LA (5 vad) ;ksx

I fLFkjoS|qfrdh 1(1) 2 (1) — 5 (1) 8 (3)

II fo|qr /kjk — 4 (2) 3 (1) — 7 (3)

III /kjk dk pqEcdh; izHkko 1 (1) 4 (2) 3 (1) — 8 (4)

vkSj pqEcdRo

IV fo|qr pqEcdh; izsj.k vkSj 1(1) 2 (1) — 5 (1) 8 (3)

izR;korhZ /kjk

V fo|qr pqEcdh; rjaxsa 1 (1) 2 (1) — — 3 (2)

VI izdkf'kdh 2 (2) 4 (2) 3 (1) 5 (1) 14 (6)

VII fofdj.k rFkk nzO; dh 1 (1) — 3 (1) — 4 (2)

Sr izÑfr

VIII ijek.kq vkSj ukfHkd — — 6 (2) — 6 (2)

IX v/Zpkyd bysDVªkWfudh 1 (1) — 6 (2) — 7 (3)

X lapkj O;oLFkk — 2 (1) 3 (1) — 5 (2)

;ksx 8 (8) 20 (10) 27 (9) 15 (3) 70 (30)

23/04/18


218

izfrn'kZ iz'u i=k IIHkkSfrdhdkk 12


lkekU; funsZ'k %

(i) lHkh iz'u vfuok;Z gSaA

(ii) bl iz'u i=k esa 30 iz'u gSaA iz'u 1 ls 8 rd osQ iz'u ,d vad osQ gSa] iz'u 9 ls 18 rd osQ izR;sd iz'u nks vadksa osQ] iz'u19 ls 27 rd osQ izR;sd iz'u rhu vadksa osQ rFkk iz'u 28 ls 30 rd osQ izR;sd iz'u ik¡p vadksa osQ gSaA

(iii) iz'u i=k esa lexz ij dksbZ fodYi ugha gSA rFkkfi] ik¡p vad osQ rhuksa iz'uksa esa vkUrfjd fodYi fn;s x;s gSaA ,sls iz'uksa esa lsvkidks osQoy ,d fodYi dk mÙkj nsuk gSA

(vi) oSQyoqQysVj osQ mi;ksx dh vuqefr ugha gSA

(v) tgk¡ vko';d gks vki fuEufyf[kr fu;rkadksa osQ ekuksa dk mi;ksx dj ldrs gSa %

c = 3 × 108 m s-1

h = 6.6 × 10-34 J s

e = 1.6 × 10-19 C

µo = 4π × 10-7 T m A-1

29

20

1 Am9 10

4 Cπε= ×

cksYV~”kleku fu;rkad] k = 1.38 × 1023 JK–1

,oksxknzks la[;k NA = 6.023 × 1023/mole

U;wVªkWu dk nzO;eku mn = 1.6 × 10–27 kg

1. fp=k esa n'kkZ, ifjiFk esa 4 µ F dk la/kfj=k la;ksftr gSA cSVjh dk vkUrfjd izfrjks/ 0.5 Ω gSA la/kfj=k dh IysVksaij vkos'k dh ek=kk gksxh&

(a) 0

(b) 4 µ C

(c) 16 µ C

(d) 8 µ C

4 Fm

10W

2.5V

2W

23/04/18

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izfrn'kZ iz'u i=k

2. nks vkosf'kr d.k fdlh ,dleku pqEcdh; ks=k B = B0 k esa iw.kZr% loZle lfiZy iFkksa ij foijhr fn'kkvksa esa xeu

djrs gSa rks buosQ

(a) laosxksa osQ z-vo;o leku gksus pkfg,A

(b) vkos'k leku gksus pkfg,A

(c) vkos'k vo'; gh d.k&izfrd.k ;qxy dks fu:fir djrs gksaxsA

(d) vkos'k ,oa nzO;eku dk vuqikr lacaèk% 1 2

0e e

m m

+ =

dh iqf"V djsxkA

3. dksbZ ifjukfydk fdlh cSVjh ls la;ksftr gS ftlosQ dkj.k mlesa vifjorhZ /kjk izokfgr gks jgh gSA ;fn bl ifjukfydkosQ Hkhrj dksbZ yksg ozQksM j[k fn;k tk, rks fo|qr èkkjk ?kVsxh vFkok c<+sxh\ Li"V dhft,A

4. izksisQlj lh- oh- je.k us ,d ikjn'khZ fuokZfrr izdks"B esa ,d NksVh gydh xsan dks ystj iaqt ls izdkf'kr dj Lora=krkiwoZdfcuk vk/kj osQ Bgjk dj fn[kk;k vkSj vius fo|kfFkZ;ksa dks vk'p;Zpfdr dj fn;kA os oS|qrpqEcdh; rjaxksa osQ fdlxq.k dks iznf'kZr dj jgs Fks\ bl xq.k dk ,d vkSj mnkgj.k nhft,A

5. ok;q;ku esa dksbZ ;k=kh

(a) dHkh Hkh bUnz/uq"k ugha ns[k ikrk gSA

(b) izkFkfed rFkk frh;d bUnz/uq"k dks laosaQnzh o`Ùkksa osQ :i esa ns[k ikrk gSA

(c) izkFkfed rFkk frh;d bUnz/uq"k dks laosaQnzh vkoZQ osQ :i esa ns[k ikrk gSA

(d) dHkh Hkh frh;d bUnz/uq"k ugha ns[k ikrk gSA

6. lw;Z osQ izdk'k osQ fy, i`Foh ij rjaxkxz dh vko`Qfr oSQlh gksrh gS\

7. dksbZ bysDVªkWu (nzO;eku m) ftldk izkjafHkd osx 0 0ˆ( 0)v v= >v i gS fdlh fo|qr ks=k 0 0

ˆ– ( 0 )E E= = >E i vpj

esa xfreku gSA t k.k ij bl bysDVªkWu dh ns&czkWXyh rjaxnS?;Z gS %

(a) 0

0

0

1eE t

m v

+

λ

(b)0

00

1eE t

mv

+

λ

(c) λ0

(d) λ0t.

8. Li"V dhft, fd rkfRod vèkZpkydksa dk mi;ksx n`'; LED cukus esa D;ksa ugha fd;ktk ldrkA

9. ik¡p vkos'k] ftuesa izR;sd q gS] ‘a’ Hkqtk osQ fdlh fu;fer iapHkqt osQ dksuksa ij j[ks

x;s gSa tSlk fp=k esa n'kkZ;k x;k gSA

A

B

CD

E

q

q

qq

q

O

r

a

23/04/18


220

(i) ;fn fdlh ,d dksus (tSls A) ls vkos'k dks gVk fn;k tk, rks O ij fo|qr ks=k fdruk gksxk\

(ii) ;fn A ij vkos'k dks –q kjk izfrLFkkfir dj fn;k tk, rks O ij fo|qr ks=k fdruk gksxk\

10. fo|qr okgd cy E1 ,oa E

2 okys nks lsyksa dk vkarfjd izfrjks/ Øe'k% r

1 ,oa r

2 gSA

buosQ ik'oZØe esa la;kstu osQ

fy, rqY; fo|qr ckgd cy dk O;atu izkIr dhft,A

11. ,d lsy ,oa ,d /kjk fu;a=kd osQ lgk;rk ls cus foHko&foHkktd dk ifjiFk vkjs[k cukb;sA vkjs[k esa fuXkZr fljksadks n'kkZb,A

12. ;fn pqacdh; ,dy /zqoksa dk vfLrRo gksrk rks pqacdRo laca/h xkml dk fu;e D;k :i xzg.k djrk\

13. vk.kfod n`f"Vdks.k ls izfrpqEcdRo] vuqpqEcdRo rFkk yksgpqEcdRo dh pqEcdh; izo`fÙk;ksa dh rki fuHkZjrk dhfoospuk dhft,A

14. ,d ySai fdlh la/kfjr osQ lkFk Js.khØe esa tqM+k gSA dc ,oa ac la;kstuksa osQ fy, vius izsk.kksa dh izkxqfDr dhft,AizR;sd izdj.k esa crkb, fd la/kfj=k dh /kfjrk de djus dk D;k izHkko gksxk\

15. 25 MHz vko`fÙk dh ,d lery oS|qrpqEcdh; rjax fuokZr esa x- fn'kk osQ vuqfn'k xfreku gSA fnDdky (space)

esa fdlh fof'k"V ¯cnq ij bldk E = 6.3 j V/m gSA bl ¯cnq ij B dk eku D;k gS\

16. ^ysal dh kerk* dh ifjHkk"kk nhft,A n'kkZb;s fd ysal dh kerk iQksdl nwjh osQ O;qRØekuqikrh gSA

17. nks f>fj;k¡ 1 feyhehVj nwj cukbZ xbZ gSa vkSj ijns dks 1 ehVj nwj j[kk x;k gSA fizaQt varjky fdruk gksxk tc500 nm rjaxnS?;Z dk uhyk&gjk izdk'k iz;ksx esa yk;k tkrk gS\

18. 10 kHz vko`fÙk rFkk 10 V f'k[kj oksYVrk osQ lans'k flXuy dk mi;ksx fdlh 1 MHz vko`fÙk rFkk 20 V f'k[kjoksYVrk dh okgd rjax dks ekMqfyr djus esa fd;k x;k gSA (i) ekMqyu lwpdkad rFkk (ii) mRiUu ik'oZ cSaM Kkr dhft,A

19. foHkoekih dh lgk;rk ls fdlh lsy osQ vkarfjd izfrjks/ osQ ekiu osQ fy, ifjiFk [khafp,A ftl fl¼kar ij ;gfof/ vk/kfjr gS mls le>kb,A

20. izfrpqEcdRo] vuqpqEcdRo rFkk yksgpqacdRo ls vki D;k le>rs gSa\

21. fdlh lwen'khZ kjk mlh vfHkn`';d osQ fy, nks fcUnqvksa esa Hksn djus osQ fy,] muosQ chp U;wure i`Fkduksa osQ

vuqikr dks Kkr dhft, tcfd inkFkZ dks iznhIr djus osQ fy, 5000 A

osQ izdk'k dk rFkk 100 V ls RofjrbysDVªkWuksa dk mi;ksx fd;k x;k gks\

22. 6.0 × 1014 Hz vko`fÙk dk ,do.khZ izdk'k fdlh yslj osQ kjk mRiUu fd;k tkrk gSA mRltZu kerk2.0 × 10–3 W gSA (i) izdk'k fdj.k&iqat esa fdlh I+kQksVkWu dh ÅtkZ fdruh gS\ (ii) lzksr osQ kjk vkSlr rkSj ij izfrlsoaQM fdrus I+kQksVkWu mRl£tr gksrs gSa\

23/04/18

221

izfrn'kZ iz'u i=k

23. gkbMªkstu ijek.kq esa bysDVªkWu osQ fy, ^vuqer dkkvkas* osQ fy, cksj dk vfHkx`ghr crkb,A ns&czkWXyh kjk bldkLi"Vhdj.k oSQls fd;k x;k\

24. β &k; izfØ;k mnkgj.k nsdj le>kb,A β− k; kjk] VªkbfV;e dh v/Z&vk;q 12.5 o"kZ gSA 25 o"kZ ckn 'kq¼VªkbfV;e osQ ,d uewus dk fdruk va'k vfo?kfVr jgsxk\

25. fn"Vdj.k D;k gS\ vafdr ifjiFk vkjs[k dh lgk;rk ls laf/ Mk;ksM osQ mi;ksx ls iw.kZ rjax fn"Vdj.k le>kb,A

26. ifjiFk vkjs[k dh lgk;rk ls le>kb, fd fdlh p-n laf/ Mk;ksM dk (i) vxzfnf'kd ck;l ,oa (ii) i'pfnf'kd ck;lesa V-I vfHkykkf.kd oSQls izkIr djrs gSa\ izkIr oØkas dk vkdkj cukb;sA

27. (i) fdlh lapkj O;oLFkk dk Cykd vkjs[k cukb,A

(ii) vk;ke ekMqfyr rjax osQ lalwpu dk rkRi;Z D;k gSA lalwpu osQ vko';d pj.kksa dk laksi esa o.kZu dhft,A

28. fdlh oS|qr f/zqo osQ dkj.k foHko osQ O;atu dh mu nwfj;ksa osQ fy, tks foHko osQ vkdkj dh rqyuk esa vR;f/d cM+h gSa] O;qRifÙk dfj,A f/qzo osQ dkj.k foHko ,dy vkos'k osQ dkj.k foHko ls oSQls fHkUu gS\

vFkok

fdlh cká ks=k esa nks vkos'kksa osQ fudk; dh fLFkfrt ÅtkZ osQ fy, O;atu izkIr dhft,A nks vkos'kksa7 µC rFkk µ2 µC tks Øe'k% (µ9 cm, 0,0) rFkk (9 cm, 0, 0) ij fLFkr gSa] dk fudk;] cká fo|qr ks=kE = A (1/r2) tgk¡ A = 9 × 105 C m–2 gS] esa fLFkr gSA fudk; dh fLFkfrt ÅtkZ dh x.kuk dhft,A

29. fdlh oqQ.Myh osQ ^Lo&izsjdRo* dh ifjHkk"kk nhft,A fdlh yacs ifjukfydk osQ ^Lo&izsjdRo* osQ fy, O;atu]ifjukfydk osQ ks=kiQy A, yEckbZ l rFkk ,dkad yEckbZ esa isQjksa dh la[;k n osQ inksa esa O;qRifÙk dhft,A n'kkZb, fdLo&izsjdRo ;kaf=kdh esa nzO;eku dk vuq:i gSA

vFkok

^vU;ksU; izsjdRo* dh ifjHkk"kk nhft,A fdu dkjdksa ij ;g fuHkZj djrk gS\ nks laosaQnzh o`Ùkkdkj oaqQMfy;k¡] ,d def=kT;k r

1 dh rFkk nwljh vf/d f=kT;k r

2 dh, ,slh fd r

1 << r

2, lekkh j[kh gSa rFkk nksuksa osQ osaQnz laikrh gSaA bl

O;oLFkk osQ fy, vU;ksU; izsjdRo Kkr dhft,A

30. fdlh izdk'k fdj.k osQ dk¡p osQ fizTe ls nksuksa viorZu dks fdj.k vkjs[k cukdj n'kkZb,A vkjs[k dh lgk;rk ls fopyudks.k dh vkiru dks.k ij fuHkZjrk le>kb,A U;wure fopyu dks.k osQ fy, fizTe dks.k rFkk fizTe osQ inkFkZ osQviorZukad osQ inksa esa O;atu izkIr dhft,A

vFkok

(i) fdlh ,dy xksyh; i`"B ls izdk'k osQ viorZu osQ lehdj.k dk mi;ksx djrs gq, ysal&esdj lw=k dh O;qRifÙkdhft,A

(ii) viouZrkad 1.55 osQ dk¡p ls nksuksa iQydksa dh leku oØrk f=kT;k osQ mHk;ksÙky ysal fu£er djus gSaA ;fn20 cm iQksdl nwjh osQ ysal fu£er djus gSa rks visfkr oØrk f=kT;k D;k gksxh\

23/04/18


222

izfrn'kZ iz'u i=k II

gy ,oa vadu ;kstuk

1. (a) (1)

2. (d) (1)

3. èkkjk ?kV tk,xhA ifjukfydk esa yksg ozQksM j[kus ij pqEcdh; ks=k esa o`f¼ gksrh gS vkSj ÝyDl c<+ tkrk gSA ysat+ osQ fu;e osQvuqlkj izsfjr fo|qr okgd cy dks bl o`f¼ dk fojksèk djuk pkfg, ftls èkkjk esa deh kjk izkIr fd;k tkrk gSA (1)

4. fo|qr pqEcdh; rjaxsa fofdj.k nkc yxkrh gSaA /weosQrq dh i¡wN lkSj fofdj.k osQ dkj.k gSA (1/2, 1/2)

5. (b) (1)

6. xksyh;] i`Foh dh f=kT;k dh rqyuk esa fo'kky f=kT;k ftlls fd ;g yxHkx lery gSA (1/2, 1/2)

7. (a) (1)

8. rkfRod v/Zpkyd osQ cSaM&varjky ,sls gksrs gSa fd mRltZu vojDr izns'k esa gksrk gSA (1/2, 1/2)

9. (i) 20

1

4

q

rπεOA oQs lfn'k (1)

(ii) 2

0

1 2

4

q

rπεOA oQs lfn'k (1)

10. 1 2I I I= + (1/2)

1 2

1 2

E V E V

r r

− −= +

1 2

1 2 1 2

1 1E EI V

r r r r

= + − +

1 2 2 1 1 2

1 2 1 2

E r E r r rV I

r r r r

+ += −

+ + (1/2)

V = Eeq

– Ireq ls rqyuk djus ij (1/2)

gesa izkIr gksrk gS, Eeq

=1 2 2 1

1 2

E r E r

r r

+

+(1/2)

23/04/18

223

izfrn'kZ iz'u i=k

C

E r

R

A

11. vkjs[k esa vko';d ifjiFk n'kkZ;k x;k gSA fuxZr foHko A rFkk C osQ eè; izkIr gksrk gSA (1, 1)

12. pqEcdRo laca/h xkml dk fu;e ;g dgrk gS fd ks=k B osQ dkj.k] fdlh can lrg ls xq”kjus okyk oqQy ÝyDl

lnSo 'kwU; gksrk gSA fdlh can lrg S osQ fy, . 0d =∫ B s (1)

;fn ,dy /qzoksa dk vfLrRo gksrk rks (fLFkjoS|qfrdh osQ xkml fu;e osQ vuq:i) lehdj.k osQ nk;ha vksj lrg Sls f?kjs ,dy /qzoksa (pqEcdh; vkos'kksa)q

m dk ;ksx vkrk vFkkZr lehdj.k dk :i gksrkA

0. md qµ=∫ B s tgk¡ qm, S ls f?kjk pqEcdh; vkos'k (,dy /zqo) gSA (1)

13. izfrpqEcdRo bysDVªkWuksa dh dkh; xfr osQ dkj.k gksrk gS tks vuqiz;qDr ks=k osQ foijhr pqEcdh; vk?kw.kZ mRiUu djrk gSA blfy,;g rki ls vfèkd izHkkfor ugha gksrkA (1)

vuqpqEcdRo vkSj yksgpqEcdRo ijek.oh; pqEcdh; vk?kw.kksZa osQ vuqiz;qDr ks=k dh fn'kk esa lajs[k.k osQ dkj.k gksrk gSA rki&o`f¼gksus ij ;g lajs[k.k fokksfHkr gks tkrk gS ftlosQ iQyLo:i nksuksa dh pqEcd'khyrk rki o`f¼ osQ lkFk ?kV tkrh gSA (1)

14. tc la/kfjr osQ lkFk fdlh dc lzksr dks tksM+rs gSa rks la/kfj=k vkosf'kr gksrk gS vkSj mlosQ iw.kZ vkos'ku osQ ckn ifjiFk esa dksbZ/kjk izokfgr ugha gksrh vkSj ySai izdkf'kr ugha gksrk gSA bl ekeys esa C dks de djus ls dksbZ ifjorZu ugha vk,xkA (1)

ac lzksr osQ lkFk] la/kfj=k (1/ωC) la/kfj=kh; izfr?kkr yxkrk gS vkSj ifjiFk esa /kjk izokfgr gksrh gSA ifj.kker% ySai izdk'knsxkA C dks de djus ls izfr?kkr c<+sxk vkSj ySai igys dh rqyuk esa nhfIr ls izdkf'kr gksxkA (1)

15. B ,oa E osQ ifjek.k ,d&nwljs ls fuEufyf[kr lehdj.k kjk lacaf/r gSaµ

–8

8

6.3V/m2.1 10 T

3 10 m/s

EB

c=

= = ××

(1)

bldh fn'kk osQ laca/ esa ge tkurs gSa fd E y-fn'kk osQ vuqfn'k gS vkSj rjax x-fn'kk osQ vuqfn'k xeu dj jgh gSA vr%B x- ,oa y-vkksa nksuksa osQ yacor fn'kk esa gksuk pkfg,A lfn'k chtxf.kr dk mi;ksx djus ij] E ××××× B dks x-fn'kk esa gksuk

pkfg,A pw¡fd (+ j ) × × × × × (+ k )= i , B z-fn'kk osQ vuqfn'k gSA

vr% B= 2.1×××××10–8 k T. (1 )

16. P = tanδ (vkjs[k lfgr)

23/04/18


224

1

/h ff

= = (1)

y?kq δ osQ fy,] tan δ ∼ δ.

P = 1/f (1)

17. fizaQt varjky D

d

λ= (1)

× ×=

×

–7

–3

1 5 100.5 mm

1 10

(1)

18. (i) ekMqyu lwpdkad = 10/10

= 0.5 (1)

(ii) 1010 kHz rFkk 990 kHz ij ik'oZ cSaM gSA (1)

19. vkjs[k (1)

E = φ l1

(1/2)

V = φ l2

E/V = l1/l

2(1/2)

E = I (r+R), V= IR

E/V = (r+ R)/R (1/2)

r = R (l1/l

2)-1. (1/2)

20. izfrpqEcdRo (1)

vuqpqEcdRo (1)

yksg pqEcdRo (1)

21. min

1.22

2sind

λ

β= (1/2)

tgk¡ β vfHkn`';d kjk fcac ij varfjr dks.k gSA

5500 A

osQ izdk'k osQ fy,

–7

min

1.22 5.5 10m

2sind

β

× ×= (1)

100 V ls Rofjr bysDVªkWuksa osQ fy, ns&czkXyh rjaxnS?;Z gS

23/04/18

225

izfrn'kZ iz'u i=k

–91.2270.13nm 0.13 10 m

100

h

pλ = = = = × (1/2)

–10

min

1.22 1.3 10'

2sind

β

× ×∴ =

(1/2)

min –3

min

0.2 10d

d= ×

' (1/2)

22. (i) izR;sd I+kQksVkWu dh ÅtkZ gksxh

E = hv = (6.63 × 10–34 J s) (6.0 × 10–14 Hz)

= 3.98 × 10–19 J (1)

(ii) ;fn lzksr osQ kjk lsoaQM mRl£tr I+kQksVkWuksa dh la[;k N gS rks fdj.k&iqat esa lapfjr kerk P izfr I+kQksVkWu ÅtkZ E osQ Nxquk gksxh ftlls fd P = NE A rc

PN

E= (1)

3

19

2.0 10 W

3.98 10 J

−

−

×=

× = 5.0 ×

1015 -iQksVku izfr lsoQaM (1)

23. vfHkx`ghr (1)

ns&czkXyh Li"Vhdj.k (2)

24. Li"Vhdj.k (1)

mnkgj.k (1)

gy : uewus dk 1/4 (1)

25. fn"Vdj.k (1/2)

vafdr vkjs[k (1/2)

Li"Vhdj.k (2)

26. vfHkykkf.kd izkIr djus osQ mi;qDr ifjiFk vkjs[k (1)

Li"Vhdj.k (1)

oØ dk vkdkj (1)

27. (i) lapkj O;oLFkk dk Cykd vkjs[k (1)

23/04/18


226

(ii) lalwpu dk Cykd vkjs[k rFkk ifjHkk"kk (1)

Li"Vhdj.k (1)

28. O;qRifÙk (4)

varj (1)

vFkok

O;qRifÙk (3)

iz'u dk gy (2)

29. ifjHkk"kk (1)

O;atu dh O;qRifÙk (2)

izwiQ 2

vFkok

ifjHkk"kk (1)

dkjdksa ij fuHkZjrk (1)

iz'u dk gy (3)

30. vafdr vkjs[k (1)

δ rFkk e osQ chp vkjs[k (1)

δm = (µ-1)A dh O;qRifÙk (3)

vFkok

(i) O;qRifÙk (3)

(ii) µ = 1.55, R1 = R (1/2)

R2 = –R, f = 20 cm.

1 2

1 1 1( 1)

f R Rµ

= − −

(1/2)

1 2

1 1 1 1.10(1.55 1)

20 R R R

= − + =

(1/2)

R=20×1.1 = 22 cm. (1/2)

23/04/18

109

mÙkj

vè;k; 1

1.1 (a)

1.2 (a)

1.3 (d)

1.4 (b)

1.5 (c)

1.6 (a)

1.7 (a)

1.8 (c), (d)

1.9 (b), (d)

1.10 (b), (d)

1.11 (c), (d)

1.12 (a), (c).

1.13 (a), (b), (c) vkSj (d).

1.14 'kwU;

1.15 (i) 21

–4

Q

Rπ , (ii) Q

R224π

1.16 fo|qr ks=k ijek.kqvksa dks ck¡/dj mnklhu vfLrRo dj nsrs gSaA vkos'kksa osQ vkfèkD; osQ dkj.kks=k mRiUu gksrs gSaA fdlh fo;qDr pkyd osQ vUrjki`"B ij vkos'k&vkf/D; ugha gks ldrkA

1.17 ugha] fo|qr ks=k vfHkyEcor gks ldrk gSA rFkkfi] bldk foijhr lR; gSA

23/04/18

iz'u izn£'kdk & HkkSfrdh

110

1.18

'kh"kZ dk n`';

ik'oZ dk n`';

1.19 (i) q

08ε , (ii) q

04ε , (iii) q

02ε , (iv) q

02ε .

1.20 Al osQ 1 eksyj nzO;eku M esa ijek.kqvksa dh la[;k NA = 6.023 × 1023

∴ m nzO;eku osQ Al osQ iSls osQ flDosQ esa ijek.kqvksa dh la[;k A

mN N

M=

vc ZAl = 13, MAl = 26.9815g

vr%] N = 6.02 × 1023 ijek.kq/eksy × eksy

0.7526.9815g/

= 1.6733 × 1022 ijek.kq

∴ q = iSls esa èkukos'k = N Ze

= (1.67 × 1022

)(13) (1.60 × 10–19

C)

= 3.48 × 104 C.

q = 34.8 kC èkukos'k;g vkos'k dh ,d fo'kky ek=kk gSA

1.212 42

2391 2 –4 22

0 1

q (3.48 10 C)Nm 1.1 10 N8.99 104 r 10 mC

Fπ ε

× = = = ××

2 –2 2–8 –8 152 1

2 12 2 21 2

r (10 m)10 10 1.1 10 N

r (10 m)F

F FF

= = = ⇒ = × = ×

2 –2 2–163 1

2 6 21 3

r (10 m)10

r (10 m)F

F= = =

F3 = 10–16 F1 = 1.1 × 107 N.

fu"d"kZ: fcUnq vkos'kksa esa i`Fkd djus ij ;s vkos'k fo'kky cy vkjksfir djrs gSaA oS|qr mnklhurkdks fokqCèk djuk vklku ugha gSA

23/04/18

mÙkj

111

1.22 (i) 'kwU;] lefefr lsA

(ii) ,d èkukRed Cs vk;u gVkuk ml vofLFkfr ls ,dy ½.kkRed Cs vk;u tksM+us osQrqY; gSA rc usV cy

2

204 r

eF

π=

∈

;gk¡ r = Cl vk;u vkSj fdlh Cs vk;u osQ chp nwjh

2 2 2 –9 2 –9(0.20) +(0.20) +(0.20) ×10 = 3(0.20) ×10F =

= 0.346 × 10–9 m

vr%] 9 –19 2

–11–9 2

(8.99×10 )(1.6 10 )192 10

(0.346×10 )F

×= = ×

= 1.92 × 10–9 N

mÙkj% 1.92 × 10–9 N, A ls Cl– dh vksj funsf'kr

1.23 fcUnq P ij fLFkr vkos'k 2q ij q osQ dkj.k cy ck;ha vksj rFkk –3q osQ dkj.k nk;ha vksj gSA

∴

2 2

2 20 0

2q 6q4 x 4 (d x)πε πε

=+

∴ (d + x)2 = 3x2

∴ 2x2 – 2dx – d2 = 0

= ±d 3d2 2

x

= + = +d 3d d

(1 3)2 2 2

x

(½.kkRed fpg~u ysus ij x dk eku q rFkk –3q osQ chp gksxk] vr% ;g ekU; ugha gSA)

1.24 (a) vkos'k A rFkk C èkukRed gSa D;ksafd ks=k js[kk,¡ buls fudyrh gSaA

(b) vkos'k C dk ifjek.k vfèkdre gS D;ksafd blls vfèkdre ks=k js[kk,¡ lac¼ gSaA(c) (i) A osQ fudVA ½.kkos'k rFkk fdlh fLFkfr osQ chp dksbZ mnklhu fcUnq ugha gSA nks

ltkrh; vkos'kksa osQ dksbZ mnklhu fcUnq gks ldrs gSaA fp=k esa ge ;g ns[krs gSa fd vkos'kksaA rFkk C osQ chp ,d mnklhu fcUnq gSA lkFk gh] nks ltkrh; vkos'kksa osQ chp mnklhufcUnq de ifjek.k osQ vkos'k osQ fudV gh gksrk gSA bl izdkj vkos'k A osQ fudV fo|qrks=k 'kwU; gSA

1.25 (a) (i) 'kwU; (ii) πε 2

0

1 q4 r

osQ vuqfn'k (iii) πε 2

0

1 2q4 r

osQ vuqfn'k

(b) mÙkj (a) osQ leku

P q

– q32q x

d

23/04/18


112

1.26 (a) eku yhft, fo'o dh f=kT;k R gSA ;g ekfu, fd gkbMªkstu ijek.kq ,dleku :i lsforfjr gSaA izR;sd gkbMªkstu ijek.kq ij vkos'k e

H = – (1 + y) e + e = – ye = |ye|

izR;sd gkbMªkstu ijek.kq dk nzO;eku izksVkWu osQ nzO;eku ~ mp osQ rqY; gSA tc R ij]

fdlh gkbMªkstu ijek.kq ij ;fn owQykWe&izfrd"kZ.k xq#Roh; vkd"kZ.k ls vfèkd gks tk,rks foLrkj vkjEHk gks tkrk gSAeku yhft, R ij fo|qr ks=k E gS] rc

4πR2 E = πε

3

o

4R N

3 ye (xkml fu;e)

E (R) = εo

N1 ˆ3

rye

R

eku yhft, R ij xq#Roh; ks=k GR gSA rc

– 4πR2 GR = 4 πG 3

p4

m R N3

π

R4

G – Gm NR3 ρπ=

ρ= πR4 ˆ( ) – Gm 3

G R rN R

bl izdkj R ij gkbMªkstu ijek.kq ij owQykWe&cy gS

ε=

2 2

o

1 e ˆ(R)3

rNy

ye RE

bl ijek.kq ij xq#Rokd"kZ.k cy gS

( )π

= 2p R p

4 ˆm G – GNm R3

rR

ijek.kq ij usV cy gS

π

ε

=

2 22p

o

1 4 ˆR – GNm R3 3

F rNy e

;g ozQkafrd eku rc gS tc

π

ε=

C2 2

2p

o

1 4R GNm R

3 3

Ny e

πε⇒ =c

2p2

o 2

m4 G

ey

–11 2 6 –62

9 2 –38

7 10 1.8 10 81 109 10 1.6 10

× × × × ×

× × ×

–3863 10×∼

–19 –18C 8 10 10y∴ ×∼ ∼

(b) bl usV cy osQ dkj.k gkbMªkstu ijek.kq fdlh Roj.k dk vuqHko djrk gS tks bl izdkjgksrk gS] fd

23/04/18

mÙkj

113

2 222

pr 2

o

1 Ny e 4pd RR – GNm Rm =

3 e 3dt

vFkok 2

2

2

d R= a R

dt tgk¡

2 222p

op

1 Ny e 4p1– GNma =

3 e 3m

bldk ,d gy at –atR = Ae + Be

pwafd ge dksbZ foLrkj [kkst jgs gSa] B = 0tR Aeα∴ =

tR Ae Rαα α⇒ = =.

bl izdkj osx osQUnz ls nwjh osQ vuqozQekuqikrh gSA

1.27 (a) leL;k dh lefefr ls ;g Kkr gksrk gS fd fo|qr ks=k vjh; gSA r < R okys fcUnqvksaosQ fy, fdlh xksyh; xkml&i`"B ij fopkj dhft,A rc ml i`"B ij

1V

o

dvρε

=∫ ∫ rE .dS

2 314 4

r

r

o o

r E k r drπ πε

′ ′= ∫

41 44o

kr

π

ε=

214r

o

E krε

∴ =

( ) 21 ˆ4 o

krrε

=E r

r > R, okys fcUnqvksa osQ fy, fdlh r f=kT;k osQ xksyh; i`"B ij fopkj dhft,

1.r

o V

d dvρε

=∫ ∫E S

2 344

R

r

o o

kr E r dr

ππ

ε= ∫

o

k R444

=π

ε

r

o

k RE

r

4

24∴ =

ε

( ) 4 2 ˆ( /4 ) ( / )ok R rr ε=E r

r

rR

S

S

23/04/18


114

(b) nksuksa izksVkWu fdlh O;kl osQ vuqfn'k osQUnz osQ foijhr ik'oksZ ij gksus pkfg,A eku yhft,izksVkWu osQUnz ls r nwjh ij gSa

bl izdkj] 34 2R

o

kr dr eπ ′ =∫

442

4k

R eπ

∴ =

4

2ek

Rπ∴ =

izksVkWu 1 ij cyksa ij fopkj dhft,A vkos'k forj.k osQ dkj.k vkd"kZ.k cy gS2 2

24

2ˆ ˆ– – –4 4r

o o

e e re kr

Rε πε= =E r r

izfrd"kZ.k cy gS ( )

2

2

1 ˆ4 2o

er

rπε

usV cy gS 2 2 2

2 4

2ˆ–

4 4 4o o

e e rr

r Rπε πε

;g usV cy 'kwU; gS] blfy,2 2 2

2 4

216 4o o

e e r

r Rπε πε=

vFkok] 4 4

4 432 8R R

r = =

1/ 4(8)R

r⇒ =

bl izdkj] izksVkWu osQUnz ls nwjh 4 8

Rr = ij gksuk pkfg,A

1.28 (a) IysV α osQ dkj.k x ij fo|qr ks=k gS ˆ–2 o

Q

S εx

IysV β osQ dkj.k x ij fo|qr ks=k gS ˆ2 o

q

S εx

bl izdkj] usV fo|qr ks=k gS

( )( )1

–ˆ–

2 o

Q q

Sε=E x

(b) Vdjkus osQ le; IysV β rFkk IysV γ ,d lkFk gSa] vr% leku foHko ij gSaA ekuyhft, β ij vkos'k q

1 rFkk γ ij vkos'k q

2 gSA fdlh fcUnq O ij fopkj dhft,A ;gk¡

fo|qr ks=k 'kwU; gksuk pkfg,A

α osQ dkj.k 0 ij fo|qr ks=k ε

= ˆ–2 o

Q

Sx

1

r

2

O

r

a b g

-Q q Qd

23/04/18

mÙkj

115

β osQ dkj.k 0 ij fo|qr ks=k ε

= 1 ˆ–2 o

q

Sx

γ osQ dkj.k 0 ij fo|qr ks=k ε

= 2 ˆ–2 o

q

Sx

( )2 1–0

2 2o o

Q q q

S Sε ε

+∴ + =

1 2–q q Q⇒ =

lkFk gh] q1 + q

2 = Q + q

1 /2q Q q⇒ = +

rFkk q2 = q/2

bl izdkj β vkSj γ ij vkos'k ozQe'k% Q + q/2 vkSj q/2 gSaA

(c) eku yhft, VDdj osQ i'pkr~ nwjh ij ossx v gSA ;fn IysV γ dk nzO;eku m gS] rc blisQjs esa vftZr xfrt mQtkZ fo|qr ks=k kjk fd, x, dk;Z osQ cjkcj gksuh pkfg,A VDdjosQ i'pkr~ γ ij fo|qr ks=k gS

( )2

/2 /2ˆ ˆ ˆ–2 2 2o o o

Q qQ q

S S Sε ε ε

+= + =E x x x

IysV γ osQ eqDr gksus ls VDdj rd fd;k x;k dk;Z F1d gS] ;gk¡ F

1 IysV γ ij cy gSA

VDdj osQ i'pkr~ blosQ d rd igq¡pus rd fd;k x;k dk;Z F2d, ;gk¡ F

2 IysV γ ij

cy gSA

( )1 1

–2 o

QQ qF E Q

Sε= =

rFkk ( )2

2 2

/2/2

2 o

qF E q

Sε= =

∴ oqQy fd;k x;k dk;Z gS

( ) ( ) ( )221 1– /2– /2

2 2o o

d dQ qQQ q qS Sε ε =+

( )22(1/2) – /22 o

dmv Q q

Sε⇒ =

( )1/2

– /2o

dv Q q

m Sε

∴ =

1.29 (i)qQ

Fr

2

2 2

[1esu ]1 =

[1cm]= =

vko's kMkbu

vFkok1 esu vkos'k = 1 (Mkbu)1/2(cm)

vr% [1 esu vkos'k] = [F]1/2 L = [MLT–2]1/2 L = M1/2 L3/2 T–1

[1 esu vkos'k] = M1/2 L3/2 T–1

b g

°o

q1 q2

23/04/18


116

bl izdkj cgs ek=kdksa esa vkos'k dks M dh 1/2 rFkk L dh 3/2 dh fHkUukRed ?kkrksaesa O;Dr fd;k tkrk gSA

(ii) nks vkos'kksa] ftuesa izR;sd dk ifjek.k 1 esu vkos'k rFkk ftuosQ chp i`Fkdu 1 cm

osQ chp cy ij fopkj dhft,Arc cy 1 Mkbu = 10–5 N.

;g fLFkfr 10–2m i`Fkdu okys xC ifj.kke osQ nks vkos'kksa osQ rqY; gSAblls izkIr gksrk gS%

2

–40

1.

4 10x

Fπ

=∈

tks gksuk pkfg, 1 Mkbu = 10–5 N

bl izdkj x

x

2 –9 2–5

–4 2 20 0

1 1 10 Nm. 10

4 10 4 Cπε πε= ⇒ =

ftlosQ lkFk 9

1[3] 10

x =×

, blls izkIr gksrk gS

2–9 2 18 2 9

20

1 Nm10 [3] 10 [3] 10

4 Cπε= × × = ×

ftlosQ lkFk [3] → 2.99792458, gesa izkIr gksrk gS2

92

0

1 Nm8.98755.... 10

4 Cπε= × rF;r%

1.30 osQUnz O osQ vuqfn'k q ij oqQy cy F

q q xF

r r r

2 2

2 20 0

22 cos – .

4 4θ

πε πε= =

2

2 2 3/20

–24 ( )

q xF

d xπε=

+

2

30

2–

4q

x kxdπε

≈ = osQ fy, x << d

bl izdkj rhljs vkos'k q ij cy foLFkkiu osQ vuqozQekuqikrh gS rFkk og nks vU; vkos'kksaosQ osQUnz dh vksj gSA vr% rhljs vkos'k dh xfr ljy vkorZ xfr gS ftldh vko`fÙk gS

2

30

24

q k

d m mω

πε= =

vkSj bl izdkj mdT

q

1/23 302

2 8π π ε

ω

=

1.31 (a) NYys osQ vk osQ vuqfn'k q dks /hjs ls fn;k x;k èkDdk fp=k (b) esa n'kkZ;h fLFkfrmRiUu djsxkA NYys osQ O;kl osQ nks fljksa ij A rFkk B nks fcUnq gSaA

q

q x

d– q d – q

23/04/18

mÙkj

117

NYys dk vk

qz

q

RA B

NYys dk ry(b)

(a)

NYys dk vkoqQy vkos'k –Q

q

Z

R

–––––––––

–

– – – – – – – – – – – – – – ––

–

–––––––

A rFkk B ij js[kk vo;oksa –

2Q

Rπ osQ dkj.k q ij cy

θπ πε

+ = 20

– 1 12. . . . .cos

2 4Q

F qR r

A B

π πε=

+ +2 2 2 2 1/ 2

–Q 1. .

R.4 ( ) ( )z

z R z R0

q

q ij NYys osQ dkj.k oqQy cy = (FA+B)(πR)

πε=

+2 2 3 /2o

– z4 ( )

Qq

z R

πε

–4

Qq z

o

z << R osQ fy,

bl izdkj cy ½.kkRed foLFkkiu osQ vuqozQekuqikrh gSA ,sls cyksa osQ vèkhu xfr ljyvkorZ xfr gksrh gSA(b) iz'u osQ Hkkx (a) ls

πε=

2

2 3– ...4

d z Qqzm

dt R0

vFkok πε

=2

2 3–4

d z Qqz

dt R0

vFkkZr ωπε

=234

Qq

mR0

. vr% πεπ=

342

mRT

Qq0

vè;k; 2

2.1 (d)

2.2 (c)

2.3 (c)

2.4 (c)

2.5 (a)

2.6 (c)

2.7 (b), (c), (d)

2.8 (a), (b), (c)

2.9 (b), (c)

2.10 (b), (c)

2.11 (a), (d)

2.12 (a), (b)

23/04/18


118

2.13 (c) vkSj (d)

2.14 vfèkd

2.15 mPp foHko

2.16 gk¡] ;fn vkeki fHkUu gSaA

2.17 ugha

2.18 pw¡fd fo|qr ks=k lajkh gS] nksuksa izdj.kksa esa fd;k x;k dk;Z 'kwU; gksxkA

2.19 eku yhft, ;g lR; ugha gSA rc i"B osQ rqjUr Hkhrj i"B dh rqyuk esa foHko fHkUu gksuk pkfg,ftlosQ iQyLo:i dksbZ foHko izo.krk gksuh pkfg,A bldk ;g vFkZ gqvk fd i"B osQ vUreZq[khvFkok cfgeqZ[kh ks=k js[kk,¡ gksuh pkfg,A pw¡fd i`"B] lefoHko i`"B gS] nwljs fljs ij ;s js[kk,¡nqckjk i`"B ij ugha gks ldrhaA bl izdkj ;g osQoy rHkh laHko gS tc ks=k js[kkvksa osQ nwljsfljs Hkhrj vkos'kksa ij gksa] tks vk/kj rF; osQ ijLij fojks/h gSaA vr% Hkhrj leLr vk;ru lekufoHko ij gksuk pkfg,A

2.20 C de gks tk,xhA

lafpr mQtkZ = 12

2CV vkSj blfy, vf/d gks tk,xhA

fo|qr ks=k vf/d gks tk,xkAlafpr vkos'k leku jgsxkAV de gks tk,xkA

2.21 fo|qr ks=k osQ vuqfn'k vkosf'kr pkyd ls vukosf'kr pkyd dh vksj osQ fdlh Hkh iFk ijfopkj dhft,A bl iFk ij foHko fujUrj de gksxkA vukosf'kr pkyd ls vuUr dh vksjosQ vU; iFk ij foHko vkSj ?kVsxkA ;g visfkr rF; dks fl¼ djrk gSA

2.22 Q

R z R2 20

qU=

4 1π ε

−

+

z osQ lkFk fLFkfrt mQtkZ esa ifjorZu dks fp=k esa n'kkZ;k x;k gSA

foLFkkfir vkos'k – q nksyu djsxkA ek=k xzkiQ dks ns[kdj ge dksbZ fu"d"kZ ugha fudkyldrsA

2.232 2

0

1 Q4

VR zπε

=+

2.24 js[kk ls nwjh r ij foHko Kkr djus osQ fy, fo|qr ks=k ij fopkj dhft,A lefefr kjk ge;g ikrs gSa fd ks=k js[kk,¡ cfgeZq[kh vjh; gksuh pkfg,A f=kT;k r rFkk yEckbZ l dk dksbZ xkmlh;i`"B [khafp,A rc

U

z

++++

++

+

+ + + + + +

++

+

++

R

Q

P

r

z

23/04/18

mÙkj

119

λε

=∫0

1.dE S l

vFkok π λε

=r0

12E rl l

λ

πε⇒ =r

02E

r

vr%] ;fn f=kT;k r0 gS] rc

λ

πε= − =∫

0

r0

00r

( ) – ( ) .d2

E lr

V r V r lnr

fdlh fn, x, V osQ fy,]

ln πε

λ= − 0

00

2[ ( ) – ( )]

rV r V r

r

πε λ πε λ− +⇒ = 0 0 02 ( )/ 2 ( )/0e .eV r V rr r

lefoHko i`"B csyukdkj gSa ftudh f=kT;k gSπε λ−= 0 02 [ ( )– ( )]

0eV r V rr r

2.25 eku yhft, ry ewy fcUnq ls nwjh x gSA rc fcUnq P ij foHko gSA

( ) ( )1/2 1/ 22 22 20 0

1 14 4/2 /2

q q

h hx d x dπε πε−

+ ++ −

;fn ;g foHko 'kwU; gS] rks

( ) ( )1/2 1/22 22 2

1 1

/2 /2h hx d x d

= + ++ −

vFkok (x-d/2)2 + h2 = (x+d/2)2 + h2

2 2 2 2/4 /4x dx d x dx d⇒ − + = + +

Or, 2dx = 0⇒ x = 0

;g ry x = 0 dk lehdj.k gSA

2.26 eku yhft, ;g U dh vafre oksYVrk gSA ;fn laèkkfj=k dh ijkoS|qr osQ fcuk èkkfjrk C rclaèkkfj=k ij vkos'k gS

Q1 = CU

ijkoS|qr gksus ij laèkkfj=k dh èkkfjrk εC gksrh gSA blfy, laèkkfj=k ij vkos'k gS2

2Q CU CUε α= =

tks laèkkfj=k vkosf'kr Fkk ml ij vkjfEHkd vkos'k gSQ

0 = CU

0

vkos'kksa osQ lajk.k lsQ0 = Q1 + Q2

vFkok CU0 = CU + ε CU2

rl

23/04/18


120

U U u20 0α⇒ + − =

UU 01 1 4

2

α

α

− ± +∴ =

1 1 624

4− ± +

= oksYV

1 625

4− ±

=

pwafd U èkukRed gS

625 1 246V

4 4U

−= = =

2.27 tc pfozQdk ryh dks Li'kZ dj jgh gS rc leLr ifêðdk lefoHko ifêðdk gSA dksbZ vkos'kq′ pfozQdk dks LFkkukUrfjr gks tkrk gSA

pfozQdk ij fo|qr ks=k

V

d=

20

Vq r

dε π′∴ = −

pfozQdk ij dk;Zjr cy gS

V Vq r

d d

22

0 2ε π′− × =

;fn pfozQdk dks mQij mBkuk gS] rc2

20 2

Vr mg

dε π =

2

20

mgdV

rπε⇒ =

2.28 d d u d u dq q q q q q

r r r0

1U= – –

4πε

( ) 9 2–19 2

–15

9×10=8 1.6×10 (1 3 ) – (2 3 )(1 3 )– (2 3 )(1 3 )

10

= 2.304 × 10–13 –141 4– = –7.68×10 J

9 9

= 4.8 × 105 eV = 0.48 MeV = 5.11 × 10–4 (mnc2)

2.29 lEioZQ ls iwoZ %

2.4 Rσ π=1Q

23/04/18

mÙkj

121

2 2.4 (2 ) 4 .4 42Q R R Q

lEioZQ osQ i'pkr~

1 2 1 2 1Q Q Q Q 5Q′′ + = + = ,

2( .4 )=5 R

leku foHko ij gksaxs

1 2

2Q Q

R R

′ ′=

2Q 2Q′ ′∴ = .

( )213Q 5 .4 Rσ π′∴ =

( )21

5Q .4 R

3σ π′∴ = vkSj ( )2

210

.4 R3

Q σ π′ =

1 5 3σ σ∴ = vkSj 2

56

2.30 vkjEHk esa : vkSj 1 21

EC

V ,V V∝ + =

1 =3V V⇒ vkSj 2 =6V V

1 1 1Q C V 6C×3 =18 C

2Q 9 C vkSj 3Q 0

ckn esa% 2 2 3Q =Q Q

lkFk gh% C2V + C3V = Q2 2

2 3

Q= (3 2)V

C +CV⇒ =

2Q 9 2 Cµ′ = vkSj 3Q 9 2 Cµ′ =

2.31 2

Q

Rσ

π=

( )( )

K1 K2

E = 9V

C1

C3 C2

R

z

r

Q

23/04/18


122

U

O

2 20

1 .24

r drdU

r z

σ π

πε=

+

R

2 20 O

24

rdrU

r z

πσ

πε∴ =

+∫

R2 2 2 2

O0 0

2 2+z – z

4 4r z R

πσ πσ

πε πε = + =

2 22

0

2Q+ – z

4R z

Rπε =

2.32 ( ) ( )1 2

2 22 2 2 20

–

q q

x y z d x y z d+ =

+ + + + +

( ) ( )

1 2

2 22 2 2 2

–

–

q q

x y z d x y z d∴ =

+ + + + +

bl izdkj] oqQy foHko 'kwU; gksus osQ fy, q1 rFkk q2 osQ fpg~u foijhr gksus pkfg,A oxZ vkSjljy djus ij gesa izkIr gksrk gS

( )

( )

21 22 2 2 2

21 2

1(2 ) 0

–1

q qx y z zd d

q q

++ + + + =

;g ml xksys dk lehdj.k gS ftldk osQUnz 2 2

1 12 2

1 1

0,0,–2–

q qd

q q

+

ij gSA

è;ku nhft, ;fn q1 = –q2 rc z = 0, eè; fcUnq ls xqtjus okyk ry gSA

2.33 ( )πε

= +

2 2

0

1 – –4 – –

q qU

d x d x

( )πε=

2

2 20

– 24 –

q dU

d x

( )π=

∈

2

22 20

d – .2 2.

d 4 –

U q d x

x d x

2

00

24

qU

dπε=

q1

z

O

q2 – d

d

23/04/18

mÙkj

123

x = 0 ij =d

0dU

x

x = 0 dksbZ larqyu fcUnq gSA

( )π

=

∈

22 2

2 2 2 32 2 20

2 8d –2 –( – )d 4 –

xU dqd xx d x

( )2

22 2 22 2 3

0

1–22 – – 8

( – )4dq

d x xd xπ

= ∈

x = 0 ij

π

= ∈

2 22

2 60

–2 1(2 )

d 4d U dq

dx d

, tks < 0.

vr% ;g vLFkk;h larqyu gSA

vè;k; 3

3.1 (b)

3.2 (a)

3.3 (c)

3.4 (b)

3.5 (a)

3.6 (a)

3.7 (b), (d)

3.8 (a), (d)

3.9 (a), (b)

3.10 (b), (c)

3.11 (a), (c)

3.12 tc dksbZ bysDVªkWu fdlh lafèk dh vksj xeu djrk gS rks ,dleku E osQ vfrfjDr og

lekU;r% lafèk osQ rkjksa osQ i`"B ij lafpr vkos'kksa (tks viokg osx dv dks fu;r j[krs gSaA)

dk lkeuk Hkh djrk gSA ;s fo|qr ks=k mRiUu djrs gSaA ;s ks=k laosx dh fn'kk ifjofrZr djnsrs gSaA

3.13 foJkfUr dky bysDVªkWuksa ,oa vk;uksa osQ osxksa ij fuHkZj gksus osQ fy, ckè; gSaA vuqizLFk fo|qrcy bysDVªkWu osQ osx dks 1mm/s dksfV dh pkyksa kjk izHkkfor djrs gS] tks dksbZ lkFkZd izHkko

23/04/18


124

ugha gSA blosQ foijhr] T esa ifjofrZr osxksa esa 102 m/s dksfV osQ izHkko mRiUu djrk gSA ;gτ esa lkFkZd izHkko yk ldrk gSA [ρ = ρ(E,T ) gS ftlesa E ij fuHkZjrk misk.kh; gS] lkekU;vuqiz;qDr oksYVrkvksa osQ fy, ]A

3.14 OghVLVksu lsrq esa 'kwU; foksi fof/ dk ;g ykHk gS fd xSYosuksehVj dk izfrjksèk larqyu fcUnqdks izHkkfor ugha djrk rFkk izfrjksèkksa ,oa xSYosuksehVj esa izokfgr èkkjk rFkk xSYosuksehVj osQvkUrfjd izfrjksèk dks Kkr djus dh dksbZ vko';drk ugha gksrh vkSj fdj[kksiQ fu;e dkifjiFk ij vuqiz;ksx djosQ vKkr izfrjksèk] R

vKkr] ifjdfyr fd;k tk ldrk gSA vU;

fofèk;ksa esa ges izfrjksèkksa rFkk xSYosuksehVj esa izokfgr lHkh èkkjkvksa rFkk xSYosuksehVj osQvkUrfjd izfrjksèk dh ifj'kq¼ ekiksa dh vko';drk gksxhA

3.15 èkkrq dh eksVh ifêð;ksa dk fuEu izfrjksèk gksrk gS ftls 'kqU;&foksi fcUnq ij foHkoekih rkjdh yEckbZ esa lfEefyr djus dh vko';drk ugha gksrhA gesa osQoy lhèks [k.Mksa (izR;sd1 yEck) osQ vuqfn'k rkjksa dh yEckbZ ekiuh gksrh gS ftls ehVj LosQy kjk vklkuh ls ekiktk ldrk gSA vkSj ;g eki ifj'kq¼ gksrh gSA

3.16 nks ckrks ij fopkj djus dh vko';drk gksrh gS% (i) èkkrq dk ewY;] rFkk (ii) èkkrq dh vPNhpkydrkA vfèkd ewY; gksus osQ dkj.k ge pk¡nh dk mi;ksx ugha djrsA blosQ i'pkr vPNspkydksa esa rk¡ck o ,syqfefu;e mi;ksx gksrs gSaA

3.17 feJkrqvksa osQ izfrjksèk dk rki xq.kkad fuEu (fuEu rki lqxzkg~;rk) rFkk izfrjksèkdrk mPpgksrh gSA

3.18 'kfDr k; PC = I2R

C

;gka] RC la;kstd rkjksa dk izfrjksèk gS2

C C2

PP R

V=

'kfDr k; PC de djus osQ fy, 'kfDr lapj.k mPp oksYVrk ij fd;k tkuk pkfg,A

3.19 ;fn R esa o`f¼ dj nsa] rks rkj ls izokfgr èkkjk de gks tk,xh vkSj bl izdkj foHko izo.krkHkh de gks tk,xh] ftlosQ dkj.k larqyu yEckbZ vfèkd gks tk,xhA vr% 'kwU; foksi fcUnqJ fcUnq B dh vksj LFkkukUrfjr gks tk,xkA

3.20 (a) E1 dk èkukRed VfeZuy X ls la;ksftr gS rFkk E

1 > E

(b) E1 dk Í.kkRed VfeZuy X ls la;ksftr gSA

3.21

E

R

V

23/04/18

mÙkj

125

3.22 ; 10E E

I IRR nR Rn

= =+ +

1 110

1 11

n nn n

n

n

+ += = =

++

n = 10.

3.231

1 1 1.......

p nR R R= + + , U; wUre U; Uw re U; Uw re U; Uw re

1 2

....... 1P n

R R R R

R R R R= + + + >

vkSj RS = R1 + ...... + Rn ≥ Rvfèkdre

.

fp=k (b) esa Rmin fp=k (a) esa èkkjk dks iznku fd, tSlk gh rqY; ekxZ iznku djrk gSA ijUrq blosQlkFk&lkFk 'ks"k (n – 1) izfrjksèkdksa osQ kjk (n – 1) ekxZ iznku fd, x, gSaA fp=k (b) esa fo|qrèkkjk > fp=k (a) esa fo|qr èkkjkA fp=k (b) esa izHkkoh izfrjksèk < RminA Li"V :i ls nwljk ifjiFkvfèkd izfrjksèk ogu djus ;ksX; gSA vki fp=k (c) rFkk fp=k (d) dk mi;ksx djosQ Rs > Rmax

fl¼ dj ldrs gSaA

3.246 – 4

0.2A2 8

I = =+

E1 osQ fljksa ij foHkokUrj = 6 – 0.2 × 2 = 5.6 V

E2 osQ fljksa ij foHkokUrj = VAB = 4 + .2 × 8 = 5.6 V

fcUnq B fcUnq A ls mPp foHko ij gSA

3.25E E

IR r r1 2

+=

+ +

V1 = E – Ir1 = E

E rr r R

11 2

2– 0=

+ +

V

Rmin

V

RmaxRmin

V

V

Rmax

(a) (b) (c) (d)

E1 E2

A B

23/04/18


126

vFkok ErE

r r R1

1 2

2=

+ +

r1

r r R

1

1 2

2=

+ +

r1 + r

2 + R = 2r

1

R = r1 – r2

3.26 A

lR –3 2(10 0.5)

ρ

π=

×

B

lR –3 2 –3 2[(10 ) – (0.5 10 ) ]

ρ

π=

×

A

B

R

R

–3 2 –3 2

–3 2

(10 ) – (0.5 10 )(.5 10 )

×=

× = 3 : 1

3.27 fp=k esa n'kkZ, vuqlkj ge fdlh Hkh 'kk[kk R osQ leLr usVooZQ dks ,d ljy ifjiFk esa ifj.krdjus dh lksp ldrs gSaA

rc R ls izokfgr èkkjk VI

R R=

+iHz kkoh

izHkkoh

foeh; :i esa VizHkkoh

= VizHkkoh

(V1, V2, ...... Vn) dh foek oskYVrk dh gS rFkk RizHkkoh

= RizHkkoh

(R1, R

2, ....... R

m) dh foek izfrjksèk dh gSA

vr% ;fn lc esa n-xquh o`f¼ gks tkrh gS] rc

V nV R n R,= =u;k u;kizHkkoh izHkkoh izHkkoh izHkkoh

vkSj R izHkkoh = nR.

bl izdkj èkkjk leku jgrh gSA

3.28 fdj[kksiQ osQ lafèk fu;e dk vuqiz;ksx djus ij

I1 = I + I

2

fdj[kksiQ osQ ik'k fu;e ls izkIr gksrk gS10 = IR + 10I

1....(i)

2 = 5I2 – RI = 5 (I1 – I) – R

I

4 = 10I1 – 10I – 2RI..... (ii)

(i) – (ii) ⇒ 6 = 3RI + 10I vFkok 2 = I R10

+3

I Veff

Reff

R

I2

I1

R

I2

10V10W

5W

2V

R

Veff

I

Reff

23/04/18

mÙkj

127

2 = (R+ RizHkkoh

)I dh VizHkkoh

= (R + RizHkkoh

)I

vkSj VizHkkoh

= 2V

RizHkkoh

= 103

Ω

3.29 mi;qDr 'kfDr = 2ek=kd/?kaVk = 2kW = 2000J/s

20009

220P

IV

= = A

rkj esa 'kfDr k; = RI2 J/s

= 2 –8–6

101.7 10 81

10l

IA

ρπ

= × × ××

J/s

4 J/s

= 0.2%

Al rkj esa 'kfDr k; = 4 1.6 4 6.4J/s=0.32%Al

Cu

ρ

ρ= × =

3.30 eku yhft, foHkoekih osQ rkj dk izfrjksèk R′ gS] rc

108

50R

R

′×< ⇒

′+ 10R ′ < 400 + 8R′

2R ′ < 400 vFkok R′ < 200Ω

108 2 80 40

10R

R RR

′×′ ′> ⇒ > ⇒ >

′+

310

4 810

R

R

′×< ⇒

′+7.5R′ < 80 + 8R′

R′ > 160 ⇒ 160 < R′ < 200

bldh 400 cm ij foHkoikr > 8V

bldh 300 cm ij foHkoikr < 8V

φ × 400 > 8V (φ → foHkokUrj )φ × 300 < 8Vφ > 2V/m

< 2

23

V/m

3.31 (a) I = 66

= 1 A = nevd A

vd = –4

29 –19 –6

1 110

10 1.6 10 10 1.6= ×

× × × m/s

e dm v nAl2

–31 –8 29 –6 –1 –17

12

1 19.1 10 10 10 10 10 2 10 J

2 2.56

= ×

= × × × × × × × ×

xfrt mQtkZ

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128

(b) vkseh k; = RI2 = 6 × 12 = 6 J/s

×

–17–172 10

s 10 s6

esa bysDVªkWu dh leLr xfrt mQtkZ u"V gks tk,xhA

vè;k; 4

4.1 (d)

4.2 (a)

4.3 (a)

4.4 (d)

4.5 (a)

4.6 (d)

4.7 (a), (b)

4.8 (b), (d)

4.9 (b), (c)

4.10 (b), (c), (d)

4.11 (a), (b), (d)

4.12 pqEcdh; ks=k osQ yEcor xeu djus okys vkosf'kr d.k osQ fy,% 2mv

qvBR

=

qB v

m Rω∴ = =

qB vT

m R

–1[ ] [ ]ω

∴ = = =

4.13 dW= . 0d =F l

. 0dt⇒ =F v

. 0⇒ =F v

F, osx fuHkZj gksuk pkfg, ftldk vFkZ ;g gS fd F rFkk v osQ chp dks.k 90° dk gSA ;fnv ifjofrZr gksrk gS (fn'kk esa) rks F Hkh (fn'kk esa) bl izdkj ifjo£rr gksxk ftlls mijksDr'krZ iwjh gks tk,A

4.14 pqEcdh; cy funsZ'k izsQe ij fuHkZj gS rFkkfi blls mRiUu usV Roj.k tM+Roh; funsZ'k izsQeksa osQfy, funsZ'k izsQe ij fuHkZj ugha djrk (vukisfkdh; HkkSfrdh)A

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129

4.15 d.k ,dkUrjr% Rofjr ,oa eafnr gksxkA vr% nksuksa Mh esa iFk dh f=kT;k vifjofrZr jgsxhA

4.16 O2 ij I1 osQ dkj.k pqEcdh; ks=k y-vk osQ vuqfn'k gSA nwljk rkj y-vk osQ vuqfn'k gS] vr%cy 'kwU; gSA

4.17 01 ˆ ˆ ˆ( + + )4 2

I

R

µ=B i j k

4.18 dksbZ foekghu jkf'k ughaA –1[ ] [ ]eB

Tm

ω = =

4.19 0 0ˆ ˆ0,0E E B= > =E i B k,

4.20 d 1l ij d 2l osQ dkj.k cy 'kwU; gSA

d 2l ij d 1l osQ dkj.k cy 'kwU;srj gSA

4.21 iG (G + R1) = 2 (0 – 2V) ifjlj osQ fy,

iG (G + R1+ R2) = 20, (0 – 2V) ifjlj osQ fy,rFkk iG (G + R1+ R2 + R3) = 200, 200V ifjlj osQ fy,izkIr gksrk gS R1 = 1990Ω

R2 = 18 kΩ

rFkk R3 = 180 kΩ

4.22 F = BIl sin θ = BIl

o

2I

Bh

µ

π=

I lF mg

h

2o

2µ

π= =

2 –7o

–3

4 10 250 25 12 2 2.5 10 9.8

I lh

mg

µ π

π π

× × × ×= =

× × ×

= 51 × 10–4 mh = 0.51 cm

4.23 tc pqEcdh; ks=k dk;Zjr ugha gS] rc 0τ =∑Mgl = W

oqQ.Myh l

500 g l = WoqQ.Myh

l

WoqQ.Myh

= 500 × 9.8 N

tc pqEcdh; ks=k yxk fn;k tkrk gS] rcMgl + mgl = W

oqQ.Myh l + IBL sin 90°l

mgl = BILl

–2–30.2 4.9 1 10

10 kg9.8

BILm

g

× × ×= = =

= 1 g

P Q

h

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4.240

1 1

VF = i lB = lB

R,

01 12 2 2 2

d V ldBF

Rτ = =

02 2 2

VF i lB lB

R= = 0

2 22 2 4 2

d V ldBF

Rτ = =

usV cy vk?kw.kZ 1 2–τ τ τ=

01

4 2

V AB

Rτ =

F1

F2

B

45°

nd

B

i1

F1

F2

l

n

Front viewV0

vxz n`f"V i'p n`f"V

4.25 pwafd B x-vk osQ vuqfn'k gS] o`Ùkh; dkk osQ fy, nks d.kksa osQ laosx y - z ry esa gSaA ekuyhft, bysDVªkWu rFkk izksVkWu osQ laosx ozQe'k% p1 rFkk p2 gSaA ;s nksuks R f=kT;k osQ o`Ùk dksfu:fir djrs gSaA ;s nksuks foijhr fn'kk osQ o`Ùkksa dk fu:i.k djrs gSaA eku yhft, p1 y

vk ls θ dks.k cukrk rks p2 dks Hkh bruk gh dks.k cukuk pkfg,A buosQ vius futh osQUnzksadks laosxksa osQ yEcor rFkk R nwjh ij gksuk pkfg,A eku yhft, bysDVªkWu dk osQUnz Ce ryikWthVªkWu dk osQUnz Cp ij gSACe osQ funsZ'kkad gSa

(0,– sin , cos )Ce R Rθ θ≡

Cp osQ funsZ'kkad gSa

θ θ≡ (0,– sin cos )3

Cp R , R–R 2

;fn nksuksa osQ osQUnzksa osQ chp dh nwjh 2R ls vfèkd gS] rks bu nksuksa osQ o`Ùk ijLij O;kiuugha djsaxsAeku yhft, Cp rFkk Ce osQ chp dh nwjh d gS] rc

θ θ

= +

22 2 3

(2 sin ) – 2 cos2

d R R R

θ θ θ= + +2

2 2 2 2 294 sin – 6 cos 4 cos

4R R R R

Z

y

x

R

1.5 R

Cp

Ce

q

B

23/04/18

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131

2 2 294 – 6 cos

4R R R θ= +

pw¡fd d dks 2R ls vfèkd gksuk pkfg,d2 > 4R2

2 2 2 294 – 6 cos 4

4R R R Rθ⇒ + >

96cos

4θ⇒ >

vFkok 3cos

8θ <

4.26 ks=kiQy 23A=

4a , A = a2, 23 3

4A a=

fo|qr èkkjk I lcosQ fy, leku gSpqEcdh; vk?kw.kZ m = n I A

2= 3m Ia∴ 3a2I 23 3a I

(è;ku nhft,% m xq.kksÙkj Js.kh esa gSA)

4.27 (a) B (z) z - vk ij leku fn'kk esa laosQr djrk gS] blhfy, J (L), L dk ,d :ih o`f¼iQyu gSA

(b) J(L) + ifjjs[kk C ij cM+h nwfj;ksa ls ;ksxnku 0Iµ=

∴ tSls&tSls L → ∞

cM+h nwfj;ksa ls ;ksxnku 0→ D;ksafd 3(B 1/r )∼

0( )J Iµ∞ −

(c) 2

02 2 3 /22( )z

IRB

z R

µ=

+

20

2 2 3/ 2– – 2( )z

IRB dz dz

z R

µ∞ ∞

∞ ∞=

+∫ ∫

;fn z = R tanθ dz = R sec2 θ d θ

/20

0– – /2cos

2z

IB dz d I

π

π

µθ θ µ

∞

∞∴ = =∫ ∫

(d) B(z)oxZ

< B (z)o`Ùkh; oqQ.Myh

( ) ( )L Lℑ ℑ∴ <oxZ oÙkh; oQq .Myh

ijUrq (b) esa fn, x, rdks± dk mi;ksx djus ij

( ) ( )ℑ ℑ∞ = ∞oxZ oÙkh; oqQ.Myh

4.28 iG .G = (i1 – iG) (S1+ S2+ S3) tc i1 = 10mA

iG (G + S1) = (i2 –iG) (S2+ S3) tc i2 = 100mA

rFkk iG (G + S1+S2) = (i3 – iG) (S3) tc i3 = 1A

ls izkIr gksrk gS S1 = 1Ω, S2 = 0.1Ω rFkk S3 = 0.01Ω

n = 4 n = 3 n = 2

–L –LO

23/04/18


132

4.29 (a) 'kwU;

(b) 0

2i

R

µ

π AO osQ yEcor~ ckb± fn'kk esa

(c) 0 i

R

µ

π AO osQ yEcor~ ckb± fn'kk esa

vè;k; 5

5.1 (c)

5.2 (a)

5.3 (c)

5.4 (b)

5.5 (b)

5.6 (a), (d)

5.7 (a), (d)

5.8 (a), (d)

5.9 (a), (c), (d)

5.10 (b), (c), (d)

5.11 2p

p

e

mµ ≈

vkSj ,2 2e

e

e h

mµ

π≈ =

e pµ µ>> D;ksafd mp >> me

5.12 0 0 MB ( )l M l I Iµ µ= = + vkSj H = 0 = I

Ml = IM = 106 × 0.1 = 105 A

5.13 χ α ?kuRo ρ A vc –3N

Cu

28g/22.4Lt 3.510

8g/c 22.4c

ρ

ρ= = × = 1.6 × 10–4

–4N

Cu

5 10χ

χ= ×

vr% ;gk¡ izeq[k vUrj ?kuRo osQ dkj.k gSA

5.14 izfr pqEcdRo bysDVªkWuksa dh dkh; xfr osQ dkj.k gksrk gS tks vuqiz;qDr ks=k osQ foijhrpqEcdh; vk?kw.kZ mRiUu djrk gSA blfy, ;g rki ls vfèkd izHkkfor ugha gksrkA

N S

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133

vuqpqEcdRo vkSj yksg pqEcdRo ijek.oh; pqEcdh; vk?kw.kksZa osQ vuqiz;qDr ks=k dh fn'kk esalajs[k.k osQ dkj.k gksrk gSA rki of¼ gksus ij ;g lajs[k.k fokksfHkr gks tkrk gS ftlosQ iQyLo:inksuksa dh pqEcd'khyrk rki of¼ osQ lkFk ?kV tkrh gSA

5.15 (i) pqEcd ls nwj

(ii) pqEcdh; vk?kw.kZ ck,a ls nk,a

5.16 03

ˆ3 . ˆ,4

m mr

µ

π= =

m rB k

2ˆ. sind d dθ θ φ=s r r

0 ,0θ π φ π≤ ≤ ≤ ≤

203

3cos. sin

4m

ds r d dr

µ θθ θ φ

π=∫ ∫B

= 0 (θ lekdyu osQ dkj.k)

q

f

m

ds

z

y

x

r

S S

NN

N

S

5.17 usV 0m = . ek=k laHkor% fp=k (b) esa n'kkZ;h xbZ gSA

5.18 E (r) = c B (r), m

pc

= . fèkzqoksa osQ nzO;eku vkSj tM+Ro vk?kw.kZ leku gSaA

5.19 2I

TmB

π=1 12 4

I I′ = × rFkk 2m

m ′ = . 12

T T′ =

5.20 NM+ ls xqtjus okyh B dh fdlh js[kk ij fopkj dhft,A ;g cUn gksuh pkfg,A eku yhft,C ,sfEi;jh&ik'k gSA

0

. . 0P P

Q Q

d dµ

= >∫ ∫B

H l l

. 0PQP

d =∫ H l

. 0Q

p

d <∫H l

P → Q NM+ osQ Hkhrj gSAvr% H vkSj dl osQ chp dk dks.k vfèkd dks.k gSA

5.21 (i) z-vk osQ vuqfn'k

03

24 r

µ

π=

mB

0 03 2 2

1 11. 2 ––

4 2 2

R R

a a

dz md m

z R a

µ µ

π π

= =

∫ ∫B l

(ii) f=kT;k R osQ pkSFkkbZ o`Ùk osQ vuqfn'k

P Q

C

S N

23/04/18


134

( )0 00 3 3

ˆ– . ––sin

4 4m

BR R

µ µθ

π π/ = =

m θθθθ

02. sin

4m

d dR

µθ θ

π=B l

20

20

B.4

mdl

R

π

µ

π=∫

(iii) x-vk osQ vuqfn'k

03

–4

m

x

µ

π

=

B

. 0d =∫B l

(iv) f=kT;k a osQ pkSFkkbZ o`Ùk osQ vuqfn'k

02

–. sin

4m

d da

µθ θ

π=B l ,

π

µ µθ θ

π π= =∫ ∫

20 0

2 20

– –. – sin

4 4B l

m md d

a a

lHkh dks tksM+us ij] . 0C

d =∫ B l

5.22 χ foekghu gSA

χ ml pqEcdh; vk?kw.kZ ij fuHkZj djrk gS tks H ijek.oh; bysDVªkWuksa ls buosQ vkos'kksa ekjk la;ksftr gksrk gSA m ij bldk izHkko èkkjk I ls gksdj gksrk gS ftlesa ‘e’ dk nwljk dkjd

lfEefyr gksrk gSA la;kstu 20" "eµ “vkos'k” Q dh foek ij fuHkZj ugha djrkA

20e m v Rα β γχ µ=

2 22

0 2 2 20 0

1 1~ . ~

e ec R

Rc c cµ

ε ε=

mQtkZ foLrkj

[ χ ] = M0L0T0Q0 = 3 –2

02 –2

ML T LL Q

TM

L T

βα γ

–1, 0, –1α β γ= = =

2 –6 –38–400

–30 –10

10 10~ ~10

10 10e

mR

µχ

×=

×

R

a1

a x xO R

z

23/04/18

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135

5.23 (i) 2 2 1/ 203 (4cos sin )

4m

R

µθ θ

π= +B

22

220

3

3cos 1

4m

R

θµ

π

= +

B , 2π

θ = ij U;wureA

B pqEcdh; fujk ij U;wure gSA

(ii) tan (ufr dks.k) = 2cotV

H

B

Bθ=

2π

θ = ij ufr dks.k 'kwU; gks tkrk gSA iqu% fcanqiFk] pqEcdh; fujk gSA

(iii) tc 1V

H

B

B= rc ufr dks.k ± 45° gSA

2 cot θ = 1θ = tan–12 fcUnqiFk gSA

5.24 layXu fp=k ij è;ku nhft,A

1. fcUnq P ry S esa gS (lqbZ mÙkj dh vksj laosQr djsxh)

fnDikr dks.k = 0;

P Hkh ,d pqEcdh; fujk gSA

∴ ufr dks.k = 0

2. Q pqEcdh; fujk ij gS

∴ ufr dks.k = 0

ijUrq fnDikr dks.k = 11.3°

5.25 1 2L

nRπ

= 2 4L

na

=

1 1 1IAm n= 2 2 2Im n A=

2L

I RR

ππ

= 2=4 4L L

Ia Iaa

=

2

1 2MR

I = (O;kl ls xqtjus okys fdlh vk osQ ifjr% tM+Ùo vk?kw.kZ)

2

2 12Ma

I =

wN

P

Q

GE

ME

11.3°

S

23/04/18


136

2 11

1

m B

Iω = 2 2

22

m B

Iω =

1 2

1 2

m m

I I=

LIa

LR Ia R

MR Ma2 2

342 4

2 12

π

π× =

vè;k; 6

6.1 (c)

6.2 (b)

6.3 (a)

6.4 (d)

6.5 (a)

6.6 (b)

6.7 (a), (b), (d)

6.8 (a), (b), (c)

6.9 (a), (d)

6.10 (b), (c)

6.11 rkj dk dksbZ Hkh Hkkx xfre; ugha gS vr% xfrd fo|qr okgd cy 'kwU; gSA pqEcd fLFkj gSvr% le; osQ lkFk pqEcdh; ks=k ifjofrZr ugha gksrkA bldk ;g vFkZ gS fd dksbZ fo|qr okgdcy mRiUu ugha gksrk vr% ifjiFk esa dksbZ èkkjk izokfgr ugha gksxhA

6.12 èkkjk c<+ tk,xhA tSls gh rkjksa dks ,d nwljs ls nwj [khapk tkrk gS fjDr LFkkuksa ls ÝyDl dkkj.k gksrk gSA ysat+ osQ fu;e osQ vuqlkj izsfjr fo|qr okgd cy bl deh dk fojksèk djrkgS ftls fo|qr èkkjk esa o`f¼ kjk iwjk fd;k tkrk gSA

6.13 èkkjk ?kV tk,xhA ifjukfydk esa yksg ozQksM j[kus ij pqEcdh; ks=k esa o`f¼ gksrh gS vkSj ÝyDlc<+ tkrk gSA ysat+ osQ fu;e osQ vuqlkj izsfjr fo|qr okgd cy dks bl o`f¼ dk fojksèk djukpkfg, ftls èkkjk esa deh kjk izkIr fd;k tkrk gSA

6.14 vkjEHk esa èkkrq osQ oy; ls dksbZ ÝyDl ugha xqtj jgk FkkA èkkjk izokfgr gksrs gh oy; ls ÝyDlxqtjus yxrk gSA ysat+ osQ fu;e osQ vuqlkj izsfjr fo|qr okgd cy bl o`f¼ dk fojksèk djsxkvkSj ;g rc gks ldrk gS tc oy; ifjukfydk ls nwj tk,A bldk foLr`r fo'ys"k.k fd;k tkldrk gS (fp=k 6.5)A ;fn ifjukfydk esa èkkjk n'kkZ, vuqlkj gS rks ÝyDl (vèkkseq[kh) esao`f¼ gksrh gS vkSj blls okekorZ (oy; osQ 'kh"kZ ls ns[kus ij) xfr mRiUu gksxhA tSls gh èkkjk

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137

dk izokg ifjukfydk esa izokfgr èkkjk osQ foijhr gksrk gS] ;s ,d nwljs dks izfrdf"kZr djsaxs rFkkoy; mQij dh vksj xfr djsxkA

6.15 tc ifjukfydk esa izokfgr fo|qr èkkjk esa deh gksrh gS] rks oy; esa èkkjk dh fn'kk] ifjukfydkosQ leku gh gksrh gSA bl izdkj ;gk¡ ,d vèkkseq[kh cy yxsxkA bldk ;g vFkZ gS fd oy;dkMZ cksMZ ij gh jgsxkA dkMZ cksMZ dh oy; ij mifjeq[kh izfrfozQ;k c<+ tk,xhA

6.16 pqEcd osQ fy,] èkkrq osQ ikbi esa Hkaoj èkkjk,¡ mRiUu gksrh gSaA ;s èkkjk,¡ pqEcd dh xfr dkfojksèk djsaxhA blhfy,] pqEcd dk vèkkseq[kh Roj.k] xq#Roh; Roj.k ls de gksxkA blosQ foijhr]pqEcfdr yksgs dh NM+ esa Hkaoj èkkjk,¡ mRiUu ugha gksaxh vkSj og xq#Roh; Roj.k ls uhps fxjsxkAvr% pqEcd fxjus esa vfèkd le; yxsxkA

6.17 oy; ls xqtjus okyk ÝyDl

φ = π ω2( )cosoB a t

ε = π ω ω2( ) sinB a t

2( ) sin /I B a t R= π ω ω

fofHkUu le;ksa ij èkkjk dk ifjek.k

( )2

;2

B at I

R

ωπ π= =

ω, j osQ vuqfn'k

; 0t Iπ

= =ω

( )23;

2

B at I

R

ωπ π= =

ω, ˆ– j osQ vuqfn'k

6.18 gesa ÝyDl osQ fy, leku mÙkj izkIr gksxkA ÝyDl dks fdlh i`"B (ge fdlh ks=kiQy∆ A ⊥ ls B rd dN = B ∆ A js[kk,¡ [khprs gSa) ls xqtjus okyh pqEcdh; ks=k js[kkvksa dhla[;k ekuk tk ldrk gSA ftl izdkj B dh js[kk,¡ fnDdky esa u rks vkjEHk gksrh gSa vkSj ugh var gksrh gSa (os cUn ik'k cukrh gSa)A i`"B S

1 ls xqtjus okyh js[kkvksa dh la[;k i`"B S

2

ls xqtjus okyh js[kkvksa dh la[;k osQ leku gksuh pkfg,A

6.19 fcUnqfdr js[kk CD osQ vuqfn'k xfrd fo|qr ks=k (v rFkk B nksuksa osQ yEcor~ rFkk v × B osQvuqfn'k) = vB

PQ osQ vuqfn'k E.M.F. = (yEckbZ PQ)×(PQ osQ vuqfn'k ks=k)

= coscos

dvB dvB× θ =

θ

vr%

dvBI

R= vkSj ;g θ ij fuHkZj ugha gSA

( ,0,0)ax

(0,0,0)

y

k

S1

S2

c

B D B

BC

q

B

B

P

Q B

Rv

23/04/18


138

6.20 èkkjk esa vfèkdre ifjorZu dh nj AB esa gSA vr% vfèkdre fojksèkh fo|qr fojksèkh cy izkIrgksus dk le; 5 s < t <10 s osQ chp gSA

;fn u = –L 1/5 3s, 1/5dI

tdt

= =

ij = e

5 s < t < 10 s ij 13 3

– – 35 5

u L L e= = =

bl izdkj t = 7 s, ij u2 = –3 e

10s < t < 30s ij

32 1

20 10 2L

u L e= = =

t > 30s ij u3 = 0

6.21 vU;ksU; izsjdRo –210

5mH2

= =

ÝyDl –3 –35 10 1 5 10= × × = × Wb

6.22 eku yhft,] lekUrj rkj y = 0 rFkk y = d gSaA le; t = 0 ij AB dh fLFkfr x=0 gS vkSj

;g osx ˆvi ls xfr djrk gSA

le; t ij] rkj dh fLFkfr gS x (t) = vt

xfrd e.m.f = ( ) ( )ˆsin –oB t vdω j

OBAC osQ vuqfn'k ks=k esa ifjorZu osQ dkj.k e.m.f

– cos ( )oB t x t d= ω ω

oqQy e.m.f ( ) ( )[ ]– cos sinoB d x vt t= ω +ω ω

OBAC osQ vuqfn'k èkkjk (nfk.kkorhZ) ( )cos sinoB dx t v t

R= ω ω + ω

i osQ vuqfn'k vko';d cy ( ) sincos sinoo

B dd B tx t v t

R= × × ωω ω + ω

( )oB dtx t v t

R

2 2

sincos sin= ωω ω + ω

6.23 (i) eku yhft, le; t ij rkj dh fLFkfr x = x (t) gSA

ÝyDl = B (t) l x (t)

( )( ) ( ) ( )– – – .

d dB tE l x B l vt t t

dt dt

φ= =

(nwljk in xfrd fo|qr okgd cy ls gS)

1I E

R=

y

xB

CA

O

v

X

B

x t( )

Bl

Y

B

Dx

C

A

R

y

23/04/18

mÙkj

139

cy ( )

( ) ( ) ( ) ˆ– –l B dBt

l x B l vt t tR dt

=

i

( )2 2 2 2

2 – –d x l B dB l B dx

m x tdt R dt R dt

=

(ii) 0,dB

dt=

2 2 2

2 0d x l B dx

dt mR dt+ =

2 2

0dv l B

vdt mR

+ =

2 2–A exp l B tv

mR

=

t = 0 ij, v = uv (t) = u exp (–l2B2t/mR)

(iii)2 2 2 2 2

2 2 2 22

( )exp(–2 / )

B l v t B lI R R u l B t mR

R R= × =

'kfDr k; 2 2

2 2 –( )2 2

01 – e2

2 2

t

l B t/mRB l mR

I R dt uR l B

= = ∫

( )2 2–2 2m m

u v t=

= xfrt mQtkZ esa deh

6.24 le; t = 0 vkSj 4

tπ

=ω

osQ chp NM+ OP Hkqtk BD ls lEioZQ cuk,xhA eku yhft, NM+

dh lEioZQ dh yEckbZ OQ fdlh le; t 04

tπ

< < ω

ij x gSA ks=kiQy ODQ ls

xqtjus okyk ÝyDl gS 1 1

QD×OD= tan2 2

B B l lφ θ= ×

21= B t a n

2l ;gk¡ tθ ω=

bl izdkj mRiUu emf dk ifjek.k gS 2 21B sec

2d

l tdt

φε ω ω= = izokfgr èkkjk gS I =

R

ε

;gk¡ R NM+ dh lEioZQ okyh yEckbZ dk izfrjksèk gS

=cos

lR x

t

λ= λ

ω

A B

C D

2l

Oql

P

lx Q

23/04/18


140

A B

C DO

q

P

llx

l

2l

A

D

B

I t( )

xo

C

l

r

drx

∴ 2

21 B Bsec cos

2 2 cosl l

I t tl t

ω ωω ω

λ λ ω= =

vUrjky 3

4t

π π< <

ω ω esa NM+ Hkqtk AB osQ lEioZQ esa gSA eku yhft, NM+ osQ lEioZQ okys

Hkkx dh yEckbZ (OQ) x gSA rc OQBD ls xqtjus okyh ÝyDl gS&

22 1

2 tanl

Bl

φ = + θ

;gk¡ θ = ωt

bl izdkj mRiUu emf dk ifjek.k gS 2

22

1 sec2 tan

d tBl

dt t

φ ωε = = ω

ω

izokfgr èkkjk gS sin

= = =t

IR x l

ε ε ε ω

λ λ=

12 sin

Bl

t

ω

λ ω

vUrjky 3

tπ π

< <ω ω

ij NM+ Hkqtk OC dks Li'kZ djsxhA rc OQABD ls xqtjus okyk

ÝyDl gS 2

22 –2 tan

lBl

t

φ =

ω

bl izdkj emf dk ifjek.k gS

2 2sec2tans

d B l t

dt t

φ ω ωε

ω= =

1 B= = =

2 sinl

IR x t

ε ε ω

λ λ ω

6.25 rkj ls nwjh r ij

ks=k ( )2

o IB r

r

µ=

π (dkxt+ osQ cfgeqZ[kh)

rkj ls nwjh r ij pkSM+kbZ dr dh fdlh ifêðdk ij fopkj dhft,

ywi ls oqQy ÝyDl gS%

ÝyDl 2 2

o

xo o

ox

I Idr xl ln

r x

µ µ= =

π π∫

A B

C DO

q

R

P

l

2l

l

Q

x

23/04/18

mÙkj

141

0

12

odI l xI ln

R dt R R x

ε µ λ

π= = =

6.26 ;fn ik'k esa izokfgr èkkjk I (t) gS] rc

1( )

dI t

R dt

φ=

;fn le; t esa izokfgr vkos'k Q gS] rc

( )dQ

I tdt

= or 1dQ d

dt R dt

φ=

lekdyu djus ij ( ) ( ) ( ) ( )1 2 1 21

– –Q t Q t t tR

= φ φ

( ) ( )φ+

′µ=

′π ∫2

1 1 12

L x

o

x

dxt L I t

x

( )1 21 ln

2oL L x

I tx

µ +=

π

vkos'k dk ifjek.k

[ ]1 2 – 0ln2o

o

L L xIQ

x

µ +=

π

1 1 2ln2

oL I L x

x

µ + =

π

6.272.

2 . .B a

bE E M Ft

ππ = =

∆ ;gk¡ E ik'k osQ pkjksa vksj mRiUu fo|qr ks=k gSA

cy vk?kw.kZ = b × cy = Q E b 2

2B a

Q bb t

π= π ∆

2

2Ba

Qt

=∆

;fn dks.kh; laosx esa ifjorZu ∆L gS] rc

∆L = cy vk?kw.kZ × ∆t

2

2Ba

Q=

A

D

B

I (t)

x C

L1

L + x2

23/04/18


142

vafre dks.kh; laosx = 0

vafre dks.kh; laosx 2

2

2QBa

mb= ω =

2

22

QBa

mbω =

6.28 ( )2

2

cossin – cos

d x B d dxm mg Bd

Rdt dt

θ = θ × θ

dv B dg v

dt mR

2 22sin – (cos )= θ θ

dv B dv g

dt mR

2 22(cos ) sin+ θ = θ

2 22

2 2 2

sinexp – (cos )

cos

g B dv A t

B d mR

mR

θ = + θ θ

[tgk¡ A ,d fLFkjkad gS ftldk eku vkjafHkd voLFkkvksa ls fu/kZfjr gksrk gSA]

2 22

2 2 2

sin1 – exp – (cos )

cosmgR B d

tB d mR

θ = θ

θ

6.29 ;fn laèkkfj=k ij vkos'k Q (t) gS (è;ku nhft,] èkkjk izokg A ls B dh vksj gS)] rc

–vBd Q

IR RC

=

Q dQ vBd

RC dt R⇒ + =

∴ [ ]

– /

– /1 –

t RC

t RC

Q vBdC Ae

Q vBdC e

= +

⇒ = (le; t = 0 ij Q = 0 = A = –vBdc)

– /t RCvBdI e

R=

6.30 –dI

L vBd IRdt

+ =

dIL IR vBd

dt+ =

B

BC

B

dv

AX

Y

S

23/04/18

mÙkj

143

– /2A e RtvBdI

R= +

t = 0 ij I = 0 –vBd

AR

⇒ =

( )– /1 – Rt LvBd

I eR

=

6.31φd

dt= ÝyDl esa ifjorZu dh nj = (πl2) Bo l

dz

dt= IR

2ol B

I vR

π λ=

izfr lsd.M mQtkZ k; = I2 R = 2 22 2

ol B v

R

(π λ)

;g fLFkfrt mQtkZ esa ifjorZu dh nj ls izkIr gksuk pkfg, = m gdz

dt= mgv

(v= fu;r gksus osQ dkj.k xfrt mQtkZ fu;r gS)

bl izdkj mgv = 2

02 2l B v

R

(π λ )

vFkok v = 2 2)o

mgR

( l Bπ λ

6.32 fdlh ifjukfydk osQ dkj.k pqEcdh; ks=k 0B nI= µ

NksVh oqQ.Myh esa pqEcdh; ÝyDl NBA=φ

;gk¡ 2A b= π

vr% φ= =

– –( )

d de NBA

dt dt

d B dN b N b nI

dt dt

2 20

( )– – ( )= π = π µ

20

I–

dN b n

dt= π µ

2 2 20 0– ( C) – 2

dNn b mt Nn b mt

dt= πµ + = µ π

20– 2e Nn b mt= µ π

½.kkRed fpg~u izsfjr emf dk ifjek.k fp=k esa n'kkZ, vuqlkj le; osQ lkFk ifjofrZr gksrkgSA

e

t

d

B

B B

B

L

B

v

AX

S

B B

23/04/18


144

vè;k; 7

7.1 (d)

7.2 (c)

7.3 (c)

7.4 (b)

7.5 (c)

7.6 (c)

7.7 (a)

7.8 (a), (d)

7.9 (c), (d)

7.10 (a), (b), (d)

7.11 (a), (b), (c)

7.12 (c), (d)

7.13 (a), (d)

7.14 pqEcdh; mQtkZ xfrt mQtkZ osQ ln`'k rFkk oS|qr mQtkZ fLFkfrt mQtkZ osQ ln`'kA

7.15 mPp vko`fÙk ij] la/kfj=k ≈ y?kq iFk (fuEu izfr?kkr) rFkk izsjd [kqyk ifjiFk (mPp izfr?kkr)

1 3Z R R≈ + tSlk rqY; ifjiFk esa n'kkZ;k x;k gSA

7.16 (a) gk¡] ;fn nksuksa ifjiFkksa esa rms oksYVrk leku gS rks vuqukn fLFkfr esa LCR esa rms èkkjkmruh gh gksxh ftruh R ifjiFk esaA

(b) ugha] D;ksafd ,R Z≤ vr% I Ia b≥

7.17 gk¡] ugha

⇒

23/04/18

mÙkj

145

7.18 cSaM pkSM+kbZ mu vko`fÙk;ksa osQ laxr gS ftu ij

1

2m maxI I= 0.7 maxI≈

;g fp=k esa n'kkZ;k x;k gS

∆ω = 1.2 – 0.8 = 0.4 rad/s

7.19 Irms

= 1.6 A fp=k esa fcUnqfdr js[kk kjk fu:firA

–3

1

0

2

–1

–2

3

T 2T

t

IA(

)

.5 1.0 1.5 2.0

0.5

1.0

Dw

0

w(rad/s)

I (A)m

7.20 ½.kkRed ls 'kwU; fiQj èkukRed] vuqukn vko`fÙk ij 'kwU;A

7.21 (a) A

(b) 'kwU;

(c) L vFkok C vFkok LC

7.22 a.c. èkkjk dh fn'kk lzksr dh vkofÙk osQ lkFk cnyrh gS rFkk vkd"kZ.k cy dk vkSlr eku 'kwU;gks tkrk gS] vr% a.c. osQ lanHkZ esa ,fEi;j dks fdlh ,sls xq.k osQ inksa esa ifjHkkf"kr fd;k tkukpkfg, tks èkkjk dh fn'kk ij fuHkZj u djrk gksA twy dk mQ"eu izHkko ,d ,slk gh xq.k gSvr% bldk mi;ksx a.c. osQ rms eku dks ifjHkkf"kr djus osQ fy, fd;k tk ldrk gSA

7.23 XL = ωL = 2pfL

= 3.14Ω

2 2Z R L= +

2 2(3.14) (1) 10.86= + =

3.3Ω

tan 3.14L

R

ωφ = =

–1tan (3.14)φ =

72°

72rad.

180π×

23/04/18


146

le;i'prk tφ

ω∆ =

72 1s

180 2 50 250π

π

×= =

× ×

7.24 PL = 60W, I

L = 0.54A

LV60

110V0.54

= =

VªkaliQkWeZj vipk;h gS rFkk fuxZr oksYVrk fuos'k oksYVrk dh vkèkh gS] vr%]

ip =

2I1

0.27A2

× =

7.25 laèkkfj=k dh IysVksa osQ chp osQ vUrjky dk izfrjksèk vuUr gksus osQ dkj.k blls gksdj fn"Vèkkjkizokfgr ugha gks ldrhA laèkkfj=k dh IysVksa osQ chp tc izR;korhZ èkkjk yxkbZ tkrh gS rks bldhIysVsa ckjh&ckjh ls vkosf'kr vkSj vukosf'kr gksrh gSaA laèkkfj=k ls gksdj izokfgr gksus okyh èkkjkblh ifjorhZ oksYVrk (;k vkos'k) dk ifj.kke gSA vr% ;fn oksYVrk vfèkd nzqr xfr ls ifjofrZrgksrh gS rks laèkkfj=k ls vfèkd èkkjk izokfgr gksxhA bldk fufgrkFkZ ;g gS fd laèkkfj=k kjk izLrqrizfr?kkr vko`fÙk c<+kus ls de gksrk gS% bldk eku gksrk gS 1/ωC

7.26 izsjd vius fljksa osQ chp ysUt osQ fu;e osQ vuqlkj fojksèkh fo|qr okgd cy fodflr djosQvius esa ls izokfgr gksus okyh èkkjk dk fojksèk djrk gSA izsfjr oksYVrk dh èkzqork bl izdkjgksrh gS fd fo|eku èkkjk dk Lrj cuk jg losQA ;fn èkkjk de gksrh gS rks izsfjr emf dh èkzqorkbl izdkj gksxh fd èkkjk c<+ losQ vkSj ;fn èkkjk c<+rh gS rks izsfjr emf dh èkzqork blosQ foijhrgksxhA D;ksafd izsfjr oksYVrk èkkjk ifjorZu dh nj osQ lekuqikrh gksrh gSA èkkjk ifjorZu dh njvfèkd gksus ij vFkkZr vko`fÙk vfèkd gksus ij èkkjk izokg osQ izfr izsjd dk izfr?kkr vfèkdgks tk,xkA vr% izsjd dk izfr?kkr vko`fÙk osQ lekuqikrh gksrk gS vkSj bldk eku ωL. kjkO;Dr fd;k tkrk gSA

7.27 'kfDr 50,00025

2000

2VP Z

Z= ⇒ = =

Z2 = R2 + (XC – X

L)2 = 625

C L– 3tan –

4X X

Rφ = =

22 2253

625 –164

R RR

= + =

R2 = 400 ⇒ R = 20Ω

23/04/18

mÙkj

147

XC– X

L = –15Ω

M

VI

Z

I

2239 A

25

2 9=12.6 A

= =

= ×

;fn R, XC, X

L lHkh dks nksxquk dj fn;k tk, rks tan φ esa dksbZ ifjorZu ugha gksrkA

Z dks nksxquk djsa rks èkkjk vkèkh gks tkrh gSA

7.28 (i) Cu osQ rkjksa dk izfrjksèk] R

–8

2–4

1.7×10 ×200004

1× 102

l

Aρ

π

= = = Ω ×

220 V ij I : VI = 106 W ;6

4100.45 10

220I = = × A

RI2 = kfr k;

= 4 × (0.45)2 × 108 W

> 106 W

;g fofèk lapj.k osQ fy, mi;ksx esa ugha ykbZ tk ldrhA

(ii) V′I′ = 106 W = 11000 I′

2110

1.1I ′ = ×

2 4 414 10 =3.3×10 W

1.21RI ′ = × ×

izfr'kfDr k; 4

6

3.3 10=3.3%

10×

=

7.29 Ri1 = v

m sin ωt 1

sinmv ti

R

ω=

22 2

2 sinm

q dqL v t

C dtω+ =

Let q2 = q

m sin (ωt + φ)

2 sin( ) sin–mm m

qq t v tL

C

ω + = ωω

φ

23/04/18


148

2

2

1, 0; – 0

1–

mm

vq L

CL

C

= φ = ω >

ω

2R

2

1, – 0

1–

mvv L

CLw

C

= φ = π ω >

22 cos( )m

dqi q t

dtφ= = ω ω +

i1 ,oa i2 leku dyk esa ugha gSaA ekuk fd 21– 0L

Cω >

1 2sin

cos1

–

m mv t vi i t

R Lc

ω+ = + ω

ωω

tgk¡ A sin ωt + B cos ωt = C sin (ωt + φ )

C cos φ = A, C sin φ = B; 2 2C A B= +

vr%]

12 2 2

1 2 2 2sin( )

[ –1/ ]m mv v

i i tR l C

ω φω ω

+ = ++

–1tan–L C

R

X Xφ =

1/2

2 2

1 11( – 1/ )R L CZ

+=

ω ω

7.30 2 21;

2

di qi di dLi Ri vi Li Li

dt c dt dt

+ + = =

= izsjd esa laxzghr mQtkZ ifjorZu dh nj

Ri2 = twy mQ"eu k;

2

2

q d qi

C dt C

=

laèkkfj=k esa laxzghr mQtkZ ifjorZu dh nj

vi = izpkyd cy kjk mQtkZ laHkj.k dh njA ;g mQtkZ iz;qDr gksrh gS (i) vkseh; k; (ii)

laxzghr mQtkZ o`f¼ esaA

23/04/18

mÙkj

149

222

0 0 0

12

T T Td q

dt Ri dt vidtidt C

+ =+

∫ ∫ ∫

0

0 ( )T

ve vidt+ + = ∫

0

0T

vidt >∫ ;g rHkh vkSj osQoy rHkh laHko gS tc dyk&vUrj] tks vpj gksrk gS]

U;wudks.k gksA

7.31 (i)2

2 sinm

d q dq qL R v t

dt Cdt+ + = ω

ekuk q = qm sin (ω t + φ) = – q

m cos (ωt + φ )

i = imsin (ω t + φ ) = qm ω sin (wt + φ )

–1

2 2

–; tan

( – )m m C L

m

C L

v v X Xi

Z RR X Xφ = = =

+

(ii)2

2 202 2

0

1 1sin ( )

– )2 2m

L

C L

vU Li L t

R X Xφ

= = ω +

+

222

02 2 2

1 1 1cos ( )

( – )2 2m

C

C L

vqU t

R X XC Cφ

= = ω +

+ ω

(iii) Lora=k NksM nsus ij ;g ,d LC nksfy=k gSA laèkkfj=k vukosf'kr gksrk tk,xk vkSj lEiw.kZmQtkZ L esa pyh tk,xhA ;g ozQe myVk gksxk vkSj ckj&ckj ;g izfozQ;k nksgjkbZ tkrh jgsxhA

vè;k; 8

8.1 (c)

8.2 (b)

8.3 (b)

8.4 (d)

8.5 (d)

8.6 (c)

23/04/18


150

i

8.7 (c)

8.8 (a), (d)

8.9 (a), (b), (c)

8.10 (b), (d)

8.11 (a), (c), (d)

8.12 (b), (d)

8.13 (a), (c), (d)

8.14 D;ksafd oS|qrpqacdh; rjaxsa lery /zqfor gksrh gSa] blfy, vfHkxzkgh ,sUVsuk rjax osQ oS|qr@pqacdh;Hkkx osQ lekarj gksuk pkfg,A

8.15 ekbozQksoso dh vko`fÙk ty osQ v.kqvksa dh vuqukn vko`fÙk ls esy [kkrh gSA

8.16 0–2 sin2C D

dqi i q t

dtπ ν πν= = =

8.17 vko`fÙk ?kVkus ij izfr?kkr 1cX

Cω= c<+sxk tks pkyu /kjk dks ?kVk,xkA bl fLFkfr esa

iD = i

C; vr% foLFkkiu /kjk de gks tk,xhA

8.18av

BI c W m

2 8 –8 220

–60

1 1 3 10 (12 10 )1.71 /

2 2 1.26 10µ

× × ×= = × =

×

8.19

T=2 /p w

S

tBZ

Ey

8.20 fo|qrpqacdh; rjaxsa fofdj.k nkc yxkrh gSaA /weosQrq dh iw¡N lkSj fofdj.k osQ dkj.k gSA

8.21 0 0 00

2 14 4 2

D EI dB

r r r dt

µ µ µ φ= = = ε

π π π

20 0 ( )2

dE r

r dt

µ ε= π

π

r dE

dt0 0

2µ ε

=

23/04/18

mÙkj

151

8.22 (a) λ1 → ekbozQksoso (lwe rjaxsa)

λ2 → ijkcSaxuh rjaxsa

λ3 → X - fdj.ksa

λ4 → vojDr rjaxsaa

(b) λ3 < λ2 < λ4 < λ1

(c) lwe rjaxsa (ekbozQksoso) - jMkj

ijkcSaxuh rjaxsa & ykfld us=k 'kY;rkX-fdj.ksa - vfLFkHkax ozQeohk.kvojDr rjaxsa - izdk'kh; lapkj

8.23 2 20 00

0

1cos ( – )

T

avS c kx t dtT

ε ω×= ∫E B D;ksafd 20( )c= ε ×S E B

20 0 0

12T

c E BT

ε= ×

2 00 0

12

Ec E

cε

= ×

0

0

Ec

B

=

∵

20 0

12

E cε=

20

02E

cµ= D;ksafd

0 0

1c

µ ε

=

8.24D

dVi C

dt=

–3 –61 10 2 10dV

dt× = ×

3110 5 10 /

2dV

V sdt

= × = ×

vr% 5 × 102 V/s dk ifjorhZ foHkokUrj yxk dj yfkr eku dh foLFkkiu èkkjk mRiUu dhtk ldrh gSA

8.25 nkc

1( )

AF p p

P FA t t

∆ ∆= = = = =

∆ ∆

cyloa xs ifjoruZ dh nj

ks=kiQy

23/04/18


152

pc t A

1 U. ( U

tc)= ∆ = = ∆

∆le; e sa rjax kjk iznku dh xb Z mQtkZ

UI

c A t

I

= =

∆

rhozrk

8.26 rhozrk ?kVdj ,d pkSFkkbZ jg tkrh gSA bldk dkj.k gS fd xksyh; ks=k osQ ks=kiQy 4π r2 esalapfjr gksus ij izdk'k iqat dk foLrkj gksrk gS ysfdu ys”kj esa foLrkj ugha gksrk vkSj blfy,rhozrk fLFkj jgrh gSA

8.27 oS|qrpqacdh; rjax dk fo|qr ks=k nksyk;eku ks=k gS vkSj fdlh vkosf'kr d.k ij blosQ kjkmRiUu fo|qr cy Hkh ,slk gh gksrk gSA iw.kZlkaf[;d pozQksa esa vkSlr ysus ij ;g fo|qr cy'kwU; gS D;ksafd bldh fn'kk izR;sd vk/s pozQ esa ifjofrZr gks tkrh gSA vr% fo|qr ks=kfofdj.k nkc esa ;ksxnku ugha djrkA

8.28ˆ ˆ

2s

oa

λ

πε=

eE j

ˆ2

oi

a

µ

π=B i

ˆ2

o vi

a

µ λ

π=

ˆ1 1 ˆ ˆ( )2 2

s o

o o o

v

a a

λ µ λ

µ µ πε π

= × = ×

jS E B j i

= 2

2 20

– ˆ4

v

a

λ

π εk

8.29 eku yhft, IysVksa osQ chp esa nwjh d gSA rc fo|qr ks=k gksxk = sin(2 )oVE t

dπν A pkyu èkkjk

?kuRo vkse osQ fu;e kjk izkIr gksxh& J c = sE = 1ρ

E

⇒ J c = 1ρ

oV

dsin (2πν t ) = sin(2 )0V

td

πνρ

= c

oJ sin 2πν t

tgk¡ ij c VJ

d0

0ρ

=

23/04/18

mÙkj

153

foLFkkiu /kjk ?kuRo izkIr gksxk d oE VJ t

t dsin(2 )

d dt∂ ∂

= ε = ε π ν

= V

vtd

o2cos(2 )

ε πνπ

d oE V

J tt d

sin(2 )d dt

ε ε π ν∂ ∂

= =

= V

td

o2cos(2 )

ε πνπν

= doJ cos(2 )tνπ , tgk¡ 0d

02

JV

d

πνε=

doo

c o oo o

2J . 2 2 80 0.25 4 10J V

V d

d

πνε ρπνερ π ε ν πε ν= = = × × = ×

= 9

10 499 10

ν=

×

8.30 (i) foLFkkiu /kjk ?kuRo fuEu laca/ ls Kkr fd;k tk ldrk gS

0D

d

dtε=

EJ

= ε0 µ

0 I

0 cos

t

∂

∂ (2πν t). ln ˆs

a

k

( )( )202

1 ˆ2 – sin ln2s

I tc a

πν πν =

k

( )2

0ˆ2 sin ln2

aI kt

c s

νπ πν

=

( )02

2 ˆln sin 2a

I ts

ππν

λ

=

k

(ii) dDI J sdsdθ= ∫

( )020

22 ln . sin 2

a

s

aI sds t

s

ππ πν

λ=

=

∫

23/04/18


154

h

4 3

21

x

y

Z

E=Ex îE

dl

Edl

E

dl

E dl

B=B0 j

z1 z2

( )2

20

0

12n .sin 2

2

a

s

aI ds l t

s

ππν

λ =

= ∫

( )2 2 22

00

2.sin 2

4

a

s

a s aI d ln t

a s

ππν

λ =

= ∫

( )2 12

00

2– ln .sin 2

4a

I d tπ

ξ ξ πνλ

= ∫

22 2 sin22 0

aI t

ππν

λ

= +

(lekdy dk eku –1 gS)

(iii) foLFkkiu èkkjk

2

0 02

sin2 2.2

d daI I t = I sin t

ππν πν

λ

=

20

0

dI a

I

π

λ

=

.

8.31 (i)

2 3 4 1

1 2 3 4

E.dl E.dl E.dl E.dl E.dl= + + +∫ ∫ ∫ ∫ ∫

2 3 4 1

1 2 3 4

cos 90° cos 0 cos 90° cos 180°E.dl E.dl E.dl E.dl= + + +∫ ∫ ∫ ∫

0 2 1[ ( – ) – ( – )]h sin kz t sin kz tω ω= E (1)

(ii) .∫B ds dk ewY;koaQu djus osQ fy, izR;sd dk ks=kiQy ds = h dz dh ifg;ksa

ls cus vk;r 1234 ij fopkj djsaA

2

1

0. cos0 ( – )Z

Z

Bds Bds B sin kz t hdzω= = =∫ ∫ ∫ ∫B ds

2 1–

[cos( – ) – cos( – )]oB hkz t kz t

kω ω= (2)

4 3

21

x

y

z

B

ds

dz

dl

B=Byj

z1

h

z2

23/04/18

mÙkj

155

4

32

1

x

y

zB

dl

B=Byj dl

dl

dl

B

B

E=Ex î

B

4

32

1

x

y

z

dlB=By j

ds

dz

E=Exî

z1 z2

h

(iii)– Bd

dt

φ=∫ E.dl

lehdj.kksa (1) rFkk (2) esa izkIr lac/ksa dk mi;ksx djosQ rFkk ljyhdj.k kjk gesa izkIrgksxk

0 2 1 2 1[ ( – ) – ( – )] [ ( – ) – ( – )]oB hE h sin kz t sin kz t sin kz t sin kz t

kω ω ω ω ω=

0 0E Bk

ω=

0

0

Ec

B=

(iv) ∫ B.dl osQ ewY;koaQu osQ fy, ywi 1234 ij yz ry esa fp=k kjk n'kkZ, vuqlkj

fopkj djsa

2 3 4 1

1 2 3 4

= + + +∫ ∫ ∫ ∫ ∫B.dl B.dl B.dl B.dl B.dl

2 3 4 1

1 2 3 4

cos0 cos 90° cos 180° cos90B dl B dl B dl B dl= + + + °∫ ∫ ∫ ∫

0 1 2[ ( – ) – ( – )]B h sin kz t sin kz tω ω= (3)

E = ∫E.dsφ dk ewY;koaQu djus osQ fy,] izR;sd ks=kiQy dh ifg;ksa ls cus vk;r

1234 ij fopkj djsaA

2

1

0 1. cos0 ( – )Z

E

Z

Eds Eds E sin kz t hdzφ ω= = = =∫ ∫ ∫ ∫E ds

2 1–

[cos( – ) – cos( – )]0E hkz t kz t

kω ω=

1 2[ ( – ) – ( – )]E 0d E hsin kz t sin kz t

dt k

φ ωω ω∴ = (4)

EdI

dt0 0.

φµ ε

= +

B dl , I = pkyu /kjk

= 0 fuokZr esa

23/04/18


156

Ed

dt0 0.

φµ ε∴ =

B dl

lehdj.kksa (3) rFkk (4) esa izkIr lac/ksa dk mi;ksx djosQ rFkk ljy djus ij gesa izkIr gksrkgS&

B Ek

0 0 0 0.ω

µ ε=

E

B0

0 0 0

1kω

µ ε= ysfdu E0/B0 = c, rFkk w = ck

;k c c0 0

1.

µ ε= vr%,

0 0

1c

µ ε= .

8.32 (i) E - ks=k dk ;ksxnku gS 2E 0

1u

2E= ε

B - ks=k dk ;ksxnku gS µ

=2

B0

12

Bu

oqQy mQtkZ ?kuRo E B

Bu u u E

22

00

1 12 2

εµ

= + = + (1)

E2 rFkk B2 osQ eku izR;sd fcUnq rFkk izR;sd k.k ij ifjofrZr gksrs gSaA vr% E2 rFkk B2 osQizHkkoh eku muosQ dkfyd eku gSaA

2 20( ) [ ( – )]2

av avE = E sin kz tω

(B 2)av

= (B 2)av = 2 2

0[ ( – )]avB sin kz tω

sin2θ rFkk cos2θ osQ xzkiQ vko`Qfr esa le:i gSa ysfdu π/2 ls LFkkukUrfjr gSa] vr% sin2θ

rFkk cos2θ osQ vkSlr eku Hkh π osQ fdlh Hkh iw.kZlkaf[;d xq.kt osQ fy, leku gSaA

rFkk sin2θ + cos2θ =1

vr% lefefr ls sin2θ dk vkSlr = cos2θ dk vkSlr = 12

2 2 2 20 0

1 1( ) ( )

2 2av avE E and B B∴ = =

+1

0 p 2p

23/04/18

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157

lehdj.k 1 esa izLFkkiu djus ij

01 14 4

22 0B

u Eεµ

= +

(ii) gesa Kkr gS E

c cB

0

0 0 0

1

µ ε= =rFkk

2 2 2 220 0 0

0 0 000 0 0

1 / 14 4 4 4

B E c EEµ ε ε

µ µ µ∴ = = =

2 2 2 20 0 0 0 0 0 0 0

1 1 1 1,

4 4 2 2av av avu E E E I u c Eε ε ε ε= + = = =rFkk

Chapter 9

9.1 (a)

9.2 (d)

9.3 (c)

9.4 (b)

9.5 (c)

9.6 (c)

9.7 (b)

9.8 (b)

9.9 (b)

9.10 (c)

9.11 (a)

9.12 (a), (b), (c)

9.13 (d)

9.14 (a), (d)

9.15 (a), (b)

9.16 (a), (b), (c)

9.17 D;ksafd yky izdk'k osQ fy, viorZukad uhys osQ fy, viorZukad ls de gS] blfy, ysalij vkifrr lekUrj izdk'k iqat yky izdk'k dh viskk uhys izdk'k dh fLFkfr esa vk dhvksj vf/d eqM+sxkA blfy, yky izdk'k dh viskk uhys izdk'k osQ fy, iQksdl nwjh degksxhA

23/04/18


158

9.18 lkekU; O;fDr dh fudV n`f"V 25 cm gSA fdlh fcac dks 10 xquk vkof/Zr ns[kus osQ fy,

Dm

f= ⇒

Df

m

2510

= = = 2.5 = 0.025m

140

0.025P = = MkbvkWIVj

9.19 ughaA ysal dks myVk djus ij izfrfcac dh fLFkfr esa ifjorZu ugha gksxkA (izdk'k dhmRozQe.kh;rk)

9.20 eku yhft, µ2 ls fcac dks ns[kus ij vkHkklh xgjkbZ O1 gSA

21

1

O3hµ

µ=

µ3 ls ns[kus ij vkHkklh xgjkbZ O

2 gSA

2 3 33 32 1

1 2 12 2

O O3 3 33

h h hh µ µ µµ µ

µ µ µµ µ

+ += = =+

ckgj ls ns[kus ij vkHkklh mQ¡pkbZ

3 23

1 hO +O

3µ

=

= 3 3

2 13

1 ++3 3h h

µ µ

µ µµ

1 2 3

1 1 1+ +

3h

= µ µ µ

9.21 U;wure fopyu ij

( )sin2

sin2

mA D

Aµ

+ =

fn;k gS Dm = A

∴ 2sin cossin 2 2 2cos

2sin sin2 2

A AA A

A A= = =µ

∴ 3

cos2 2A

= vFkok 2A

= 30° ∴ A = 60°

O

m3

m2

m1

h/3

h/3

h/3

O3

O2

O1

23/04/18

mÙkj

159

9.22 eku yhft, fcac osQ nks fljs ozQe'k% fcac nwjh u1= u – L/2 rFkk u2 = u + L/2 ij gSa] ftlls

|u1–u2|= LA eku yhft, nks fljkas osQ izfrfcac v1 rFkk v2 ij curs gSa] bl izdkj izfrfcac

dh yEckbZ gksxh 1 2–L v v′ = . D;ksafd fu

vu v f u f

1 1 1–

+ = =;k , nks fljksa dk izfrfcac

gksxk ( )

1– /2

– – /2

f u Lv

u f L= ij

( )2

/2– /2

f u Lv

u f L

+=

+ ij

vr%

( )

2

1 2 2 2| – |

/4–

f LL v v

Lu f′ = =

×

D;ksafd fcac NksVk gS rFkk iQksdl ls nwj j[kk x;k gS blfy, ge ik,¡xsL2/4 << (u –f )2

vr% vfUrer%

( )

2

2 .–

fL L

u f′ =

9.23 fp=k osQ lanHkZ esa] nzo Hkjus ls igys vkifrr fdj.k dh fn'kk AM gSA nzo Hkjus osQ i'pkrvkifrr fdj.k dh fn'kk BM gSA nksuksa fLFkfr;ksa esa viofrZr fdj.k AM osQ vuqfn'k ,d ghgSA

1 sin sin

sin sini i

rµ α= =

2 2

–sin

( – )

a Ri

d a R=

+ rFkk

2 2sin cos(90 – )

( – )

a R

d a Rα α

+= =

+

izfrLFkkfir djus ij gesa izkIr gksxk 2 2

2 2

( – )

( ) – ( – )

a Rd

a R a R

µ

µ=

+

9.240.5

O O¢

50.0

;fn dkVk u tkrk rks fcac eq[; vk 00′ ls 0.5 cm dh mQ¡pkbZ ij gksrkA

1 1 1–

v u f=

1 1 1 1 1 1–50 25 50v u f

∴ = + = + =

∴ v = 50 cm

O

90 - aa

a

a

A BC

id

Ma a

a

R R

23/04/18


160

vko/Zu m = 50–

50v

u= = –1

vr% izfrfcac izdkf'kd osQUnz ls 50 cm nwj rFkk eq[; vk ls 0.5 cm uhps cusxkAbl izdkj dVs gq, ysal dh dksj ls xq”kjus okyh X vk osQ lkisk izfrfcac osQ funsZ'kkad(50 cm, –1 cm) gSaA

9.25 ysal lw=k

1 1 1–

f v u=

dks ns[kus ij u rFkk v dh mRozQe.kh;rk ls ;g Li"V gSA ,slh nks fLFkfr;k¡ gSa ftuosQ fy, ijnsij izfrfcac cusxkAeku yhft, igyh fLFkfr og gS tc ysal O ij gSAfn;k gS –u + v = D⇒ u = –(D – v)bls ysal lw=k esa j[kus ij

1 1 1–D v v f

+ =

⇒ – 1

( – )v D v

D v v f

+=

⇒ v2 – Dv + Df = 0

⇒ 2D – 4

2 2

DfDv = ±

u = –(D – v) = 2 – 4–

2 2D DfD

±

bl izdkj ;fn fcac nwjh 2 – 4

–2 2

D DfD gS rks izfrfcac

2 – 4

2 2

D DfD+ ij gksxkA

;fn fcac nwjh 2 – 4

2 2

D DfD+ gS rks izfrfcac

2 – 4– .

2 2

D DfD ij gksxkA

bu nks fcac nwfj;ksa osQ fy, izdkf'kd osQUnzksa osQ chp dh nwjh gS

2 22– 4 – 4D– – 4–2 2 2 2

D DfD D fD D Df

+ =

ekuk d = 2 – 4D Df

;fn u = 2 2D d

+ rc izfrfcac gksxk v = –2 2D d

ij

u vO

23/04/18

mÙkj

161

∴ vko/Zu m1 = D–d

D d+

;fn u = D–

2d

rc v = D+

2d

∴ vko/Zu m2 =

D+D –

d

d vr%

dm

dm

22

1

D +D –

=

9.26 eku yhft, fMLd dk O;kl d gSA fcanq vn'; gks tk,xk ;fn fcanq ls i"B 2d

ij vkifrr fdj.ksa

ozQkafrd dks.k ij gksaA eku yhft, vkiru dks.k i gS

rc sin i = 1µ

vc /2d

h = tan i

⇒ –1

2tan –12d

h i h µ = =

∴2

2

–1

hd

µ=

9.27 (i) eku yhft, lkekU; foJkUr us=k osQ fy, nwj fcanq ij kerk Pf gSA

rc Pf =

1 1 10.1 0.02f

= + = 60 MkbvkWIVj

la'kks/d ysal osQ lkFk nwj fcanq ij fcac nwjh ∞ gSA

1 1 150D

0.02fPf

′ = = + =′ ∞

p'es osQ lkFk foJkar us=k dh izHkkoh kerk us=k rFkk p'es osQ ysalksa Pg dk ;ksx gSA

∴ fP ′ = Pf + Pg

∴ Pg = – 10 D

(ii) lkekU; us=k osQ fy, mldh leatu kerk 4 MkbvkWIVj gSA eku yhft, fd lkekU; us=kdh fudV n`f"V dh kerk P

n gSrc 4 = Pn – Pf or Pn = 64 D

eku yhft, mldk fudV fcanq xn gks] rc

n nx x

1 1 164 50 64

0.02+ = + =vFkok

nx

114=

23/04/18


162

∴ xn = 1

0.07m14

(iii) p'es osQ lkFk 4 54n fP P′ ′= + =

1 1 154 50

0.02n nx x= + = +

′ ′

nx

14=

′

∴ 1

0.25m4nx ′ = =

9.28 dksbZ fdj.k tks dks.k i ls izos'k djrh gS] AC osQ vuqfn'k funsZf'kr gksxh ;fn iQyd AC

ls cuk;k x;k dks.k (φ ) ozQkafrd dks.k ls vf/d gSA

⇒ sin ≥ 1µ

⇒ cos r ≥ 1µ

vFkok 1 – cos2r ≤ 1 – 2

1µ

i.e. sin2r ≤ 1 – 2

1µ

D;ksafd sin i = µ sin r

2

1µ

sin2i ≤ 1 – 2

1µ

;k sin2i ≤ µ2 – 1

tc i = 2π

rks φ NksVs ls NksVk dks.k gksxkA ;fn ;g ozQkafrd dks.k ls cM+k gS rc lHkh nwljs

vkiru dks.k ozQkafrd dks.k ls vf/d gksaxsAvr% 1 ≤ µ2 –1

;k µ2 ≥ 2

⇒ µ ≥ 2

9.29 nzo osQ vUnj x rFkk x + dx osQ chp ,d fdj.k osQ fdlh Hkkx ij fopkj dhft,A eku yhft,x ij vkiru dks.k θ gS vkSj eku yhft, ;g irys LraHk esa y mQ¡pkbZ ij izos'k djrh gSA caduosQ dkj.k ;g dks.k θ + dθ ls y + dy mQ¡pkbZ ij rFkk x + dx fuxZr gksxhA LuSy osQ fu;els&µ(y) sin θ = m(y+dy) sin (θ+dθ)

;k µ(y) sinθ ( )d

y dydy

µµ

+

(sinθ cosdθ + cosθ sin dθ )

f

A C

DB

ri

23/04/18

mÙkj

163

( )sin ( )cos sind

y y d dydy

µµ θ µ θ θ θ+ +

vFkok µ(y) cosθdθ –

sind

dydy

µθ

dθ –1

tand

dydy

µθ

µ

ysfdu tanθ = dx

dy (fp=k ls)

∴ dθ = –1 ddx

dy

µ

µ

∴ θ = –1 d

o

ddx

dy

µ

µ ∫ = –1 dd

dy

µ

µ

9.30 r rFkk r + dr ij nks ryksa ij fopkj djsaA eku yhft, ry r ij izdk'k θ dks.k ls vkifrrgksrk gS rFkk r + dr ls θ +dθ dks.k ls ckgj fudyrk gSA

rc Lusy osQ fu;e ls

n(r) sinθ = n(r + dr) sin (θ + dθ )

⇒ n(r) sinθ ( )dn

n r drdr

+

(sinθ cos dθ + cosθ sin dθ )

( )dn

n r drdr

+

(sinθ + cosθ dθ )

vody xq.ku iQyksa dks NksM+us ij

( ) ( )dn

n r sin n r sin drdr

θ θ + sinθ + n(r) cosθdθ

⇒ – tan ( )dn d

n rdr dr

θθ =

⇒ 2 2 2

2 2tan 1

GM d dGM

r c dr drrc

θ θθ = ≈+

∴ 2 2

0 –

2GM tanodr

dc r

θ θθ

∞

∞

=∫ ∫

vc r2 = x2 +R2 rFkk tanθ = R

x

dx

dyy q

q q+ d

( )y + dy

q + dq

rqR

M

dr

r + dr r

23/04/18


164

2rdr = 2xdx

322 20 – 2

2GM

( )

oR xdx

dc x

x R

θ

θ∞

∞

=

+∫ ∫

x = R tan φ jf[k,

x = R tan φ

dx = R Sec2 φ d φ

∴

/2 2

0 2 3 3– /2

2GMR sec =

c secR d

R

π

π

φ φθ

φ∫

= /2

2– /2

2cos

GMd

Rc

π

π

φ φ∫ = 2

4GM

R c

9.31 D;ksafd inkFkZ –1 viorZukad dk gS] θr ½.kkRed gS rFkk rθ ′ /ukRed gSA vc i r rθ θ θ ′= =

ckgj fudyus okyh fdj.k dk vUnj vkus okyh fdj.k ls oqQy fopyu 4θi gSA fdj.ksa xzkgh

IysV rd ugha igq¡psaxh ;fn

34

2 2i

π πθ≤ ≤ (dks.k y &vk ls nfk.kkorZ ekis x, gSa)

38 8i

π πθ≤ ≤

vc sin i

x

Rθ =

–1 3sin

8 8x

R

π π≤ ≤

vFkok 3

8 8x

R

π π≤ ≤

vr% 38 8

R Rx

π π≤ ≤ osQ fy, lzksr ls mRlftZr izdk'k xzkgh IysV rd ugha igq¡psxkA

9.32 (i) S ls P1 rd ikjxeu dk le; gS

2 2 21

1 2

11

2

SP u b u bt

c c c u

+ = = +

eku yhft, b << u

0

P1 ls O rd ikjxeu dk le; gS

2 2 21

2 2

11

2

P O v b v bt

c c c v

+ = = +

23/04/18

mÙkj

165

ysal ls ikjxeu dk le; gS

( –1) ( )l

n w bt

c= tgk¡ n viorZukad gSA

vr% oqQy le; gS

21 1 1 1( –1) ( )

2t u v b n w b

c u v

= + + ++

. 1 1 1D u v

= + jf[k,

rc 2 2

0

1 1( –1)

2b b

t u v n wc D α

= + + + +

iQjeSV osQ fl¼kUr ls

2( –1)0 –

dt b n b

db CD cα= =

2( – 1)α = n D

vr% ;fn 2( –1)α = n D rks vfHklj.kdkjh ysal cusxkA ;g b ls LorU=k gS vkSj blfy, S

ls vkus okyh lHkh mikkh; fdj.ksa O ij vfHklfjr gksaxh (vFkkZr b << n rFkk b << v

fdj.kksa osQ fy,)A

D;ksafd 1 1 1D u v

= + , iQksdl nwjh gSA

(ii) bl fLFkfr esa

t = ( )2

21

1 11

2 Db k

u v k lnnc b

+ + + −

10 – ( –1)dt b k

ndb D b

= =

⇒ b2 = (n – 1) k1D

∴ b = 1( –1)n k D

vr% mQ¡pkbZ ls xqtjus okyh lHkh fdj.ksa izfrfcac cukus esa ;ksxnku nsaxhA fdj.k iFk kjk cuk;kx;k dks.k

1 1 12 2

( –1) ( – 1) ( –1)( ) ( )

n k Db n k uv n k u

v v v u v u v vβ = = =

+ +

vè;k; 10

10.1 (c)

10.2 (a)

10.3 (a)

10.4 (c)

10.5 (d)

P1

S u v O

b

23/04/18


166

10.6 (a), (b), (d)

10.7 (b), (d)

10.8 (a), (b)

10.9 (a), (b)

10.10 gk¡

10.11 xksyh;

10.12 xksyh;] i`Foh dh f=kT;k dh rqyuk esa fo'kky f=kT;k ftlls fd ;g yxHkx lery gSA

10.13 èofu rjaxksa dh vko`fÙk;k¡ 20 Hz ls 20 kHz gksrh gSaA laxr rjaxnS?;Z ozQe'k% 15m rFkk15mm gSA foorZu izHkko fn[kkbZ nsxk ;fn f>fj;ksa dh pkSM+kbZ a ,slh gks fd

a λ∼

izdk'k rjaxksa osQ fy, rjaxnS?;Z ∼ 10–7mA vr% foorZu izHkko fn[kkbZ nsxk tc–710∼a m

tcfd èofu rjaxksas osQ fy, ;s fn[kkbZ nsaxs15mm 15ma< <

10.14 nks fcanqvksa osQ chp jSf[kd nwjh –22.54cm 0.84 10 cm

300l = × gSA Z cm nwjh ij ;g

dks.k –2

–4

0.84 10 cm/ 14.5cm

5.8 10l

l z zφφ

×∴ = =

×∼ ∼

10.15 osQoy fo'ks"k fLFkfr;ksa esa tc (III) dh ikfjr vk (I) ;k (II) osQ lekUrj gS rks dksbZ izdk'kfuxZr ugha gksxkA nwljh lHkh fLFkfr;ksa esa izdk'k fuxZr gksxk D;ksafd (II) dh ikfjr vk (III)osQ yacor ugha gSA

10.16 ijkorZu kjk èzkqo.k rc gksrk gS tc vkiru dks.k czwLVj dks.k osQ cjkcj gks vFkkZr~2

1

tan B

n

nθ = tgk¡ n2 < n1

tc ,sls ekè;e esa izdk'k xeu djrk gS rks ozQkafrd dks.k gS 2

1

sin c

n

nθ = tgk¡ n

2 < n

1.

D;ksafd cM+s dks.kksa osQ fy, |tan θB|>|sin θc| B Cθ θ<

blfy, ijkorZu kjk fuf'pr :i ls èkzqo.k gksxkA

10.17 min1.222sin

dλ

β=

tgk¡ β vfHkn`';d kjk fcac ij varfjr dks.k gSA

5500 Å osQ izdk'k osQ fy,

23/04/18

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167

–7

min

1.22 5.5 10m

2sind

β

× ×=

100V ls Rofjr bysDVªkWuksa osQ fy, ns czkXyh rjaxnS?;Z gS

–91.2270.13nm 0.13 10 m

100

h

pλ = = = = ×

–10

min1.22 1.3 10

'2sin

dβ

× ×∴ =

–10–3min

–7min

' 1.3 100.2 10

5.5 10d

d

×∴ = ×

×∼

10.18 T2P = D + x, T1 P = D – x

2 21 1 1 1S P (S T ) (PT )= +

= [D 2 + (D – x)2]1/2

S2P = [D 2 + (D + x)2]1/2

fufEu"B izkIr gksxk tc

[D 2 + (D + x)2]1/2 – [D2 + (D – x)2]1/2 =2λ

;fn x = D

(D2 + 4D2)1/2 =2λ

(5D2)1/2 =2λ

2 5D

λ∴ = .

10.19 cxSj P osQ

11A A A⊥= +

1 2 0 0A A A A sin( – )+A sin( – )kx t kx tω ω φ⊥ ⊥ ⊥ ⊥ ⊥= + = +

(1) (2)11 11 11A A A= +

23/04/18


168

011 11A A [sin( – ) sin( – ]kx wt kx tω φ= + +

tgk¡ 0A ⊥ , 011A fdlh Hkh fdj.k iaqt osQ ⊥ rFkk 11 èkzqo.kksa esa vk;ke gSaA

∴ rhozrk

( ) kx tkx wt2 2 2 2 2 20 0

11[sin (1+cos 2sin )+sin ( – ) sin ]–A A φ φ ω φ

⊥= ++ vklS r

2 20 011

1 .2(1+cos )A A2

φ⊥

= +

= 220 0.(1 cos )sinceA A⊥ ⊥

+ φ vkSlr 011A= vkSlr

P osQ lkFk%

ekuk 12A⊥ vo#¼ gS

rhozrk = = 1 2 2 1 211 11(A A ) (A )⊥+ +

2 20 0 1(1 cos ) .A A

2φ

⊥ ⊥= + +

fn;k gS: I0 =

204 A⊥ = cxSj iksysjkbtj osQ eq[; mfPp"B rhozrk

iksysjkbtj osQ lkFk eq[; mfPp"B ij rhozrk

20 12A

2⊥

= +

05

I8

=

iksysjkbtj osQ lkFk eq[; mfPp"B ij rhozrk

( )

2020 A

A 1 –12⊥

⊥= +

0

8I

=

10.20 iFkkarj = 2 sin ( –1)d lθ µ+

∴ eq[; mfPp"B osQ fy,

2 sin 0.5 0d lθ + =

23/04/18

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169

0– –1

sin4 16 4

l dl

dθ

= = = ∵

∴ 0OP tan –16D

D θ= ≈

izFke fufEu"B osQ fy,

∴ 12 sin +0.5 = 2

d lλ

θ ±

1/2 – 0.5 /2 – /8 1 1

sin –2 2 4 16

l

d

λ λ λθ

λ

± ±= = = ±

èkukRed fn'kk esa: 3

sin16

θ + =

½.kkRed fn'kk esa: – 5sin –

16θ =

èkukRed fn'kk esa izFke eq[; mfPp"B dh nwjh

2 2 2

sin 3tan

1 – sin 16 – 3D D D

θθ

θ

++ = = O osQ mQij

½.kkRed fn'kk esa nwjh gksxh –

2 2

5tan

16 – 5D θ = O osQ uhps

10.21 (i) R1 tks A ls d nwjh ij gS] ij fokksHkksa osQ ckjs esa fopkj djsaA eku yhft, A osQ dkj.k

R1 ij rjax gS Y

A = a cos ωtA A ls laosQr dk B ls iFkkUrj λ/2 gS rFkk bl izdkj

dykUrj π gSA

bl izdkj B osQ dkj.k R1 ij rjax gS

By a t a tcos( – ) – cosω π ω= =

C ls laosQr dk A ls iFkkUrj π gS vkSj bl izdkj dykUrj 2π gSA

vr% C osQ dkj.k R1 ij rjax gS y

c = a cos ωtA D rFkk A ls

laosQr osQ chp iFkkUrj gS

( )2

2 /22

d dλ

λ

+ − −

R1 A B C

D

l/2

l/2 l/2

R2

23/04/18


170

1/2

2124

d dd

λλ = − ++

1/22

2128

d dd

λλ = − ++

iFkkUrj 2λ

∼ vkSj blfy, dykUrj π gSA

cosDy a tω∴ = −

R1 ij izkIr gksus okyk laosQr gS

yA + y

B + y

C + y

D = 0

eku yhft, B ls R2 ij izkIr gksus okyk laosQr gS y

B = a1 cos ωtA B rFkk D ij

laosQrksa osQ chp iFkkUrj λ/2 gS

Dy a t1– cosω∴ =

A rFkk B ij laosQr osQ chp iFkkUrj gS

1/22 22

2( ) 1

2 4d d d d

d

λ λ + − = −+

2

2

18 d

λ∼

∴ dykUrj gS d d

2

2

2. 0

8 4π λ πλ

φλ

= = ∼

vr% yA = a1 cos (ωt-φ)

blh izdkj yC = a1 cos (ωt-φ)

∴ R2 kjk p;fur laosQr gSy

A + y

B + yC + y

D = y = 2a1 cos (ωt-φ)

2 2 21| | 4 cos ( – )y a tω φ∴ =

212aI∴ =

vr% R1 o`gr laosQr p;u djrk gSA

(ii) ;fn B dks cUn dj fn;k tk,R

1 p;u djrk gS y = a cos ω t

121

2RI a∴ =

R2 p;u djrk gS y = a cos ω t

221

12

RI a∴ =

23/04/18

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171

bl izdkj R1 rFkk R2 leku laosQr p;u djrs gSaA(iii);fn D dks cUn dj fn;k tk,

R1 p;u djrk gS y = a cos ω t

121

2RI a∴ =

R2 p;u djrk gS y = 3a cos ω t

221

92

RI a∴ =

bl izdkj R2, R

1 rqyuk esa o`gr laosQr p;u djrk gSA

(iv) bl izdkj R1 ij laosQr n'kkZrk gS fd B cUn dj fn;k x;k gS rFkk R

2 ij ,d o`gr

laosQr n'kkZrk gS D dks cUn dj fn;k x;k gSA

10.22 (i) eku yhft, fd vfHkèkkj.kk lgh gS] rc nks lekUrj fdj.ksa fp=k esa n'kkZ, vuqlkj vxzljgksrh gSaA eku yhft, ED rjaxkxz dks n'kkZrk gS rks bl ij reke fcanq leku dyk esagksus pkfg,A leku izdkf'kd iFk yEckbZ osQ lHkh fcanq leku dyk esa gksuspkfg,A

vr% r r r rAE BC CD– –ε µ ε µ=

;k ( )r r CD AEBC ε µ= −

pwafd BC > 0, CD > AE

;g n'kkZrk gS fd vfHkèkkj.kk ;qfDrlaxr gSA rFkkfi] ;fn izdk'k mlh izdkjvxzflr gksrk gS tSls ;g lkèkkj.k inkFkksZa esa gksrk gS (vFkkZr] pkSFks prqFkkZa'kesa fp=k 2)

rc r r r rAE BC CD– –ε µ ε µ=

;k] ( )r rBC CD AEε µ= −

D;ksafd AE > CD, BC < O

;g n'kkZrs gq, fd ,slk lEHko ugha gSA vr% vfHkèkkj.kk lgh gSA(ii) fp=k 1 ls

BC = AC sin θi rFkk CD-AE = AC sin θr:

D;ksafd ( )r r BCAE CDε µ− =−

–n sin θr = sin θi.

10.23 dks.k i ij vkifrr ,d fdj.k ij fopkj djsaA bl fdj.k dk ,d Hkkx ok;q&fiQYe vUrjki"Bls ijkofrZr gksrk gS rFkk ,d Hkkx vUnj viofrZr gksrk gSA ;g fiQYe&dk¡p vUrjki`"B ijva'kr% ijkofrZr rFkk va'kr% ikjxr gksrh gSA ijkofrZr fdj.k dk ,d Hkkx fiQYe&ok;qvUrjki`"B ij ijkofrZr gksrk gS rFkk ,d Hkkx r

2 dh rjg ikjxr r

1 osQ lekUrj ikjxr gksrk

gSA okLro esa ozQfed ijkorZu rFkk ikjxeu rjax osQ vk;ke dks ?kVkrs jgsaxsA vr% r1 rFkk r

2

fdj.ksa O;ogkj ij NkbZ jgsaxhA ;fn vkifrr izdk'k ysal kjk ikjxfer gks rks r1 rFkk r

2 esa

fouk'kh O;frdj.k gksuk pkfg,A A rFkk D nksauksa ij ijkorZu fuEu ls mPp viorZukaddh vksj gksaxs vr% ijkorZu ij dksbZ dyk ifjorZu ugha gksxkA r

2 rFkk r

1osQ chp izdkf'kd

iFkkUrj gS

qi qi

qiqr

ED

CB

A

E

D

C

B

A

ekè;e

ok;q

ekè;e

ok;q

fp=k 1

fp=k 2

23/04/18


172

n (AD + CD) – AB

;fn d fiQYe dh eksVkbZ gS rks

cosd

AD CDr

= =

sinAB AC i=

tan2

ACd r=

2 tanAC d r∴ =

vr% AB = 2d tanr sini

vr% iFkkUrj gS

2 2 tan sincos

dn d r i

r−

sin sin2. 2 sin

sin cos cosi d r

d ir r r

= −

21 sin2 sin

sin cosr

dr r

−=

= 2nd cosr

bu rjaxksa osQ fouk'kh O;frdj.k osQ fy, ;g λ/2 osQ cjkcj gksuk pkfg,A

2 cos2

nd rλ

⇒ =

;k nd cos r = λ/4

oSQejs osQ ysal osQ fy,] lzksr mQèokZèkj ry esa gS vkSj blfy,

0i r

4nd

λ∴ .

5500 A1000 A

1.38 4d⇒ =

×

23/04/18

mÙkj

173

vè;k; 11

11.1 (d)

11.2 (b)

11.3 (d)

11.4 (c)

11.5 (b)

11.6 (a)

11.7 (a)

11.8 (c)

11.9 (c), (d)

11.10 (a), (c)

11.11 (b), (c)

11.12 (a), (b), (c)

11.13 (b), (d)

11.142

/ / 8 :12

p d x p

p p

m Ep p

m E

α αλ λ = = =

11.15 (i) Emax = 2hν – φ

(ii) ,d gh bysDVªkWu kjk nks iQksVkWu vo'kksf"kr djus dh izkf;drk vR;Ur fuEu gSA vr%bl izdkj osQ mRltZu ux.; gSaA

11.16 igyh fLFkfr esa iznÙk (ckgj fudyh) mQtkZ laHkfjr mQtkZ ls de gSA nwljh fLFkfr esa D;ksafdmRlftZr iQksVkWu esa vf/d mQtkZ gksrh gS blfy, inkFkZ dks mQtkZ vkiwfrZ djuh iM+rh gSA LFkk;hinkFkksZa osQ fy, ,slk gksuk laHko ugha gSA

11.17 ugha] vf/dak'k bysDVªkWu èkkrq esa izdh.kZ gks tkrs gSaA osQoy oqQN gh èkkrq osQ i`"B ls ckgj vkrsgSaA

11.18 oqQy E fu;r gSA

eku yhft, n1 rFkk n2 X-fdj.kksa rFkk n`'; ks=k osQ iQksVkWu dh la[;k gSA

n1E

1 = n

2E

2

1 21 2

hc hcn n

λ λ=

23/04/18


174

n

n1 1

2 2

λ

λ=

1

2

1500

n

n=

11.19 laosx èkkrq dks LFkkukarfjr gks tkrk gSA lwe Lrj ij] ijek.kq iQksVkWu dks vo'kksf"kr djrs gSarFkk bldk laosx eq[; :i ls ukfHkd rFkk bysDVªkWuksa dks LFkkukarfjr gks tkrk gSA mÙksftrbysDVªkWu mRlftZr gksrk gSA laosx lajk.k ukfHkd rFkk bysDVªkWuks dks laosx LFkkukarfjr djusosQ fy, laosx lajk.k osQ ifjdyu dh vko';drk gSA

11.20 vfèkdre mQtkZ = hν – φ

11230 1230– –

2600 400φ φ

=

12301.02eV

1200φ = =

11.21 x p∆ ∆

–34–25

–9

1.05 10 Js1.05 10

10 mp

x

×∆ = ×

∆

×= = = ×

× × ×

2 –25 2 2 2–19

–31

(1.05 10 ) 1.05 1.0510 J= eV

2 2 9.1 10 18.2 18.2 1.6p

Em

= 3.8 × 10–2eV

11.22 I = nAn

A = nBν

B

2A B

B A

n

n

ν

ν= =

iqat B dh vko`fÙk A ls nqxuh gSA

11.23 A B

A B c c

h h h hp p

λ λ λ λ= + = + = =cp if p

A, p

B > 0 or p

A, p

B < 0

vFkok A Bc

A B

λ λλ

λ λ=

+

;fn pA > 0, pB < 0 vFkok p

A < 0, pB > 0

–.

B Ac

A B c

hp h= =

λ λ

λ λ λ

B Ac

A B

.–

λ λλ

λ λ=

23/04/18

mÙkj

175

11.24 2d sinθ = λ = d =10–10 m

–34–21

–10 –10

6.6 106.6 10 kg m/s

10 10h

p×

= = = ×

–24 2 2–19 –2

–27

(6.6 10 ) 6.61.6 10 1.6 10 V

2 (1.7 10 ) 2 1.7E e

×= × × = × ×

× × ×

= 20.5 × 10–2eV = 0.21eV

11.25 Na osQ 6 × 1026 ijek.kqvksa dk Hkkj = 23 kg

y; dk vk;ru = (10–4 × 10–3) = 10–7m3

lksfM;e dk ?kuRo = (d) = 0.97 kg/m3

6 × 1026 Na ijek.kqvksa dk vk;ru = 323m

0.97 = 23.7 m3

1 Na ijek.kq dk vk;ru 326

23m

0.97 6 10=

× × = 3.95 × 10–26 m3

y; esa Na ijek.kqvksa dh la[;k = –7

–26

103.95 10×

= 2.53 × 1018

iQksVkWu dh la[;k izfr lsoaQM rFkk 10–4 m2 = n

mQtkZ izfr lsoaQM rFkk nhν = 10–4 J × 100 = 10–2 W

hν (λ = 660nm osQ fy,) = 1234.5

600

= 2.05eV = 2.05 × 1.6 × 10–19 = 3.28 × 10–19J

n = –2

16–19

103.05 10 /s

3.28 10= ×

×

n = 17 161

10 3.1 103.2

× = ×

;fn izfr ijek.kq mRltZu dh izkf;drk P gS] izfr iQksVkWu] iQksVksbysDVªkWu dh izfr lsoaQMmRltZZu dh la[;k

16 183.1 10 2.53 10P= × × × ×

èkkjk = P × 3.1 × 10+16 × 2.53 × 1018 × 1.6 × 10–19 A

= P × 1.25 × 10+16 A

;g 100µA osQ cjkcj gksuh pkfg, vFkok

23/04/18


176

P = –6

16

100 101.25 10+

×

×

∴ P = 8 × 10–21

bl izdkj ,dy ijek.kq ij ,dy iQksVkWu kjk iQksVks mRltZu dh izkf;drk 1 ls cgqr degSA (blfy, ,d ijek.kq kjk nks iQksVkWu dk vo'kks"k.k ux.; gSA)

11.26 cká ,tsalh kjk fd;k x;k dk;Z = 2 2

20 0

1 1 1. .

4 4 4 4d

q qdx

x dπε πε

∞

+ =∫

d = 0.1nm ls] mQtkZ = –19 9

–10 –19

(1.6 10 ) 9 10eV

4(10 ) 1.6 10× × ×

× ×

= 1.6 9

eV4×

= 3.6 eV

11.27 (i) B osQ fy, mPp vko`fÙk ij fujks/h foHko = 0

vr% bldk dk;ZiQyu mPp gS

(ii) <ky = h

e = 14

2(10 – 5) 10×

A osQ fy,

= 14

2.5(15 –10) 10×

B osQ fy,

–19–14 –341.6 10

2 10 6.04 10 Js A5

h×

= × × = × oQs fy,

–19 –141.6 10 2.5 105

× × ×= = 8 × 10–34 Js osQ fy, B

D;ksafd h dk eku vyx&vyx vkrk gS blfy, iz;ksx fl¼kUr osQ laxr ugha gSA

11.28 mAv = m

Av

1 + mBv

2

2 2 21 2

1 1 12 2 2A A Bm v m v m v= +

21 1

1 1( – )( )

2 2A A B Bm v v v v m v/ /

∴ + =/ /

∴ v + v1 = v

2

vFkok v = v2 – v

1

23/04/18

mÙkj

177

1 2

– 2,A B A

A B A B

m m mv v v v

m m m m

∴ = = + +

rFkk

ikz jfa EHkdA

h

m vλ∴ =

vafre

( )( – )

A B

A A BA

h m mh

m m m vm vλ

+= =

)– 1

–A B

A BA

m mh

m mm vλ

+ ∴ ∆ =

11.29 (i) 195 10 /( / )

dN Psec

dt hc λ= = ×

(ii) 02.49eV :hc

Wλ

= > gk¡

(iii)2

02.4

rP t W

d

π

π∆ = , 28.4st∆ =

(iv)2

2 24

rdNN t

ddt

π

π

= × × ∆ =

vè;k; 12

12.1 (c)

12.2 (c)

12.3 (a)

12.4 (a)

12.5 (a)

12.6 (a)

12.7 (a)

12.8 (a), (c)

12.9 (a), (b)

12.10 (a), (b)

12.11 (b), (d)

r

d

23/04/18


178

12.12 (b), (d)

12.13 (c), (d)

12.14 vkbaLVhu osQ nzO;eku&mQtkZ lacaèk ls gesa izkIr gksrk gS% E = mc2. vr% gkbMªkstu osQ ,d

ijek.kq dk nzO;eku gS 2+ −p e

Bm m

c, tgk¡ B ≈ 13.6 eV caèku&mQtkZ gSA

12.15 D;ksafd bysDVªkWu osQ nzO;eku dh rqyuk esa nksuksa ukfHkd vR;fèkd Hkkjh gSaA

12.16 D;ksafd bysDVªkWu osQoy oS|qr pqEcdh; :i ls ikjLifjd fozQ;k djrs gSaA

12.17 gk¡] D;ksafd cksgj&lw=k esa osQoy vkos'kksa dk xq.kuiQy fufgr gSA

12.18 ugha] D;ksafd cksgj izfr:i osQ vuqlkj 2

13.6–=nE

n, vkSj fHkUu&fHkUu mQtkZ osQ bysDVªkWu

fofHkUu n& eku okys Lrjksa ls lEc¼ gksrs gSa% vr% muosQ dks.kh;&laosx fHkUu gksaxs] D;ksafd

nhmvr

2π=

12.19 cksgj osQ lw=k 4

2 20

–8ε

=n

meE

n h esa 'm' lekuhr nzO;eku gSA H-ijek.kq osQ fy, m ≈ me

iksftVªksfu;e osQ fy, /2em m≈ vr% ,d iksftVªksfu;e osQ fy, E1≈ – 6.8eV

12.20 2e vkos'k okys ukfHkd rFkk –e vkos'k okys bysDVªkWuksa osQ fy,] Lrj gSa& 4

2 2 20

4–

8ε=n

meE

n h

fuEurj Lrj esa nks bysDVªkWu gksaxs] ftuesa izR;sd dh mQtkZ E rFkk fuEure Lrj dh oqQymQtkZ –(4×13.6)eV gksxhA

12.21 v = bysDVªkWu dk osx

a0= cksgj f=kT;k

∴,dkad le; esa pozQ.kksa dh la[;k 02π=

a

v

∴ èkkjk 02π=

a

ve

12.22 νU;wure ( )

22 2

1 1cRZ

nn p

−=

+ ,

tgk¡ m = n + p, (p = 1, 2, 3, ...) ,oa R fjM~cxZ fu;rkoaQ gSA

p << n osQ fy,

23/04/18

mÙkj

179

pcRZ

n nn

–22

2 2

1 11ν

= −+

U;uw re

pcRZ

n n n

22 3 2

1 2 1–ν

= −

U; wure

p cRZcRZ p

n n

22

3 3

2 2ν

=

U;uw re

bl izdkj νU;wure

dk yxHkx ozQe gS& 1, 2, 3...........

12.23 ckej Js.kh esa Hγ , n = 5 ls n = 2 osQ laozQe.k osQ laxr gSA vr% U;wure Lrj n = 1

osQ bysDVªkWu dks igys n = 5 esa j[kuk pkfg,A vko';d mQtkZ = E1 – E5 = 13.6 – 0.54= 13.06 eV

;fn dks.kh; laosx lajfkr jgrk gS] rks iQksVku dk dks.kh; laosx = bysDVªkWu osQ dks.kh; laosx

esa ifjorZu –345 2– 5 – 2 3 3 1.06 10= = = = × ×L L

= 3.18 × 10–34 kg m2/s

12.24 H osQ fy, lekuhr nzO;eku 1–1

e eH e

e

m mm

m MM

µ = = +

D osQ fy, lekuhr nzO;eku 1 – 1– 12 2 2

e e eD e e

m m mm m

M M Mµ

= = +

( – ) .ij i jh E E=ν α µ vr%] 1λ α

µij

;fn gkbMªkstu@M~;wVhfj;e osQ fy, rjaxnS?;Z /λ λH D gS

–1 11 –1

2 18402

λ µ

λ µ

= + ×

D H e

H D

m

M

(0.99973)λ λ= ×D H

vr% js[kk,¡ gSa 1217.7 Å , 1027.7 Å, 974.04 Å, 951.143 Å

12.25 ukfHkdh; xfr dks lfEefyr djrs gq,] fLFkj voLFkk esa mQtkZ,¡ gkasxh& 2 4

2 2 20

1–

8n

Z eE

h n

=

µ

ε

eku fy;k Hµ gkbMªkstu dk rFkk Hµ M~;wVhfj;e dk lekuhr nzO;eku gSA rc gkbMªkstu

dh izFke ykbeu js[kk dh vko`fÙk gS 4 4

2 2 2 20 0

31.1 –

8 4 84

µ µν

ε ε

= =

H HH

e eh

h h vr% laozQe.k

23/04/18


180

dh rjaxnS?;Z gS 4

2 30

34 8

HH

e

h c

µλ

ε= A M~;wVhfj;e osQ fy, laozQe.k dh mlh js[kk dh

rjaxnS?;Z gS 4

2 30

34 8

µλ

ε= H

D

e

h c

–λ λ λ∴ ∆ = D H

vr% vUrj&izfr'kr gS&

– –100 100 100

λ λ λ µ µ

λ λ µ

∆× = × = ×D H D H

H H H

–( ) ( )

100/( )

e D e H

e D e H

e H e H

m M m M

m M m M

m M m M

+ += ×

+

–1 100e H D

e D H

m M M

m M M

+ = × +

D;ksafd me << M

H < M

D

1 /100 –1 100

1 /e HH D

e DH D H

m MM M

m MM M

λ

λ

+ ∆ × = × × +

= –1 100(1 / )(1 / ) –1 × + + e H e Dm M m M

(1 – –1 100e e

H D

m m

M M

+ ×

eH D

mM M

1 1– 100

≈ ×

–31–27 –27

1 19.1 10 100–

1.6725 10 3.3374 10

= × × × ×

[ ]–49.1 10 1000.5979 – 0.2996= × ×

= 2.714 × 10–2 %

12.26 H-ijek.kq esa] ,d fcanq&ukfHkd osQ fy,

fuEure Lrj:2 2

20

1, – .

4B B

mv emvr

r r πε= =

23/04/18

mÙkj

181

2 2

2 2 20

1 1.

4πε

∴ = +

B B B

em

m r r r

Brm e

20

2

4. 0.51A

°πε∴ = =

fLFkfrt mQtkZ

2 22

2 2 20

1 1– . –27.2 ; . . 13.6eV

2 24 2B B B

mveeV K E m

rr m r mr

= = = = = +

π

R f=kT;k osQ ,d xksyh; ukfHkd osQ fy, ;fn

R < rB, ogh ifj.kkeA

;fn R >> rB: bysDVªkWu Br ′ ( Br ′ = u;h cksgj f=kT;k) f=kT;k osQ xksys osQ Hkhrj xfreku gSA

3

3B

B

rr e

R

′′ =

oQs Hkhrj vko's k

2 30

32

4B

B

Rr

m re

πε ′∴ = ′

4 3(0.51A). .Br R°

′ = R 10 A°

=

4510(A)°

=

Br R1/4(510) A .°

∴ ≈ <′

22 2 2

1 1. .

2 2 2B B

mmv

m r m r= = =

′ ′

xfrt mQtkZ

22 2

1/22 2

(0.51) 3.54. (13.6eV) 0.16eV

(510) 22.62B

B B

r

mr r

= = = =

′

2 2 2

30

– 3.4 2

Be r R

Rπε

′= +

fLFkfrt mQtkZ

B B

B

e r r R

r R

2 2 2

30

1 ( – 3..4πε

′= +

23/04/18


182

0.51( 510 – 300)(27.2eV)1000

= +

–141(27.2eV). –3.83eV

1000= + =

12.27 D;ksafd ukfHkd Hkkjh gS] ijek.kq dk izfrfkIr laosx ux.; gS rFkk laozQe.k dh oqQy mQtkZ dksvksts&bysDVªkWu dks LFkkukUrfjr eku ldrs gSa D;ksafd Cr esa ,d la;ksth bysDVªkWu gS] mQtkZvoLFkkvksa dks cksgj izfr:i kjk iznÙk ekuk tk ldrk gSA noha voLFkk dh mQtkZ

22

1–=nE Z R

n tgk¡ R fjM~cxZ fu;rkaoQ gS rFkk Z 24=

n = 2 ls n = 1 osQ laozQe.k esa eqDr mQtkZ gS E Z R Z R2 2311 –

44

∆ = =

n = 4 bysDVªkWu dks mRksfir djus osQ fy, vko';d mQtkZ 24

116

=E Z R

vr% vksts bysDVªkWu dh xfrt ÅtkZ gS&

2 3 1. –

4 16 =

K E Z R 2116

= Z R

1124 24 13.6eV

16= × × ×

= 5385.6 eV

12.28 mpc2 = 10–6 × bysDVªkWu nzO;eku × c2

–610 0.5MeV≈ ×

–6 –1310 0.5 1.6 10≈ × × ×

–190.8 10 J≈ ×

–34 8

2 –19

10 3 100.8 10

× ×= =

×p p

c

m c m c

–74 10 m≈ × >> cksgj f=kT;k

2

20

1 exp(– )4e

rr r

λλ

πε

= + F

tgk¡ –1 –74 10 m B

p

rm c

λ = ≈ × >>

23/04/18

mÙkj

183

B

B

rr

11λ λ∴ << << vFkkZr

2

0

exp(– )( ) – .

4λ

πε=

e rU r

r

=mvr ∴ =vmr

;g Hkh 2 2

20

1:

4mv e

r r r

λ

πε

=≈ +

2 2

3 20

14

λ

πε

∴ = +

e

mr r r

2 22

0

[ ]4

λπε

∴ = +

er r

m

;fn 02

40; .

πελ = = =Br r

m e

2 2

0

.4πε

= B

er

m

D;ksafd –1 ,B Br r rλ δ>> = + j[ksa

2 2 2( 2 );B B B Br r r rδ λ δ δ δ∴ = + + + + ux.; gSA

vFkok 20 (1 2 )λ δ λ= + +B Br r

B B B Br r r r2 2(1 – 2 ) – 1δ λ λ λ λ= = << D;ksafd

2

0

exp(– – )( ) – .

4λδ λ

πε δ∴ =

+B

B

e rV r

r

2

0

1 1 –( ) – .(1 – )4

δλ

πε

∴ =

B

BB

eV r r

rr

(–27.2eV)≅ vifjo£rr jgrk gSA

23/04/18


184

xfrt mQtkZ 21–

2mv=

2

2

1.

2m

mr=

2

22( )Br δ=

+

2

2

21 –

2 BBrr

δ =

[ ](13.6eV) 1 2 Brλ= +

oqQy mQtkZ = [ ]2 2

20

– 1 24 2 B

B B

er

r rλ

πε+ +

[ ]–27.2 13.6 1 2 eVBrλ= + +

mQtkZ esa ifjorZu 13.6 2 eV 27.2 eVB Br r= × =λ λ

12.29 ekuk 2ε δ= +

1 2 0 02 2

0

.4q q R R

Fr r

δ δ

δ δπε + += = ∧ , tgk¡ 1 2

0

,4q q

π ε= ∧ –19 2 9(1.6 10 ) 9 10∧ = × × ×

–2923.04 10= ×

2

=mv

r

2 01

δ

δ+

∧=

Rv

mr

(i) mvr n= , 1/2

1/2 /2

0

mn nr r

Rmv m

+ = = ∧

δδ

bls r osQ fy, gy djus ij

12 2 1–

0

δ

δ

=

∧ n

nr

m R

n = 1 osQ fy,] rFkk fLFkjkad osQ eku j[kus ij] gesa izkIr gksrk gS

12 1–

10

rm R

δ

δ

=

∧

12 –68 2.9

1 –31 –28 19

1.05 109.1 10 2.3 10 10

r+

×=

× × × × = 8 × 10–11 = 0.08 nm

(< 0.1 nm)

(ii) n

n

nv

mr=

=

11–

02 2

m Rn

n

δ δ ∧

n = 1 osQ fy,, 11

vmr

=

= 1.44 × 106 m/s

23/04/18

mÙkj

185

(iii) xfrt mQtkZ = 2 –191

19.43 10 J=5.9eV

2mv = ×

LFkfrt mQtkZ R0 rd

0

–R

∧=

R0 ls r rd fLFkfrt mQtkZ

00

00 2 1

1–1 –

δδ

δ δδ+ +

∧ = + ∧ = + ∫

rr

RR

dr RR

r r

01 1

0

1 1––

1

δ

δ δδ

+ +

∧ = +

R

r R rd

fLFkfrt mQtkZ 01

0

1– –

1

δ

δδ +

∧=

+

R

r R

δ

+ δ

∧ + δ= +

+ δ

01

0 0

1 1– –

1R

R Rr

∧=

– 1 .90– 0 . 9

0

1 . 9– –

– 0 . 9R

Rr

–18 0.92.310 [(0.8) –1.9]

0.9= × J = – 17.3 eV

oqQy mQtkZ gS (–17.3 + 5.9) = –11.4 eV

vè;k; 13

13.1 (c)

13.2 (b)

13.3 (b)

13.4 (a)

13.5 (a)

13.6 (b)

13.7 (b)

13.8 (a), (b)

13.9 (b), (d)

23/04/18


186

13.10 (c), (d)

13.11 ugha] He3 dh caèku ÅtkZ rqyukRed :i ls vfèkd gSA

13.12

N

d N

d t

13.13 B dh vkSlr vk;q de gS D;ksafd B osQ fy, λ dk eku vfèkd gSA

13.14 mÙksftr bysDVªkWu] D;ksafd bysDVªkWfud ÅtkZ Lrjksa dh ÅtkZ dh ijkl eV esa gS] MeV esa ughaAγ -fofdj.k dh ÅtkZ MeV gSA

13.15 nks iQksVku mRiUu gksrs gSa] tks ÅtkZ&lajk.k gsrq foijhr fn'kkvksa esa xfr djrs gSaA

13.16 izksVku èkukosf'kr gksrs gSa rFkk ,d nwljs dks fo|qrh; :i ls izfrdf"kZr djrsa gSaA 10 ls vfèkdizksVkuksa okys ukfHkd esa ;g izfrd"kZ.k bruk vfèkd gks tkrk gS fd U;wVªkuksa dh vfèkdrk tksosQoy vkd"kZ.k cy mRiUu djrh gS] LFkkf;Ro osQ fy, vko';d gks tkrh gSA

13.17

ijek.kqvksa dh la[;

k

A

B

le;

t = 0 ij NA = N

O tcfd N

B = 0 tSls&tSls le; esa o`f¼ gksrh gS] N

A dk pj ?kkrkadh :i

ls iru gksrk gS] B osQ ijek.kqvksa dh la[;k c<+rh gS] vfèkdre gksrh gS vkSj vUr esa¥ ij 'kwU; gks tkrh gS (pj ?kkrkadh fo?kVu fu;ekuqlkj)

13.18 01ln

Rt

Rλ=

23/04/18

mÙkj

187

= 5760 16

ln0.693 12

= 5760 4

ln0.693 3

= 5760 4

2.303log0.693 3

× = 2391.12 o"kZ

13.19 d nwjh ij i`FkDo`Qr nks oLrqvksa dks vyx djus gsrq vUos"kh flXuy dh rjaxnS?;Z λ, d ls degksuh pkfg,A vr% U;wfDy;ku osQ Hkhrj vyx&vyx Hkkxksa dk lalwpu djus osQ fy,] bysDVªkWudh rjaxnS?;Z 10–15 m ls de gksuh pkfg,A

h hcK pc K pc

pλ

λ= ≈ ⇒ ≈ =vkSj

34 8

–19 –15

6.63 10 3 10eV

1.6 10 10× × ×

=× ×

= 109 eV. = 1 GeV

13.20 (a) 2311 Na : Z1 = 11, N1 = 12

∴ 2311 Na dk niZ.k lEHkkjh = 23

12 Mg

(b) D;ksafd Z2 > Z1, Mg dh cUèku ÅtkZ Na ls vfèkd gSA

13.2138 38 38

2.48 h 0.62 hS Cl Ar → →

ekuk t le; ij] 38S osQ ikl N1(t ) lfozQ; ukfHkd rFkk 38Cl osQ ikl N2(t ) lfozQ;

ukfHkd gSaA

NN

t

3811 1

d– Cl

dλ= = oQs cuu s dh nj

21 2 1 1

d–

dN

N Nt

λ λ= +

ysfdu 1–1 0

tN N e λ=

1–21 0 2 2

d– –

dtN

N e Nt

λλ λ=

2e td tλ ls xq.kk djosQ iqu% O;ofLFkr djus ij

2 2 2 1( – )2 2 2 1 0N d = Nt t te dN e t e dtλ λ λ λλ λ+

nksuksa ikksa dks lekdfyr djus ij

2 2 1( – )0 1

2 1

NC

–t t

2N e eλ λ λλ

λ λ= +

D;ksafd t = 0, N2 = 0, 0 1

2 1

C=––

N λ

λ λ

23/04/18


188

2 12 ( – )1

2 1

( –1)–

tt 02

NN e e

λ λλ λ

λ λ∴ =

2– , –1

2 1

( – )–

λ λλ

λ λ= t t0

2

NN e e

vfèkdre fxurh osQ fy, 02dN

dt=

gy djus ij 11 2

2

ln /( – )λ

λ λλ

=

t

2.48ln /(2.48 – 0.62)

0.62=

ln 4 2.303 log 41.86 1.86

= =

= 0.745 s.

13.22 ÅtkZ ljak.k ls]

22

2 2pn

n p

ppE B K K

m m− = + = + (1)

laosx ljak.k ls]

+ =n p

Ep p

c(2)

;fn E = B, izFke leh- ls izkIr gksrk gS pn = p

p = 0 vkSj blfy, frh; leh- lUrq"V ugh

dh tk ldrh] rFkk izfozQ;k ?kfVr ugha gks ldrhA

izfozQ;k osQ ?kfVr gksus osQ fy, ekuk E = B + λ, tgk¡ λ <<B rc leh- (1) ls leh- (2)esa p

n dk eku j[kus ij

( )( )22 2 21 1( ) /

2 2p n ppp p p E cp

m mλ = + = −+

22

2

22 02 λ

∴ − + =−

p p

E Ep p m

c c

22 2

22 / 4 / 8 2

4p

EE c E c m

cp

λ

± − −

∴ =

D;ksafd pp osQ okLrfod gksus osQ fy,] lkfjf.kd dks èkukRed gksuk pkfg,

23/04/18

mÙkj

189

2 2

2 2

4– 8 02

E Em

c cλ

=−

vFkok] 2

2

416 λ =

Em

c,

2 2

2 24 4λ∴ = ≈

E B

mc mc.

13.23 H ijek.kq esa caèku ÅtkZ 4

2 20

13.6eV8me

Ehε

= = (1)

;fn izksVku vkSj U;wVªkWu izR;sd ij vkos'k e′ Fkk rFkk os ,dleku oS|qrLFkSfrd cyksa osQ vèkhuFks] rc mijksDr lehdj.k esa bysDVªkWfud nzO;eku m dks izksVku&U;wVªkWu osQ lekuhr nzO;ekum ′ rFkk bysDVªkWfud vkos'k e dks e′ ls izfrLFkkfir djus dh vko';drk gS%

1836918

2 2M m

m m′ = = =

∴ cUèku ÅtkZ 2 20

9182.2MeV

8m e

hε

′= = (fn;k gS) (2)

(2) dks (1) ls Hkkx nsus ij

4 2.2MeV918

13.6eVe

e

′ =

11e

e

′⇒ ≈

13.24 β fo?kVu ls iwoZ] U;wVªkWu fojke esa gSa] vr% En = mnc

2, pn = 0

β fo?kVu osQ i'pkr laosx ljak.k ls

= +p p pn p e

;k 0+ = ⇒ = =p pp p p ep e p

12 4 2 2 2( )p p pE m c p c= + ,

1 12 4 2 2 2 4 22 2( ) ( )= + = +e e e e pE m c p c m c p c

ÅtkZ lajk.k ls

1 12 4 2 2 2 4 2 2 22 2( ) ( )+ + + =p e nm c p c m c p c m c

23/04/18


190

0 1 2 3 4

–1.04

–2.08

–3.11

–4.16

t(h)

ln(R/R )0

2 2 2936MeV, 938MeV, 0.51MeVp n em c m c m c≈ ≈ =

D;ksafd n rFkk p osQ eè; ÅtkZUrj U;wu gS] pc dk eku U;wu gksxkA pc << mpc2, tcfd pc,

mec2 ls vfèkd gks ldrh gSA

2 22 2

2 4 –2

⇒ +p n

p

p cm c m c pc

m c

izFke ozQe rd 2 2– 938MeV – 936MeV 2MeVn ppc m c m c = =

blls laosx izkIr gksrk gSA

rc]

12 4 2 2 2 22( ) 936 2 936MeVp pE m c p c= + = +

12 4 2 2 2 22( ) (0.51) 2 2.06MeVe eE m c p c= + = +

13.25 (i) t1/2 = 40 feuV (yxHkx)

(ii) xzkiQ dk <ky = –λ

vr% –4.16+3.11– 1.05h1

λ = =

vr% 1/20.693

0.66h 39.6 401.05

t or= = = feuV feuV (yxHkx)

13.26 (i) SpSn

= (M119,70 + MH – M120,70)c

2

= (118.9058 + 1.0078252 – 119.902199)c2

= 0.0114362 c2

SpSb = (M120,70 + MH – M121,70)c

2

= (119.902199 + 1.0078252 – 120.903822)c2

= 0.0059912 c2

pw¡fd SpSn

> SpSb

, Sn ukfHkd] Sb ukfHkd ls vfèkd LFkk;h gSA

(ii) ;g ukfHkd osQ fy, mlh izdkj dh dksf'k; lajpuk dks izn£'kr djrk gS tSlk fd ijek.kqesa gksrk gSA ;g caèku mQtkZ rFkk U;wDyku la[;k osQ chp f[akps oozQ esa mifLFkrf'k[kjksa dh Hkh O;k[;k djrk gSA

23/04/18

mÙkj

191

vè;k; 14

14.1 (d)

14.2 (b)

14.3 (b)

14.4 (d)

14.5 (b)

14.6 (c)

14.7 (b)

14.8 (c)

14.9 (a), (c)

14.10 (a), (c)

14.11 (b), (c), (d)

14.12 (b), (c)

14.13 (a), (b), (d)

14.14 (b), (d)

14.15 (a), (c), (d)

14.16 (a), (d)

14.17 ekfnr fd, tkus okys ijek.kq dk lkbt ,slk gksuk pkfg, fd ;g 'kq¼ v¼Zpkyd osQfdLVy tkyd dh lajpuk dks rks foo`Qr u djs ijUrq Si ;k Ge osQ lkFk lg&la;ksth caèkljyrkiwoZd fufeZr dj ,d vkos'k okgd dk ;ksxnku dj losQA

14.18 ijek.kq lkbt osQ vuqlkj Sn osQ fy, mQtkZ vUrjky 0 eV, C osQ fy, 5.4 eV, Si osQfy, 1.1 eV rFkk Ge osQ fy, 0.7eV gSA

14.19 th ugha] D;ksafd lafèk&izfrjksèk dh rqyuk esa oksYVehVj dk izfrjksèk vR;qPp gksuk gh pkfg,]tcfd lafèk izfrjksèk yxHkx vuUr gSA

14.20

+1V

0

14.21 (i) 10 × 20 × 30 × 10–3 = 6V

(ii) ;fn dc iznk; oksYVrk 5V gS rks vfèkdre fuxZe Vcc 5V ls vfèkd ugha gks ldrkAvr%] V0 = 5V

23/04/18


192

14.22 ugha] vkofèkZr fuxZe osQ fy, okafNr vfrfjDr 'kfDr DC lzksr ls izkIr gksrh gSA

14.23 (i) tsuj lafèk Mk;ksM rFkk lkSj lsy

(ii) tsuj Haktd oksYVrk

(iii) Q- y?kq iFku èkkjk

P- [kqys ifjiFk dh oksYVrk

14.24 vkifrr izdk'k osQ iQksVkWu dh mQtkZ

–34 8

–7 –19

6.6 10 3 102.06e

6 10 1.6 10hv V

× × ×= =

× × ×

vkifrr fofdj.k] iQksVksMk;ksM kjk lalwfpr gks losQ blosQ fy, vkifrr fofdj.k iQksVkWuksa dhmQtkZ cSaM&vUrjky ls vfèkd gksuh pkfg,A ;g 'krZ osQoy D2 kjk iwjh gksrh gSA vr% osQoyD2 gh bu fofdj.kksa dks lalwfpr djsxkA

14.25

1

–BB BEB

V VI

R=

;fn R1 dk eku c<+k;k tk,xk rks I

B dk eku de gksxkA D;ksafd I

c= βI

b, ifj.kke ;g gksxk

fd IC Hkh de gks tk,xk vFkkZr ,ehVj vkSj oksYVehVj osQ ikB~;kad de gks tk,¡xsA

14.26

OR kj dk fuxZe uhps nh xbZ lR;eku lkj.kh osQ vuqlkj gksrk gS%

A B C

0 0 0

0 1 1

1 0 1

1 1 1

23/04/18

mÙkj

193

14.27

fuos'k fuxZr

A A

0 1

1 0

14.28 rRoh; v¼Zpkydksa osQ mQtkZ&vUrjky ,sls gksrs gSa fd mRltZu IR ks=k esa gksrk gSA

14.29 lR;eku lkj.kh

A B Y

0 0 0

0 1 0

1 0 0

1 1 1

AND kj

14.30 max 0.2A 200mAZ

Z

PI

V= = =

s ZS

Z

V VR

I max

– 210

0.2= = = Ω

14.31 I3 'kwU; gS D;ksafd bl 'kk[kk esa yxk Mk;ksM i'p&ck;flr gSA AB ,oa EF esa ls izR;sd esa

izfrjksèk (125 + 25) Ω = 150 Ω gSA

D;ksafd AB ,oa EF loZle lekUrj 'kk[kk,¡ gSa] budk izHkkoh izfrjksèk gS] 150

752

= Ω

∴ ifjiFk esa oqQy izfrjksèk = (75 + 25) Ω = 100 Ω

∴ èkkjk 15

0.05A100

I = =

D;ksafd AB vkSj EF osQ izfrjksèk cjkcj gSa rFkk I1 = I2 + I3 + I4, I5 = 0

2 40.05

0.025A2

I I∴ = = =

14.32 D;ksafd Vbe = 0, Rb ij foHkoikr 10V gSA

3

1025

400 10bI Aµ∴ = =×

23/04/18


194

D;ksafd Vce = 0, Rc, ij foHkoikr I

cR

c 10V.

–33

103.33 10 3.33m

3 10cI A∴ = = × =×

.

–32

–6

3.33 101.33 10 133.

25 10c

b

I

Iβ

×∴ = = = × =

×

14.33

A

B

C1

C2

0

0

0

0

1

1

1

1

2

2

2

2

3

3

3

3

4

4

4

4

5

5

5

5

t (s)

14.34 fuxZe vfHkykkf.kd oozQ osQ fcUnq Q ij] VCE

= 8V & IC = 4mA

VCC

= ICR

C + V

CE

–CC CEc

C

V VR

I=

–3

16 – 82K

4 10cR = = Ω×

pw¡fd

VBB

= IBR

B + V

BE

–6

16 – 0.7510K

30 10BR = = Ω×

vc]–3

–6

4 10133

30 10C

B

I

Iβ

×= = =

×

oksYVrk yfCèk = – CV

B

RA

Rβ=

3

3

2 10–133

510 10×

= ××

= 0.52

23/04/18

mÙkj

195

'kfDr yfCèk = Ap = VAβ ×

2– C

B

R

Rβ=

32

3

2 10(133)

510 10×

= ××

= 69

14.35 tc fuosf'kr oksYVrk 5V ls vfèkd gksrh gS rks Mk;ksM ls èkkjkizokfgr gksrh gSA tc fuos'k 5V ls de gksrk gS rks Mk;ksM ,d[kqyk ifjiFk gksrk gSA

14.36 (i) ‘n’ ks=k esa As osQ dkj.k e– dh la[;k

ne = N

D = 1 × 10–6 × 5 × 1028 ijek.kq/m3

ne = 5 × 1022/m3

vYiak'k okgdksa (gksyksa) dh la[;k

2 16 2 32

22 22

(1.5 10 ) 2.25 105 10 5 10

ih

e

nn

n

× ×= = =

× ×

nh = 0.45 × 10/m3

blh izdkj tc cksjkWu dk vkjksi.k fd;k tkrk gS] rks ‘p’ izdkj fu£er gksrk gSA ftlesagksyksa dh la[;k

nh

= NA = 200 × 10–6 × 5 × 1028

= 1 × 1025/m3

;g ml n- izdkj dh ijr esa fo|eku e– dh la[;k dh rqyuk esa cgqr vfèkd gS ftlesacksjkWu folfjr fd;k x;k FkkA

bl izdkj fu£er ‘p’ ks=k esa vYika'k okgdksa dh la[;k

2 32

25

2.25 101 10

ie

h

nn

n

×= =

×

= 2.25 × 107/m3

(ii) vr% i'p ck;flr djus ij n- ks=k esa fo|eku 0.45 × 1010/m3 gksy] p- ks=k osQ2.25 × 107/m3 vYika'k e– dh rqyuk esa i'p lar`fIr èkkjk osQ fy, vfèkd ;ksxnkudjsaxsA

23/04/18


196

14.37

AB

A

B

A

B

B.A

AB

A.B+A.B

14.38

A

B C

1KW

14.39 IC ≈ I

E∴ I

C (R

C + R

E) + VCE =12 V

RE = 9 – R

C = 1.2 KΩ

∴ VE = 1.2 V

VB = V

E + V

BE =1.7 V

0.085mA20K

BVI = =

12–1.7 10.3108K

/ 0.085 0.01 1.085B

C

RI β

= = = Ω+ +

14.40 IE = I

C + I

BIC = β I

B(1)

ICR

C + V

CE + I

ER

E = V

CC(2)

RIB + V

BE + I

ER

E = V

CC(3)

lehdj.k (3) ls Ie ≈ I

C = β I

B

(R + β RE)= V

CC – V

BE,

– 11.5mA

200CC BE

B

E

V VI

R Rβ= =

+

lehdj.k (2) ls

2+ (12 – 3)K 1.56K

11.5

1.56 –1 0.56K

CC CE CC CEC E

C B

C

V – V V – VR R

I I

R

β= = = Ω = Ω

= = Ω

23/04/18

mÙkj

197

vè;k; 15

15.1 (b)

15.2 (a)

15.3 (b)

15.4 (a)

15.5 (b)

15.6 (c)

15.7 (b)

15.8 (b)

15.9 (c)

15.10 (a), (b), (d)

15.11 (b), (d)

15.12 (b), (c), (d)

15.13 (a), (b), (c)

15.14 (b), (d)

15.15 (i) vuq:i

(ii) vuq:i

(iii) vadh;

(iv) vadh;

15.16 ugha] 30 MHz ls vfèkd vko``fÙk osQ flXuy] vk;ue.My kjk ijkofrZr ugha gksaxs cfYdvarosZèku djsaxsA

15.17 viorZukad] vko`fÙk c<+us osQ lkFk&lkFk c<+rk gS ftldk vFkZ ;g gS fd mPprj vko`fÙkrjaxksa osQ fy, viorZu dks.k de gksrk gS] vFkkZr eqM+uk de gksrk gSA vr% iw.kZ vkUrfjdijkorZu dh n'kk vfèkd nwjh r; djus ij izkIr gksrh gSA

15.18 Ac + Am = 15, Ac – Am = 3

∴ 2Ac = 18, 2Am = 12

∴ 23

m

c

Am

A= =

15.191

1MHz2π

=LC

23/04/18


198

6

1LC

2 10π=

×

15.20 vk;ke&ekMqyu esa] okgh rjaxksa dk rRdkfyd foHko ekMqyd rjax foHko kjk ifjofrZrgksrk gSA lEizs"k.k esa ukW;t flXuy Hkh tqM+ ldrs gSa vkSj xzkgh] ukW;t dks] ekMqysfVaxflXuy osQ ,d Hkkx dh Hkk¡fr O;ogkj djrk gSA ijUrq vko`fÙk ekMqyu esa] ekMqyd foHkoosQ rRdkfyd foHkokuqlkj okgh rjax vkofÙk ifjofrZr dh tkrh gSA ;g osQoy feJ.k@ekMqyuLrj ij fd;k tk ldrk gS] flXuy osQ pSuy es lapj.k osQ nkSjku ughaA vr% ukW;t vko`fÙkekMqfyr flXuy dks izHkkfor ugha djrhA

15.21 lapj.k iFk esa gqbZ gkfu

= – 2 dB km–1 × 5 km = – 10 dB

izoèkZd dk oqQy ykHk = 10 dB + 20 dB

= 30 dB

flxuy dk lEiw.kZ ykHk = 30 dB – 10 dB

= 20 dB

10log

o

i

P

P= 12 vFkok P

o = P

i × 102

= 1.01 mW × 100 = 101 mW

15.22 (i) ijkl = 62 6.4 10 20× × × = 16 km

vkPNkfnr ks=kiQy = 803.84 km2

(ii) ijkl = 6 62 6.4 10 20 2 6.4 10 25× × × + × × ×

= (16 + 17.9) km = 33.9 km

vkPNkfnr ks=kiQy = 3608.52 km2

(iii) ks=kiQy esa izfr'kr o`f¼

= (3608.52 – 803.84)

100803.84

×

= 348.9%

15.23 2 22( )m Td R h= +

8RhT = 2(R+h

T)2 ( 2 2 )Tdm Rh=∵

2 24 2T T TRh R h Rh= + +

23/04/18

mÙkj

199

(R – hT)2 = 0

R = hT

D;ksafd osQoy vkdk'k rjax vko`fÙk iz;qDr gqbZ gS l << hT vr% osQoy ehukj dh

mQ¡pkbZ dk fopkj djsaA

f=kfoeh; vkdk'k esa] 6 ,UVsuk&ehukj iz;qDr gksaxsA hT = R

15.24 F1 ijr osQ fy,

5 × 106 = 9(Nmax

)1/2 or Nmax

= 2

6510

9

×

= 3.086 × 1011 m–3

F2 ijr osQ fy,

8 × 106 = 9 (Nmax

)1/2 or

Nmax

= 11 –368

7.9 10 m109

= ××

= 7.9 × 1011 m–3

15.25 ωc – ωm, ωc ,oa ωm+ ωm esa ls osQoy ωc + ωm ;k ωc – ωm esa lwpuk fufgr gSA vr% ωc +

ωm, rFkk ωc – ωm, nksuksa dks lEizsf"kr djosQ ykxr de dh tk ldrh gSA ωc + ωm oωc – ωm

15.26 (i)14

=o

I

I, vr% ln

1–

4α =

x

vFkok ln4 = ax vFkok 4α

=

lnx

(ii) 10log10

–o

Ix

Iα= tgk¡ 'a' es kh.ku gS dB/km

;gk¡ 12

=o

I

I

vFkok 10log 1–50 log2 = 5

2α α

=

vFkok

vFkok log2 0.30100.0602 B/km

5 5dα = = =

15.272x

= osxle;

2x = 3 × 108 m/s × 4.04 × 10–3s

512.12 × 10= m

2x

dm

R

R

hT

xhs

d

23/04/18


200

x = 6.06 × 105m = 606 km

2 2 2 2 2– (606) – (600)= =sd x h

= 7236; d = 85.06 km

lzksr rFkk xzkgh osQ eè; nwjh

= 2d ≅170 km

2 2m Td Rh=

2d = dm

4d2 = 8 RhT

2

2 T

dh

R= =

72362 6400×

≈ 0.565 km

hT = 565m

15.28 fp=k ls]

Vmax

= 100

2 = 50V, V

min =

202

= 10 V

(i) izfr'kr ekMqyu

max min

max min

– 50 –10(%) 100 100

50 10µ

= × = × + +

V V

V V= 40

10060

× = 66.67%

(ii) 'kh"kZ okgh foHko Vc = max min

2V V+

= 50 10

30V2+

=

(iii) 'kh"kZ lwpuk foHko = Vm = µVc

230 20V

3= × =

15.29 (i) 1 21 2( )= A(A sin sin sin )m m m m c cv t t A t A tω ω ω+ +

1 1 2 2

2( sin sin sin )m m m m c cB A t A t A tω ω ω+ + +

2 21 1= ( sin sin sin )m m m m c cA A t A t A tω ω ω+ +

m m m c c

c m m m c

B A t A t A t

A A t A sin t

1 1 2

1 2

2 2 2

1

(( sin ) sin

2 ( sin )

ω ω

ω ω

+ + +

+ +

23/04/18

mÙkj

201

m m m c c

m m m m m m m m

c c c m m c m m c

A A t A t A t

B A t A sin t A A t t

A t A A sin t t A t

1 1 2 2

1 1 2 2 1 2 1 2

1 1 2 2

2 2 2 2

2 2

( sin sin sin )

[ sin 2 sin sin

sin 2 ( sin sin sin ]

ω ω ω

ω ω ω ω

ω ω ω ω ω

= + +

+ + +

+ + + +

m m m m c c

m m m m c c

m m

m m m m

A A t A t A t

B A t A sin t A t

A At t

21 1 2

2 21

1 22 1 1 2

2 2 2 2 2 21

( sin sin sin )

[ sin sin

2[cos( – ) – cos( ) ]

2

ω ω ω

ω ω ω

ω ω ω ω

= + +

+ + +

+ +

21 1

2[cos( – ) – cos( ) ]

2c m

c m c m

A At tω ω ω ω+ +

12 2

2[cos( – ) – cos( ) ]

2c m

c m c m

A At tω ω ω ω+ +

∴ fo|eku vko`fÙk;k¡

1 2, ,ω ω ωm m c

2 1 1 2( – ),( )m m m mω ω ω ω+

1 1( – ),( )c m c mω ω ω ω+

2 2( – ),( – )c m c mω ω ω ω

(i) vk;ke dk ω osQ lkFk oozQ fp=k esa n'kkZ;k x;k gSA

1mω2mω

1 2m mω ω+

2–c mω ω

2 1–m mω ω 1c mω ω+

cω2c mω ω+

1–c mω ω

(ii) tSlk fd ns[kk tk ldrk gS fd vkofÙk LisDVªe ωc ij lefer ugh gSA ω < ω

c ij LisDVªe

dk la?kuu fo|eku gSA

(iii) vfèkd ekMqyu flXuy osQ tqM+us ij ω < ωc esa vfèkd la?kuu gksrk gS vkSj flXuy osQ

fefJr gksus dh lEHkkouk c<+ tkrh gSA

(iv) vfèkd flXuyksa dks lfEefyr djus osQ fy, cS.M pkSM+kbZ rFkk ωc c<+kuh pkfg,A ;g

izn£'kr djrk gS fd cM+h okgh vkofÙk vfèkd lwpuk (vfèkd ωm) dk ogu dj ldrh

gS vkSj tks ifj.kker% cS.M pkSM+kbZ dks c<+k,xkA

23/04/18


202

15.30 fm = 1.5kHz, –310.7 10

mf= × s

fc = 20MHz, –710.5 10

cf= × s

(i) RC = 103 × 10–8 = 10–5 s

vr% 1 1

<< <c m

RCf f

larq"V gksrk gS

vr% ;g foekMqfyr gks ldrh gSA

(ii) RC = 104 × 10–8 = 10–4 s

;gk¡ 1 1

<< <c m

RCf f

vr% ;g Hkh foekMqfyr gks ldrh gSA

(iii) RC = 104 × 10–12 = 10–8 s

;gk¡ 1>

c

RCf

, vr% ;g foekMqfyr ugha gks ldrhA

23/04/18

vè;k; 1 os|qr vkos'k rfkk {ks=k · 2019-01-30 · 1.20 dksbz flddk al-mg fejkrq dk cuk gs...

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