1. XvKv †evW©-2016 - WordPress.com...2017/03/02 · c`v_©weÁvb wØZxq cÎ: m„Rbkxj...

c`v_©weÁvb wØZxq cÎ: m„Rbkxj cÖ‡kœi mgvavb

c`v^Æweævb

1. XvKv †evW©-2016

1 bs cÖ‡kœi DËi

K mymsMZ Drm n‡Z Drcbœ †Kv‡bv Zi‡½i mÂvi‡Yi Awfgy‡L †h †iLv ev Zj eivei me¸‡jv KYv mg`kvm¤úbœ Zv‡K H Zi‡½i

Zi½ gyL e‡j|

L Kv‡P Av‡jvK ermi 6.271012 km ej‡Z eySvq KvP gva¨‡g Av‡jv GK eQ‡i 6.271012 km ~̀iZ¡ AwZµg Ki‡e|

M Awfj‡ÿï †ÿ‡Î: †j‡Ýi †dvKvm ~̀iZ¡, f0 = 0.02m = 2cm

e¯‘i ~̀iZ¡, u0 = 0.24m = 24 cm

cÖwZwe‡¤î `~iZ¡ v0 n‡j,

1v0

+ 1u0

= 1f0

ev, 1v0

= 1f0

– 1u0

= 12 –

124 =

1124

v0 = 2.1818 cm.

Awf‡b‡Îi †ÿ‡Î: †dvKvm ~̀iZ¡, fe = 0.05 m = 5 cm

G‡ÿ‡Î, cÖwZwe¤^wU Awfj‡ÿï †cQ‡b wKš‘ Awf‡b‡Îi mvg‡b MwVZ

nIqvq cÖwZwe¤^wU Awf‡b‡Îi Rb¨ Aev Í̄e|

cÖwZwe‡¤î ~̀iZ¡, ve = – 0.12 m = – 12 cm

e¯‘i ~̀iZ¡ ue n‡j,

1ue

+ 1ve

= 1fe

ev, 1ue

= 1fe

– 1ve

= 15 +

112 =

1760

ue = 3.529 cm

hš¿wUi ˆ`N©̈ , L = v0 + ue = (2.1818 + 3.529) cm

= 5.7108 cm (Ans.)

N †jÝØq Ae¯’vb cwieZ©‡bi Av‡M weea©‡bi ivwkgvjv:

GLv‡b,

Awf‡bÎ Øviv m„ó P‚ovšÍ we‡¤î ~̀iZ¡, v2 = – 25 cm

[†h‡nZz ¯úó `k©‡bi b~¨bZg `~i‡Z¡ †dvKvm Kiv nq]

Awf‡b‡Îi †dvKvm ~̀iZ¡, fe = 0.05m = 5 cm

awi, Awf‡b‡Îi jÿë ‘̄i ~̀iZ¡, ue = ?

Avgiv Rvwb, 1ue

+ 1ve

= 1fe

ev, 1ue

= 1fe

– 1ve

= 1

5cm + 1

25cm

ue = 4.17cm

Avevi, Awfj‡ÿï †dvKvm ~̀iZ¡, fo = 0.02m = 2 cm

b‡ji ˆ`N©̈ , L = 5.7108cm

Awfj‡ÿï we‡¤î ~̀iZ¡, vo = L – ue

= (5.7108 – 4.17) cm

= 1.5408 cm

Awfjÿ¨ †_‡K e ‘̄i ~̀iZ¡, uo = ?

GLb, 1uo

+ 1vo

= 1fo

ev, 1uo

= 1fo

– 1vo

= 1

2 cm – 1

1.5408 cm

uo = – 0.15 cm

myZivs hš¿wUi weea©b, mm = –vouo

1 +

Dfe

= – 1.5408

0.15

1 +

255 = 61.632

|mm| = 61.632

†jÝØq Ae¯’vb cwieZ©‡bi ci weea©‡bi ivwkgvjv :

G‡ÿ‡Î, Awfj‡ÿï †dvKvm ~̀iZ¡, fo = 5 cm

Awf‡b‡Îi †dvKvm ~̀iZ¡, fe = 2 cm

G‡ÿ‡Î, hš¿wU `~iexÿY hš¿ wn‡m‡e KvR Ki‡e|

weea©b, mT = fofe

1 +

feD =

52

1 +

225 = 2.7

|mT| = 2.7 < |mm|

†jÝØq Ae¯’vb cwieZ©‡bi ci weea©b K‡g hv‡e|


K ỳwU PvwR©Z e ‘̄i AvKvi hw` Zv‡ì gaëZ©x ~̀i‡Z¡i Zzjbvq Lye †QvU nq Z‡e Zv‡ì‡K we› ỳ PvR© ejv nq|

L †Kv‡bv PvwR©Z cwievnx †Mvj‡Ki Af¨šÍ‡i †Kv‡bv PvR© _v‡K bv, mg¯Í PvR© Ae¯’vb K‡i Gi c„‡ô| Zwor ej †iLv wbM©Z nq PvR©

†_‡K, ZvB ejv hvq PvwR©Z †MvjvKvi cwievnxi Af¨šÍ‡i †Kv‡bv ej

†iLv _v‡K bv| ZvB PvwR©Z †Mvj‡Ki Af¨šÍ‡i †Kvb wefe cv_©KÏ

_v‡K bv A_©vr cÖ‡Z¨K we› ỳi wefe mgvb _v‡K| GRb¨ PvwR©Z

cwievnx †Mvj‡Ki †K‡›`ª cÖvej¨ k~b¨ nq|

M Avgiv Rvwb, avi‡K mwÂZ kw³,

GLv‡b,

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c`v^Æweævb

U = 12 QV

= 12 2 C 2 V

Pv‡R©i cwigvY, Q = 2 C

cvZØ‡qi wefe cv_©K¨, V = 2 V

mwÂZ kw³, U = ?

= 2 J

AZGe, wPÎ (i) Gi avi‡Ki mwÂZ kw³ 2J. (Ans.)

N GLv‡b, wPÎ (i)Gi avi‡Ki–

cv‡Zi †ÿÎdj, A1 = 4 cm2

awi, cvZØ‡qi gaëZ©x ~̀iZ¡ = d1

Ges wPÎ (ii)Gi avi‡Ki-

cv‡Zi †ÿÎdj, A2 = 2 cm2

awi, cvZØ‡qi gaëZ©x ~̀iZ¡ = d2

myZivs cÖ_g avi‡Ki aviKZ¡, C1 = A10K

d1

Ges wØZxq avi‡Ki aviKZ¡, C2 = A20K

d2

kZ©vbymv‡i, Dfq avi‡Ki aviKZ¡ mgvb n‡Z n‡e

A10K

d1 =

A20Kd2

ev, d1d2

= A1A2

= 4 cm2

2 cm2 = 2

ev, d1 = 2d2

MvwYwZK we‡kølY †_‡K †`Lv hvq, 1g avi‡Ki cvZØ‡qi gaëZ©x

`~iZ¡ wØZxq avi‡Ki cvZØ‡qi gaëZ©x ~̀i‡Z¡i wØ¸Y Kiv n‡j, D³

aviKØ‡qi aviK‡Z¡i gvb mgvb n‡e|

myZivs wPÎ (i) I (ii) Gi aviK ỳwUi cvZØ‡qi gaëZ©x ~̀i‡Z¡i

AbycvZ 2 t 1 n‡j Dfq avi‡Ki aviKZ¡ mgvb n‡e|


K GKwU gvÎ eZ©bx‡Z Zwor cÖev‡ni cwieZ©‡bi d‡j A_ev †Kv‡bv †PŠ¤^K‡ÿ‡Î eZ©bxi MwZi d‡j eZ©bxi mv‡_ mswkøó †PŠ¤^K d¬v‡·i

cwieZ©‡bi Rb¨ †h Zwor †PŠ¤^K Av‡ek N‡U Zv‡K ¯̂Kxq Av‡ek

e‡j|

L Pz¤^‡Ki †PŠ¤̂K †ÿ‡Îi cÖfve‡K Kv‡R jvwM‡q ê ỳ¨wZK kw³ ˆZwi Kiv hvq| GKwU e× KzÛjxi mv‡_ GKwU M¨vjfv‡bvwgUvi hy³

K‡i GKwU Pz¤^K `Ð‡K KzÐjxi mv‡c‡ÿ MwZkxj Kiv n‡j Gi mv‡_

hy³ M¨vjfv‡bvwgUviwU wewÿß n‡Z †`Lv hvq| G †_‡K †evSv hvq

MwZkxj Pz¤^K e× KzÐjx‡Z Zwor cÖevn m„wó K‡i|

M Avgiv Rvwb, ZwoZevnx j¤̂v †mvRv Zv‡ii Avkcv‡ki †Kv‡bv we›`y‡Z m„ó †PŠ¤^K †ÿ‡Îi gvb,

B = μ0I2πa

B = (4π 10–7) (5 A)

2π 0.5 m

GLv‡b, Zwor cÖevn, I = 5A

Zvi n‡Z C we› ỳ‡Z ̀ ~iZ¡, a = 0.5m

†PŠ¤^K †ÿÎ, B = ?

= 210–6 T

= 2 μT (Ans.)

N †d¬wgs‡qi Wvb n Í̄ wbqgvbymv‡i AB Zv‡i Zwor cÖev‡ni Rb¨ Y we›`y‡Z m„ó †PŠ¤̂K †ÿ‡Îi w`K n‡e KvMR Z‡ji mv‡_ j¤̂ eivei

wfZ‡ii w`‡K| †d¬wgs‡qi evg n Í̄ wbqgvbymv‡i Y we› ỳ‡Z Zworevnx

CD Zv‡ii Dci †PŠ¤̂K e‡ji w`K n‡e CD Zv‡ii Dci j¤̂ Ges AB

†h w`‡K Av‡Q Zvi wecixZ w`‡K|

Avevi †d¬wgs‡qi Wvb n¯Í wbqgvbymv‡i CD Zv‡i Zwor cÖev‡ni Rb¨

X we›`y‡Z m„ó †PŠ¤^K †ÿ‡Îi w`K n‡e KvMR Z‡ji mv‡_ j¤̂ eivei

wfZ‡ii w`‡K| †d¬wgs‡qi evg n¯Í wbqgvbymv‡i X we›`y‡Z Zworevnx

AB Zv‡ii Dci †PŠ¤̂K e‡ji w`K n‡e AB Zv‡ii Dci j¤̂ Ges CD

†h w`‡K Av‡Q Zvi wecixZ w`‡K|

X I Y we›`y‡Z Zv‡ii Dci wµqvkxj ejØ‡qi w`‡K †_‡K †evSv hvq

ZviØq ci¯úi‡K weKl©Y Ki‡e|


K ci¯ú‡ii mv‡c‡ÿ aªæe †e‡M MwZkxj †h mKj cÖm½ KvVv‡gv‡Z wbDU‡bi MwZ m~Î¸‡jv AR©b Kiv hvq, Zv‡ì‡K Ro cÖm½ KvVv‡gv

e‡j|

L wbw`©ó avZzi c„ô n‡Z B‡jKUªb‡K gy³ Ki‡Z GKwU b~¨bZg kw³i cÖ‡qvRb hv‡K Kv‡h©v‡cÿK e‡j| Av‡jvK Zwor wµqvi

†Kvqv›Uvg ZË¡vbymv‡i GB b~¨bZg kw³i mieiv‡ni Rb¨ GKwU

b~¨bZg K¤úvs‡Ki Av‡jv cÖ‡qvRb hvi †P‡q Kg K¤úvsK wewkó

Av‡jv avZzi Kv‡h©v‡cÿ‡Ki mggv‡bi kw³ B‡jKUªb‡K mieivn

Ki‡Z cv‡i bv| GB K¤úvsKB n‡jv m~Pb K¤úvsK| m~Pb K¤úvsK

hZ Kg nq| wbw ©̀ó e‡Y©i I ZxeªZvi Av‡jvi Rb¨ (e„nËi K¤úvsK)

avZzi d‡Uv B‡jKUª‡bi †eM ZZ ev‡o d‡j Av‡jvK Zwor Gi gvbI

ev‡o| m~Pb K¤úvsK hZ e„w× cvq, Av‡jvK kw³i ZZ †ewk Ask

B‡jKUªb‡K gy³ Ki‡Z e¨q nq| ZvB d‡Uv Zwor Gi gvb I K‡g

hvq| A_v©r avZzi Av‡jvK Zwor wµqv Gi m~Pb K¤úvs‡Ki Dci

wbf©ikxj|

M wPÎ (i) Abymv‡i B‡jKUªbwU cÖ_g Kÿc‡_ Av‡Q| Avgiv Rvwb, nvB‡Wªv‡Rb cigvYyi n-Zg Kÿc‡_i e¨vmva©,

0.5 m

B A

C D

X

Y

5 A

5 A


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c`v^Æweævb

2

0

22

me

hnrn

GLv‡b, n = 1

0 = 8.85 10 – 12 C2 N– 1 m– 2

B‡jKUª‡bi fi, m = 9.1 10 – 31 kg

B‡jKUª‡bi PvR©, e = 1.6 10 – 19 C

cø̈ v‡¼i aªyeK, h = 6.63 10 – 34 J s

Kÿc‡_i e¨vmva©, rn = r1 = ?

myZivs, cÖ_g Kÿc‡_i e¨vmva©,

21931

212122342

1)C 106.1)(kg 101.9)(14.3(

)mNC 1085.8()sJ 1063.6)(1(

r

= 0.53 10 – 10 m = 0.53 Å (Ans.)

N n I (n + 1) Zg Kÿc‡_ kw³i e¨eavb,

E = me4

8h202

1

n2 – 1

(n + 1)2

me©vwaK Zi½‰`N©¨ max n‡j, B‡jKUªb‡K KÿPz¨Z Ki‡Z cÖ‡qvRbxq kw³

hc

max =

me4

8e202

1

n2 – 1

(n + 1)2

ev, max = 8h302C

me4 1

1n2 –

1(n + 1)2

ev, max = 8h302C

me4 1

11 –

122

ev, max= 8 (6.63 10–34)3 (8.85 10–12)2 3 108

9.11 10–31 (1.6 10–19)4

43

ev, max = 1.1953 10–7m

max = 1195.3125 Å

DÏxc‡Ki Dfq wP‡ÎB AvewZ©Z †Kv‡Yi Zi½‰`N©¨ max Gi Zzjbvq †ewk|

myZivs †Kvb †ÿ‡ÎB B‡jKUªb KÿPz¨Z n‡e bv|


K †KvqvK© n‡jv c`v‡_©i †gŠwjK KYv I †gŠwjK cÖ‡qvRbxq Dcv`vb hv Øviv c`v_© MwVZ|

L iƒ×Zvcxq cÖwµqvq †Kv‡bv iƒc Zv‡ci Av`vb cÖ`vb nqbv, ZvB dQ = 0| myZivs, ZvcMwZwe`¨vi cÖ_g m~Îbymv‡i,

0 = U + W

U = – W

A_©vr, iƒ×Zvcxq cÖwµqvq M¨vm Zvi AšÍt¯’ kw³i wewbg‡q KvR

K‡i| iƒ×Zvcxq cÖmvi‡Yi †ÿ‡Î wm‡÷g Øviv KvR Kiv nq e‡j

dW abvZ¥K nq| Avi ZvB, dU = – dW mgxKiY Abymv‡i wm‡÷‡gi Af¨šÍixY kw³ n«vm cvq|

M 1 bs eZ©bxwU GKwU AND †MB‡Ui| Gi Dfq BbcyU A_ev †h‡Kv‡bv GKwU BbcyU 0 (k~b¨) n‡jB AvDUcyU 0 (k~b¨) n‡e Ges †Kej gvÎ Dfq BbcyU 1 n‡jB AvDUcyU 1 n‡e| myZivs Gi mZ¨K mviwY n‡”Q–

A B X 0 0 0 1 0 0 0 1 0 1 1 1

N eywjqvb exRMwY‡Zi mvnv‡h¨ wjL‡j DÏxc‡K cÖ`Ë mZ¨K mviwYwU OR Acv‡ikb‡K mg_©b K‡i| KviY P A_ev Q A_ev DfqB 1 n‡j R = 1 nq| A_©vr P + Q = R| ZvB cÖ`Ë mviwYwU OR †MB‡Ui| wb‡P Gi eZ©bx I cÖZxK †`qv nj|

eZ©bxwUi AvDUcy‡U GKwU NOT †MBU hy³ Ki‡j eZ©bxwU n‡e wb¤œiƒc

GwU GKwU NOR †MBU| Gi mZ¨K mviwY n‡”Q-

P Q R S

0 0 0 1

0 1 1 0

1 0 1 0

1 1 1 0


K GKK abvZ¥K PvR©‡K eZ©bxi †Kv‡bv GK we› ỳ †_‡K Drmmn m¤c~Y© eZ©bx Nywi‡q cybivq H we› ỳ‡Z Avb‡Z †h KvR nq ev Dr‡mi

†h kw³ e¨q nq Zv‡K Dr‡mi Zwo”PvjK ej e‡j|

L mxmv I wU‡bi (mxmv 75% Ges wUb 25%) mswgkÖ‡Y ˆZwi GKwU miy Zvi‡K wbivcËv wdDR wn‡m‡e e¨envi Kiv nq| G Zv‡ii

eZ©bx

R

P

Q R = P + Q P

Q

cÖZxK

R = P + Q

P

Q S = R–


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c`v^Æweævb

Mjbv¼ Kg (cÖvq 300C)| Zv‡ii ga¨ w`‡q AwZwi³ Zwor cÖevwnZ n‡j ZviwU Mig n‡q D‡V Ges Zv M‡j wM‡q we ỳ¨r mieivn e›a

K‡i †`q| g~jZ Mjbv¼ Kgvevi Rb¨ wbivcËv wdD‡R weï× avZz

e¨envi Kiv nq bv|

M Avgiv Rvwb, M¨vjfv‡bvwgUvi cÖevn,

GLv‡b,

ig = S

G + S i

ev, 10-2 A (G + S) = S 1 A

ev, G + S = 100 S

ev, 99 S = 100

g~j cÖevn, i = 1 A

M¨vjfv‡bvwgUvi †iva, G = 100

M¨vjfv‡bvwgUvi cÖevn,

ig = 10 mA = 10-2 A

mv›U †iva, S = ?

S = 1.01 (Ans.)

N nviæb M¨vjfv‡bvwgUv‡ii eZ©bx m¾vi cwieZ©b ỳfv‡e Ki‡Z cv‡i

(i) mv›UwU cwieZ©b Ki‡Z cv‡i

mv‡›Ui gvb cwieZ©b K‡i S gv‡bi mv›U e¨venvi Ki‡j

Avgiv Rvwb, M¨vjfv‡bvwgUvi cÖevn,

ig = S

G + S i

ev, 10-2 A (G + S ) = S 10 A

ev, G + S = 1000 S

ev, 999 S = 100

S = 0.1

GLv‡b,

g~j cÖevn, i = 10 A

M¨vjfv‡bvwgUvi †iva, G = 100

M¨vjfv‡bvwgUvi cÖevn,

ig = 10 mA = 10-2 A

mv›U †iva, S = ?

(ii) Av‡iv GKwU mv›U e¨envi Ki‡Z cv‡i|

cÖ̀ Ë eZ©bxi M¨vjfv‡bvwgUvi I mv›U‡K GK‡Î GKwU A¨vwgUvi

we‡ePiv Ki‡j Gi cvjøv n‡e 1 A Ges Zzj¨ †iva n‡e,

R = GS

G + S = 100 1.01

100 + 1.01 = 0.9999

GLb A¨vwgUv‡ii cvjøv 10 A Ki‡Z n‡j G cvjøv n‡e Avw` cvjøvi 10 ¸Y

A¨vwgUv‡ii cvjøv e„w×i m~Î †_‡K Rvwb, Gi mv‡_ hy³ mv›U †iva,

S1 = 0.9999

10 – 1 = 0.1111

2. ivRkvnx †evW©-2016

1bs cÖ‡kœi DËi

K `ywU mgvb I wecixZ AšÍwiZ we›`y Avavb Aí ~̀i‡Z¡ Aew¯’Z _vK‡j Zv‡K Zwor wØ‡giæ e‡j|

L †Kv‡bv wm‡÷‡gi G›Uªwc evovi mv‡_ mv‡_ †mLvb †_‡K KvR cvIqvi m¤¢vebv †hgb K‡g hvq †Zgwb wm‡÷‡gi wek„•LjvI e„w×

cvq| †Kv‡bv wm‡÷‡gi Dci evB‡i †_‡K kw³ cÖ‡qvM K‡i hw`

k„•Lj Avbvi †Póv Kiv nq Zvn‡j wm‡÷‡gi G›Uªwc K‡g hv‡e| e ‘̄

hLb †KjvwmZ Ae ’̄vq _v‡K ZLb Aby¸‡jv mymse× myk„•Lj

mgv‡e‡k _v‡K, †m Kvi‡Y KwVb Ae¯’vq e ‘̄i G›Uªwc Kg| myZivs

G›Uªwc I wek„•Ljv IZ‡cÖvZfv‡e m¤úwK©Z| G Kvi‡Y ejv hvq,

†Kv‡bv wm‡÷‡gi wek„•Ljvi m~PK cwigvc‡Ki ivwk G›Uªwc|

M DÏxcK Abymv‡i,

A we›`y‡Z ¯’vwcZ Avavb, q1 = 2C

B we›`y‡Z ¯’vwcZ Avavb, q2 = 2C

C we›`y‡Z ¯’vwcZ Avavb, q3 = 2C

eM©‡ÿÎwUi, AB = BC = CD = DA = 1m

wc_v‡Mviv‡mi m~Îvbyhvqx, BD2 = AB2 + AD2

ev, BD2 = 12 + 12

ev, BD2 = 2

BD = 2 m

D we› ỳ‡Z wefe, VD = 1

4o

q1

AD + q2BD +

q3CD

= 9 109

2

1 + 2

2 +

21

= 2.327 1010V (Ans.)

N ÔMÕ Ask n‡Z cvB, BD = 2 m

A we›`y‡Z ¯’vwcZ Avav‡bi Rb¨ D we›`y‡Z cÖvej¨,

E1 = 1

4o .

q1AD2

= 9 109 212

= 1.8 1010 NC1

Gi w`K AD eivei

B we›`y‡Z ¯’vwcZ Avav‡bi Rb¨ D we›`y‡Z cÖvej¨,


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c`v^Æweævb

E2 = 1

4o

q1BD2

= 9 109 2

( 2)2

= 9 109 NC1

Gi w`K DB eivei|

C we›`y‡Z ¯’vwcZ Avav‡bi Rb¨ D we›`y‡Z cÖvej¨,

E3 = 1

4o

q3CD2

= 9 109 212

= 1.8 109 NC1

Gi w`K CD eivei|

E1 I E3 Gi gaëZ©x †KvY, 1 = 90

E1 I E3 Gi jwä cÖvej¨,

E4 = E12 + E32 + 2E1 E3 cos 90

= (1.8 1010)2 + (1.8 1010)2 + 0

= 2.55 1010 NC1

E1 I E4 Gi gaëZ©x †KvY 1 n‡j,

tan1 = E3 sin1

E1 + E3 cos1

= 1.8 109 sin 90

1.8 109 + 1.8 109 cos 90

= 1.8 109

1.8 109

ev, 1 = tan1(1)

1 = 45

E4 I E2 ci¯úi wecixZgyLx e‡j,

jwä cÖvej¨, E = E4 E2

= 2.55 1010 9 109

= 1.65 1010 NC1

awi, jwä cÖvej¨ E, E2 Gi mv‡_ †KvY Drcbœ K‡i|

E4 I E2 Gi gaëZ©x †KvY, = 180

tan = E4 sin

E2 + E4 cos

= 2.55 1010 sin 180

9 109 + 2.55 1010 cos 180

= 0

9 109 2.55 1010

= 0

= tan1 (0) = 0

AZGe, D we› ỳ‡Z jwä cÖvej¨ 1.65 1010 NC1 Ges Gi w`K BD eivei|

2bs cÖ‡kœi DËi

K †Kv‡bv Zwor †ÿ‡Î †Kv‡bv e× KwíZ Z‡ji ga¨ w`‡q AwZµvšÍ

†gvU Zwor d¬v‡·i cwigvY H Zj Øviv mxgve× Pv‡R©i

1

0 ¸‡Yi

mgvb|

L `ywU c`v_© hLb Nl©Y Kiv nq ZLb c`v_© `ywUi g‡a¨ hvi cigvYy‡Z B‡jKUª‡bi eÜb A‡cÿvK…Z wkw_j Zv †_‡K wKQy

B‡jKUªb wew”Qbœ n‡q AciwU‡Z P‡j hvq| Gi d‡j †h e ‘̄ †_‡K

B‡jKUªb wew”Qbœ nq †mB e¯‘wU‡Z B‡jKUª‡bi msL¨v K‡g hvIqvq

Zv abvZ¥K Pv‡R© PvwR©Z nq Ges Ab¨ e¯‘wU‡Z B‡jKUª‡bi AvwaK¨

NUvq GwU FYvZ¥K Pv‡R© PvwR©Z nq| d‡j e ‘̄wU AvwnZ nq| wKš‘

†Kv‡bv e ‘̄‡K nvZ Øviv Nl‡j e ‘̄wU AvwnZ nq bv †Kbbv nvZ †_‡K

B‡jKUªb H e ‘̄‡Z ¯’vbvšÍwiZ nq bv|

M DÏxcK n‡Z cvB, eZ©bxi

†iva, R1 = 12

†iva, R2 = 6

†iva, R3 = 3

wefe, V = 8V

R2 I R3 †ivaØq mgvšÍiv‡j hy³ _vKvq Zv‡ì Zzj¨ †iva Rp n‡j,

1Rp

= 1R2

+ 1R3

ev, 1Rp

= 16 +

13

Rp = 2

Avgiv Rvwb, V = I1R1

ev, I1 = VR1

= 8

12 = 0.67A

E

D E

E E

C

BA


Teac

hing

bd.co

m



c`v^Æweævb

Avevi, V = I2 Rp

ev, I2 = VRp

= 82 = 4 A

g~j cÖevn, I = I1 + I2

= (4 + 0.67)A

= 4.67 A (Ans.)

N wP‡Î D‡jøwLZ †iva¸‡jv‡K †kÖwY mgev‡q mvwR‡q AswKZ wPÎwU wb¤œiƒc n‡e:

Zzj¨ †iva, Rs = R1 + R2 + R3

= (12 + 6 + 3)

= 21

Avgiv Rvwb, V = IRs

ev, I = VRs

= 8

21 = 0.38 A

ÔMÕ Ask n‡Z cvB g~j cÖevn = 4.67A

g~j cÖev‡ni cwieZ©b = (4.67 0.38)A

= 4.29 A

AZGe, wP‡Î D‡jøwLZ †iva¸‡jv‡K †kÖwY mgev‡q mvRv‡j g~j cÖevn

4.29A n«vm cv‡e|

3bs cÖ‡kœi DËi

K †h †PŠ¤̂K †ÿ‡Î 1 Kzj¤^ Avavb †ÿ‡Îi w`‡Ki mv‡_ mg‡Kv‡Y 1ms1 †e‡M MwZkxj n‡j 1N ej Abyfe K‡i †mB †PŠ¤̂K †ÿ‡Îi gvb‡K 1 †Umjv e‡j|

L ̄ ^Kxq Av‡ek ¸Yv¼ 5 †nbwi ej‡Z eySvq †Kv‡bv KzÐjx‡Z Zwor cÖevn cÖwZ †m‡K‡Û GK A¨vw¤úqvi nv‡i cwiewZ©Z n‡j D³

KzÐjx‡Z 5 †fvë Zwo”PvjK kw³ Avweó nq|

M †Ìqv Av‡Q,

Kÿc‡_i e¨vmva© Z_v B‡jKUªb I †cÖvU‡bi gaëZ©x ~̀iZ¡, r = 5.3 1011 m

B‡jKUª‡bi Avavb = †cÖvU‡bi Avavb = e = 1.6 1019C

†K‡›`ª Kzj¤^ ej, Fe = ?

Avgiv Rvwb, Fe = C e e

r2

= 9 109 e2

r2

= 9 109 (1.6 1019)2

(5.3 1011)2

= 8.2 108 N (Ans.)

N DÏxcK n‡Z cvB,

B‡jKUª‡bi ª̀æwZ, v = 2.185 106 ms1

B‡jKUª‡bi fi, m = 9.1 1031 kg

e„ËvKvi c‡_i e¨vmva©, r = 5.3 1011 m

†K›`ªgyLx ej, Fc = ?

Avgiv Rvwb, Fc = mv2

r

= 9.1 1031 (2.185 106)2

5.3 1011

= 8.2 108 N

ÔMÕ Ask n‡Z cvB, †K‡›`ª Kzj¤^ ej, Fe = 8.2 108 N

Avgiv Rvwb, †K› ª̀gyLx ej hLb Kzj¤^ e‡ji mgvb nq ZLb †K‡› ª̀i

wecixZ w`‡K †K› ª̀gyLx e‡ji mgvb GKwU ej KvR K‡i hv‡K

†K›`ªwegyLx ej ejv nq| †K› ª̀gyLx ej †K› ª̀wegyLx e‡ji mgvb n‡j

e„ËvKvi c‡_ N~Y©vqgvb †Kvb e¯‘ Kÿc‡_B Ae ’̄vb K‡i| GLv‡b,

Fe = Fc| Avi ZvB N~Y©biZ B‡jKUªbwU cigvYyi Kÿc_ †_‡K wQU‡K co‡e bv|

4bs cÖ‡kœi DËi

K †h mKj wcÖR‡gi cÖwZmviK †KvY 6-Gi †P‡q eo bq Zv‡ì‡K miæ wcÖRg e‡j|

L AYyexÿY I ~̀iexÿY h‡š¿i MVbMZ cv_©K¨ wb‡¤œi ZvwjKvq wjwce× Kiv n‡jv:

AYyexÿY hš¿ `~iexÿY hš¿

1. Awfj‡ÿï †dvKvm ~̀iZ¡ I

D‡š§l A‡cÿvK…Z †QvU|

1. Awfj‡ÿï †dvKvm ~̀iZ¡ I

D‡š§l A‡cÿvK…Z eo|

2. Awf‡b‡Îi †dvKvm ~̀iZ¡ I

D‡š§l A‡cÿvK…Z eo| 2. Awf‡b‡Îi †dvKvm ~̀iZ¡ I

D‡š§l A‡cÿvK…Z †QvU|

M DÏxcK n‡Z cvB, wP‡oi gaëZ©x `~iZ¡, d = 0.3mm = 0.3 103 m

c`©vi ~̀iZ¡, D = 1m

R1 = 12 R2 = 6 R3 = 3

8V I


Teac

hing

bd.co

m



c`v^Æweævb

8g D¾¡j cwÆi `~iZ¡, x8 = 6.2 mm = 6.2 103 m

Av‡jvi Zi½‰`N©¨, = ?

Avgiv Rvwb, x8 = 8D

d

ev, = d x88 D

= 0.3 103 6.2 103

8 1

= 2.32 107m (Ans.)

N DÏxcK n‡Z cvB,

wP‡oi ga¨eZ©x ~̀iZ¡, d = 0.3mm = 0.3 103m

c`©vi ~̀iZ¡, D = 1 m

cvwbi cÖwZmiv¼, w = 43

evqyi cÖwZmiv¼, a = 1

ÔMÕ Ask n‡Z cvB, evqy‡Z Zi½ ˆ`N©¨, a = 2.32 107m

Avgiv Rvwb, w w = a a

ev, w = a aw

= 4 2.32 107

4/3

= 1.74 107 m

evqy gva¨‡g cwÆ ev Svj‡ii cÖ¯’, xa = aD2d =

2.32 107 1

2 0.3 103

= 386.67 106 m

cvwbi g‡a¨ cwÆ ev Svj‡ii cÖ¯’, xw = w D

2d

= 1.74 107 1

2 0.3 103

= 290 106 m

cwÆ ev Svj‡ii cÖ‡¯’i ciweZ©b,

x = xa xw

= (386.67 106 290 106)m

= 96.67 106 m

AZGe, DÏxc‡Ki e¨e ’̄vwU cvwbi g‡a¨ _vK‡j cwÆ ev Svj‡ii cȪ ’

96.67 106m n«vm cv‡e|

5bs cÖ‡kœi DËi

K h‡_vchy³ D”P K¤úv¼wewkó Av‡jvKiwk¥ †Kv‡bv avZec„‡ô AvcwZZ n‡j Zv †_‡K B‡jKUªb wbtm„Z nq, G NUbv‡K Av‡jvK

Zwor wµqv e‡j|

L †Kvb †ZRw¯µq c`v‡_©i fvO‡bi nvi wbf©i K‡i bgybvq Dcw¯’Z †gvU cigvYy msL¨vi Dci| ZvB mg‡qi mv‡_ GB nvi Kg‡Z _v‡K|

fvO‡bi d‡j †ZRw¯µq cigvYyi msL¨v hLb LyeB Kg n‡q hvq,

ZLb GB nviI bMb¨ n‡q hvq| †h‡nZz cigvYyi msL¨v GKwU c~Y©

msL¨v, ZvB fvO‡bi nvi Lye bMb¨ n‡j g~jZ Zv `xN© mgq e¨vcx

cigvYywUi w ’̄wZkxjZv wb‡`©k K‡i| ZvB GB fvOb KL‡bv †kl nq

bv|

g‡b Kwi, †Kv‡bv †ZRw¯µq c`v‡_©i bgybvq Avw` ev cÖviw¤¢K

cigvYyi msL¨v No Ges Aeÿq aªæeK | t mg‡q Aewkó cigvYyi msL¨v, N = Noet

N = 0 n‡Z n‡j, Noet = 0

ev, et = 0

ev, 1

et = 0

ev, et = 10

ev, et =

ev, t =

t =

AZGe, †Kv‡bv †ZRw¯µq c`v‡_©i wbt‡kl Kvj Amxg|

M DÏxcK n‡Z cvB,

Y cv‡Zi Kvh©v‡cÿK, Wo = 1.85eV = 1.85 1.6 1019J

Av‡jvi ª̀æwZ, c = 3 108 ms1

cø̈ v‡¼i aªæeK, h = 6.63 1034 J.s

m~PK Zi½‰`N©¨, o = ?

Avgiv Rvwb, Wo = hc

o

ev, o = hcWo

= 6.63 1034 3 108

1.85 1.6 1019


Teac

hing

bd.co

m



c`v^Æweævb

= 6.72 107m (Ans.)

N †Ìqv Av‡Q,

Y cv‡Zi Kvh©v‡cÿK, Wo = 1.85eV

†Kv‡li ZworPvjK ej, E = 4.2V

Y †_‡K X G 1 wU B‡jKUªb‡K wb‡q †h‡Z K…ZKvR, W = eE

= 4.2 eV

†dvU‡bi m‡e©v”P Zi½‰`N©¨ max n‡j, hc

max = e (W0 + W)

ev, max = hc

e(W0 + W)

ev, max = 6.63 10–34 3 108

1.6 10–19 (1.85 + 4.2)

max = 2054.75Å; hv ̀ „k¨gvb Av‡jvi Zi½‰`‡N©ï (4000Å – 8000Å) Gi Zzjbvq A‡bK Kg|

A_©vr „̀k¨gvb Av‡jvi mvnv‡h¨ B‡jKUªb‡K Y cvZ †_‡K X cv‡Z Avbv m¤¢e bq|


K †Kv‡bv ’̄vqx wbDwK¬qv‡mi fi Gi MVbKvix Dcv`vbmg~‡ni gy³ve ’̄vq f‡ii †hvMd‡ji †P‡q wKQyUv Kg n‡Z †`Lv hvq| f‡ii

H cv_©K¨‡K fiÎæwU e‡j|

L cig k~b¨ ZvcgvÎvq Aa©-cwievnxi mn‡hvRx eÜb¸‡jv LyeB mej nq Ges me¸‡jv †hvRb B‡jKUªbB mn‡hvRx eÜb ˆZwi‡Z

e¨¯Í _v‡K, d‡j †Kv‡bv gy³ B‡jKUªb _v‡K bv| Aa©-cwievnx‡Z Zvc

w`‡j Zvckw³i Kvi‡Y wKQy msL¨K mn‡hvRx eÜb †f‡½ hvq Ges

wKQy B‡jKUªb gy³ nq| GB ch©v‡q wefe cv_©K¨ cÖ‡qvM Kiv n‡j

gy³ B‡jKUªb¸‡jv Zwor cÖevn m„wó K‡i| G Kvi‡Y Aa©-cwievnx‡K

Zvc w`‡j cwievnxi b¨vq AvPiY K‡i|

M DÏxcK n‡Z cvB,

†em cÖev‡ni cwieZ©b, Ib = (22 8)mA = 14 mA

GwgUvi cÖev‡ni cwieZ©b, Ie = 16 mA

awi, Kv‡j±i cÖev‡ni cwieZ©b = Ic

cÖevn weea©b ¸YK, = ?

Avgiv Rvwb, Ie = Ib + Ic

ev, Ic = Ie Ib

= (16 14) mA

= 2 mA

Avevi, = IcIe

= 2

16

= 0.125 (Ans.)

N DÏxc‡Ki UªvbwR÷viwUi weea©b e„w× Ki‡Z n‡j Gi AšÍM©vgx eZ©bx‡K me©`v m¤§yLx eZ©bx‡Z evqvm Kiv nq Ges Zv Kivi Rb¨

AšÍM©vgx eZ©bx‡Z AšÍM©vgx ms‡K‡Zi AwZwi³ GKwU wW.wm †fv‡ëR

cÖ‡qvM Ki‡Z nq hv‡K evqvm †fv‡ëR e‡j| m¤§yLx †SuvK †Ìqvq

AšÍM©vgx eZ©bx‡Z †iva Lye Kg nq| wbtmviK msMÖvnK eZ©bx A_©vr

ewnM©vgx eZ©bx‡Z Vcc e¨vUvwii gva¨‡g wegyLx †SuvK cÖ`vb Kiv nq|

wbtmviK cxV Rsk‡b cÖhy³ ms‡K‡Zi abvZ¥K Aa©P‡µi mgq

Rvsk‡bi m¤§yL †SuvK e„w× cvq d‡j AwaK cwigvY B‡jKUªb

wbtmviK †_‡K cxV Gi ga¨ w`‡q msMÖvn‡K cÖevwnZ nq Ges

msMÖvnK cÖevn e„w× cvq| GB †e‡o hvIqv msMÖvnK cÖevn (Ic) †jvW †iwR÷¨vÝ RL-G AwaK cwigvY wefe cZb m„wó K‡i| A_©vr ewnM©vgx‡Z AwaK †fv‡ëR cvIqv hvq|

3. w`bvRcyi †evW©-2016


K `ywU wbw`©ó we›`y PvR© GKB wbw`©ó `~i‡Z¡ _vK‡j k~b¨ ev evqy gva¨‡g Zv‡ì g‡a¨ wµqvkxj ej Ges GKB ~̀i‡Z¡ Ab¨ †Kv‡bv

gva¨‡g Zv‡ì g‡a¨ wµqvkxj e‡ji AbycvZ‡K civ‰e ỳ¨wZK aªæeK

e‡j|

L Zwor †ÿ‡Îi †Kv‡bv we›`yi wefe 15 V ej‡Z eySvq, Amxg †_‡K cÖwZ Kzj¤^ abvZ¥K Avavb‡K Zwor‡ÿ‡Îi H we› ỳ‡Z Avb‡Z

15 J KvR m¤úbœ nq|

M GLv‡b,

C1 = 1 F

C2 = 2 F

C3 = 3 F

DÏxc‡Ki wP‡Î, C1 Ges C2 aviKØq mgvšÍiv‡j _vKvq G‡ì ZzjäviKZ¡ Cp n‡j,

Cp = C1 + C2

= 1 F + 2 F = 3 F

IB

Aš—M©vgx

ms‡KZ

RL

VBB VCC

n-p-n

+ –

ewnM©v

B

C

+

Ri E


Teac

hing

bd.co

m



c`v^Æweævb

Avevi,

C2 aviK, Cp Gi mv‡_ †kÖYx‡Z _vKvq G‡`i Zzj¨ aviKZ¡ Cs n‡j,

1Cs =

1C3

+ 1CP

= 1

3 F +

1

3 F =

2

3 F

Cs = 1.5 F

eZ©bxwUi Zzj¨ aviKZ¡ 1.5F (Ans.)

N GLv‡b,

cÖ̀ Ë eZ©bxi Zzj¨ aviKZ¡, C = 1.5uF

= 1.5 10–6 F

eZ©bxi wefe, V = 10 V

cÖ̀ Ë eZ©bxi mwÂZ kw³, U = 12 CV

2

= 12 1.5 10

–6 F (10 V)2

= 7.5 10–5 J

Avevi, C1, C2 Ges C3 aviK¸‡jv‡K mgvšÍiv‡j ms‡hvM Ki‡j G‡`i Zzj¨ aviKZ¡ C n‡j,

C = C1 + C2 + C3

= 1 F + 2 F + 3 F

= 6 F

= 6 10–6 F

aviK¸‡jv‡K mgvšÍiv‡j hy³ Ki‡j eZ©bxi mwÂZ kw³,

U = 12 CV

2

= 12 6 10

–6 F (10 V)2

= 3 10–4 J

†h‡nZz, U > U

AZGe, eZ©bxwUi mKj aviK‡K mgvšÍiv‡j ms‡hvM Ki‡j cÖvß

mwÂZ kw³, cÖ`Ë eZ©bxi mwÂZ kw³ A‡cÿv †ewk n‡e|


K †Kv‡bv eZ©bx‡Z Zwor cÖevn hw` GKwU wbw`©ó mgq cici w`K cwieZ©b K‡i Ges wbw`©ó mgq cici m‡e©v”P I me©wb¤œ gvb cÖvß

nq †mB Zwor cÖevn‡K w`K cwieZx© cÖevn e‡j|

L †Kv‡bv Zvi KzÐjxi ̄ ^Kxq Av‡ek ̧ YvsK 10 †nbix ej‡Z eySvq, H KzÐjx‡Z ZworcÖevn cÖwZ †m‡K‡Û GK A¨vw¤úqvi nv‡i cwieZx©Z

n‡j, KzÐjxwU‡Z cÖevn cwieZ©‡bi wecix‡Z 10 †fvë Zwo”PvjK kw³ Avweó nq|

M GLv‡b,

w`K cwieZx© cÖev‡ni mgxKiY, i = 40 sin t

kxl©gvb, i = 40 A

w`K cwieZx© cÖev‡ni eM©g~jxq Mo gvb, irms = ?

Avgiv Rvwb,

irms = io

2

= 40A

2

= 28.28 A (Ans.)

N GLv‡b,

w`K cwieZx© cÖev‡ni mgxKiY, i = 40 sin t

kxl©gvb, i = 40 A

hLb, t = 3T4 ZLb, i = 40 sin

3T4

= 40 sin

2

T 3T4

= 40 sin

3

2

= 40 (–1) = – 40 A = –io

AZGe, MvwYwZK we‡køl‡Y †`Lv hvq, DÏxc‡K hLb t = 3T4 ZLb

w`K cwieZx© cÖev‡ni gvb Gi kxl©gv‡bi mgvb|


K mv`v Av‡jvK iwk¥ wcÖR‡gi ga¨ w`‡q cÖwZmi‡Yi d‡j mvZwU g~j e‡Y©i Av‡jv‡Z wef³ nIqv‡K Av‡jv‡Ki we”QziY e‡j|

L Kv‡Pi mgeZ©b †KvY 57 ej‡Z eySvq, AmgewZ©Z Av‡jvK iwk¥ Kv‡P 57 †Kv‡Y AvcwZZ n‡j cÖwZdwjZ iwk¥ me©vwaK cwigvY mgeZx©Z n‡e|

M GLv‡b, DËj †j‡Ýi cÖ_g c„‡ôi eµZvi e¨vmva©, r1 = 6 cm

wØZxq c„‡ôi eµZvi e¨vmva©, r2 = –12 cm

†j‡Ýi cÖwZmivsK, = 32

†j‡Ýi †dvKvm ~̀iZ¡, f = ?


Teac

hing

bd.co

m



c`v^Æweævb

Avgiv Rvwb,

1f = ( – 1)

1

r1 –

1r2

=

3

2 – 1

1

6 cm – 1

–12 cm = 12

1

6 – 1

–12 cm–1

= 18 cm

–1

f = 8 cm

AZGe, DÏxc‡Ki †jÝwUi †dvKvm ~̀iZ¡ 6 cm| (Ans.)

N GLv‡b, evqy‡Z †j‡Ýi cÖwZmiv¼, ag = 32

Ges †dvKvm ~̀iZ¡, a = 8 cm [ÔMÕ bs n‡Z]

cvwbi cÖwZmivsK, aw = 43

awi, cvwb‡Z †dvKvm ~̀iZ¡ = w

†j‡Ýi `yB c„‡ôi eµZvi e¨vmva© r1 I r2 n‡j

Avgiv Rvwb, 1

= ( –1)

1

r1 –

1r2

evZv‡mi †ÿ‡Î, 1

a = (ag – 1)

1

r1 –

1r2

... (i)

cvwbi †ÿ‡Î, 1

w = (wg – 1)

1

r1 –

1r2

... (ii)

(i) (ii) bs n‡Z cvB,

w

a =

ag – 1

wg – 1 =

ag – 1

ag

aw – 1

=

32 – 1

32

43

– 1

=

12

18

= 4

w = 4 a = (4 8) cm = 32 cm

AZGe, MvwYwZK we‡køl‡Y †`Lv hvq †h, DÏxc‡Ki †jÝwU‡K hw`

cvwb‡Z Wzev‡bv nq Z‡e Gi †dvKvm ~̀iZ¡ c~‡e©i †dvKvm ~̀i‡Z¡i 4 ¸Y n‡e Ges †dvKvm ~̀i‡Z¡i gvb n‡e 32 cm|


K `ªæZMwZ m¤úbœ B‡jKUªb †Kvb avZz‡K AvNvZ Ki‡j Zv †_‡K D”P K¤úvsK I †f`b ÿgZvm¤úbœ ARvbv cÖK…wZi GK cÖKvi

wewKiY Drcbœ nq, G wewKiY‡K G·-†i e‡j|

L Avgiv Rvwb 23592 U †K wbDUªb 10n Øviv AvNvZ Ki‡j wbDwK¬q wdkb

N‡U| G‡Z 23592 U wbDwK¬qvm wefvwRZ n‡q Kg f‡ii ỳwU wbDwK¬qvm

m„wó nq Ges ỳwU ev wZbwU wbDUªb 10n wbM©Z nq|

wewµqvq AskMÖnYKvix 10n I

23592 U Gi †gvU fi A‡cÿv Drcbœ

wbDwK¬qvmØq I wbDUªb¸wji †gvU fi mvgvb¨ Kg nq| A_©vr wbDwK¬q

wdk‡b wKQy fi nvivq| AvBb÷vB‡bi fikw³ mgxKiY E = mc2 Abymv‡i GB nviv‡bv fi kw³‡Z iƒcvšÍwiZ nq| BnvB wbDwK¬q

wdkb wewµqvq kw³ Drc‡bœi KviY|

M GLv‡b,

f‚-c„‡ô i‡K‡Ui ˆ`N©̈ , Lo = 10 m

f‚-c„‡ô w¯’i ch©‡eÿ‡Ki mv‡c‡ÿ i‡K‡Ui †eM, v = 3 107 ms–1

i‡K‡Ui Pjgvb ˆ`N©¨, L = ?

Av‡jvi †eM, c = 3 108 ms–1

Avgiv Rvwb,

L = Lo 1 – v2

c2 = 10 1 – (3 107)2

(3 108)2 = 9.9498 m

AZGe, i‡K‡Ui Pjgvb ˆ`N©¨ n‡e 9.9498 m (An.s)

N GLv‡b, f‚-c„‡ô i‡K‡Ui fi, mo = 5000 Kg

cÖ_g †ÿ‡Î, i‡K‡Ui †eM, v1 = 3 107 ms–1

wØZxq †ÿ‡Î, i‡K‡Ui †eM, v2 = 2v1 = 2 3 107 ms–1

= 6 107 ms–1

Av‡jvi †eM, c = 3 108 ms–1

cÖ_g †ÿ‡Î i‡K‡Ui Pjgvb fi m1 n‡j

Avgiv Rvwb,

m1 = mo

1 – v12

c2

= 5000 kg

1 – (3 107ms–1)2

(3 108ms–1)2

= 5025.189 kg

Avevi, wØZxq †ÿ‡Î i‡K‡Ui Pjgvb fi m2 n‡j,

m2 = mo

1 – v22

c2

= 5000 kg

1 – (6 107ms–1)2

(3 108ms–1)2

= 6250 kg

†h‡nZz, m2 > m1

AZGe, DÏxc‡K i‡K‡Ui †eM wØ¸Y Kiv n‡j Gi fi †e‡o hv‡e|


K wbDwK¬qvm MVbKvix Dcv`vbmg~‡ni f‡ii mgwó A‡cÿv wbDwK¬qv‡mi fi wKQyUv Kg nq| f‡ii G cv_©K¨‡K fiÎæwU e‡j|

L iv`vi‡dv‡W©i g‡Z cigvYyi †K‡›`ª i‡q‡Q wbDwK¬qvm †hLv‡b mg¯Í abvZ¥K Avavb Ges fi †K›`ªxf‚Z _v‡K| GB wbDwK¬qv‡mi

Pviw`‡KB wewÿß Ae ’̄vq i‡q‡Q B‡jKUªb mg~n| A_v©r cigvYyi

Af¨šÍixY AwaKvsk AÂjB duvKv| ZvB abvZ¥K Avavb hy³

AwaKvsk -KYv ¯̂Y©cv‡Zi ga¨ w`‡q hvIqvi mgq cÖvq k~b¨


Teac

hing

bd.co

m



c`v^Æweævb

RvqMvi ga¨ w`‡q †mvRv c‡_ †ei n‡q hvq| †h me -KYv wbDwK¬qv‡mi cÖvq KvQvKvwQ Avm‡e Zviv wbDwK¬qv‡mi abvZ¥K Avavb

Øviv weKwl©Z n‡q nvjKv †eu‡K hv‡e| Avi †h me -KYv wbDwK¬qv‡mi w`‡K gy‡LvgywL n‡e Zviv weKwl©Z n‡q wd‡i Avm‡e|

M GLv‡b, †iwWqv‡gi,

cÖv_wgK cigvYyi msL¨v, No = 6.023 1023wU

†f‡½ hvIqv cigvYyi msL¨v = 6.000 1023wU

Aewkó cigvYyi msL¨v, N = (6.023 – 6.000) 1023wU

= 2.3 1021wU

mgq, t = 1y

†iwWqv‡gi Aeÿq aªæeK n‡j Avgiv Rvwb,

NNo

= e–t

ev, n

N

No = –t

ev, =

n

N

No

–t

=

n

2.3 10

21

6.023 1023

–1 y

= 5.568 y–1

Avevi, Avgiv Rvwb,

Aa©vqy, T12

= 0.693

=

0.6935.568 y–1 = 0.124 y

AZGe, †iwWqvg †gŠjwUi Aa©vqy 0.124 eQi (Ans.)

N wØZxq eQ‡ii ïiæ‡Z AÿZ cigvYy msL¨v,

No = 2.3 1021wU

G mgq †_‡K 1 eQi ci cigvYy msL¨v N n‡j,

N = No e–t

= 2.3 10–21 e–5.568 y–1 1 y

= 8.78 1018

GLv‡b,

= 5.56 y–1

myZivs wØZxq eQ‡i †f‡½ hvIqv cigvYy msL¨v,

No – N = 2.3 1021 – 8.78 1018 = 2.29 1021

GLv‡b, cÖ_g GK eQi n‡Z cieZ©x GK eQ‡i †f‡½ hvIqv cigvYyi

msL¨v Kg|

AZGe, cieZ©x GK eQ‡i †f‡½ hvIqv cigvYyi msL¨v c~e©eZ©x

GKeQ‡i †f‡½ hvIqv cigvYyi msL¨vi †ewk n‡e bv|


K Zwor cwievwnZv e„w×i D‡Ï‡k¨ PZz‡h©vRx Aa©cwievnxi g‡a¨ cÄ‡hvRx ev wÎ‡hvRx c`v‡_©i cigvYy wgwk‡q Gi cwievwnZv e„w×i

cÖwµqv‡K †Wvwcs e‡j|

L GKwU P-UvBc I GKwU N-UvBc Aa©-cwievnx‡K we‡kl e¨e ’̄vax‡b mshy³ Ki‡j ms‡hvM c„ô‡K P-N Rvskb e‡j| P-N Rvsk‡bi †h cv‡k P-UvBc AÂj †mLv‡b msL¨v¸iæ evnK †nvj Ges †h cv‡k N-UvBc AÂj †mLv‡b B‡jKUª‡bi AvwaK¨ A‡bK †ewk| hLb P-UvBc AÂj Ges P-UvBc AÂj hy³ nq ZLb N-AÂ‡ji B‡jKUªb¸‡jv P-AÂ‡ji †nvj Øviv AvK…ó n‡q e¨vcb wµqvi gva¨‡g Rvsk‡bi w`‡K Qy‡U hvq| GKBfv‡e P-AÂ‡ji †nvj¸‡jv N-AÂ‡ji B‡jKUªb Øviv AvK…ó n‡q e¨vc‡bi gva¨‡g ms‡hvM ’̄‡ji

w`‡K Qy‡U hvq| P-N Rvskb ’̄‡j B‡jKUªb I †nvj cigvYy wgwjZ n‡q wbi‡cÿ n‡q hvq| G Kvi‡Y P-N Rvskb Wv‡qv‡Wi wW‡cøkb †jqvi mvgwMÖKfv‡e Zwor wbi‡cÿ|

M GLv‡b,

IE = 0.80 mA

Ges IB = 0.05 mA

cÖevn jvf, = ?

Avgiv Rvwb,

= ICIB

wKš‘, IE = IC + IB

IC = IE – IB

= IE – IB

IB

= 0.80 mA – 0.05 mA

0.05 mA

= 15

AZGe, DÏxc‡Ki UªvbwR÷iwUi cÖevn jvf 15| (Ans.)

N GwU GKwU PNP UªvbwR÷i mvaviY cxV weea©K eZ©bx (eZ©bx‡Z cÖ‡qvRbxq ms‡kvab K‡i †`qv n‡jv)|

RL

IE = 0.80 mA; IB = 0.05 mA

G‡Z wbtmiK I cxV BbcyU Ges cxV I msMÖvnK AvDUcyU wn‡m‡e

KvR K‡i| wbtmiK Wv‡qvW‡K m¤§yLx evqvm Kivi Rb¨ wbtmiK I

cx‡Vi g‡a¨ evqvm wefe Vee Ges msMÖvnK Wv‡qvW‡K wegyLx evqvm Kivi Rb¨ msMÖvnK I wbtmi‡Ki g‡a¨ evqvm wefe Vcc cÖ‡qvM Kiv nq| BbcyU evqvm wefe Vbb BbcyU ms‡K‡Zi we Í̄vi wefe †_‡K eo n‡Z n‡e †hb BbcyU ms‡KZ evqvm wef‡ei wecix‡Z wµqv Ki‡jI

Zv m¤§yLx evqvm wewkó nq| BbcyU eZ©bx‡Z †kÖwY mgev‡q hy³ Ri


Teac

hing

bd.co

m



c`v^Æweævb

†iv‡a BbcyU ms‡KZ cÖ‡qvM Kiv nq Ges AvDUcyU eZ©bx‡Z †kÖwY

mgev‡q hy³ D”P fvi †iva RL †_‡K AvDUcyU ms‡KZ MÖnY Kiv nq|

BbcyU ms‡KZ wefe VS Gi cwieZ©‡b wbtmiK I cx‡Vi g‡a¨ wefe Vbe cwieZ©xZ nq, d‡j ie-I cwiewZ©Z nq| Vbe e„w× †c‡j cxV msMÖvnK †iva n«vm cvq d‡j msMÖvnK cÖevn ic e„w× cvq| G‡Z cxV msMÖvnK wefe n«vm cvq Ges fvi †iva RL Gi ỳB cÖv‡šÍi wefe ev AvDUcyU wefe VR e„w× cvq| GKBfv‡e Vbe n«vm †c‡j wbtmiK

msMÖvnK †iva e„w× cvq d‡j msMÖvnK cÖevn ic n«vm cvq| G‡Z wbtmiK msMÖvnK wefe e„w× cvq Ges fvi †iva RL Gi ỳB cÖv‡šÍi wefe ev AvDUcyU wefe VR n«vm cvq| RL Gi †iva Lye †ewk nIqvq ic Gi mvgvb¨ cwieZ©‡b VR Gi cwieZ©b Lye †ewk nq| myZivs, ejv hvq, VS Gi mvgvb¨ cwieZ©‡b VR Gi cwieZ©b Lye †ewk nq| ZvB Bbcy‡U GKwU Kg we¯Ív‡ii ms‡KZ cÖ‡qvM Kiv n‡j AvDUcy‡U GKwU

†ewk we¯Ív‡ii ms‡KZ cvIqv hvq A_©vr ms‡KZwU weewa©Z nq|

4. Kzwgjøv †evW©-2016


K †h cÖwµqv wecixZgyLx n‡q cÖZ¨veZ©b Ki‡Z cv‡i Ges m¤§yLeZ©x I wecixZgyLx cÖwµqvi cÖwZ¯Í‡i Zvc I Kv‡Ri djvdj

mgvb I wecixZ nq, †mB cÖwµqv‡K cÖZ¨veZ©x cÖwµqv e‡j|

L Zvc BwÄb D”P ZvcgvÎvi Drm n‡Z Zvc MÖnY K‡i Kvh© m¤úv`b K‡i Ges Aeën„Z Zvc wb¤œ ZvcgvÎvi ZvcMÖvn‡K ewR©Z

K‡i|

†iwd«‡R‡iUi wb¤œ ZvcgvÎvi Drm †_‡K Zvc MÖnY ev AcmviY K‡i

I D”P ZvcgvÎvi Avav‡i eR©b K‡i| Gi Rb¨ evB‡i †_‡K kw³

mieivn Ki‡Z nq|

M GLv‡b BwÄb KZ…©K M„wnZ Zvc, Q1 = 1260J BwÄb KZ…©K ewR©Z Zvc, Q2 = 930J

Avgiv Rvwb, BwÄ‡bi `ÿZv,

= 1 Q2Q1

= 1 930

1260 = 0.262

= 26.2%

AZGe BwÄ‡bi `ÿZv = 26.2% (Ans.)

N ÔMÕ n‡Z BwÄbwUi `ÿZv, = 26.2%

BwÄbwU cÖZ¨vMvgx n‡j Gi `ÿZv n‡e,

= 1 T2T1

= 1 310420

= 0.262

= 26.2%

GLv‡b,

Dr‡mi ZvcgvÎv, T1 = 147C

= 420K

MÖvn‡Ki ZvcgvÎv, T2 = 37C

= 310K

=

†h‡nZz BwÄbwUi `ÿZv cÖZ¨vMvgx BwÄ‡bi `ÿZvi mgvb ZvB

BwÄbwU cÖZ¨vMvgx|


K Zwor wØ‡giæi †h †Kvb GKwU Pv‡R©i gvb Ges G‡ì gaëZ©x `~i‡Z¡i ¸Ydj‡K wØ-†giæ åvgK e‡j|

L avi‡K kw³ mÂq Ki‡Z n‡j avi‡K wKQy PvR© Rgv Ki‡Z n‡e| G PvR© avi‡K GKev‡i †`qv m¤¢e bq| GKUz GKUz K‡i PvR© Rgv

Ki‡Z nq| KviY GwU wKQy PvR© jvf Kivi ci cieZ©x PvR© cÖ`v‡b

evav †`q| ZvB †Kv‡bv aviK‡K PvwR©Z Ki‡Z wKQy KvR Ki‡Z nq

ev wKQy kw³ e¨q nq| G e¨wqZ kw³ avi‡K Zwor kw³ wn‡m‡e Rgv

_v‡K|

M

5 4

E = 24 Volt

r = 2

5 4

I

GLv‡b, Zwo”PvjK ej, E = 24V

Af¨šÍixY †iva, r = 2

GLv‡b, 4 Ges 5 †kÖwY mgev‡q _vKvq Zv‡ì Zzj¨‡iva, R1 = 4 + 5 = 9

Avevi, 5 Ges 4 †iva †kÖwY mgev‡q _vKvq Zv‡ì Zzj¨‡iva, R2 = 5 + 4 = 9

R1 Ges R2 ci¯úi mgvšÍiv‡j mshy³ _vKvq eZ©bxi Zzj¨‡iva R n‡j,

1R

= 1R1

+ 1R2

= 1

9 +

1

9 =

1 + 1

9 =

2

9

R = 92

= 4.5

Avgiv Rvwb, Zwor cÖevn, I = E

R + r =

24V

4.5 + 2

ev, I = 3.69A

AZGe, eZ©bxi Zwor cÖevn, I = 3.69A (Ans.)

N

R1 = 4

i2

i4 R4 = 4

i1 R2 = 5

i3 G

ig

A B P

Q C D

R3 = 5


Teac

hing

bd.co

m



c`v^Æweævb

P I Q we›`y‡Z wKik‡di cÖ_g m~Îvbymv‡i,

i1 = i3 + ig

i2 = i4 ig

Avevi, APQDA I PBCQP jy‡c wØZxq m~Î cÖ‡qvM K‡i cvB,

R1i1 + igG R3i2 = 0

R2i3 R4i4 igG = 0

ev, 4i1 + igG 5i2 = 0

5i3 4i4 igG = 0

4i1 + 5i3 5i2 4i4 = 0

4i3 + 4ig + 5i3 5i4 + 5ig 4i4 = 0

9i3 + 9ig 9i4 = 0

ig = i4 i3

†h‡nZz R4 R2

†m‡nZz i4 i3

myZivs ig abvZ¥K

A_©vr ig Gi w`K P †_‡K Q Gi w`‡K|


K †Kvb ’̄v‡b GKB mg‡q GKwU Zwor‡ÿÎ I GKwU †PŠ¤̂K‡ÿÎ we`¨gvb _vK‡j †mLv‡b GKwU MwZkxj Avavb †h jwä ej Abyfe

K‡i Zv‡K j‡iÄ ej e‡j|

L †Kvb KzÐjxi ¯̂Kxq Av‡ek ¸YvsK 8H ej‡Z eySvq, †mB KzÐjx‡Z cÖwZ †m‡K‡Û Zwor cÖevn 1A nv‡i cwiewZ©Z n‡j D³

KzÐjx‡Z cÖevn cwieZ©‡bi wecix‡Z 8V Zwor PvjK kw³ Avweó nq|

M GLv‡b, A Zv‡i Zwor cÖevn, i1 = 12A

B Zv‡i Zwor cÖevn, i2 = 15A

ZviØ‡qi gaëZ©x ~̀iZ¡, r = 5 cm = 0.05m

A Zv‡ii cÖwZ GKK ˆ`‡N©¨ †PŠ¤̂K e‡ji gvb, Fl = ?

Avgiv Rvwb,

Fl = 0i1i22r

= 4 107Wb/Am 12A 15A

2 0.05

= 7.2 104 N/m

AZGe, A-Zv‡ii cÖwZ GKK ˆ`‡N©¨ †PŠ¤̂K e‡ji gvb 7.2 104 N/m (Ans.)

N GLv‡b, A-Zv‡i Zwor cÖevn, i1 = 12A

B-Zv‡i Zwor cÖevn, i2 = 15A

ZviØ‡qi gaëZ©x ~̀iZ¡, r = 5cm = 0.05m

A Zvi n‡Z P we›`yi ~̀iZ¡ = B Zvi n‡Z P we›`yi ~̀iZ¡, d = 0.025 m

A Zv‡ii Rb¨ P we›`yi †PŠ¤̂K‡ÿ‡Îi cÖvej¨,

B1 = 0i12d

= 4 107Wb/mA 12A

2 0.025

= 9.6 105 Wb/m2

†d¬wgs Gi Wvbn Í̄ wbqgvbyhvqx, B1 Gi w`K KvMR Z‡ji j¤̂ eivei †fZ‡ii w`‡K|

Avevi,

B Zv‡ii Rb¨ P we› ỳ‡Z †PŠ¤^K‡ÿ‡Îi cÖvej¨,

B2 = 0i12d

= 4 107Wb/Am 15A

2 0.025 m

= 1.2 104 Wb/m2

†d¬wgs Gi Wvbn Í̄ wbqgvbyhvqx B2 Gi w`K KvMR Z‡ji j¤^ eivei evB‡ii w`‡K A_ev B1 Gi wecixZ w`‡K|

myZivs, P we› ỳ‡Z jwä †PŠ¤^K cÖvej¨, B = B2 B1

= 1.2 104 Wb/m2 9.6 105 Wb/m2

= 2.4 105 Wb/m2

B Gi w`K n‡e KvMR Z‡ji mv‡_ j¤^ eivei evB‡ii w`‡K|

Avevi, B Zv‡ii cÖevn wecixZgyyLx Ki‡j †d¬wgs Gi Wvbn Í̄ wbqgvbyhvqx B2 †PŠ¤̂K‡ÿ‡Îi w`K cwiewZ©Z n‡e Ges Zvi w`K n‡e KvMR Z‡ji j¤̂ eivei †fZ‡ii w`K A_©vr B1 Gi w`‡Ki Abyiƒc|

AZGe, P we›`y‡Z jwä cÖvej¨, B = B1 + B2

= 1.2 104 Wb/m2 + 9.6 10–5 Wb/m2

= 2.16 104 Wb/m2 2.4 10–5 Wb/m2

B Gi w`K n‡e KvMR Z‡ji mv‡_ j¤^ eivei wfZ‡ii w`‡K

myZivs, P we› ỳ‡Z †PŠ¤^K‡ÿ‡Îi gvb I w`K DfqB cwiewZ©Z n‡e|


K Av‡jvi iwk¥ GK we›`y †_‡K Ab¨ we›`y‡Z hvevi mgq m¤¢ve¨ mKj c‡_i g‡a¨ †mB c_ AYymiY K‡i †h c‡_ mgq me †_‡K Kg

jv‡M|

L Avgiv Rvwb, GKwU wbw`©ó e‡Y©i Av‡jvi Rb¨ †Kv‡bv gva¨‡gi cÖwZmiYvsK GKwU aªæe msL¨v| wKš‘ wewfbœ e‡Y©i Av‡jvi Rb¨ GB

msL¨v wewfbœ| wewfbœ e‡Y©i Av‡jvi cÖwZmiv¼ wewfbœ nIqvq †hŠwMK

Av‡jv GK gva¨g †_‡K Ab¨ gva¨‡g cÖwZmi‡Yi mgq GKB †Kv‡Y

AvcwZZ n‡jI wewfbœ e‡Y©i cÖwZmiY †KvY wewfbœ nq| d‡j

eY©̧ ‡jv ci¯úi †_‡K Avjv`v n‡q c‡o| wcÖR‡g Av‡jv cÖwZmi‡Yi

†ÿ‡Î ỳB evi f‚wgi w`‡K †eu‡K hvq| ZvB wewfbœ Av‡jvK iwk¥i

Rb¨ AvcZb †KvY GK n‡jI wbM©gb †KvY i2 wfbœ nq| Avgiv Rvwb wcÖR‡gi wePz¨wZ, = (i1 + i2) A| i2 wfbœ nIqvi Kvi‡Y wewfbœ e‡Y©i wePz¨wZ wfbœ nq| G Kvi‡Y mv`v Av‡jv wcÖR‡gi ga¨ w`‡q cÖwZmi‡Yi

mgq we”QzwiZ nq|

M †Ìqv Av‡Q,


Teac

hing

bd.co

m



c`v^Æweævb

Zi½‰`N©¨, = 3800 A = 3800 10–10m

S, S2 = wPoØ‡qi ~̀iZ¡ = d = 0.5mm = 0.5 10–3 m

D = wPo n‡Z c ©̀vi ~̀iZ¡ = 1m, n = 5

cÂg AÜKvi †Wvivi ~̀iZ¡, xn = ?

Avgiv Rvwb, n Zg AÜKvi †Wvivi ~̀iZ¡, xn = (2n 1) D2d

= (2 5 1) 3800 1010m 1m

2 0.5 103m

= 3.42 103m

AZGe, 5g AÜKvi †Wvivi ~̀iZ¡ = 3.42 103 m

= 3.42 mm

N Avgiv Rvwb,

= S2P S1P = xdD

= 6.46 103m 0.5 103m

1m

= 3.23 106m

GLv‡b,

x = 6.46 103m

d = 0.5 103m

D = 1m

= 3800 1010m

e¨vwZPv‡ii kZ© †_‡K Rvwb,

g‡b Kwi,

c_ cv_©K¨ =

= n

n = S2P S1P

= 3.23 106m

3800 1610m

= 172

= 17 12

n c~Y© msL¨v n‡j MVb g~jK Avi A‡a©‡Ki †e‡Rvo ¸wYZK n‡j aŸsmvZ¥K e¨vwZPvi n‡e|

GLv‡b, n, 12

Gi †e‡Rvo ¸wYZK

myZivs P we› ỳ‡Z aŸsmvZ¥K e¨vwZPvi m„wó n‡e|


K mvaviY cxV web¨v‡mi †ÿ‡Î †Kv‡bv UªvbwR÷‡ii wbtmiK

cÖev‡ni cwieZ©‡bi mv‡c‡ÿ msMÖvnK cÖev‡ni cwieZ©‡bi nvi icie

†K cÖevn weea©b ¸YK e‡j|

L Aa© cwievnx‡Z †hvRb e¨vÛ c~Y© Ges cwienb e¨v‡Û †Kv‡bv B‡j±ªb _v‡K bv, wKš‘ †hvRb e¨vÛ I cwienb e¨v‡Ûi g‡a¨ kw³

e¨eavb Lye Kg _v‡K| mvaviY ZvcgvÎvq †hvRb e¨v‡Ûi wKQy

B‡jKUªb †hvRbx eÜb †f‡½ cwienb e¨v‡Û P‡j hvq d‡j Giv

mvgvb¨ cwievnx nq| ZvcgvÎv e„w×i mv‡_ mv‡_ GKwU wbw`©ó

ZvcgvÎv ch©šÍ †hvRb e¨v‡Ûi wKQy B‡jKUªb Zvcxq kw³ MÖnY K‡i

cwienb e¨v‡Û P‡j Av‡m A_©vr cwienb e¨v‡Û B‡jKUªb msL¨v e„w×

cvq ZvB ZvcgvÎv e„w×‡Z Aa© cwievnxi cwievwnZv e„w× cvq Ges

†iva n«vm cvq|

M GLv‡b, wbe„wË wefe, V0 = 2V

B‡jKUª‡bi fi, m = 9.1 1031 kg

B‡jKUª‡bi m‡e©v”P †eM, vmax = ?

Avgiv Rvwb, 12

m vma2

x = eV0

ev, vmax2 =

eV0 2m

= 1.6 1019C 2v 2

9.1 1031kg

ev, vma2

x = 7.0329 1011 m2/s2

vmax = 8.386 105 m/s

AZGe, d‡UvB‡jKUª‡bi m‡e©v”P MwZ‡eM = 8.386 105 m/s (Ans.)

N GLv‡b,

AvcwZZ †dvU‡bi Zi½‰`N©¨, = 4 107m

wbe„wË wefe, V0 = 2V

cø̈ v‡¼i aªæeK, h = 6.63 1034Js

Av‡jvi †eM, c = 3 108 m/s

jvj Av‡jvi Zi½‰`N©¨, R = 6.8 107m

Avgiv Rvwb,

AvcwZZ †dvU‡bi kw³, E = hc

= (6.63 1034Js) 3 108m/s

4 107m

= 4.973 1019J

GLb, Kvh©v‡cÿK, W = E eV0

= 4.973 1019J (1.6 1019C 2V)

= 1.773 1019J

jvj e‡Y©i †dvU‡bi kw³, ER = hc

= (6.63 1034 Js) 3 108 m/s

6.8 107m

= 2.925 1019J

†h‡nZz, ER W

myZivs, jvj Av‡jv e¨envi Ki‡j d‡UvZwor cÖevn NU‡e|


Teac

hing

bd.co

m



c`v^Æweævb


K Zwor Dr‡mi abvZ¥K I FYvZ¥K cÖvšÍ‡K h_vµ‡g Rvsk‡bi P I n AÂ‡ji mv‡_ hy³ Kiv n‡j Rsk‡bi wefe cÖvPxi n«vm cvq Ges cÖevn mnR nq e‡j G ai‡bi ms‡hvM‡K m¤§yLx †SuvK e‡j|

L Awbqwš¿Z wbDwK¬qvi wewµqvi cÖwZ P‡µ cigvYyi fvO‡bi mv‡_ mv‡_ wewµqv msNUbKvix wbDUªb gy³ nq Ges cÖwZwU gy³ wbDUª‡bi

AvNv‡Z cieZx© cigvYywUI fv‡O Ges 3wU K‡i wbDUªb gy³ nq| Gfv‡e cÖwZP‡µ wbDUª‡bi msL¨v e„w× cvq Ges kw³ Drcv`‡bi

nviI evo‡Z _v‡K| AZGe, ejv hvq †h wdkb GKwU ¯̂ZtùzZ©

wewµqv| GKevi G wewµqv ïiæ K‡i w`‡j Zv Awbqwš¿Z fv‡e Pj‡Z

_v‡K Ges cÖPzi kw³ Drcbœ K‡i| ZvB Awbqwš¿Z wbDwK¬qvi

wewµqvq AwZwi³ kw³i cÖ‡qvRb nq bv|

M GLv‡b, mvaviY f‚wg n-p-n eZ©bx‡Z,

BbcyU cÖevn, IE = 25 mA

AvDUcyU cÖevn, IC = 20 mA

f‚wg cÖevn, IB = ?

Avgiv Rvwb, IE = IB + IC

IB = IE IC

= 25 mA 20 mA = 5 mA (Ans.)

N DÏxc‡K ivBmv cÖ_‡g GKwU †÷c-WvDb UªvÝdg©vi eënvi K‡i 220V Gwm‡K 12V Gwm‡Z bvwg‡q Av‡b| UªvÝdg©viwUi g~L¨ I †MŠY KzÐjxi †fv‡ëR h_vµ‡g EP = 220V I Es = 12V n‡j Ges g~L¨ I †MŠY KzÐjxi cvKmsL¨v h_vµ‡g np I ns n‡j,

EpEs

= npns

ev, 220V12V

= npns

12V

220V

ev, npns

= 553

AZGe, ivBmv cÖ_‡g (55 t 3) Abycv‡Z GKwU †÷cWvDb UªvÝdg©v‡ii mvnv‡h¨ 12V G bvwg‡q G‡b‡Q|

wØZxq †ÿ‡Î ivBmv GKwU c~Y©Zi½ †iKwUdvqvi eënvi K‡i 12V Gwm‡K 12V wWwm‡Z cwiewZ©Z Kivq wUwfwU Pj‡Z Avi¤¢ KiwQj| wb‡P c~Y©Zi½ †iKwUdvqvi eZ©bxi wPÎ †`qv n‡jv|

12 V AC O

+

A D1

P

B

RL

mgq

D2

D1 D2 D1 D2

c~Y©Zi½ †iKwUdvqviwU‡Z Gwm AšÍM©vgx Dr‡mi ỳyB PµB Kv‡R

jvMv‡bv nq| GRb¨ eZ©bx‡Z `ywU Wv‡qvW D1 I D2 eënvi Kiv nq| Wv‡qvW ỳwU‡K UªvÝdg©viwUi †MŠYKzÐjxi AB As‡ki mv‡_ ms‡hvM †Ìqv n‡q‡Q| Wv‡qvW D1 Gwm AšÍM©vgx Dr‡mi †MŠbKzÐjxi OA As‡k AvMZ Dc‡ii Aa©Pµ‡K †iKwUdvB K‡i Ges Wv‡qvW D2 †MŠYKzÐjxi OB As‡k AvMZ wb‡Pi Aa©Pµ‡K †iKwUdvB K‡i| Gwm AšÍM©vgxi cÖ_g abvZ¥K Aa©P‡µi Rb¨ A abvZ¥K nq| d‡j Wv‡qvW D1 m¤§~Lx †SuvK cÖvß nIqvq Gi ga¨ w`‡q Zwor cÖevwnZ nq| wKš‘ D2 Wv‡qvW wegyLx †SuvK cÖvß nIqvq Gi ga¨ w`‡q Zwor cÖevwnZ n‡Z cvv‡i bv| G‡ÿ‡Î O A D1 P O c‡_ Zwor cÖevwnZ nq|

AšÍM©vgxi wØZxq Aa©P‡µi Rb¨ A cÖvšÍ FbvZ¥K Ges B cÖvšÍ abvZ¥K nq| d‡j Wv‡qvW D2 m¤§yLx †SvK cÖvß nIqvq Gi ga¨ w`‡q Zwor cÖevwnZ nq wKš‘ D1 wegyLx †SuvK cÖvß nIqvi Gi g‡a¨ w`‡q †Kv‡bv Zwor cÖevwnZ nq bv| G‡ÿ‡Î O B D2 P O c‡_ Zwor cÖevwnZ nq| eZ©bxi R2 †iv‡ai ’̄v‡b wUwfwU‡K ’̄vcb Ki‡j Dfq †ÿ‡ÎB wUwfi ga¨ w`‡q GKB w`‡K Zwor cÖevwnZ nq A_©vr wUwfwUi ga¨ w`‡q

GKgyLx Zwor ev wWwm cÖevn cÖevwnZ nq|

5. PÆMÖvg †evW©-2016


K †Kvb wm‡÷‡gi AšÍf‚©³ c`v_©mg~‡ni Af¨šÍi ’̄ AYy-cigvYy I †gŠwjK KYvmg~‡ni ̂ iwLK MwZ, ̄ ú›`b MwZ I N~Y©bMwZ Ges Zv‡ì

g‡a¨Kvi e‡ji Kvi‡Y D™¢‚Z kw³ hv Kvh© m¤úv`b Ki‡Z cv‡i, Ab¨

kw³‡K iƒcvšÍwiZ n‡Z cv‡i Ges hvi gvb I cÖK…wZ c`v‡_©i Zvcxq

Ae¯’v, `kv BZ¨vw` wba©viY K‡i, ZvB Af¨šÍixY kw³|

L cÖK…wZ‡Z mewKQyB mvg¨ve ’̄v †c‡Z †Póv K‡i| GKwU wm‡÷g hZB mvg¨ve ’̄vi w`‡K GwM‡q hvq ZZB Zvi KvQ †_‡K KvR cvIqvi

m¤¢vebv K‡g hvq, mvg¨ve ’̄vq †cŠQ‡j wm‡÷g †_‡K Avi KvRB

cvIqv hvq bv| wm‡÷‡gi GB kw³ iƒcvšÍ‡ii AÿgZvB n‡”Q

G›Uªwc| GK ev GKvwaK wm‡÷g hZ mvg¨ve ’̄vi w`‡K GwM‡q hvq

Zv‡ì G›UªwcI ZZ evo‡Z _v‡K| mvg¨ve ’̄vq G›Uªwc me‡P‡q †ewk

nq| †h‡nZz cÖK…wZ‡Z mewKQyB mvg¨ve ’̄v †c‡Z hvq, ZvB ejv hvq

RM‡Z G›Uªwc µgvMZ evo‡Q| RM‡Z G›Uªwc hLb m‡e©v‡”P †cŠuQv‡e

ZLb me wKQyi ZvcgvÎv GK n‡q hv‡e| d‡j Zvckw³‡K Avi

hvwš¿K kw³‡Z iƒcvšÍwiZ Kiv hv‡e bv| GB Ae ’̄v‡K RM‡Zi

Z_vKw_Z Zvcxq g„Zz¨ bv‡g AwfwnZ Kiv n‡q‡Q|

M DÏxcK n‡Z cvB

Dr‡mi ZvcgvÎv, T1 = 900C = 1173K

MÖvn‡Ki ZvcgvÎv, T2 = 30C = 303K

`ÿZv, = ?

Avgiv Rvwb,

=

T1 – T2

T1 100%

=

1173 – 303

1173 100%

= 74.168% (Ans.)

N BwÄbwUi Zvcxq `ÿZv,

=

1 –

T2T1

100%

= 100% n‡j,


Teac

hing

bd.co

m



c`v^Æweævb

1 –

T2T1

100% = 100%

ev, 1 – T2T1

= 1

ev, T2T1

= 0;

wKš‘ Zv ZLbB m¤¢e hw` T2 = OK A_ev T1 = nq|

myZivs Zvc BwÄ‡bi Kg©`ÿZv 100% †c‡Z n‡j Dr‡mi ZvcgvÎv Amxg ev wms‡¼i ZvcgvÎv cig k~b¨ n‡Z n‡e|


K evwn¨K Zwor †ÿ‡Îi cÖfv‡e †h mKj gva¨‡gi cÖwZwU cigvYy GK GKwU Zwor wØ‡giæ‡Z cwiYZ nq Zv‡K civwe ỳ¨r ev

WvBB‡jKwUªK e‡j|

L AwaK cwigvY cÖevn wM‡q hv‡Z M¨vjfv‡bvwgUvi‡K bó Ki‡Z bv cv‡i Zvi Rb¨ M¨vjfv‡bvwgUv‡ii mv‡_ mgvšÍivj mgev‡q GKwU

Aí gv‡bi †iva kv›U wn‡m‡e mshy³ Kiv nq| Gi d‡j g~j cÖevn

`yÕfv‡M wef³ n‡q hvq Ges kv‡›Ui †iva Kg nIqvq †ewk cwigvY

cÖevn Gi †fZi w`‡q cÖevwnZ nq Ges Aí cwigvY cÖevn

M¨vjfv‡bvwgUv‡ii ga¨ w`‡q cÖevwnZ nq| G‡Z M¨vjfv‡bvwgUvi bó

nIqvi nvZ †_‡K iÿv cvq|

M DÏxcK n‡Z cvB;

aviKZ¡, C1 = C2 = C3 = 180F = 180 10–6F

wefe cv_©K¨, V = 3V

Zzj¨ aviKZ¡, Cs = ?

mwÂZ wefe kw³, U = ?

Avgiv Rvwb, 1Cs

= 1C1

+ 1C2

+ 1C3

ev, 1Cs

= 1

180 10–6 +

1

180 10–6 +

1

180 10–6

Cs = 6 10–5 F

Avevi, U = 12 CsV

2 = 12 6 10

–5 (3)2

= 2.7 10–4 J (Ans.)

N †ikgv †Kvl wZbwU‡K †kÖYx mgev‡q hy³ K‡i Zwo”PvjK kw³

E = 3 + 3 + 3 = 9 V a‡i wnmve K‡i, Zwor cÖevn I wbY©q K‡i,

I = ER =

950 = 0.18 A

†ikgvi fzj n‡jv, †m Zwor †Kvl¸‡jv‡K mgvšÍiv‡j hy³ bv K‡i

†kÖYx mgev‡q hy³ K‡i Zwo”PvjK kw³ 9 V a‡iwQj|

wkÿ‡Ki wb‡ ©̀kbv †gvZv‡eK mwVK eZ©bxwU n‡e wb¤œiƒc :

Avgiv Rvwb, mgvb Zwo”PvjK e‡ji KZK¸‡jv †Kv‡li mgvšÍivj

mgev‡q Zwo”PvjK ej GKwU †Kv‡li Zwo”PvjK e‡ji mgvb nq|

EP = 3V

R = 50

IP = EPR =

350

= 0.06 A (Ans.)


K †Kvb cvZ AvK…wZi Zworevnx cwievnx‡K †PŠ¤^K †ÿ‡Îi mv‡_ j¤^fv‡e ̄ ’vcb Kiv n‡j ZworcÖevn I †PŠ¤̂K †ÿÎ Df‡qi mv‡_ j¤̂

eivei ỳB wecixZ c„‡ô GKwU wefe cv_©K¨ m„wó nIqvi NUbvB nj

wµqv|

L 220V D.C Øviv hw` †Kv‡bv e¨w³ ˆe`y¨wZK kK cvb Zvn‡j wZwb m‡e©v”P 220V ØvivB kK cvb| wKš‘ †Kv‡bv e¨w³ hw` 220V A.C Øviv

kK cvb Z‡e wZwb m‡e©v”P 2 200V = 311V Øviv kK cv‡eb| G Kvi‡Y DC 220V A‡cÿv AC 220V †ewk wec¾bK|

M DÏxcK n‡Z cvB,

w`K cwieZx© cÖev‡ni kxl©gvb, Io = 2A

mgq, t = 7.5 T

4

Zwor cÖevn I = ?

Avgiv Rvwb,

I = Io sin t

= 2 sin

2

T 7.5 T

4

= 2 sin

180 7.5

2

= 2 sin 675

= – 1.414 A

Zwor cÖev‡ni gvb, I = 1.414 A (Ans.)

N DÏxcK n‡Z cvB,

†MŠY KzÐjxi †iva, Rs = 17.5

†MŠY KzÐjxi ÿgZv, Ps = 140 W

R = 50

3V

3V

3V


Teac

hing

bd.co

m



c`v^Æweævb

gyL¨ KzÐjxi cÖev‡ni kxl©gvb, Io = 2 A

Avgiv Rvwb,

IP = 0.707 Io

= 0.707 2

= 1.414 A

Avevi, PS = I2

S RS

ev, IS = PSRS

= 14017.5 = 2.828 A

Avevi,

NPNS

= ISIP

ev, NPNS

= 2.8281.414

NPNS

= 2

AZGe, UªvÝdg©viwUi †MŠY KzÐjx‡Z 140 W ÿgZv †c‡Z n‡j gyL¨

KzÐjx I †MŠY KzÐjxi cvKmsL¨vi AbycvZ 2 : 1 Ki‡Z n‡e|


K cvkvcvwk Aew¯’Z ỳwU mymsMZ Drm †_‡K wbM©Z mgvb K¤úv¼ I we Í̄v‡ii ỳwU Av‡jvK Zi‡½i DcwicvZ‡bi d‡j ch©vqµ‡g

D¾¡j I AÜKvi Ae ’̄vi m„wó nIqv‡K Av‡jvi e¨wZPvi e‡j|

L Kv‡Pi msKU †KvY 42 ej‡Z eySvq, k~b¨ gva¨g (ev evqy) I Kv‡Pi we‡f`Z‡j KvP †_‡K 42 †Kv‡Y AvcwZZ iwk¥ we‡f`Zj †Nu‡l cÖwZmwiZ n‡e| AvcZb †Kv‡Yi gvb 42 Gi †P‡q †ewk n‡j Av‡jvK iwk¥ cÖwZmwiZ bv n‡q KuvP gva¨‡g c~Y© Af¨šÍixY fv‡e

cÖwZdwjZ n‡e|

M DÏxcK n‡Z cvB,

jÿ¨ e¯‘i ~̀iZ¡, u = 15 cm

jÿ¨ e¯‘i ˆ`N©¨, = 5 cm

we‡¤î ˆ`N©¨, = 10 cm

Avgiv Rvwb, |M| =

=

10 cm5 cm = 2.

Avevi, |M| = vu

ev, 2 = vu

v = 2u

†h‡nZz we¤^wU Aev Í̄e,

v = – 2u = –2 15 cm = – 30 cm

Avgiv Rvwb, 1f =

1u +

1v =

115 –

130 =

130

f = 30 cm = 0.3 m

Avevi, P = 1f =

10.3 = 3.33 D (Ans.)

N †jÝwU‡K mij AYyexÿY hš¿ wn‡m‡e eënvi K‡i ̄ úó cÖwZwew¤^ cvIqvi Rb¨ Aev Í̄e we¤^wU †Pv‡Li ̄ úó `k©‡bi wbKU we› ỳ‡Z MwVZ

n‡Z n‡e|

A_©vr G‡ÿ‡Î, we‡¤̂i ~̀iZ¡, v = – D = – 25 cm

ÔMÕ Ask n‡Z cvB, †jÝwUi †dvKvm ~̀iZ¡, f = 30 cm

e¯‘ n‡Z †j‡Ýi ~̀iZ¡ u n‡j,

1u +

1v =

1f

ev, 1u =

1f –

1v =

130 +

125 =

11150

u = 13.64 cm

AZGe, †jÝwU‡K mij AbyexÿY hš¿ wn‡m‡e eënvi K‡i ¯úó

cÖwZwe¤^ †`L‡Z n‡j e¯‘ †_‡K †jÝwU‡K 13.64 cm ̀ ~‡i ̄ ’vcb Ki‡Z

n‡e|

5bs cÖ‡kœi DËi

K ch©‡eÿ‡Ki mv‡c‡ÿ MwZkxj _vKvi Kvi‡Y †Kv‡bv `‡Ði ˆ`N©¨ msKzwPZ g‡b nIqvi NUbv‡K ˆ`N©¨ ms‡KvPb e‡j|

L B‡jKUª‡bi Zvcxq wbtmiY I d‡UvZwor wbtmi‡Yi g‡a¨ ỳwU cv_©K¨ wb‡P D‡jøL Kiv n‡jv :

(i) d‡UvZwor wbtmi‡Yi Rb¨ h‡_vchy³ K¤úvsK wewkó Av‡jvK iwk¥i cÖ‡qvRb| B‡jKUª‡bi Zvcxq wbtmi‡Yi †ÿ‡Î wfbœ avZzi

`yBwU Zv‡ii ms‡hvMØ‡q wfbœ ZvcgvÎvi cv_©K¨ _v‡K|

(ii) d‡UvZwor wbtmiY GKwU ZvrÿwYK NUbv| B‡jKUª‡bi Zvcxq wbtmiY GKwU mgq mv‡cÿ NUbv|

M DÏxcK n‡Z cvB,

B †gŠ‡ji Aa©vqy, T12

= 9 days

B †gŠ‡ji Mo Avqy, = ?

Avgiv Rvwb,

T12

= 0.693

ev, =

T12

0.693 = 9

0.693 = 12.987 days (Ans.)

N GLv‡b,


Teac

hing

bd.co

m



c`v^Æweævb

A †gŠ‡ji Aa©vqy, T12

= 6d

A †gŠ‡ji Aeÿq aªæeK, A = 0.693

T12

= 0.693

6d = 0.11155d1

Avevi,

B †gŠ‡ji Aa©vqy, T12

= 9d

B †gŠ‡ji Aeÿq aªæeK, B = 0.693

T12

= 0.693

9d = 0.077d1

awi, †gŠjØ‡qi cÖv_wgK cigvYyi msL¨v N0 Ges Aewkó cigvYyi msL¨v N| AZGe, N = N0 Gi 40%| †gŠjØ‡qi ÿq n‡Z cÖ‡qvRbxq mgq, tA I tB n‡j,

NN0

= eAtA

ev, 0.40 = e0.1155 tA

tA = 7.93d

NN0

= eBtB

ev, 0.44 = e0.077 tB

tB = 11.9d

†h‡nZz tB > tA, †m‡nZz DÏxc‡Ki †gŠjØ‡qi 56% ÿq n‡Z B †gŠ‡ji AwaK mgq jvM‡e|

DËi: B Gi mgq †ewk jvM‡e|


K gy³fv‡e †h‡Kvb Z‡j N~Y©‡b mÿg †Kvb Pz¤^K kjvKvi Aÿ †Kvb wbw`©ó ¯’v‡b Abyf‚wgK Z‡ji mv‡_ †h †Kv‡bv Drcbœ K‡i, ZvB

webwZ|

L †n·v‡Wwm‡gj c×wZ‡Z †gvU we‡Ui msL¨v 16 wU| A_©vr 24 | A_©vr †n·v‡Wwm‡gj c×wZi e„nËg weU (D) †K cÖKvk Ki‡Z evBbvix c×wZi 4 wU we‡Ui cÖ‡qvRb| GRb¨ evBbvix cÖwZ 4wU weU GK‡Î †n·v‡Wwm‡g‡ji GKwU we‡Ui mgZzj¨ gvb cvIqv hvq|

GRb¨ †n·v‡Wwm‡gj c×wZ‡Z m‡e©v”P 4 weU cvIqv hvq|

M DÏxc‡Ki eZ©bxwU bi-†MU (NOR-gate) Gi| GB †M‡Ui wPÎwU wb¤œiƒc :

(NOR-gate) Gi mZ¨K mviYx

BbcyU AvDUcyU

A B C = A + B

0 0 1

1 0 0

0 1 0

1 1 0

N DÏxc‡Ki eZ©bxi AvDUcy‡Ui mv‡_ GKwU bU †MU (NOT-gate) hy³ Ki‡j Ggb GKwU †MU cvIqv hv‡e hvi †h †Kvb GKwU BbcyU

jwRK mZ¨ n‡j AvDUcyU jwRK mZ¨ n‡e| GB ai‡bi †MU‡K Ai

(OR) †MU e‡j|

A_©vr, NOR gate + NOT gate = OR gate.

wb‡P Gi cÖZxK I Kvh©µg mZ¨K mviYxi gva¨‡g †`Lv‡bv n‡jv :

mZ¨K mviwY

BbcyU AvDUcyU

A B C =

A + B

0 0 0

0 1 1

1 0 1

1 1 1

6. wm‡jU †evW©-2016


K †Kvb cvZ AvKv‡ii Zworevnx cwievnK‡K †PŠ¤̂K‡ÿ‡Î j¤̂fv‡e ¯’vcb Ki‡j Zwor cÖevn I †PŠ¤̂K †ÿÎ Df‡qi mv‡_ j¤̂ eivei

A_©vr cv‡Zi cÖ¯’ eivei GKwU wefe cv_©‡K¨i m„wó nq Z_v †fv‡ëR

Drcbœ nq| GB NUbv‡K nj wµqv e‡j|

C = A + B A B

wPÎ: NOR gate

A B

A + B A + B


Teac

hing

bd.co

m



c`v^Æweævb

L UªvÝdg©v‡ii gyL¨ KzÐjx‡Z hw` DC †fv‡ëR cÖ‡qvR Kiv nq Zvn‡j †Kv‡ii ga¨ w`‡q aªæegv‡bi †PŠ¤̂Kd¬v· AwZµg Ki‡e|

ZLb ddt = 0 nIqvq Zvwor †PŠ¤̂K Av‡ek msµvšÍ d¨viv‡Wi wØZxq

m~Îvbymv‡i

= – N

ddt †MŠY KzÐjx‡Z Avweó ZworPvjK e‡ji gvb

k~b¨| G Kvi‡Y UªvÝdg©vi Øviv DC †Wv‡ë‡Ri gvb cwieZ©b Kiv hvq

bv|

M GLv‡b,

AC Dr‡mi we Í̄vi Z_v kxl©gvb, o = 220V

Avgiv Rvwb, = 2f = 2 50 = 100

Avevi †h †Kvb mgq t G kxl©gvb o Ges †KŠwYK †eM n‡j,

= o sin t

= 220 sin 100t

A_©vr DÏxc‡Ki cwieZ©x Zwo”PvjK e‡ji mgxKiY,

= 220 sin 100t (Ans.)

N GLv‡b,

AC Dr‡mi we Í̄vi, o = 220V

wnUv‡ii †iva, R = 1000

DC Dr‡mi wefe, Z_v Kvh©Ki †fv‡ëR, V = 220V

AC Dr‡mi †ÿ‡Î,

Kvh©Ki †fv‡ëR, rms = o

2 =

220

2 = 155.56V

Gwm Dr‡mi mv‡_ hy³ Ki‡j wnUv‡ii ÿgZv,

P = 2rms

R = (155.56)2

1000 = 24.2 watt

Avevi, wW. wm Dr‡mi mv‡_ hy³ Ki‡j ÿgZv,

P = V2

R = (220)2

1000 = 48.4 watt

†h‡nZz wW. wm Dr‡mi †ÿ‡Î wnUv‡ii ÿgZv †ewk, AZGe wW. wm

Dr‡mi ms‡hv‡M wnUviwU †ewk Kvh©Ki|


K †Kv‡bv †ZRw¯µq bgybvq cigvYy msL¨v †h mg‡q †f‡½ A‡a©‡K cwiYZ nq †m mgq‡K H †ZRw¯µq †gŠ‡ji Aa©vqy e‡j|

L X-ray †Kvb AvwnZ KYv bq| GwU GKwU Zwor Pz¤^Kxq Zi½| †h‡nZz X-ray †Kvb PvwR©Z KYvi cÖevn bq, ZvB X-ray †PŠ¤̂K †ÿÎ I Zwor‡ÿÎ Øviv wePz¨Z nq bv|

M GLv‡b,

1g K‡ÿi e¨vmva©, r1 = 0.53A

Kÿc_, n = 3,

n Zg Kÿc‡_i e¨mva©, rn = ?

Avgiv Rvwb,

rn = n2.r1 = 32 0.53A = 4.77 A

A_©vr 3q Kÿc‡_i e¨vmva© = 4.77 A (Ans.)

N AvcwZZ †dvU‡bi kw³,

E = hf

= 6.63 10–34Js 2.46 1015 Hz

= 1.631 10–18J = 10.2 eV

nvB‡Wªv‡R‡bi cÖ_g Kÿc‡_ B‡jKUª‡bi kw³, E1 = – 13.6 eV

wØZxq Kÿc‡_ B‡jKUª‡bi kw³, E2 = – 13.6

22 eV

= – 3.4 eV

myZivs cÖ_g Kÿc_ †_‡K 2q Kÿc‡_ B‡jKUªb †h‡Z cÖ‡qvRbxq

kw³,

E = E2 – E1

= – 3.4 eV – (– 13.6 eV)

= 10.2 eV

AvcwZZ †dvU‡bi kw³ = B‡jKUªbwU cÖ_g Kÿc_ †_‡K wØZxq Kÿc‡_ †h‡Z cÖ‡qvRbxq kw³

myZivs B‡jKUªbwU wØZxq Kÿc‡_ Mgb Ki‡e|


K †cÖvUb I wbDUªb¸‡jv‡K wbDwK¬qv‡m GK‡Î †e‡a ivL‡Z †h kw³i cÖ‡qvRb Zv‡K wbDwK¬qv‡mi eÜb kw³ e‡j|

L m~h© K…ò wee‡i cwiYZ n‡j Gi AvKvi AZ¨šÍ †QvU n‡e wKš‘ f‡ii †Kvbiƒc cwieZ©b n‡e bv Ges m~‡h©i fi‡K›`ª †_‡K c„w_exi

`~i‡Z¡i †Kv‡bv cwieZ©b n‡e bv| G‡Z m~h© I c„w_exi AvKl©Y e‡ji

I †Kv‡bv cwieZ©b n‡e bv| d‡j c„w_ex m~‡h©i Pviw`‡K Nyi‡Z

_vK‡e|

M GLv‡b, avZe `‡Ûi,

w¯’wZkxj ˆ`N©̈ , Lo = 1m

†eM, v = 0.9c

MwZkxj ˆ`N©̈ , L= ?

Avgiv Rvwb,

L = Lo 1 – v2

c2

= 1 1 –

0.9c

c

2


Teac

hing

bd.co

m



c`v^Æweævb

= 1 1 – 0.81

= 0.435m

MwZkxj KvVv‡gv‡Z avZe e ‘̄wUi ˆ`N©̈ = 0.435m (Ans.)

N GLv‡b, †eM, v = 0.9c

w¯’wZkxj ˆ`N©̈ , Lo = 1m

MwZkxj ˆ`N©̈ , L = 0.435m [M †_‡K]

w¯’wZkxj Ae¯’vi NbZ¡, o = 19.3 103 kgm–3

MwZkxj Ae ’̄vq NbZ¡, = ?

†h‡nZz `ÛwU‡K cvebx ˆ`N©¨ eivei MwZkxj K‡ib AZGe ˆ`N©¨

eiveiB ïay ms‡KvPb n‡e|

awi, `‡Ûi cÖ¯’‡”Q‡ì †ÿÎdj = A

Avgiv Rvwb, m = mo

1 – v2

c2

wKš‘ m = V

V = oVo

1 – v2

c2

ev, AL = oALo

1 – v2

c2

ev, L = oLo

1 – v2

c2

ev, = 19.3 103 1

0.435 1 –

0.9c

c

2

= 101.78 103 kgm–3

A_©vr, > o cvebx e ‘̄wUi NbZ¡ nvmvb mv‡ne A‡cÿv †ewk cv‡e|


K †h †Kvb ỳwU Avav‡bi g‡a¨ wbw`©ó `~i‡Z¡ k~b¨¯’v‡b wµqvkxj ej Ges H ỳB Avav‡bi g‡a¨ GKB ~̀i‡Z¡ Ab¨ †Kvb gva¨‡g wµqvkxj

e‡ji AbycvZ‡K H gva¨‡gi civ ê`y¨wZK aªæeK e‡j|

L Zwor cÖev‡ni mgq Zwor e‡ji cÖfv‡e Gi wfZ‡ii gy³ B‡jKUªb¸‡jvi †eM e„w× cvq Avevi cwievnxi cigvYyi mv‡_

av°vRwbZ evavi d‡j †eM n«vm cvq| G evavB cwievwni †iva|

ZvcgvÎv e„w×‡Z AYy¸‡jvi K¤úb e„w× cvq, d‡j Gi ga¨ w`‡q

cÖevwnZ B‡jKUª‡bi msNl© msL¨v e„w× cvq, ZvB ZvcgvÎv e„w×‡Z

cwievwni †iva e„w× cvq|

M GLv‡b, Awfj‡ÿï †dvKvm ~̀iZ¡, fo = 0.02m

Awf‡b‡Îi †dvKvm ~̀iZ¡, fe = 0.07m

Awfj‡ÿï e ‘̄i ~̀iZ¡, uo = 0.023m

weea©b, M = ?

Avgiv Rvwb,

1vo

+ 1uo

= 1fo

ev, 1vo

= 1fo

– 1uo

ev, 1vo

= 1

0.02m – 1

0.023m

ev, vo = 0.153m

Avevi, weea©b,

M = – vouo

1 +

Dfe

[D = 0.25m †h‡nZz †Mvjv‡ci †PvL

ÎæwUnxb Ges P‚ovšÍ we¤^ Aev Í̄e]

= – 0.153m 0.023m

1 +

0.25m0.07m = – 30.4

A_©vr †Mvjvc 30.4 ¸Y weewa©Z we¤^ †`L‡Z cv‡e| (Ans.)

N ÔMÕ †_‡K,

Awfj‡ÿï we‡¤î ~̀iZ¡, vo = 0.153m

Awf‡b‡Îi †dvKvm ~̀iZ¡, fe = 0.07m

†Mvjv‡ci Rb¨,

Awf‡b‡Îi we‡¤̂i ~̀iZ¡, ve = – 0.25m

Awf‡b‡Îi e ‘̄i ~̀iZ¡, ue = ?

h‡š¿i ˆ`N©̈ , L = ?

Avgiv Rvwb, 1ve

+ 1ue

= 1fe

ev, 1ue

= 1fe

– 1ve

ev, 1ue

= 1

0.07m + 1

0.25m

ev, ue = 0.054 m

h‡š¿i ˆ`N©¨, L = vo + ue = 0.153 m + 0.054m = 0.207m

AvRv‡ì Rb¨,

Awf‡b‡Îi we‡¤̂i ~̀iZ¡, ve = – 0.4m


Teac

hing

bd.co

m



c`v^Æweævb

1ve

+ 1ue

= 1fe

ev, 1ue

= 1fe

– 1ve

= 1

0.07m – 1

– 0.4m

ev, 1ue

= 1

0.07m + 1

0.4m

ue = 0.059m

h‡š¿i ˆ`N©¨, L = vo + ue = 0.153m + 0.059m = 0.212m

A_©vr ø̄vBW ch©‡eÿ‡Y Df‡qi †ÿ‡Î h‡š¿i ˆ`N©¨ GKB wQj bv|


K †Kvb GKwU KzÛjx‡Z Zwor cÖevn cwieZ©b Ki‡j wbKUeZ©x Ab¨ GKwU KzÛjx‡Z †h Zvwor †PŠ¤̂K Av‡ek m„wó nq Zv‡K cvi¯úwiK

Av‡ek e‡j|

L †Kvb cwievn‡Ki cwievnxZv 0.2 wm‡gÝ ej‡Z †evSvq †h, H cwievn‡Ki ỳB cÖv‡šÍi wefe cv_©K¨ 1V n‡j Zvi ga¨ w`‡q 0.2A

Zwor cÖevn P‡j| wm‡gÝ cwievnxZvi GKK hv †iv‡ai GKK Ing

Gi wecixZ ivwk|

M GLv‡b, Zwor cÖevn, I = 4A

Zvi †_‡K ~̀iZ¡, a = 0.16m

o = 4 10–7 TmA–1

H we›`y‡Z †PŠ¤^K‡ÿÎ, B = ?

Avgiv Rvwb,

†mvRv Zv‡ii Rb¨,

B = oI

2a =

4 10–7 4

2 0.16 = 5 10–6T

ZviwU n‡Z 0.16m ~̀‡i †PŠ¤̂K‡ÿ‡Îi gvb 5 10–6T (Ans.)

N †mvRv Zv‡ii Rb¨ †PŠ¤̂K‡ÿÎ, B = 5 10–6T

GLb ZviwU‡K †cuwP‡q GK cv‡Ki e„ËvKvi KzÛjx‡Z cwiYZ Ki‡j,

2r1 = 2

ev, r1 = 1

= 0.318m

Ges o = 4 10–7 TmA–1

I = 4A

GK cv‡Ki e„ËvKvi KzÛjxi †K‡›`ª †PŠ¤̂K‡ÿÎ,

B = oI2r1

= 4 10–7 4

2 0.318 = 7.89 10–6T

hv †mvRv Zv‡ii †PŠ¤̂K‡ÿ‡Îi †P‡q †ewk A_©vr B > B

Avevi, †cwP‡q N = 10 cv‡Ki KzÛjx ˆZwi Ki‡j

2r2 N = 2

ev, r2 = 1

N =

r1N

eZ©gv‡b †K‡› ª̀ †PŠ¤^K‡ÿÎ, B = oNI2r2

B

B = oNI2r2

2r101

= Nr1r2

= Nr1r1N

= N2 = 102 = 100

B = 100 B

myZivs DÏxc‡Ki e³e¨ mwVK|


K †h cÖwµqv wecixZgyLx n‡q cÖZ¨veZ©b K‡i Ges m¤§yLeZx© I wecixZgyLx cÖwµqvi cÖwZ ¯Í‡i Zvc I Kv‡Ri djvdj mgvb I

wecixZ nq †mB cÖwµqv‡K cÖZ¨vMvgx cÖwµqv e‡j|

L Kv‡b©v BwÄb Øviv Kv‡R iƒcvšÍwiZ Zvckw³ I BwÄb Øviv †kvwlZ Zvckw³i AbycvZ‡K Kv‡b©v BwÄ‡bi `ÿZv e‡j| Kv‡b©v BwÄ‡bi

`ÿZv, = T1 – T2

T1 100% mgxKi‡Y, T1 n‡jv Dr‡mi ZvcgvÎv

Ges T2 MÖvn‡Ki ZvcgvÎv| D³ mgxKiY Abymv‡i, T2 Gi gvb hZ

n«vm cv‡e, (T1 – T2) Gi gvb ZZ e„w× cv‡e| T1 – T2 Gi gvb hZ

evo‡e Kv‡b©v BwÄ‡bi `ÿZv ZZ evo‡e| G Kvi‡Y ZvcMÖvn‡Ki

ZvcgvÎv n«vm †c‡j Kv‡b©v BwÄ‡bi `ÿZv e„w× cvq|

M DÏxcK Abymv‡i, = 1.33

cÖv_wgK ZvcgvÎv, T1 = 27C = (273 + 27) K

= 300 K

cÖv_wgK Pvc, P1 = 1 evqygÐjxq Pvc

P‚ovšÍ Pvc, P2 = 2 evqygÐjxq Pvc

P‚ovšÍ ZvcgvÎv, T2 = ?

Avgiv Rvwb, T1P1

1 –

= T2P2

1 –

ev, T2 = T1 P1

P2

1 –

= 300 1

2

1 – 1.331.33

= 356.297 K

= 83.297C (Ans.)

N DÏxcK Abymv‡i,


Teac

hing

bd.co

m



c`v^Æweævb

cÖv_wgK NbZ¡, 1 = 100 kgm–3

cÖv_wgK ZvcgvÎv, T1 = 27C = 300 K



ÔMÕ Ask n‡Z cvB,

P‚ovšÍ ZvcgvÎv, T2 = 356.297 K

P‚ovšÍ NbZ¡, 2 = ?

Nb‡Z¡i cwieZ©b, = ?

Avgiv Rvwb,

1T1P1

= 2T2P2

ev, 2 = 1 T1 P2

P1 T2

= 100 300 2

1 356.297

= 168.4 kgm–3

= (2 – 1)

= (168.4 – 100) kgm–3

= 68.4 kgm–3

AZGe, †P¤̂viwUi P‚ovšÍ ZvcgvÎvq M¨v‡mi NbZ¡ 68.4 kgm–3 e„w× cv‡e|

7. h‡kvi †evW©-2016


K †Kvb wm‡÷‡gi kw³ iƒcvšÍ‡ii AÿgZv ev Am¤¢ve¨Zv‡K ev iƒcvšÍ‡ii Rb¨ kw³i AcÖvßZv‡K GbUªwc e‡j|

L ỳwU e ‘̄i Zvc aviY ÿgZv wfbœ nIqvi Kvi‡Y GKB cwigvY Zvc ỳwU wfbœ e¯‘‡Z mieivn Kiv n‡jI ZvcgvÎvi cwigvY wfbœ

nq|

Zvc n‡jv e ‘̄‡Z kw³i cwigvc wKš‘ ZvcgvÎv n‡jv e ‘̄i Af¨šÍixY

AYymg~‡ni MZxq Aw¯’iZv| wfbœ wfbœ e¯‘i AvšÍtAvYweK MVb wewfbœ

nIqvi Kvi‡Y GKB Zvc w`‡j I ZvcgvÎvi cwigvY wfbœ n‡Z cv‡i|

M GLv‡b, D”P ZvcgvÎv, T1 = 327C = 600K

wb¤œ ZvcgvÎv, T2 = 27C = 300K

Zvc Drm †_‡K M„nxZ Zvc, Q1 = 6000 J

Zvc MÖvn‡K ewR©Z Zvc, Q2 = ?

Avgiv Rvwb, Q1T1

= Q2T2

ev, Q2 = Q1T2

T1

= (6000 J) (300 K)

(600 K) = 3000 J (Ans.)

N GLv‡b,

cÖ_g †ÿ‡Î,

D”P ZvcgvÎv, T1 = 327C = 600 K

wb¤œ ZvcgvÎv, T2 = 27C = 300 K

Kg©`ÿZv, 1 = ?

Avgiv Rvwb,

1 = 1 – T2T1

= 1 – 300 K600 K = 0.5

GLv‡b,

wØZxq †ÿ‡Î Kg©`ÿZv, 2 = 21 = 2 0.5 = 1

Zvn‡j, D”P ZvcgvÎv, T1 = 600 K

wb¤œ ZvcgvÎv, T2 = ?

Avgiv Rvwb,

2 = 1 – T2

T1

ev, T2

T1 = 1 – 2

ev, T2 = (1 – 2) T1

= (1 – 1) 600 K

= 0 K

†h‡nZz `ÿZv wØ¸Y Ki‡j Zvc MÖvn‡Ki ZvcgvÎv 0 K Ki‡Z nq hv ev Í̄‡e m¤¢e bq| ZvB Kg©`ÿZv wØ¸Y Kiv m¤¢e bq|


K cÖwZ GKK Avavb‡K †Kvl m‡gZ †Kvb eZ©bxi GK we›`y †_‡K m¤ú~Y© eZ©bx Nywi‡q Avevi H we› ỳ‡Z Avb‡Z †h KvR m¤úbœ nq

A_©vr †Kvl †h Zwor kw³ mieivn K‡i Zv‡K H †Kv‡li Zwo”PvjK

kw³ e‡j|

L Zwor cwievn‡K †ek wKQy msL¨K gy³ B‡jKUªb _v‡K| cwievn‡Ki ỳB we›`yi g‡a¨ wefe cv_©K¨ m„wó n‡j gy³

B‡jKUªb¸‡jv AvšÍtAvYweK ’̄v‡bi ga¨w`‡q cwievn‡Ki wb¤œ wefe


Teac

hing

bd.co

m



c`v^Æweævb

†_‡K D”P wef‡ei w`‡K Pj‡Z _v‡K, d‡j Zwor cÖev‡ni m„wó nq|

GB B‡jKUªb¸‡jv Pjvi mgq cwievn‡Ki cigvYyi mv‡_ msN‡l© wjß

nq Ges B‡jKUª‡bi MwZkw³ cigvYy‡Z mÂvwjZ nq Ges cigvYyi

MwZkw³ Av‡iv e„w× cvq| GB ewa©Z MwZkw³ Zv‡c iƒcvšÍwiZ nq|

GRb¨ Zwor cÖev‡ni d‡j eZ©bx‡Z Zv‡ci D™¢e nq|

M GLv‡b,

cÖ_g †Mvj‡Ki e¨vmva©, r1 = 0.2 m

cÖ_g †Mvj‡Ki wefe, V1 = 5V

†MvjKwUi PvR©, q1 = ?

1

4o = 9 109 Nm2C–2

Avgiv Rvwb, †Mvj‡Ki wefe

V1 = 1

4o q1r1

ev, q1 = V1r1

1

4o

= (5V) (0.2 m)

(9 109 Nm2C–2)

= 1.11 10–10C (Ans.)

N GLv‡b,

wØZxq †Mvj‡Ki e¨vmva©, r2 = 0.3 m

wØZxq †Mvj‡Ki wefe, V2 = 10 V

†MvjKwUi PvR©, q2 = ?

Avgiv Rvwb,

V2 = 1

4o q2r2

ev, q2 = V2r2

1

4o

= (10 V) (0.3 m)

(9 109 Nm2C–2)

= 3.33 10–10 C

awi,

cÖ_g †MvjK n‡Z x ~̀i‡Z¡ A we›`y‡Z cÖvej¨ k~b¨ n‡e|

A_©vr, E1 = E2 n‡e|

GLv‡b, E1 = 1

4o q1x2

ev, E1 = (9 109 Nm2C–2) 1.11 10–10 C

x2

Avevi, E2 = 1

4o

q2(1 – x)2

ev, E2 = (9 109 Nm2C–2) (3.33 10–10 C)

(1 – x)2

GLb, E1 = E2

ev, 1.11 10–10 C

x2 = (3.33 10–10 C)

(1 – x)2

ev, (1 – x)2

x2 = 3.33 10–10 C

1.11 10–10 C

ev,

1 – x

x2 = 3

ev, 1 – x

x = 3

ev, 1x – 1 = 3

ev, 1x = 3 + 1

ev, x = 1

3 + 1

= 0.37 m

A_©vr, cÖ_g †MvjKwU †_‡K 0.37 m ~̀i‡Z¡ cÖvej¨ k~b¨ n‡e|


K ZvcgvÎv e„w× Ki‡Z _vK‡j †h ZvcgvÎvq †Kv‡bv †d‡iv-†PŠ¤̂K c`v_© c¨viv‡PŠ¤^K c`v‡_© cwiYZ nq Zv‡K H †d‡iv‡PŠ¤̂K c`v‡_©i

Kzixwe›`y e‡j|

L †KŠwYK †e‡Mi cwieZ©‡bi Kvi‡Y N~Y©vqgvb B‡jKUª‡bi Kÿxq †PŠ¤^K †gv‡g›UI cwiewZ©Z nq| †KŠwYK †eM n«vm †c‡j †PŠ¤^K

†gv‡g‡›Ui gvb n«vm cvq, Avi †eM e„w× n‡j †gv‡g‡›Ui gvb ev‡o|

myZivs, †`Lv hv‡”Q †h Wvqv‡PŠ¤̂K c`v‡_©i Dci †PŠ¤̂K‡ÿÎ

B cÖ‡qvM Ki‡j GKwU †PŠ¤̂K †gv‡g›U Avweó nq Ges Gi AwfgyL

ewnt ’̄ †PŠ¤̂K‡ÿÎ

B Gi wecixZ, d‡j weKl©Y nq| ZvB Wvqv‡PŠ¤̂K c`v_© †PŠ¤^K c`v_© nIqv m‡Ë¡I Pz¤^K Øviv weKwl©Z nq|

M GLv‡b,

KzÐjxi ˆ`N©¨, L = 3 cm = 3 10–2m

KzÐjxi cÖ¯’, b = 2 cm = 2 10–2m

KzÐjxi †ÿÎdj, A = Lb

= (3 10–2m) (2 10–2m)

= 6 10–4m2

KzÐjxi cvK msL¨v, N = 1

E1 = A

x 1


Teac

hing

bd.co

m



c`v^Æweævb

cÖevn, I = 2A

†PŠ¤^K‡ÿÎ, B = 1.5 103 Am–1

KzÐjxZj †PŠ¤̂K‡ÿ‡Îi mv‡_ j¤̂ n‡j, Zj †f±i †PŠ¤̂K †ÿ‡Îi

mgvšÍivj nq, †m‡ÿ‡Î = 0 n‡e

wµqvkxj UK©, = ?

Avgiv Rvwb,

= NIAB sin

= 1 (2A) (6 10–4m2) (1.5 103 Am–1) (sin 0)

= 0 (Ans.)

N GLv‡b, KzÐjxi †ÿÎdj, A = 6 10–4m2

KzÐjxwU †PŠ¤^K‡ÿ‡Îi Z‡ji mv‡_ 90 †Kv‡Y wewÿß n‡j K…Z KvR

n‡e,

W =

o

/2

d

=

o

/2

NIAB sin d

= NIAB

o

/2

sin.d

= NIAB [–cos]0/2

= NIAB [–cos /2 + cos 0]

= NIAB [0 + 1]

= NIAB

= 1 2 6 10–4 1.5 103

= 1.8 J

1.8 J KvR Ki‡Z n‡e| (Ans.)


K Av‡jv †Kv‡bv gva¨‡gi ga¨ w`‡q Mg‡bi ci Av‡jvK Zi‡½i K¤úb GKwU wbw ©̀ó Z‡j nIqvi NUbv‡K Av‡jvi mgeZ©b e‡j|

L ỳwU Drm †_‡K mg`kvq ev †Kvb wbw`©ó `kv cv_©‡Kï GKB Zi½‰`‡N©ï `ywU Av‡jvK Zi½ wbtm„Z n‡j Zv‡ì mymsMZ Drm

e‡j| mvaviYZ ỳwU Avjv`v Drm‡K mymsMZ Drm wn‡m‡e MY¨ Kiv

hvq bv, †Kbbv †Kvb Dr‡mi wbtm„Z Av‡jv Ab¨ Dr‡mi Dci †Kvb

fv‡eB wbf©i K‡i bv| ZvB Avjv`v ̀ ywU Drm GKwU wbw`©ó ̀ kv m¤úK©

eRvq ivL‡Z cv‡i bv| d‡j G‡ì g‡a¨ Zi½ ˆ`N©¨ I we¯Ív‡i †ek

cv_©K¨ †`Lv hvq| ZvB cÖK…wZ‡Z †Kvb mymsMZ Drm †bB|

M GLv‡b, cÖwZmviK †KvY, A = 60

cÖwZmiv¼, = 2

b~¨bZg wePz¨wZ †KvY, m = ?

Avgiv Rvwb, =

sin

A + m

2

sin A2

ev, 2 =

sin

60 + m

2

sin 60

2

ev, sin

60 + m

2 = 2 sin 30 = 2 12 =

1

2 = sin 45

ev, 60 + m

2 = 45

ev, m = 30 (Ans.)

N GLv‡b, wcÖR‡gi cÖwZmviK †KvY, A = 60

Avgiv Rvwb, †Kvb wcÖR‡gi wePz¨wZ †KvY,

= i1 + i2 – A

wKš‘ b~¨bZg wePz¨wZ Ae¯’v‡b, = m Ges i1 = i2

AZGe,

m = i1 + i2 – A

ev, m = 2i1 – A

ev, 2i1 = m + A

ev, i1 = m + A

2

ev, i1 = 30 + 60

2 [M bs n‡Z]

ev, i1 = 45 = cÖ_g AvcZb †KvY

AZGe, MvwYwZK we‡køl‡Y †`Lv hvq †h, wcÖR‡gi b~¨bZg wePz¨wZ

Ae¯’v‡b cÖ_g AvcZb †KvY (i1) wbY©q Kiv m¤¢e Ges cÖ_g AvcZb

†Kv‡Yi gvb 45|


K cwievnxZv e„w×i D‡Ï‡k¨ Aa©cwievnx‡Z mvgvb¨ cwigvY myweavRbK wbw ©̀ó †gŠwjK c`v_© †fRvj †`qv nq| †fRvj c`v‡_©i

ev®ú DËß Ae ’̄vq weï× Aa©cwievnxi ga¨ w`‡q Pvjbv K‡i †fRvj

†`qvi c×wZ‡K †Wvwcs ejv nq|

L nvB‡Rbev‡M©i AwbðqZv bxwZi m~Î

xP

h

2 eënvi K‡i

wbw`©ó MvwYwZK we‡køl‡Y cvIqv hvq †h, B‡jKUª‡bi wbDwK¬qv‡mi


Teac

hing

bd.co

m



c`v^Æweævb

Af¨šÍ‡i _vK‡Z n‡j G‡K 37.6 MeV kw³i AwaKvix n‡Z n‡e|

wKš‘ cixÿvjä djvdj †_‡K †`Lv hvq †h, B‡jKUª‡bi kw³ 4 MeV

Gi AwaK nq bv| myZivs wbDwK¬qv‡mi Af¨šÍ‡i B‡jKUªb _vK‡Z

cv‡i bv|

M GLv‡b,

AvcwZZ Av‡jvi Zi½‰`N©¨, = 2500 A

= 2500 10–10 m

avZzi Kvh©v‡cÿK, = 2.3 eV

= 2.3 1.6 10–19 J

= 3.68 10–19 J

Av‡jvi ª̀æwZ, c = 3 108 ms–1

cø̈ v¼ aªæeK, h = 6.63 10–34 Js

d‡UvB‡jKUª‡bi m‡e©v”P MwZ‡eM, vmax = ?

B‡jKUª‡bi fi, m = 9.1 10–31 kg

Avgiv Rvwb,

h = Kmax +

ev, h = 12 m(vmax)

2 +

ev, 12 m(vmax)

2 = h –

ev, 12 m(vmax)

2 = hc

–

ev, 12 m(vmax)

2 = (6.63 10–34 Js) (3 10ms–1)

(2500 10–10m) – (3.68 10–19

J)

ev, 12 m(vmax)

2 = 4.28 10–19 J

ev, vmax = 2 (4.28 10–19J)

m

= 2 4.28 10–19J

9.1 10–31 kg

= 9.7 105 ms–1 (Ans.)

N GLv‡b,

Kvh©v‡cÿK, = 2.3 eV

= 3.68 10–19 J

cøv‡¼i aªæeK, h = 6.63 10–34 Js

m~Pb K¤úv¼, o = ?

Avgiv Rvwb,

= hf0

ev, 0 =

h

= 3.68 10–19J

6.63 10–34 J

= 5.55 1014 Hz

Avevi,

AvcwZZ iwk¥i Zi½ ˆ`N©¨, = 5897A

= 5897 10–10m

K¤úv¼, = ?

Avgiv Rvwb,

c =

ev, = c

= 3 108 ms–1

5897 10–10m = 5.09 1014 Hz

A_©vr, K¤úv¼ , m~Pb K¤úvsK o A‡cÿv ÿz`ªZi ( < o)| A_©vr

5897A Zi½‰`‡N©̈ i Av‡jvi Rb¨ B‡jKUªb gy³ n‡e bv|


K †Kvb Ro KvVv‡gv‡Z msNwUZ ỳwU NUbvi gaëZx© mgq eëavb A‡cÿv H KvVv‡gvi mv‡c‡ÿ MwZkxj †Kvb Ro KvVv‡gv‡Z

cwigvcK…Z GKB NUbvØ‡qi gaëZx© mgq eëavb †ewk nq| G‡KB

Kvj `xN©vqb e‡j|

L weï× Aa©cwievnx B‡jKUªwb· G †Kv‡bv Kv‡R jv‡M bv| ZvB weï× Aa©cwievnx‡Z mvgvb¨ cwigvY myweavRbK †gŠwjK c`v_©

mywbqwš¿Z fv‡e †fRvj w`‡j Gi cwievnxZv e„w× cvq| mvaviYZ ̀ yB

ai‡bi †fRvj w`‡q P UvBc I n UvBc Aa©cwievnx ˆZwi Kiv nq|

P-N Rskb I UªvbwR÷i B‡jKUªwb‡·i mKj Kv‡R eën„Z nq|

M GLv‡b,

†ZRw¯µq X-cigvYyi Mo Avqy, = 2294 eQi

Aa©vqy, T12

= ?

Avgiv Rvwb,

T12

= 0.693 = 0.693 2294 eQi = 1589.742 eQi| (Ans.)

N GLv‡b,

†ZRw®µq X-cigvYyi Mo Avqy, = 2294 eQi

Aeÿq aªæeK, = ?

Avgiv Rvwb,


Teac

hing

bd.co

m



c`v^Æweævb

= 1

ev, = 1

2294 eQi

= 4.36 10–4 y–1

GLb, hLb, N1 = 0.5 No ZLb mgq t1 n‡j,

N1 = No e–t1

ev, 0.5 No = No e–t1

ev, 0.5 = e–t1

ev, n (0.5) = –t1

ev, t1 = – n(0.5)

= – n(0.5)

(4.36 10–4 y–1)

= 1589.742 y = T12

(M bs †_‡K)

Avevi, hLb, N2 = 0.25No ZLb mgq t2 n‡j,

t2 = – n(0.25)

= 3179.57 yr = 2 T1

2

Avevi, N3 = 0.125No Gi Rb¨ mgq t3 n‡j,

t3 = – n(0.125)

= 4768.36 yr = 3 T1

2

A_©vr, †jLwPÎwU †ZRw¯µq ÿq m~Î †g‡b P‡j|

8. ewikvj †evW©-2016


K †h cÖwµqv wecixZgyLx n‡q cÖZ¨veZ©b K‡i Ges m¤§yLeZx© I wecixZgyLx cÖwµqvi cÖwZ ¯Í‡i Zvc I Kv‡Ri djvdj mgvb I

wecixZ nq †mB cÖwµqv‡K cÖZ¨vMvgx cÖwµqv e‡j|

L Kv‡b©v BwÄb Øviv Kv‡R iƒcvšÍwiZ Zvckw³ I BwÄb Øviv †kvwlZ Zvckw³i AbycvZ‡K Kv‡b©v BwÄ‡bi `ÿZv e‡j| Kv‡b©v BwÄ‡bi

`ÿZv, = T1 – T2

T1 100% mgxKi‡Y, T1 n‡jv Dr‡mi ZvcgvÎv

Ges T2 MÖvn‡Ki ZvcgvÎv| D³ mgxKiY Abymv‡i, T2 Gi gvb hZ n«vm cv‡e, (T1 – T2) Gi gvb ZZ e„w× cv‡e| T1 – T2 Gi gvb hZ evo‡e Kv‡b©v BwÄ‡bi `ÿZv ZZ evo‡e| G Kvi‡Y ZvcMÖvn‡Ki

ZvcgvÎv n«vm †c‡j Kv‡b©v BwÄ‡bi `ÿZv e„w× cvq|

M DÏxcK Abymv‡i, = 1.33

cÖv_wgK ZvcgvÎv, T1 = 27C = (273 + 27) K

= 300 K



P‚ovšÍ ZvcgvÎv, T2 = ?

Avgiv Rvwb,

T1P1

1 –

= T2P2

1 –

ev, T2 = T1 P1

P2

1 –

= 300 1

2

1 – 1.331.33

= 356.297 K

= 83.297C (Ans.)

N DÏxcK Abymv‡i,

cÖv_wgK NbZ¡, 1 = 100 kgm–3

cÖv_wgK ZvcgvÎv, T1 = 27C = 300 K



ÔMÕ Ask n‡Z cvB,

P‚ovšÍ ZvcgvÎv, T2 = 356.297 K

P‚ovšÍ NbZ¡, 2 = ?

Nb‡Z¡i cwieZ©b, = ?

Avgiv Rvwb,

1T1P1

= 2T2P2

ev, 2 = 1 T1 P2

P1 T2

= 100 300 2

1 356.297


Teac

hing

bd.co

m



c`v^Æweævb

= 168.4 kgm–3

= (2 – 1)

= (168.4 – 100) kgm–3

= 68.4 kgm–3

AZGe, †P¤̂viwUi P‚ovšÍ ZvcgvÎvq M¨v‡mi NbZ¡ 68.4 kgm–3 e„w× cv‡e|


K wZb †mŠi f‡ii mgvb ev †ewk f‡ii bÿ‡Îi mycvi †bvfv we‡ùvi‡Yi ci Gi AšÍe©¯‘ Awb©wÏófv‡e msKzwPZ n‡Z _v‡K|

ms‡KvP‡bi Kvi‡Y AvqZb cÖvq k~b¨ Ges NbZ¡ Amxg nIqvq gnvKl©

†ÿÎ Ggb cÖej nq †h, G RvZxq e¯‘ †_‡K Gi gnvKl©‡K KvwU‡q

†Kvb cÖKvi Av‡jv GgbwK ms‡KZI †ewi‡q Avm‡Z cv‡i bv| ZvB

e¯‘wU‡K Avi †`Lv hvq bv| bÿ‡Îi GB Ae ’̄v‡K ejv nq K…ò

MnŸi|

L ci¯ú‡ii mv‡c‡ÿ aªæe‡e‡M MwZkxj †h mKj cÖm‡½ KvVv‡gv‡Z wbDU‡bi MwZm~Î AR©b Kiv hvq Zv‡`i‡K Ro cÖm½ KvVv‡gv e‡j|

N~Y©bkxj e¯‘i †eM cÖwZwbqZ cwiewZ©Z nq e‡j GwU aªæe‡e‡M

MwZkxj bq A_©vr N~Y©bkxj e ‘̄i Z¡iY _v‡K| Avgiv Rvwb †h mKj

cÖm½ KvVv‡gvi Z¡iY _v‡K Zv‡`i‡K ARo cÖm½ KvVv‡gv e‡j| G

Kvi‡Y N~Y©bkxj KvVv‡gv Ro cÖm½ KvVv‡gv bq| eis GwU ARo

cÖm½ KvVv‡gv|

M DÏxcK n‡Z cvB,

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