12th Physics ,aw;gpay; ghl tpdhj;jhs; jpl;l tiuT (BLUE PRINT)

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12th Physics 1

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7

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8

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2

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4

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• • • • •

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•

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•

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19

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•

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20

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+ E2 cos

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x cos

2 x

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21

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1

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2

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!!!!!!!!!!!!!!!

•

)

( 1(

V =

!!!!!!!!!!!!!!!!! V =

),

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( 1+

V =

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) ]

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! d.-jmoutqbqz
!

!

!

!!lqe
[

=

]

!!!!!!!!-V!km
!

!

gi^
X, Y!!km
!

! -j{k
C=

! ! ! ! ! 25

8/!lqe
hg
C1,C2,C3!lqe
C1,C2,C3!lqe
lqe
!

!

!

wz
wz
V1 =

q 1 = C 1V ;

; V2 =

; V3 =

q 2 = C 2V ; q 3 = C 3V

q = q1 + q2 + q3 V = V1 + V2 + V3 q = C pV

V= !!!!!!!!! q q q q = + + C1 C2 C3 !!! C s

CPV = V(C1+C2+C3)

CP = C1 + C2 + C3 !

1 1 1 1 = + + C s C1 C 2 C 3 ! !

9/!uie<.c.gqvi0h
fqjzlqe
kk
! •

dOzigg
26

•

Ogitk
!

•

gh
•

gh
•

sQh
•

sQh
osbz
sQh
•

fqjzlqe
•

okimi
•

dbi
!

hbe
!

!!n[g
!!!!!!!!hbe
nzG!–7 gkqi
4/!hbe
! 24/!fqjzl!lx
! 31/!!yV!dOzigk
,

λ0 = 6. 902 x 10 m or λ0 = 6902 A° -7

! ! 32/! yV! wzg
!

λ=

= λ = 1. 121 x 10-10m

(or)

λ = 1. 121 A° 33/! ! ! !

jam
= = 3.14 x 0.53 x 10-10 x 8 = 13.313 x 10-10m = 13. 313 A°

30

5 kjpg;ngz; tpdh-tpilfs; ! 2.xsp kpd;Ndhl;lj;jpd; kPJ gLk; fjph;tPr;rpd; nrwptpd; tpisT • gLk;fjph;tPr;rpd; nrwpit khw;wp mjw;Fhpa xspkpd;Ndhl;lk; mse;jwpag;gLfpwJ (kpd;dOj;jk; kw;Wk; mjph;ntz; khwpyp)

• • •

nrwpT mjpfhpf;Fk;NghJ xspkpd;Ndhl;lk; Neh;f;Nfhl;Lg; gFjpahf mjpfhpf;Fk;. xspkpd;Ndhl;lk; xU tpdhbapy; ckpog;gLk; vyf;l;uhd;fspd; vz;zpf;iff;F Neh;j;jfT. xU tpdhbapy; ckpog;gLk; vyf;l;uhd;fspd; vz;zpf;if gLfjph;tPr;rpd; nrwpTf;F Neh;j;jfT.

2. xspkpd; tpisT> xspkpd; ckpo;jypd; tpjpfs;: • xspkpd; tpisT: rpy cNyhfg; nghUs;fspd; kPJ -fjph;fs;> x-fjph;fs;> GwCjhf; fjph;fs; kw;Wk; fl;GydhFk; xsp Nghd;wit gLk;NghJ vyf;l;uhd;fs; ckpog;gLk; epfo;T. • xspkpd; ckpo;jypd; tpjpfs;: 1. Fwpg;gpl;l xsp czh;jpwd; kpf;f nghUSf;F xspapd; nrwpT vt;tsT mjpfkhf ,Ug;gpDk; ve;j mjph;ntz;Zf;Ff; fPo; xspkpd; ckpo;jy; Kw;wpYk; epfohNjh> gLfjphpd; me;jr; rpWk mjph;ntz; gad; njhlf;f mjph;ntz; vdg;gLk;. 2. mjph;ntz; gad;njhlf;f mjph;ntz;iz tpl mjpfk; vdpy;> xspkpd;Ndhl;lk; gLk; fjph;tPr;rpd; nrwpTf;F Neh;j;jfT. 3. xspkpd; ckpo;T cldb epfo;T. 4. xsp vyf;l;uhd;fspd; ngUk ,af;f Mw;wy; gLfjphpd; mjph;ntz;Zf;F Neh;j;jfT. Mdhy; nrwpitr; rhh;e;jjy;y. 3. xspkpd;fydpd; mikg;G> nray;ghL • xsp Mw;wiy kpd;dhw;wyhf khw;Wk; fUtp. mikg;G: • ntw;wplkhf;fg;gl;l fz;zhb my;yJ Fthh;l;]; Fkpo;. • Nfj;NjhL-Fiwe;j ntspNaw;W Mw;wy; nfhz;l rPrpak; - Mf;irL G+rg;gl;l miu cUis tbtj; jfL, MNdhL - nky;ypa gpshl;bdf; fk;gp. nray;ghL: • xsp Nfj;NjhL kPJ tpOk;NghJ vyf;l;uhd;fs; ckpog;gl;L MNdhil milAk;. • kpd;Ndhl;lk; ikf;Nuh mk;kPl;lh; %yk; msf;fg;gLk;. • xspkpd;Ndhl;lk; gLk; xspapd; nrwpTf;F Neh;j;jftpy; mikAk;.

31

4. xspkpd;fydpd; gad;fs;: 1. ciyfspd; ntg;gepiyiaf; fl;Lg;gLj;j. 2. njUtpsf;Ffisj; jhdhf ,af;f. 3. tpz;ntspg;gazj;jpd; NghJ #hpa xspapypUe;J kpd;dhw;wiyg;ngw. 4. fjTfisj; jhdhfj; jpwf;fTk;> %lTk;. 5. xspapd; nghypTj;jd;ikia mstpLk; fUtpfspy.; 5. gUg;nghUspd; b-gpuhyp miyePsk; • •

g;shq;f; rkd;ghL: Id;];Bd; rkd;ghL:

•

E = hυ E = mc2

h υ = mc 2

h

c

λ

= mc2

( υ= )

h mc • c = v vdpy; h • my;yJ λ= mv 6. vyf;l;uhdpd; b-gpuhyp miyePsk;

λ=

,af;fMw;wy;

v=

λ=

λ=

h m

h p

1 mv 2 = eV 2

2eV m

λ=

λ =

2eV m

12.27 V

=

h mv

h 2 meV

A0

E = eV vdpy;>

λ=

h 2mE

7. mZitg;gw;wpa miy ,ae;jputpay; fUj;J h • bgpuhyp miyePsk; λ = mv • ntt;NtW tl;lg; ghijapy; nry;Yk; vyf;l;uhd;fs; miyfisg; Nghy ,aq;Fk;.

32

tl;lg;ghijapd; Rw;wsT (2πr) bgpuhypmiyePsj;jpd; KOklq;fhf (nλ)

•

,Ue;jhy; ghij epiyj;jd;ik ngw;w ghij.mjhtJ 2πr = nλ (n=1, 2, 3, . . . )

2 r = n( m vr =

•

)

nh 2π

bgpuhypapd; fUj;J Nghhpd; vLNfhis cWjpg;gLj;jpaJ.

8. xspkpd; tpistpw;fhd Id;];Bd; rkd;ghL • Fthz;lk; nfhs;ifapd; gb xspkpd; tpisT tpsf;fg;gLfpwJ. • /Nghl;lhDf;Fk; vyf;l;uhDf;Fk; ,ilNaahd gpd;dpanray; tpistpdhy; vyf;l;uhd;fs; ckpog;gLfpd;wd. • /Nghl;lhdpd; Mw;wy; i) cNyhfg;gug;gpypUe;J vyf;l;uhid ntspNaw;w (xspkpd; ntspNaw;W Mw;wy;) kw;Wk; ii) ntspNaWk; vyf;l;uhDf;F ,af;f Mw;wyhff; nfhLf;fg;gLk;. 1 hυ = W + m v 2 2 •

•

Mw;wy; ,og;G ,y;iy vdpy; v = vngUkk; 1 hυ = W + mv 2 ngUkk; 2 mjph;ntz; υ> gad;njhlf;f mjph;ntz;Zf;F (υ0) rkk; vdpy; W = hυ0 1 hυ = hυ 0 + mv 2 ngUkk; 2 1 h (υ − υ 0 ) = mv 2 ngUkk; 2

9.nyhud;]; - /gpl;];n[uhy;L FWf;fk; (ePsf;FWf;fk;) •

S>

S' vd;w

Fwpg;ghaq;fisf;

fUJNthk;.

S

Fwpg;ghaj;jpy;

cs;s

Ma;thsUf;Fj; jz;bd; ePsk; l 0 . S' Fwpg;ghak; v jpirNtfj;jpy; nrd;why; jz;bd; ePsk; l vd;Nghk;.

33

•

l = l0 1−

•

l < l0

• •

1−

v2 c2

v2 vd;w msT ePsk; FWf;fkilAk; c2

v.fh. Ntfkhf efUk; Ma;thsUf;F tl;l tbtg; nghUs; ePs;tl;lkhfj;

njhpAk;. 11. fhyePl;bg;G •

S' Fwpg;ghaj;jpy; xU fbfhuk; ntsptpLk; iriffspd; fhy,ilntsp t0 . S Fwpg;ghaj;jpy; Ma;thsuhy; fzf;fplg;gLk; fhy ,ilntsp t.

•

t0

t=

1− •

•

v2 c2

t > t0 fhy ,ilntsp

1

msT ePz;L fhzg;gLk;.

v2 1− 2 c

•

v.fh.

,aq;Fk;

tpz;ntspf;

fyj;jpy;

cs;s

fbfhuk;

Gtpapy;

fbfhuq;fis tpl nkJthfr; nry;Yk;. 12. Id;];Bd; - epiw Mw;wy; ,iz khw;W rkd;ghL: •

nghUspd; Xa;T epiw m0 >v jpirNtfj;jpy; mjd; epiw m vd;f.

•

epA+l;ldpd; ,uz;lhk; tpjpg;gb F =

•

rhh;gpay; nfhs;ifapd;gb> F =m

•

dv dm +v dt dt

d (mv) dt

→ (1)

→ (2)

nghUspd; ,af;f Mw;wy; mjpfhpg;G dEk = F dx

34

cs;s

dEk =m v d v + v 2dm •

→ (3)

Id;];Bd; rhh;gpay; nfhs;ifg;gb m=

m0 1−

v2 c2

tifapl> c2dm = mv dv + v2dm •

→ (4)

rkd; (3)> (4) ypUe;J dEk = c2 dm

∫

Ek

0

→ (5) m

dE k = c 2 ∫ dm m0

,af;f Mw;wy; Ek = mc2 - m0c2 •

nkhj;j Mw;wy; = ,af;f Mw;wy; + Xa;T epiw Mw;wy; E = Ek +m0c2 E = mc2 – moc2 + moc2 E = mc2

nzG!9!n[g
! 2/!JOsiOmih
!

4/!JOsiOmie
!

5/!n[g
! 6/!n[fqjx!nzG!)2!amu*!we
x 6 c12n[uqe
1 amu = 1.66 x 10 -27 kg ! 7/!2amu!g
! 22/!gkqiqbg
2:/!n[g
38/!gi^
!

! 45/!94Po325gkqiqbg
Z + 2 + 2 – 1 – 1 = 84 Z + 2 = 84 ⇒ Z = 84 – 2 ⇒ Z = 82 0A =!317! Z =!93!

!

35. 92U238JOsiOmih
+ 2 He 4 + 2 He 4 + 2 He 4 + -1eo+ -1eo A+4+4+4= 238 A= 238 – 12 = 226 Z + 2 + 2 + 2 – 1 -1 = 92 Z= 92-6+2 Z=88 Z =99!!weOu!JOsiOmih
U349!

!

zX

A

! 47/!Ovmieqe
! ! !

! ! !

τ= 1.443 T½! τ= 1.443 x 3. 8 τ= 5. 4834!fim
! ! 48/!6!njv!NBm
wR
sqjkujmf
! !! ! ! ! ! ! ! !

olik
40

= 5!!!!!!!!

! 4:/!ciqcbk
wR
I!)23/!6!N{
sqjkujmf
!

II )36!n{
!

2!-!

!

2!-!

!

olik
! 0!36!N{
5 kjpg;ngz; tpdh-tpilfs; 1.

BE A

•

•

•

•

•

tisNfhl;bd; rpwg;gpay;Gfs;.

BE BE kjpg;G NtfkhfTk; A > 20 vdpy; kjpg;G A A nkJthfTk; mjpfhpf;fpwJ. A < 20 vdpy;>Z = N vdTk;> A ehd;fpd; klq;fhfTk;> ,ul;ilg;gil vz;zhfTk; mikAk; mZf;fUf;fs; kPz;Lk; kPz;Lk; KfLfspy; mikfpd;wd. A = 40 Kjy; 120 tiu tiuNfhL Vwf;Fiwa fpilf;NfhlhFk;. BE kjpg;G 8.8 MeV. vdNt ,Uk;G mjpf A =56 vdpy; 26 Fe 56 A epiyg;ghLilaJ. BE A=40Kjy; A=120tiu ruhrhp kjpg;G 8.5 MeV. vdNt ,e;j A mZf;fUf;fs; mjpf epiyj;jd;ikAilaitahFk;. BE mjpf epiw vz; kjpg;Gfspy; kjpg;G Fiwe;J ANudpaj;jpw;F 7.6MeV A MFk;. vdNt ,e;j mZf;fUf;fs; fjphpaf;fj;jpw;F cl;gLk;> epiyj; jd;ikaw;witahFk;. BE fdkhd kw;Wk; ,Nyrhd mZf;fUf;fspd; Fiwe;j kjpg;Gfs; mit A mZf;fUg;gpsT kw;Wk; mZf;fU ,izTf;F cl;gLtijf; fhl;Lfpd;wd.

epiw vz; A = 20 tiu

(

)

2. mZf;fUtpir> mZf;fU tpirapd; gz;Gfs;. Neh;kpd;D}l;lk; nfhz;l GNuhl;lhd;fSf;F ,ilNa nray;gLk; tpul;L tpiria tpl typikahd tpir mZf;fUtpDs; nray;gl;L GNuhl;lhd;fisAk; epA+l;uhd;fisAk; gpizf;fpd;wJ. ,t;tpir mZf;fUtpir vdg;gLk;. mZf;fU tpirapd; gz;Gfs;: tpir.(n – p), (p – p), (p – n)vd;w %d;W Nrhb • kpd;D}l;l rhh;gw;w mZf;fUj; Jfs;fspilNa rktpir Vw;gLk;. epiy kpd;dpay; tpir my;y.

41

• • •

fz;lwpag;gl;l tpirfspNyNa typikahd tpir.
thAf;fis madpahf;fk; nra;Ak;. (madpahf;Fk; jpwd; = 100 ×β fjph;fspd;

• • •

madpahf;fk; kw;Wk; 10000×γ fjph;fspd; madpahf;fk;) xspg;glj;jfLfisg; ghjpf;Fk;. xsph;jiy Vw;gLj;Jk;. CLUT jpwd; kpff;FiwT.

4. β-fjph;fspd; gz;Gfs; • • • • • •

0.3 c Kjy; 0.99 c tiu jpirNtfk; cilait. kpd;kw;Wk; fhe;jg; Gyq;fshy; tpyfyilAk;. thAf;fis madpahf;Fk;> madpahf;Fk; jpwd; α- fjph;fis tpl FiwT. xspg;glj;jfLfisg; ghjpf;Fk;. xsph;jiy Vw;gLj;Jk;. CLUT jpwd; α - fjph;fis tpl mjpfk;.

5. γ-fjph;fspd; gz;Gfs; • xspapd; jpirNtfj;jpy; ( c ) nry;Yk;. • kpd; kw;Wk; fhe;j Gyq;fshy; tpyfy; miltjpy;iy. • madpahf;Fk; jpwd; kpff;FiwT • xspg;glj;jfLfisg; ghjpf;Fk;. • xsph;jiy Vw;gLj;Jk;. • CLUT jpwd; kpf mjpfk;. 6.fjphpaf;f ,lg;ngah;r;rp tpjpfs; my;yJ rhb - g[d; fjphpaf;fr; rpijT tpjpfs; • α - rpijT fjphpaf;f mZf;fU α-Jfis ntsptpl;L rpijtile;jhy; mZ vz; 2 FiwAk;> epiw vz; 4 FiwAk.; v.fh. 88 Ra 226 →86 Rn222 + 2 He4 • β - rpijT fjphpaf;f mZf;fU β-Jfis ntsptpl;L rpijtile;jhy; mZ vz; 1 $Lk;> epiw vz; khwhJ. v.fh. 90Th234 →91 Pa234 + −1e0 •

γ - rpijT fjphpaf;f mZf;fU γ-Jfis ntsptpLk;NghJ mZ vz; kw;Wk; epiw vz; khwhJ. mZf;fUtpd; Mw;wy; kl;lk; kl;Lk; khWk;. v.fh. Nubak; Nulhdhf khWk; rpijtpy; Nulhd; fpsh;rr ; p epiyapypUe;J mbepiyf;Fj; jpUk;Gk;NghJ 0.187MeV Mw;wy; nfhz;l γ-fjph; ntspg;gLk;.

7. epA+l;uhd;fspd; gz;Gfs; • i`l;u[idj; jtpu midj;J mZf;fUf;fspYk; epA+l;uhd;fs; cs;sd. • GNuhl;lhd;fis tpl rw;Nw epiw mjpfkhd> Rop kpd;D}l;lk; nfhz;l eLepiyj;Jfs;fs;. 42

•

mZf;fUtpDs; epiyg;ghLilait. mZf;fUtpw;F epiyg;ghlw;wit. epA+l;uhd;fspd; miu MAl;fhyk; 13 epkplq;fs;. 0

• •

ntspNa

n1 →1 H 1 + −1 e 0 + υ

mZf;fUf;fis vspjpy; CLUtpr; nry;Yk;. ,af;f Mw;wy; mbg;gilapy; i) FiwNtf epA+l;uhd; (0–1000eV) ii) NtfepA+l;uhd; (0.5MeV-10MeV) iii) ntg;gepA+l;uhd; (0.025eV) vd tifg;gLj;jyhk;.

8. fjphpaf;f INrhNlhg;Gfspd; kUj;Jtg; gad;ghLfs; •

fjphpaf;f Nfhghy;l;( Co 60 )Gw;WNeha; rpfpr;irf;Fg; gad;gLfpwJ.

•

fjphpaf;f Nrhbak; Na 24 ,uj;j ehsq;fspy; cs;s milg;Gfisf; fz;lwpaTk;> ,jaj;jpd; nray;ghl;il mwpaTk; gad;gLfpwJ.

•

fjphpaf;f mNahbd; I ijuha;L ,lkwpaTk; gad;gLfpwJ.

•

59 fjphpaf;f ,Uk;G Fe ,uj;j Nrhifiaf; fz;lwpag; gad;gLfpwJ.

•

fjphpaf;f

(

)

( ) 131

( ) gh];gu]; (P ) Njhy; 32

rpfpr;irf;Fk;>

%isf;foiyfis

Neha; rpfpr;irf;Fg; gad;gLfpwJ.

9. caphpaypy; fjph;tPr;Rfspy; jPatpisTfs; • γfjph; kdpj clypy; nry;Yk; NghJ Vw;gLk; cly;top kw;Wk; kuG top ghjpg;Gfis %d;W gphpTfshfg; gphpf;fyhk;. i) kPsf;$ba FWfpafhy tpisTfs; ii) kPsKbahj ePz;lfhy tpisTfs; iii) kuGtop tpisTfs; • fjph;tPr;rpd; msT kw;Wk; ngwg;gLk; tPjk;> fjph;tPr;Rf;F cl;gLk; clypd; gFjp Mfpatw;iwr; rhh;e;J kdpj clypd; xU mq;fk; ghjpf;fg;gLtJ mikAk;. • kPsf;$ba FWfpa fhy tpisTfs; - rpwpa fjph;tPr;Rfshy; Vw;gLk; Njhy; ghjpg;G> Kbcjph;jy;. • kPsKbahj ePz;l fhy tpisTfs; - fjph;tPr;R 100 R vdpy; Y}f;nfkpah (,uj;jg;Gw;WNeha;). 600 R vdpy; kuzk; Vw;gLk;. ghJfhg;ghd fjph;tPr;R msT xU thuj;jpy; 250 mR. • kuG toptpisTfs; - ,dg;ngUf;fr; nry;fspy; cs;s kuG mZf;fisg; ghjpf;Fk;. 10. i`l;u[d; Fz;bd; jj;Jtk;> nray;ghL • mZf;fU ,izT %yk; Vuhskhd Mw;wiy ntspg;gLj;Jk; ntbf;Fk; mikg;G i`l;u[d; Fz;L MFk;. • mZf;fU ,iztpw;Fj; Njitahd cah;ntg;gepiy (50 kpy;ypad; bfphp nry;rpa];) mZFz;L xd;wpid ntbf;fr; nra;J ngwg;gLfpwJ. • mZFz;L ntbg;Gf;F mUfpy; jFe;j msT bA+l;uhDk;> bhpl;lhDk; itf;fg;gl;bUf;Fk;. • rhjfkhd ntg;gepiyapy; fl;Lg;ghlw;w mZf;fU ,izT epfo;T eilngw;W Vuhskhd ntg;gMw;wy; ntspg;gLk;. 3 2 4 1 • 1 H +1H → 2 He + 0 n + Mw;wy;.

43

11.mZFz;bd; jj;Jtk; kw;Wk; nray;ghL

jj;Jtk;: fl;Lg;ghlw;w mZf;fUg; gpsit njhlh;tpid gpsitg;nghUs;: 239 • U235 my;yJ Pu mikg;G: • khWepiy gUkidtpl Fiwthd gUkd; nfhz;l U 235 my;yJ Pu 239 My; Md ,U miuf;Nfhsq;fs; rpwpa ,ilntspapy; gphpj;J itf;fg;gl;Ls;sd. nray;ghL: • khWepiy epiwiatpl Fiwthd epiwAila U 235 my;yJ Pu 239 vd;w %d;whtJ ,aq;Fk; cUis> miuf;Nfhsq;fSf;F ,ilapy; rhpahfg; nghUe;Jk;gb nra;jhy; khWepiy epiwiatpl nkhj;j epiw mjpfkhfpwJ. • fl;Lg;ghlw;w njhlh;tpid Vw;gl;L gaq;fukhf ntbj;Jr; rpjWfpwJ. tpisTfs;: • Vuhskhd ntg;g Mw;wy;> xsp> fjph;tPr;Rfs; Vw;gLk;. • gykpy;ypad; bfphp nry;rpa]; ntg;gepiyAk;> gykpy;ypad; tspkz;ly mOj;jKk; caUk;. • mjph;r;rp miyfs; Vw;gLk;. • γfjph;fs;> epA+l;uhd;fs; cly; eyf;Nfl;il Vw;gLj;Jk;. 12. fh];kpf; fjph; nghopT epfo;T

•

mUtpf;nfhs;ifapd;gb fh];kpf; fjph;nghopTfs; i) fjph;tPr;R Nkhjy; ii) Nrhb cUthjy; Mfpatw;why; Vw;gLk;. • fh];kpf; fjphpYs;s e − or e + , thA mZf;fUf;fspd; kPJ NkhjYw;W Mw;wiy ,of;fpd;wd. Mw;wy; ,og;G Nghl;lhdhf ntspg;gLk;. • Nghl;lhd; mZf;fUTld; tpidGhpe;J vyf;l;uhd;(e-) kw;Wk; ghrpl;uhd; (e+) Nrhbia cUthf;Fk;.

44

•

vyf;l;uhd;> ghrpl;uhd; Nrhb NkYk; NkYk; mZf;fUf;fSld; NkhjYw;W mjpf Nghl;lhd;fisAk;> Nghl;lhd;fs; mjpf vz;zpf;ifapy; vyf;l;uhd;> ghrpl;uhd; NrhbfisAk; cUthf;Fk;. xt;nthU Jfspd; Mw;wYk; khWepiy Mw;wiytpl Fiwthf ,Uf;Fk; tiu ,e;epfo;T eilngw;W ngUf;fk; Vw;gLk;.

•

21!lkqh
mikg;G:

!

• Neh;kpd; madpfw;iw s1, s2 we
! osbz
kqjsOugk
Bqv=qE v=E/B •

v kqjsOugl
•

-r
B'qv=mv2/R m=B'qR/v v=E/B J!hqvkqbqm m=BB'qR/E • • •

ouu
3/!gkqiqbg
,q;F

λ-rpijT

khwpyp

• t=0 vdpy; N=N0 •

loge N0 loge N =

+ loge N0

loge(N/N0)= •

•

,

N/N0=

N=N0

jdpkj;jpd; mZf;fspd; vz;zpf;if fhyk; mjpfhpf;Fk;NghJ mLf;Ff;Fwp Kiwg;gb FiwfpwJ.

miu MAl;fhyk;: • fjpupaf;fj; jdpkj;jpy; cs;s mZf;fspdy; ghjpasT mZf;fs; rpijtila MFk; fhyk;. rpijT tpjpg;gb N=N0

t=T1/2

vdpy; N=N0/2

N0/2 = N0 e-λT½ loge2 = λT1/2

T1/2 =

,

46

T1/2 =

2.3026

T1/2 = • miu MAl;fhyk;> rpijT khwpypf;F vjph;j;jftpy; mikAk; ruhrup MAl;fhyk;> miu MAl;fhyj;jpw;F ,ilNaahd njhlh;G>

T1/2 = 0.6931τ ! 4/!fqB,m
ohikfhe;j Gyq;fshy; tpyfyilahj fjph;tPr;R ntspg;gLtijf; fz;ldh;.! Kjypy; mit γ- fjph;fs; vdf; fUjg;gl;lJ.! Inudp fpA+hp kw;Wk; N[hypal; ,f;fjph;tPr;Rfs; ghu/gpd; nkOF topahfr; nry;Yk;NghJ GNuhl;lhd;fis ntspg;gLj;Jtijf; fz;ldh;.! 1932 –y; rhl;tpf; GNuhl;lhd; epiwf;Fr; rkkhd kpd;D}l;lkw;w Jfs;fs; ,f;fjph;tPr;rpy; ,Ug;gijf; fz;Lgpbj;jhh;.! rhl;tpf; epA+l;uhd;fs; (on1 )!we!ohbiqm
!h{ Rop kpd;D}l;lk; nfhz;l eLepiyj;Jfs;fs;. 3. mZf;fUtpDs; epiyg;ghLilait. mZf;fUtpw;F ntspNa epiyg;ghlw;wit. epA+l;uhd;fspd; miu MAl;fhyk; 13 epkplq;fs; 1 1 0 0 n → 1 H + −1 e + υ 4. mZf;fUf;fis vspjpy; CLUtpr; nry;Yk;. 5. ,af;f Mw;wy; mbg;gilapy; i) FiwNtf epA+l;uhd; (0–1000eV) ii) NtfepA+l;uhd; (0.5MeV-10MeV) iii) ntg;gepA+l;uhd; (0.025eV) vd tifg;gLj;jyhk;.

4. nfa;fh; Ky;yh; vz;zp jj;Jtk;: mZf;fUtpd; fjph;tPr;Rf;fs; thAf;fis madpahf;Fk;.

mikg;G: • • • • •

fz;zhbahy; R+og;gl;l cNyf Foha;[C] Nfj;NjhL. Fohapy; cs;s nky;ypa lq;];ld; fk;gp[W] MNdhL. Fohapy; Fiwe;j mOj;jj;jpy; Mh;fhd; Nghd;w ke;j thA cs;sJ. Fohapd; xU Kidapy; nky;ypa ikf;fh jfL cs;sJ ,jd; topNa fjph; tPr;R cs;Ns nry;Yk;. 1000Vkpd;dOj;j NtWghL 100 nkfh Xk; kpd;jil topahf nrYj;jg;gLfpwJ.

nray;ghL: •

fjph;tPr;Rf;fs; nfa;fh; Ky;yh; vz;zpapy; EiofpwJ.

47

• • • • • • • •

Kjd;ik madpahf;fj;jhy; xU rpy madpfs; Njhd;Wk;. cah;kpd; mOj;jj;jhy; ,it KLf;Ftpf;fg;gl;L NkYk; madpahf;fk; nra;Ak;. Nkhjy; fhuzkhf madpfspd; vz;zpf;if caUk;. ,jdhy; mjpf vyf;l;uhd;fs; cUthfp xU kpd;Ndhl;lj; Jbg;ig cUthf;Fk;. ,J kpd;jil topNa gha;e;J xU vyf;l;uhdpay; vz;zpiar; nray;gLj;JfpwJ. vyf;l;uhd; vz;zpapd; vz;zpf;if fjph; tPr;rpd; nrwpTf;F Neh;j;jftpy; ,Uf;Fk;. madpahf;fk; fjph; tPr;rpd; tifiag; nghUj;jJ my;y. fjph;tPr;rpd; tifapid czu tpy;rd; Kfpy; $lk; gad;gLfpwJ.

5. mZf;fU ciyapd; Kf;fpa ghfq;fs; mZf;fU ciyapy; fl;Lg;ghlhd> jw;rhu;Gila mZf;fUg; gpsT eilngWk;.

mZf;fU ciyapd; ghfq;fs;: •

vhpnghUs;> jzpg;ghd;> epA+l;uhd; %yk;> fl;Lg;gLj;Jk; jz;L> Fsph;tpf;Fk; mikg;G> epA+l;uhd; vjpnuhspg;ghd;> ghJfhg;G mikg;G.

1.vhpnghUs;:

• • • • • 2.

• • •

gpsitf;F cl;gLk; nghUs; vhpg;nghUs; vdg;gLk;. v.fh 92U235, rpy ciyfspy; Pu239kw;Wk; U233INrhNlhg;Gfs; gad;gLfpwJ. cah; mOj;j fdePh; mZf;fU ciyfspy; vhpnghUs;- ANudpak; Mf;i]L cah; mOj;j ePh; mZf;fU ciyfspy; vhpnghUs;-nrwpT+l;lgl;l ANudpak; fhkpdp mZf;fU ciyapy; vhpnghUs; - U233

jzpg;ghd;: jzpg;ghd;fs; 2MeV Ntf epA+l;uhd;fis 0.025eV ntg;g epA+l;uhd;fshf khw;WfpwJ. epA+l;uhdpd; Ntfj;ijf; Fiwg;gJ jzpg;ghd;fs;. v.fh- fdePh;> rhjhuz ePh;> fpuh/igl;.

3. epA+l;uhd; %yk;: • •

mZf;fU gpsT njhlu; tpidiaj; njhlq;f epA+l;uhd; %yk; Njit. v.fh- G@l;Nlhdpak; kw;Wk; nghpypak; fye;j fyit my;yJ Nubak; kw;Wk; nghpypak; fye;j fyit.

4. fl;Lg;gLj;Jk; jz;L: • • 5.

• •

6.

njhlh; tpidiaf; fl;Lg;gLj;j gad;gLfpwJ. epA+l;uhd;fis mjpf mstpy; cl;ftUk;. v.fh- Nghuhd;> fhl;kpak;> Nghuhd; fhh;igL.

Fsph;tpf;Fk; mikg;G: mZf;fU ciyapy; ntg;gj;ij ePf;Fk; mikg;G Fsph;tpf;Fk; mikg;G. ey;y Fsph;tpg;ghd; cah; jd; ntg;g Vw;Gj;jpwDk;> mjpff; nfhjpepiyAk; ngw;wpUj;jy; Ntz;Lk;. v.fh- fdePh;> rhjhuz ePh;> jput Nrhbak;.

epA+l;uhd; vjpnuhspg;ghd;: • •

epA+l;uhd;fis vjpnuhspj;J kPz;Lk; mZf;fU ciyapy; nrYj;JtJ epA+l;uhd; vjpnuhspg;ghd; MFk;. v.fh –0.7% f;Fk; Fiwthd 92U235I nfhz;Ls;s ANudpak;> Njhhpak;.

48

7. ghJfhg;G mikg;G: •

fjph;tPr;rpd; ghJfhg;G fUjp mZf;fU ciyapy; 2 Kjy; 2.5 kP jbkd; nfhz;l fhd;fphPl; Rth; cs;sJ.

mZf;fU ciyapd; gad;fs;: i) kpd;jpwd; cw;gj;jp; f;F ii) fjphpaf;f INrhl;Nlhg;Gfs; cUthf;f iii) epA+l;uhd; %yq;fshf.

6. tpz;kPd; Mw;wy; #hpadpd; ntg;gepiy kw;Wk; tpz;kPd; Mw;wYf;Ff; fhuzk; mZf;fU ,izT. GNuhl;lhd;-GNuhl;lhd; Rw;W: 1 1H

+ 1H1

1 1H

+ 1H2

2 2He3

2 1H 2He

2He

4

3

+1e0+ ν(ghrpl;uhd; kw;Wk; ePA+l;upNdh ntspg;gLjy;) + γ(fhkhf; fjph; ntspg;gLjy;)

+2 1H1

nkhj;jtpid:

4 1H1

4 2He

+ 2 1e0+ 2

+ Mw;wy; (26.7MeV)

fhh;gd; - iel;u[d; Rw;W: 1 1H

+ 6C12

13* 7N

14 7N +

γ (fhkhf; fjph; ntspg;gLjy;)

15* 8O +

1 14 1H + 7N 15* 8O

ν (ghrpl;uhd; kw;Wk; epA+l;upNdh ntspg;gLjy;)

13 0 6C +1e +

1 13 1H +6C

γ (fhkhf; fjph; ntspg;gLjy;)

13* 7N +

15 0 7N +1e +

1 15 1H + 7N

6C

γ (fhkhf; fjph; ntspg;gLjy;)

ν (ghrpl;uhd; kw;Wk; epA+l;upNdh ntspg;gLjy;)

12

+ 2He4

nkhj;jtpid:

4 1H1

2He

4

+ 2 1e0+ 2 + Mw;wy; (26.7MeV)

7. fh];kpf; fjpu;fs;-FWf;Ff;Nfhl;L tpisT> Fj;Jau tpisT. •

fhkhf;fjph;fis

tpl

gy

klq;F

madpahf;Fk;

jpwd;-nfhz;l

fh];kh];

vdg;gLk; Gwntspapd; midj;J jpirfspYk; ,Ue;J Gtpia milAk;; fjph;tPr;Rfs; fh];kpf; fjph;fs; vdg;gLk;. fh];kpf; fjph;fs; Kjd;ik fh];kpf; fjph;fs;, Jiz fh];kpf; fjph;fs; vd ,uz;L tifg;gLk;.

FWf;Ff;Nfhl;L tpisT: • FWf;Ff;Nfhl;bidg;

nghWj;J fh];kpf; FWf;Ff;Nfhl;L tpisT vdg;gLk;. 49

fjph;fspd;

nrwpT

khWgLtJ

• JUtg;gFjpapy; nrwpT ngUkk;> eLtiuf;Nfhl;Lg;gFjpapy; nrwpT rpWkk;. • 42 f;Fk; 90 f;Fk; ,ilapy; nrwpT khwpyp.

• eLtiuf; Nfhl;Lg; gFjpapy; nrwpT Fiwtjw;fhd fhuzk; Gtp;f; fhe;jg;Gyk;. • JUtq;fspy; kpd;D}l;lk; ngw;w Jfs;, fhe;j tpir NfhLfSf;F ,izahf tUk;. vdNt nrwpT ngUkk;. • eLtiuf;

Nfhl;by;

kpd;D}l;lk;

ngw;w

Jfs,;

fhe;j

tpir

NfhLfSf;Fr;

nrq;Fj;jhf tUk.; vdNt nrwpT rpWkk;.

Fj;Jau tpisT: • Fj;Jauj;ijg; nghWj;J fh];kpf; fjph;fspd; nrwpT khWgLtJ Fj;Jau tpisT vdg;gLk;. • cauk; mjpfhpf;Fk;NghJ nrwpT mjpfhpf;Fk;. • Vwj;jho 20fp.kP cauj;jpy; nrwpT ngUkk;. • mjw;F Nky; nrwpT FiwAk;.

50

myF– 2 kpd;Ndhl;ltpay; 3 kjpg;ngz; tpdh tpilfs; 1. kpd;Ndhl;lk; tiuaW. mjd; myF ahJ? flj;jp xd;wpd; xU gFjp topNa kpd;D}l;lk; ghAk; tPjk; kpd;Ndhl;lk; vd tiuaWf;fg;gLfpwJ. mjhtJ myF : Mk;gpah;(A) 2. ,Og;Gj;jpirNtfk; tiuaW. mjd; myF ahJ? ntspg;Gwj;jpypUe;J nray;gLk; kpd;Gyj;jpdhy; flj;jpapd; topNa fl;Lg;ghlw;w ,af;fj;jpy; cs;s vyf;l;uhd;fspd; kPJ jpzpf;fg;gLk; jpirNtfk; ,Og;Gj;jpirNtfk; vd tiuaWf;fg;gLfpwJ. myF: ms-1 3. ,af;f vz;iz tiuaW. mjd; myF ahJ? XuyF typik nfhz;l kpd;Gyj;jpdhy; ngwg;gLk; ,Og;Gj;jpirNtfk; ,af;f vz; vd tiuaWf;fg;gLfpwJ. myF: m2V-1s-1 4. kpd;Ndhl;l mlh;j;jp tiuaW. mjd; myF ahJ? xU Gs;spapy; kpd;Ndhl;l mlh;j;jp vd;gJ> mg;Gs;spapy;> kpd;D}l;lk; ,aq;Fk; jpirf;Fr; nrq;Fj;jhff; fUjg;gLk; XuyF gug;gpd; topNa XuyF fhyj;jpy; ghAk; kpd;D}l;lj;jpd; msT vd tiuaWf;fg;gLfpwJ. mjhtJ J = myF: Am-2 5. Xkpd; tpjpiaf; $Wf. khwh ntg;gepiyapy; flj;jp xd;wpd; topNa ghAk; rPuhd kpd;Ndhl;lk; flj;jpapd; KidfSf;F ,ilg;gl;l kpd;dOj;j NtWghl;bw;F Neh;j;jftpy; ,Uf;Fk;. mjhtJ I α V⇒ V = IR 6. kpd;jil tiuaW : myF jUf. flj;jp xd;wpd; KidfSf;F ,ilg;gl;l kpd;dOj;j NtWghl;bw;Fk; mjd; topNa ghAk; kpd;Ndhl;lj;jpw;Fk; cs;s jfT flj;jpapd; kpd;jil vd tiuaWf;fg;gLfpwJ. R= myF : ohm 7. xU nghUspd; jd;kpd;jil vz; tiuaW. XuyF ePsKk;> XuyF FWf;F ntl;Lg; gug;Gk; nfhz;l flj;jp xd;W kpd;Ndhl;lj;jpw;F Vw;gLj;Jk; kpd;jil mf;flj;jpg; nghUspd; jd;kpd;jil vz; vdg;gLk;. (myF: Ω m) 8. kPf;flj;Jk; jpwd; vd;why; vd;d? kpff;Fiwe;j ntg;gepiyfspy; xU rpy cNyhfq;fs; mitfspd; Nrh;kq;fs; kw;Wk; cNyhff;fyitfspd; kpd;jil Rop kjpg;ig milAk;. Rop kpd;jilAld; kpd;Ndhl;lj;ijf; flj;Jk; ,g;nghUs;fs; kPf;flj;jpfs; vdg;gLk;. mtw;wpd; jd;ik kPf;flj;J jpwd; vdg;gLk;. 9. khWepiy ntg;gepiy tiuaW rhjhuz flj;jpfs;> jq;fs; kpd;jiliaj; jpBnud ,oe;J kPf;flj;jpfshf khWfpd;w ntg;gepiy ngah;T ntg;gepiy my;yJ khWepiy ntg;gepiy vdg;gLk;.

51

10. xU flj;jp kPf;flj;jpahf khWk; ngah;T ntg;gepiyapy; Vw;gLk; khWghLfis vOJf. i) jd;kpd;jil vz; RopahfpwJ. ii) kpd;flj;J vz; Kbtpyh kjpg;ghfpwJ. iii) fhe;jg;ghaf;NfhLfs; nghUspypUe;J xJf;fpj; js;sg;gLfpd;wd. 11. kpd;;jil ntg;gepiy vz;- tiuaW. 10C ntg;gepiy cah;thy; Vw;gLk; kpd;jil khWghl;bw;Fk; 00C ,y; cs;s kpd;jilf;Fk; cs;s jfT kpd;jil ntg;gepiy vz; vd tiuaWf;fg;gLfpwJ. (α = ; myF / 0 C 12. fph;r;r/gpd; (i) kpd;Ndhl;l tpjp (ii) kpd;dOj;j tpjpiaf; $Wf. i) kpd;Ndhl;l tpjp: xU kpd;Rw;wpy; ve;jnthU re;jpg;gpYk; re;jpf;fpd;w kpd;Ndhl;lq;fspd; Fwpapay; $l;Lj; njhif RopahFk; (kpd;D}l;l moptpd;ik tpjpapd;gb mikAk;). ii) kpd;dOj;j tpjp: xU %ba kpd;Rw;wpd; nttN;tW gFjpfspy; cs;s kpd;jil kw;Wk; kpd;Ndhl;lk; Mfpatw;iwg; ngUf;fp tUk; msTfspd; Fwpapay; $l;Lj;njhif mk;%ba Rw;wpy; cs;s kpd;dpaf;F tpirfspd; Fwpapay; $l;Lj;njhiff;Fr; rkk; (Mw;wy; moptpd;ik tpjpapd;gb mikAk;). 13. kpd;dOj;jkhdpapd; jj;Jtj;ijf; $Wf. kpd;fydpd; kpd;dpaf;Ftpir (E), kpd;dOj;jkhdpf; fk;gpapd; rkd; nra;Ak; ePsj;jpw;F( ) Neh;j;jftpy; mikAk;. mjhtJ E 14. kpd;dOj;jkhdpapy; jhkpuf; fk;gp gad;glhJ Vd;? jhkpuj;jpd; (i) kpd;jil vz; FiwT ii) kpd;jil ntg;gepiy vz; mjpfk;.

15 kpd;dpaf;F tpirf;Fk; kpd;dOj;j NtWghl;bw;Fk; cs;s NtWghLfs;ahit? kpd;dpaf;F tpir kpd;dOj;j NtWghL t.vz; jpwe;j kpd;Rw;wpy; kpd;fyj;jpd; %ba kpd;Rw;wpy; ve;j ,uz;L 1 ,UKidfSf;F ,ilNaahd Gs;spfSf;Fk; ,ilNaahd kpd;dOj;j NtWghlhFk;. kpd;dOj;j NtWghlhFk;. ntspg;Gw kpd; jiliar; ntspg;Gw kpd;jiliar; rhh;e;J 2 rhh;e;J khWtjpy;iy. khWk;. 16. thl; kPl;lh; nray;gLk; tpjj;ijf; $Wf. • gad;gLj;jg;gLk; kpd;jpwid mstpl gad;gLk; thl;kPl;lh; fUtpapy; epiyahfg; nghUj;jg;gl;l thpr;RUs; Nghd;w xUNrhb fk;gpr;RUs;fSf;fpilNa ,aq;F RUs; cs;sJ. • ,aq;F RUSld; FwpKs; xd;W ,izf;fg;gl;L> FwpKs; tl;l msTNfhypw;F Kd;ghf ,aq;ff; $bajhf mikAk;. • fk;gpr;RUspy; kpd;Ndhl;lk; ghAk;NghJ FwpKs;spd; tpyf;fk; kpd;jpwDf;F Neh;j;jftpy; mikAk;.

52

17. kpd;jpwd;> kpd;dhw;wy; NtWgLj;Jf. t.vz; kpd;jpwd; 1. kpd;Ndhl;lj;jpdhy; xU tpdhbapy; nra;ag;gLk; Ntiyapd; msT kpd;jpwd;. 2. kpd;jpwd; P = VI 3.

myF: thl; (W)

kpd;dhw;wy; Ntiy nra;Ak; jpwikahdJ kpd;dhw;wy;. kpd;dhw;wy; E = VIt myF: [Py; (J) eilKiw myF KWh

18. kpd;dhw;gFj;jy; vd;why; vd;d? jputk; xd;wpd; topNa ghAk; kpd;Ndhl;lk; Ntjpkhw;wq;fis cUthf;FfpwJ. ,r;nray; kpd;dhw;gFj;jy; vdg;gLk;. 19. /ghuNlapd; kpd;dhw;gFj;jy; tpjpfisj; jUf. Kjy;tpjp:kpd;thapy; ntspg;gLk; nghUspd; epiwahdJ kpd;gF jputj;jpd; topNa ghAk; kpd;D}l;lj;jpw;F Neh;j;jftpy; mikAk;. mjhtJ m α q ⇒ m α It (or) m=ZIt. ,uz;lhk; tpjp:kpd;gF jputj;jpd; topNa Fwpg;gpl;l msT kpd;D}l;lk; nrYj;jg;gLk;NghJ xUkpd;thapy; ntspg;gLk; jdpkj;jpd; epiw mj;jdpkj;jpd; Ntjpa ,izkhw;Wf;F Neh;j;jftpy; mikAk;. mjhtJ m α E 20. kpd; Ntjpa vz; : tiuaW. myF jUf. kpd;gF jputk; xd;wpd; topNa 1 $Yk; kpd;D}l;lk; nry;Yk;NghJ ntspg;gLk; jdpkj;jpd; epiw mj;jdpkj;jpd; kpd;Ntjpa vz; vd tiuaWf;fg;gLfpwJ. myF : kg C-1 21. Jiz kpd;fyd;fspd; gad;ghLfs; ahit? i) Jiz kpd;fyd;fs; kPz;Lk; kpd;Ndw;wk; nra;ag;glf;$bait. ii) Jiz kpd;fyd;fspd; mfkpd;jil FiwT. vdNt Njitf;Nfw;g mjpf kpd;Ndhl;lj;ij Vw;gLj;Jk;. iii); ,tw;iw kPz;Lk; kPz;Lk; kpd;Ndw;wk; nra;ayhk;. iv) Jiz kpd;fyd;fs; fhh;fs;> ,Urf;fu thfdq;fs;> buf;Ffs; Nghd;wtw;wpy; gad;gLfpd;wd. 22. Kjd;ik kpd;fyd;> Jizkpd;fyd; NtWgLj;Jf. t.vz; Kjd;ik kpd;fyd; Jizkpd;fyd; 1 kPs ,ayh Ntjp tpidfs; eilngWk;. kPs; Ntjp tpidfs; eilngWk; 2 kPz;Lk; kpd;Ndw;wk; nra;a ,ayhJ. kPz;Lk; kpd;Ndw;wk; nra;a ,aYk; 3 mf kpd;jil mjpfk;. mf kpd;jil FiwT 4 ePz;l Neuj;jpw;F xNu rPuhd ePz;l Neuj;jpw;F rPuhd kpd;Ndhl;lj;ij Vw;gLj;jhJ. kpd;Ndhl;lj;ij Vw;gLj;Jk; 23. flj;jp xd;wpd; FWf;F ntl;bd; topNa xU tpdhbapy; 6.25x1018vyf;l;uhd;fs; fle;J nrd;why; kpd;Ndhl;lj;ijf; fzf;fpLf. (e = 1.6x10-19C). I= ⇒I= jPh;T = 1A

I=

24. kpd;tpsf;F xd;W 240 V kpd;dOj;jj;jpy; nray;gLk;;. mjd; kpd;Ndhl;lk; 0.5A vdpy; tpsf;fpd; kpd;jiliaf; fzf;fpLf. jPh;Î: kpd;jil R= R= R= R = 480 53

25. 2 m ePsKk; 0.4 mm tpl;lKk; cila khq;fdpd;fk;gpapd; kpd;jil70Ω. nghUspd; jd;kpd;jil vz;izf; fzf;fpLf. jPh;T : kpd;jil vz; ρ = = = 1.57 x 7 x 4 x 10-7 ρ = 4.396x10-6 Ω m

26. gpd;tUk; Rw;Wtiyapy; A kw;Wk; B f;F ,ilg;gl;l njhFgad; kpd;jiliaf; fzf;fpLf.

R1 = 15Ω A

B

jPh;T: -

R2 = 15Ω

R1, R2 gf;f ,izg;gpy; cs;sd. ,

= 7.5 Ω

,

27.xt;nthU kpd;jilf;Fk; ,ilg;gl;l kpd;dOj;j NtWghLfisf; fhz;f. R1 = 5 Ω R2 = 3 Ω R3 = 2 Ω V2

V1

V3

10V

jPh;T:njhFgad; kpd;jil Rs = R1 + R2 + R3 Rs = 5 + 3 + 2 ⇒ Rs = 10 Ω Rw;wpy; ghAk; kpd;Ndhl;lk; I = Xkpd; tpjpg;gb

=

=1A

V = IR V1 = IR1 = 1 x 5 = 5V V2 = IR2 = 1 x 3 = 3V V3 = IR3 = 1 x 2 = 2V V1 = 5V; V2 = 3V; V3 = 2V

54

28. nfhLf;fg;gl;l kpd;Rw;wpy; nkhj;j kpd;jil kw;Wk; kpd;fyd; jUk; kpd;Ndhl;lj;ijf; fzf;fpLf. 2Ω

3Ω

jPh;T:

3Ω

3Ω

6V

3Ω, 3Ω, 3Ω gf;f ,izg;gpy; cs;sd. =

+

=

+ +

=

+

Rp = 1Ω

jw;NghJ Rp = 1Ω kw;Wk; 2Ω njhlhpizg;gpy; cs;sd. / njhFgad; kpd;jil Rs = Rp + R4 Rs = (1+2)Ω ⇒ Rs = 3Ω kpd;fyd; jUk; kpd;Ndhl;lk; I =

= = 2A

I = 2A 29. rkePsk; nfhz;l xU cNyhfj;jhyhd ,U flj;jpfspd; kpd; jilfs; KiwNa 5Ω kw;Wk; 10Ω mf;flj;jpfspd; Muq;fspd; tpfpjq;fisf; fzf;fpLf. jPh;T:

R1 = 5Ω, R2 = 10Ω, ℓ1 = ℓ2 = ℓ vd;f = =

= r1 : r2 =

:1

55

30. fPo;fhZk; kpd; Rw;wpy; kpd;Ndhl;lj;jpidf; fzf;fpLf. kpd;Ndhl;lk; nry;Yk; jpiriaf; Fwpg;gpLf. A

10V

2V

5Ω

B

7Ω 3Ω

D 5Ω 8V C jPh;T:Rw;wpy; ghAk; kpd;Ndhl;lk; I vd;f ABCDA jpirapy; kpd;Ndhl;lk; gha;tjhff; nfhz;lhy;> fph;r;r/g; ,uz;lhk; tpjpapidg; gad;gLj;j> 5 I + 7I + 3I + 5I = 10 + 2 – 8 20 I = 4, I = ⇒ I = 0.2 A kpd;Ndhl;lk; tyQ;Ropahfr; nry;Yk; my;yJ ABCDA

tyQ;Ropahf

topNa mikAk;.

31. fPo;f;fhZk; kpd;Rw;wpy; kpd;Ndhl;lj;jpidf; fzf;fpLf. kpd;Ndhl;lk; nry;Yk; jpiriaf; Fwpg;gpLf. A

5Ω

10V

10Ω

B

D 20 V 5Ω jPh;Î : fph;r;r/gpd; ,uz;lhk; tpjpapidg; gad;gLj;j> 5 I + 10 I + 5 I = 10 + 20, 20 I = 30⇒ I = ⇒I = 1.5 A

C

kpd;Ndhl;lk; tyQ;Ropahfr; nry;Yk; my;yJ ABCDA topNa mikAk;. 32. fPo;f;fhZk; fzf;fpLf.

kpd;Rw;wpy; kpd;Ndhl;lj;jpd;; jpiriaAk; vz;kjpg;igAk; 5

10V

10 B

A

D 20V 5 jPh;T:- kpd;Ndhl;lk; tyQ;Ropapy; gha;tjhff; fUJf. fph;r;r/gpd; ,uz;lhk; tpjpapidg; gad;gLj;j> 5I+10I+5I = 10-20 20I = -10 I= I=I=-0.5A kpd;Ndhl;lj;jpd; vz;kjpg;G = 0.5A kpd;Ndhl;lk; ,lQ;RopahfTk; my;yJ ADCBA topahfTk;; ghAk;. 56

C

33.

O0C y; epf;Nuhk; fk;gpapd; kpd;jil10 Ω mjd; kpd; jil ntg;gepiy vz; 0. 004 / 0C ePhpd; nfhjpepiyapy; mjd; kpd;jiliaf; fzf;fpLf. Kbitg; gw;wpa tpsf;fj;ijj; jUf. jPhT:-;:-

Rt = Ro (1 + αt) R100 = Ro (1+100α) R100 = 10 (1+ 100 x 0.004) =10 (1 + 0.4) = 10 x 1.4 R100 = 14 Ω

ntg;gepiy caUk;NghJ kpd;jilAk; caUk;. 34. 00C y; gpshl;bdk; fk;gpapd; kpd;jil4Ω gpshl;bdj;jpd; kpd;jil ntg;gepiy vz; 0.038 / 0C vdpy; 100oC ,y;; fk;gpapd; kpd;jil vd;d? jPh;T:-

Rt = Ro (1 + α t) R100 = Ro (1 + 100 α) R100= 4 (1 + 100 x 0.0038) = 4 (1 + 0.38) = 4 x 1.38 R100 = 5.52 Ω

35. 1.5V kpd;dpaf;F tpir cila fhh;gd;-Jj;jehfk; gir kpd;fyk; 1000 kpd;jilahf;fpAld; ,izf;fg;gl;Ls;sJ. kpd;Ndhl;lj;ijAk; jpwidAk; fzf;fpLf. jPh;T:- i) kpd;Ndhl;lk; I = = I = 1.5x10-3 A ii) kpd;jpwd;

P= VI P=1.5x1.5x10-3 P=2.25x10-3 W

36. 400 W kpd;jpwd; nfhz;l xU kpd; ryitg;ngl;b jpdKk; 30 epkplq;fSf;Fg; gad;gLj;jg;gLfpwJ. xU A+dpl; jpwDf;fhd fl;lzk; 75 igrh vdpy; ryitg; ngl;bia xU thu fhyk; gad;gLj;jpdhy; Vw;gLk; nryitf; fzf;fpL. E= Pxt jPh;T:- nrytopf;fg;gl;l kpd;dhw;wy; E = 400 x x 7 E = 1400 Wh E = 1.4 Unit 1A+dpl;Lf;fhd fl;lzk; = &. 0.75 1.4 A+dpl;Lf;fhd fl;lzk; = 1.4 x 0.75 nryT

57

=

& 1.05.

5 kjpg;ngz; tpdh-tpilfs; 1.

kpd;Ndhl;lj;jpw;Fk; ,Og;Gj;jpirNtfj;jpw;Fk; ,ilNa njhlh;G: ntspg;Gwj;jpypUe;J nray;gLk; kpd;Gyj;jpdhy;> flj;jpapd; topNa fl;Lg;ghlw;w ,af;fj;jpy; cs;s vyf;l;uhd;fs; kPJ jpzpf;fg;gLk; jpirNtfk; ,Og;Gj; jpirNtfk; vd tiuaWf;fg;gLfpwJ.

• • • • •

L ePsKk; A FWf;Fntl;Lg;gug;Gk; nfhz;l flj;jpapd; KidfSf;fpilNa E typik nfhz;l kpd;Gyk; nray;gLj;jg;gLfpwJ. XuyF gUkdpy; vyf;l;uhd;fspd; vz;zpf;if n vd;f. flj;jpapy; ghAk; kpd;D}l;lk; q = (nAL)e L kpd;D}l;lq;fs; nry;y MFk;fhyk; t = vd q ( nAL) e flj;jpapy; ghAk; kpd;Ndhl;lk; I = = t L   v   d

I = nAe vd 2.

kPf;flj;jpfspd; gad;fs; • • • • •

kPf;flj;J ,aw;wpfs; Mw;wy; Nrkpg;Gj;jpwd; mbg;gilahf cs;sd. kPf;flj;jp fhe;jq;fs; ,uapy; tz;bfisj; jz;lthsq;fspypUe;J cah;j;jp kpf mjpf Ntfj;Jld; ,af;fg; gad;gLk;. ,uhf;nfl; Jizapd;wp nraw;iff;Nfhis Vtg; gad;gLk;. kpd;Ndhl;lj;jpd; typik khwhky; ,Ug;gjhy; kpd; mDg;gpf; fk;gpapy; gad;gLk;. fzpdpfspy; epidT mbg;gilf; $Wfshfr; nray;gLk;.

3. gy kpd;jilahf;fpfs; njhlhpizg;gpy; ,izf;fg;gl;lhy; njhFgad; kpd;jil

• • • •

ehd;F kpd;jilahf;fpfs; njhlhpizg;gpy; ,izf;fg;gl;L V kpd;dOj;j NtWghL mspf;fg;gLfpwJ. njhlhpizg;gpy; kpd;Ndhl;lk; khwhJ. V1 = I R1 ; V2 = I R2, V3 = I R3, V4 = I R4 nkhj;j kpd;dOj;jk; V = V1+V2+V3+V4 V = I[R1+R2+R3+R4] (1) njhFg;gpd; kpd;jil Rs vd;f. V = I Rs (2) rkd;ghLfs; 1> 2 ypUe;J Rs = R1+R2+R3+R4

58

4. gy kpd;jilahf;fpfs; gf;f ,izg;gpy; ,izf;fg;gl;lhy; njhFgad; kpd;jil

• • • •

•

•

ehd;F kpd;jilahf;fpfs; gf;f ,izg;gpy; ,izf;fg;gl;L V kpd;dOj;j NtWghL mspf;fg;gLfpwJ. gf;f ,izg;gpy; kpd;dOj;jk; khwhJ. V V V V I1 = ; I 2 = ; I 3 = ; I 4 = R1 R2 R3 R4 nkhj;j kpd;Ndhl;lk; I = I1 + I2 + I3 + I4 V V V V I= + + + R1 R2 R3 R4  1 1 1 1   I = V  + + +  R1 R2 R3 R4  njhFg;gpd; kpd;jil Rp vd;f. V I= Rp 1 1 1 1 1 rkd;ghLfs; 1> 2 ypUe;J = + + + R p R1 R2 R3 R4

----→ 1

------→ 2

5.ntg;gepiyiar; rhh;e;j kpd;jil khWghL (tiuglj;Jld;) • ntg;gepiy caUk;NghJ flj;jpfspd; kpd;jil mjpfhpf;Fk;. Rt = Ro (1 + α t) > α = kpd;jil ntg;gepiy vz; • 10C ntg;gepiy cah;thy; Vw;gLk; kpd;jil khWghl;bw;Fk;> 00C cs;s kpd;jilf;Fk; cs;s jfT kpd;jil ntg;gepiy vz; MFk;. R − R0 α= t R0t

• •

cNyhfq;fSf;F kpd;jil ntg;gepiy vz; Neh;f;Fwp kpd;fhg;Gg;nghUl;fs;> Fiwf;flj;jpfSf;F(njh;kp];lh;fSf;F) kpd;jilntg;gepiy vz; vjph;Fwp. cNyhff;fyitfSf;F kpd;jil ntg;gepiy vz; FiwT.

59

6.Nthy;l; kPl;liuf; nfhz;L kpd;fydpd; mfkpd;jiliaf; fzf;fply;

• •

•

•

rhtp jpwe;Js;s epiyapy; Nthy;l;kPl;lh; fhl;Lk; mstPL kpd;dpaf;F tpir E

rhtpia %ba epiyapy; Nthy;l; kPl;lh; fhl;Lk; mstPL kpd;jil R f;F ,ilg;gl;l kpd;dOj;j NtWghL V V = IR 1 kpd;fydpd; mfkpd;jil(r)apdhy;>VMdJ E I tpl FiwT V = E – Ir Ir = E – V 2 rkd;ghL 2 ÷ rkd;ghL 1>

=  E −V  r = R  V  7. fph;r;r‡gpd; ,uz;lhk; tpjp tpsf;fk; • tpjp: xU %ba Rw;wpd; ntt;NtW gFjpfspy; cs;s kpd;jil kw;Wk; kpd;Ndhl;lk; Mfpatw;iwg; ngUf;fp tUk; msTfspd; Fwpapay; $l;Lj;jd;ik mk;%ba Rw;wpy; cs;s kpd;dpaf;F tpirfspd; Fwpapay; $l;Lj;njhiff;Fr; rkk;. • Mw;wy; moptpd;ik tpjpg;gb mikAk;. • kpd;Rw;wpy; tyQ;Ropahfg; ghAk; kpd;Ndhl;lq;fs; Neh;f;Fwp> kpd;Rw;wpy; ,lQ;Ropahfg;ghAk; kpd;Ndhl;lq;fs; vjph;f;Fwp • glj;jpy; fhl;bAs;s kpd;Rw;Wf;F ABCDA vd;w %ba ghijf;F I1 R1 + I2 R2 + I2 r2 + I3 R3 + I1 r1 = E1 – E2 8. tPl;];ld; rkdr;Rw;wpd; Roptpyf;fj;jpw;fhd epge;jid. • gpd;tUk; Rw;W tPl;];ld; rkdr;Rw;W MFk;.

• •

fph;r;r/gpd;; Kjy;tpjpg;gb re;jp B y; I1 – Ig – I3 = 0 → (1) re;jp Dy; I2 + Ig – I4 = 0 → (2) fph;r;r/gpd; ,uz;lhk; tpjpg;gb ABDAvd;w %ba ghijf;F> 60

•

•

I1P + IgG – I2R = 0 → (3) fph;r;r/gpd; ,uz;lhk; tpjpg;gb ABCDA vd;w %ba ghijf;F> I1 P + I3 Q – I4 S – I2 R = 0 → (4) Roptpyf;fj;jpw;F Ig = 0 I1 = I3 → (5) I2 = I4 → (6) I1P = I2R→ (7) rkd; 5> 6>7 d; kjpg;Gfisr; rkd; 4 ,y; gpujpapl> I1(P+Q) = I2(R+S) → (8) rkd (8) [ rkd; (7) My; tFf;f I1 ( P + Q ) R+S = I1 P R Q S 1+ = 1+ P R P R = Q S

9. kpd;dOj;jkhdpapd; jj;Jtk;:

•

kpd;dOj;jkhdpf; fk;gpapd; KidfSf;fpilNa Bt, K (rhtp) njhlhpizg;gpy; ,izf;fg;gLfpwJ - Kjd;ikr; Rw;W.

•

Kjd;ik kpd;fyd;> fhy;tdhkPl;lh;> cah;kpd;jil> njhLNfhy; Mfpait njhlhpizg;gpy; A Ald; ,izf;fg;gl;Ls;sd - Jizr;Rw;W

•

XuyF ePsf; fk;gpapd; kpd;jil r vd;f. Ig = 0 vdpy; AJ d; kpd;dOj;j NtWghLk;> kpd;fydpd; kpd;dpaf;F tpirAk; rkk;.

•

rkd; nra;Ak; ePsk; l vdpy; AJ d; kpd;dOj;j NtWghL Ir l E = I rl Eα l

•

kpd;fydpd; mikAk;.

kpd;dpaf;Ftpir

(E)>

61

rkd;nra;Ak;

ePsj;jpw;F

Neh;j;jftpy;

10. ,U Kjd;ik kpd;fyd;fspd; kpd;dpaf;F tpirfspd; xg;gpLjy;

•

kpd;dOj;jkhdp fk;gpapd; KidfSf;fpilNa Bt> rhtp> njhlhpizg;gpy; ,izf;fg;gLfpwJ - Kjd;ikr; Rw;W.

•

E1, E2 kpd;dpaf;FtpirAila kpd;fyd;fs; DPDT rhtpapd; C1 D1 kw;Wk;

kpd;jilkhw;wp

C2 D2 Kidfspy; ,izf;fg;gLfpd;wd. •

Kjd;ikr;Rw;wpy; ghAk; kpd;Ndhl;lk; I> XuyF ePsf; fk;gpapd; kpd;jil r vd;f.

•

E1 Jizr;Rw;Wld; ,izg;G ngw;why; E1 =

•

rkd;nra;Ak; ePsj;jpw;F

→ (1)

E2 Jizr;Rw;Wld; ,izg;G ngw;why; E2=

1

l 2 rkd;nra;Ak;

ePsj;jpw;F

→ (2)

rkd;ghL 1 ÷ 2 ⇒

E1 l 1 = E2 l 2

11 . kpd;dhw;gFj;jy; /ghuNl Kjy; tpjp rhpghh;j;jy;:

tpjp:-kpd;dhw;gFj;jypd;NghJ kpd;thapy; ntspg;gLk; jdpkj;jpd; epiw kpd;gFjputj;jpd; topNa ghAk; kpd;D}l;lj;jpw;F Neh;jftpy; ,Uf;Fk;. • glj;jpy; fhl;bathW kpd; ,izg;Gfs; nfhLf;fg;gLfpd;wd. • ‘t’ fhy msTf;F I1 kpd;Ndhl;lk; gha;fpwJ. ntspg;gLk; jdpkj;jpd; epiw ‘m1’ m1α I1 • ‘t’ fhy msTf;F I2 kpd;Ndhl;lk; gha;fpwJ. ntspg;gLk; jdpkj;jpd; epiw ‘m2’ m2α I2 m1 I1 = ⇒ mα I • m2 I 2 (1) • I kpd;Ndhl;lkhdJ t1 fhyj;jpw;F gha;fpwJ. ntspg;gLk; jdpkj;jpd; epiw ‘m3’ m3α t1 • I kpd;Ndhl;lkhdJ t2 fhyj;jpw;F gha;fpwJ.ntspg;gLk; jdpkj;jpd; epiw ‘m4’ 62

m4α t2 • •

m 3 t1 = mαt m4 t2 rkd;ghLfs; (1)> (2) ypUe;J mαIt

(2)

12. kpd;dhw;gFj;jy; /ghuNl ,uz;lhk; tpjp rhpghh;j;jy;:

kpd;gFj;jputj;jpd; topNa Fwpg;gpl;lmsT kpd;D}l;lk; tpjp: nrYj;jg;gLk;NghJ kpd;thapy; ntspg;gLk; jdpkj;jpd; epiw mj;jdpkj;jpd; Ntjpa ,iz khw;Wf;F Neh;jftpy; ,Uf;Fk;. • glj;jpy; fhl;bathW kpd;dpizg;Gfs; nfhLf;fg;gLfpd;wd. • ‘t’ fhy msTf;F I kpd;Ndhl;lk; gha;fpwJ. • jhkpu kpd;thapy; ntspg;gLk; jdpkj;jpd; epiw ‘m1’ m1α E1 (E1 Kjy; jdpkj;jpd; Ntjpa ,iz khw;W) • nts;sp kpd;thapy; ntspg;gLk; jdpkj;jpd; epiw ‘m2’ m2α E2 (E2 ,uz;lhk;jdpkj;jpd; Ntjpa ,iz khw;W) m1 E1 = m2 E2 mαE 13. Nthy;lh kpd;fyk;: mikg;G : Neh;kpd;tha; → jhkpuk; vjph;kpd;tha; → Jj;jehfk; kpd;gFjputk; → ePh;j;j fe;jf mkpyk; ghj;jpuk; → fz;zhb nray;ghL: Jj;jehfj; jfL H2SO4 cld; tpidGhpe;J Zn++ madpfis ntspNaw;wp ,U ngw;W vjph;kpd;D}l;lk; ngWk;. • • •

vyf;l;uhd;fisg;

jhkpuk;; 2H+ madpfis eLepiyahf;fp Neh; kpd;D}l;lk; ngWk;. ntspr;Rw;wpy; jhkpuj;jpypUe;J Zn f;F kpd;Ndhl;lk; gha;fpwJ. kpd;dpaf;F tpir→ 1.08V

63

14. Nldpay; kpd;fyk;: ePz;lNeuj;jpw;F kpd;Ndhl;lj;ijr; nrYj;j ,ayhJ.

mikg;G : Neh; kpd;tha; → jhkpuk; vjph;kpd;tha; → Jj;jehfk; kpd;gFjputk; → jhkpu ry;Ngl; fiury;> ePh;j;j fe;jf mkpyk; nray;ghL : • Jj;jehfj; jfL H2SO4 cld; tpidGhpe;J Zn++madpfis ntspNaw;wp ,U vyf;l;uhd;fisg; ngw;W vjph;kpd;D}l;lk; ngWk;. • Ez;Jisg; ghz;lj;jpd; Jis topNa nry;Yk; Zn++ madpfs; CuSO4Tld; tpid Ghpe;J cUthFk; Cu++madpfs; jhkpuf;fydpy; gbe;J jhkpuf;fyd; Neh; kpd;D}l;lk; ngWk;. • Jj;jehfj;jpy; ,Ue;J jhkpuj;jpw;F ,U vyf;l;uhd;fs; Rw;wpd; topNa nrd;W jhkpu madpfis eLepiyahf;Fk;. • ntspr;Rw;wpy; jhkpuj;jpypUe;J Zn f;F kpd;Ndhl;lk; gha;fpwJ. • kpd;dpaf;F tpir→ 1.08V 15. nyf;yhQ;rp kpd;fyk;: mikg;G :

Neh; kpd;tha;

→ fhh;gd; jz;L

vjph;kpd;tha;

→ Jj;jehfk;

kpd;gFjputk;

→ mk;Nkhdpak; FNshiuL fiury;

ghj;jpuk; → fz;zhb nray;ghL: • Jj;jehfj;jz;L NH4Cl cld; tpidGhpe;J Zn++ madpfshf ntspNaw;wp vjph;kpd;D}l;lk; ngWk;. • Zn++ + 2NH4Cl → 2NH3 + ZnCl2 + 2H+ + 2e-

64

•

2H+ madpfspd; Neh;kpd;D}l;lk; fhh;gd; jz;Lf;F khw;wg;gl;L Neh; kpd;D}l;lk;ngWk;. Jj;jehfj;jpy; cs;s ,U vyf;l;uhd;fs; fhh;gd; jz;il mile;J mjd; Neh;kpd;D}l;lj;ij eLepiyahf;Fk;. ntspr;Rw;wpy; fhh;gdpypUe;J Zn f;F kpd;Ndhl;lk; ghAk;.

•

kpd;Ndhl;lk; → 0.25A

•

kpd;dpaf;F tpir → 1.5V

•

16. fhhPa mkpy Nrkf;fyk;: mikg;G: Neh; kpd;tha; → fhhPa Mf;irL vjph;kpd;tha;

→ fhhPak;

kpd;gFjputk; →ePh;j;jfe;jf mkpyk; ghj;jpuk; → ug;gh; my;yJ fz;zhb nray;ghL: vjph;kpd;thapy; eilngWk; Mf;rp[Ndw;w tpidahy; PbSO4 cUthfp ,U vyf;l;uhd;fs; vjph;kpd;thapy; Vw;gLfpwJ. • • •

Neh;kpd;thapy; Mf;rp[dpwf;f tpidahy; PbSO4 cUthfp ,Uvyf;l;uhd;fSk; eLepiyahf;fg;gLfpwJ. mfkpd;jil FiwT vd;gjhy; mjpf kpd;Ndhl;lj;ijj; juty;yJ. Gjpa kpd;dpaf;F tpir→2.2V

•

kpd;dpwf;fk; nra;Ak;NghJ kpd;dpaf;F tpir → 2V

4. kpd;fhe;jj;J}z;lYk; khWjpir kpd;Ndhl;lKk; ; 3 kjpg;ngz; tpdh-tpilfs; 1. fhe;jg;ghak; tiuaW : myF ahJ? fhe;jg;ghak; vd;gJ nfhLf;fg;gl;l gug;G topNa nry;Yk; fhe;j tpirf; NfhLfspd; nkhj;j vz;zpf;if MFk;. mjhtJ

myF : ntgh; (Wb)

2. kpd;fhe;jj;J}z;ly; vd;why; vd;d? xU %lg;gl;l Rw;Wld; njhlh;G nfhz;l fhe;jg;ghaj;jpy; khw;wk; Vw;gLk; nghOJ mr;Rw;wpy; kpd;dpaf;F tpir J}z;lg;gLk; epfo;T kpd;fhe;jj; J}z;ly; vdg;gLk;. 3. kpd;fhe;jj;J}z;ly; gw;wpa /ghuNl tpjpfisf; $Wf. i) xU %lg;gl;l Rw;NwhL njhlh;G nfhz;l fhe;j ghak; khWk; nghOJ me;jr; Rw;wpy; kpd;dpaf;F tpir J}z;lg;gLfpwJ. fhe;jghaj;jpy; khw;wk; epfo;e;J nfhz;bUf;Fk; tiuapy; kl;LNk J}z;lg;gl;l kpd;dpaf;F tpir ePbf;Fk;. ii) %lg;gl;l Rw;wpy; J}z;lg;gl;l kpd;dpaf;F tpirapd; vz; kjpg;G (e) Rw;Wld; njhlh;G nfhz;l fhe;j ghak; khWk; tPjj;jpw;F Neh;j;jftpy; ,Uf;Fk;.

e α

65

4. kpd;fhe;jj; J}z;ly; gw;wpa nyd;]; tpjpiaf; $Wf. xU Rw;wpy; J}z;lg;gl;l kpd;Ndhl;lj;jpd; jpir vg;NghJk; mij cUthf;ff; fhuzkhf ,Ue;j fhe;jg;gha khw;wj;ij vjph;f;Fk; tifapy; mikAk;. mjhtJ 5. /gpskpq; tyJif tpjpiaf; $Wf. tyJ ifapd; Ms;fhl;b tpuy;> eLtpuy; kw;Wk; ngUtpuy; Mfpa %d;iwAk; xd;Wf;nfhd;W nrq;Fj;jhf itj;Jf; nfhs;sTk;> Ms;fhl;b tpuy; fhe;jg;Gyj;jpd; jpiriaAk;> ngUtpuy; flj;jp ,aq;Fk; jpiriaAk; Fwpg;gjhff; nfhz;lhy; eLtpuyhdJ J}z;lg;gl;l kpd;Ndhl;lj;jpd; jpiriaf; Fwpf;Fk;. 6. jd;kpd;J}z;ly; vd;why; vd;d? xU fk;gpr;RUspy; ghAk; kpd;Ndhl;lj;jpy; khw;wk; Vw;gLk;nghOJ mf;fk;gpr;RUspy; xU vjph;kpd;dpaf;F tpir J}z;lg;gLk; epfo;T jd;kpd;J}z;ly; vdg;gLk;. 7.

jd;kpd; J}z;ly; vz; tiuaW. fk;gpr; RUs; xd;wpy; ghAk; kpd;Ndhl;lk; xU tpdhbf;F xU Mk;gpah; vd;w tPjj;jpy; khWk; nghOJ mf;fk;gpr;RUspy; J}z;lg;gLk; vjph; kpd;dpaf;Ftpir vz;zstpy; mr;RUspd; jd;kpd;J}z;ly; vz;zpw;Fr; rkk;. myF : henry (H)

8. jd;kpd; J}z;ly; vz;zpd; myif tiuaW. jd;kpd; J}z;ly; vz;zpd; myF – n`d;wp (H). fk;gpr;RUs; xd;wpy; ghAk; kpd;Ndhl;lk; xU tpdhbf;F xU Mk;gpah; vd;w tPjj;jpy; khWk;NghJ> mf;fk;gpr;RUspy; J}z;lg;gLk; vjph;kpd;dpaf;Ftpir 1 Nthy;l; vd mikAkhdhy;> mr;RUspd; jd;kpd; J}z;ly; vz; 1 n`d;wp vd tiuaWf;fg;gLfpwJ. 9. ghpkhw;W kpd;J}z;ly; vd;why; vd;d? xU RUspy; ghAk; kpd;Ndhl;lj;jpy; khw;wk; Vw;gLk;nghOJ kw;nwhU RUspy; kpd;dpaf;F tpir J}z;lg;gLk; epfo;T ghpkhw;W kpd;J}z;ly; vdg;gLk;. 10. ghpkhw;W kpd;J}z;ly; vz; tiuaW. myF jUf. fk;gpr;RUs; xd;wpy; ghAk; kpd;Ndhl;lk; xU tpdhbf;F 1 Mk;gpah; vd;w tPjj;jpy; khWk;nghOJ> kw;nwhU fk;gpr;RUspy; J}z;lg;gLk; vjph;kpd;dpaf;F tpir vz;zstpy; mt;tpU RUs;fspd; ghpkhw;W kpd;J}z;ly; vz;zpw;Fr; rkk;. myF : henry (H) 11. ghpkhw;W kpd;J}z;ly; vz;zpd; myif tiuaW : ghpkhw;W kpd;J}z;ly; vz;zpd; myF - henry. (H) fk;gpr;RUs; xd;wpd; topNa ghAk; kpd;Ndhl;lk; xU tpdhbf;F 1 Mk;gpah; vd;w tPjj;jpy; khWk; nghOJ> kw;nwhU fk;gpr;RUspy; J}z;lg;;gLk; vjph; kpd;dpaf;F tpir 1 Nthy;l; vd mikAkhdhy; mt;tpU fk;gpr;RUs;fspd; ghpkhw;W kpd;J}z;ly; vz; 1 n`d;wp MFk;. 12. ghpkhw;W kpd;J}z;ly; vz; rhh;e;Js;s fhuzpfs; ahit? i) RUspd; ghpkhzk;> tbtk;> Rw;Wfspd; vz;zpf;if kw;Wk; cs;sfkhfg; gad;gLk; nghUspd; fhe;j cl;GFjpwd; Mfpatw;iwAk; ii) fk;gpr;RUs;fs; xd;Wf;nfhd;W vt;tsT mUfpy; cs;sd vd;gijAk; rhh;e;jJ.

66

13. J}z;lg;gl;l kpd;dpaf;F tpiriaj; Njhw;Wtpf;Fk; Kiwfs; ahit? i) fhe;jj; J}z;liy (B) khw;Wtjd; %yk;. ii) RUs; cs;slf;fpa gug;gpid (A) khw;Wtjd; %yk;. iii) fhe;jGyj;ijg; nghWj;J RUspd; jpir mikg;ig (θ) khw;Wtjd; %yk; J}z;lg;gl;l kpd;dpaf;F tpiriag; ngwyhk;. 14. A.C. kpd;dpaw;wpapd; jj;Jtj;ijf; $Wf. fk;gpr;RUs; xd;W rPuhd fhe;jg;Gyj;jpy; Row;wg;gLk;NghJ mjpy; kpd;dpaf;F tpir J}z;lg;gLk; (kpd;fhe;jj; J}z;ly;) 15. Roy; kpd;Ndhl;lk; (/Nghfhy;l; kpd;Ndhl;lk;) vd;why; vd;d? cNyhff;fl;b xd;W fhe;jg;Gyj;jpy; ,aq;Fk;nghOJ my;yJ epiyahf cs;s cNyhff; fl;bapd; topNa nry;Yk; fhe;jg;ghak; khWk; nghOJ cNyhff;fl;bapDs; kpd;Ndhl;lk; J}z;lg;gLfpwJ. cNyhff; flj;jpapDs; J}z;lg;gLk; ,k;kpd;Ndhl;lk; Roy; kpd;Ndhl;lk; my;yJ /Nghfhy;l; kpd;Ndhl;lk; vdg;gLk;. 16. kpd;khw;wp vd;why; vd;d? mjd; jj;Jtk; ahJ? Fiwe;j khWjpir kpd;dOj;jj;ij mjpf khWjpir kpd;dOj;jkhfTk; mjpf khWjpir kpd;dOj;jj;ij Fiwe;j khWjpir kpd;dOj;jkhfTk; khw;w cjTk; rhjdk; kpd;khw;wp vdg;gLk;. jj;Jtk; : kpd;fhe;jj;J}z;ly; (ghpkhw;W kpd;J}z;ly;) 17. Vw;W kpd;khw;wp> ,wf;F kpd;khw;wp NtWgLj;Jf. t. vz; 1. 2. 3.

4.

Vw;W kpd;khw;wp

,wf;F kpd;khw;wp

kpd;dOj;jj;ij mjpfhpf;fpwJ. Es > Ep kpd;Ndhl;lj;ijf; Fiwf;fpwJ Is < Ip Kjd;ikr; RUspd; Rw;Wfspd; vz;zpf;ifiatpl Jizr;RUspd;Rw;Wfspd; vz;zpf;if mjpfk;. Ns > Np kpd;khw;wp tpfpjk; k >1

kpd;dOj;jj;ijf; Fiwf;fpwJ. Es < Ep kpd;Ndhl;lj;ij mjpfhpf;fpwJ. Is > Ip Kjd;ikr; RUspd; Rw;Wfspd; vz;zpf;ifiatpl Jizr;RUspd;Rw;Wfspd; vz;zpf;if FiwT Ns < Np kpd;khw;wp tpfpjk; k<1

18. kpd;khw;wpapd; gaDWjpwd; tiuaW. kpd;khw;wpapd; gaDWjpwd; vd;gJ ntspaPL jpwDf;Fk; cs;sPL jpwDf;Fk; cs;s jfT vd tiuaWf;fg;gLfpwJ. η

=

ntspaP ŋ L jpwd; cs;sPL jpwd;

= Es I s

Ep I p

19. D. C. mk;kPl;lh; khW jpir kpd;Ndhl;lj;ij mstplhJ. Vd;? khWjpir kpd;Ndhl;lj;jpd; xU KOr;Rw;Wf;fhd ruhrhp kjpg;G RopahFk;. vdNt D.C. mk;kPl;liu A.C. kpd;Rw;wpy; ,izj;jhy; mjd; Fwp Ks; Rop msitNa vg;NghJk; fhl;Lk;. 20. khWjpir kpd;Ndhl;lj;jpd; rms kjpg;G (gaDW kjpg;G ) tiuaW. khWjpir kpd;Ndhl;lkhdJ xU kpd;jilahf;fp xd;wpd; topahf Fwpg;gpl;l Neuk; ghAk;nghOJ cUthf;Fk; ntg;g Mw;wiy> mNj Neuj;jpy; mNj kpd;jilapy; cUthf;Fk; khwhj Neh;kpd;Ndhl;lj;jpd; kjpg;G> khWjpir kpd;Ndhl;lj;jpd; rms kjpg;G vdg;gLfpwJ. 67

21. kpd;J}z;bapd; kpd;kWg;G vd;why; vd;d? xU fk;gpr;RUs; my;yJ kpd;J}z;b khWjpir Vw;gLj;Jk; kpd;jil mjd; kpd;kWg;G (XL) vdg;gLk;. XL= L

kpd;Ndhl;lj;jpw;F myF : ohm

22. kpd;Njf;fpapd; kpd;kWg;G vd;why; vd;d? xU kpd;Njf;fp khWjpir kpd;Ndhl;lj;jpw;F Vw;gLj;Jk; kpd;jil mjd; kpd;kWg;G(Xc) vdg;gLk;. Xc= myF : ohm 23. kpd; Njf;fp D.C. jLf;Fk; A.C I mDkjpf;Fk; Vd;? • xU kpd;Njf;fpapd; kpd;kWg;G • d.c f;F mjph; ntz; ( • ,jdhy; D.C. f;F Xc = mjhtJ kpd;kWg;G Kbtpyh kjpg;ig miltjhy; • D.C. I kpd;Njf;fp mDkjpf;fhJ. • vd;w rkd;ghl;bd;gb A.C. I kl;Lk; mDkjpf;Fk;. 24. RLC njhlh; Rw;wpy; kpd;dOj;j %yj;jpd; mjph;ntz;iz mjpfhpj;jhy; kpd;Ndhl;lj;jpd; kjpg;G vd;dthFk;? kpd;dOj;j %yj;jpd; mjph;ntz;iz mjpfhpj;jhy; Rw;wpd; kpd;kWg;G Fiwe;J kpd;Ndhl;lk; mjpfhpf;Fk;. xj;jpirT mjph; ntz;zpy; kpd;Ndhl;lk; ngUk kjpg;igg; ngWk;. xj;jpirT mjph;ntz;iz tpl mjpfkhdhy; kpd;Ndhl;lk; gbg;gbahff; FiwAk;. 25. RLC njhlhpizg;Gr; Rw;wpy; xj;jpirT mjph;ntz; vd;why; vd;d? RLC njhlhpizg;Gr; Rw;wpy; ve;jf; Fwpg;gpl;l mjph;ntz;Zf;Fr; Rw;wpd; kpd;ndjph;g;G rpWkkhfTk;> kpd;Ndhl;lk; ngUkkhfTk; khWNkh me;jf; Fwpg;gpl;l mjph;ntz; Rw;wpd; xj;jpirT mjph;ntz; ( 0) vdg;gLk;. 26.juf;fhuzp vd;gjid tiuaW. njhlh; xj;jpirTr; Rw;wpd; juf;fhuzp vd;gJ fk;gpr;RUs; my;yJ kpd;Njf;fpapd; FWf;Nf cs;s kpd;dOj;j NtWghl;bw;Fk; nrYj;jg;gLk; kpd;dOj;jj;jpw;Fk; cs;s jfT vd tiuaWf;fg;gLfpwJ . L my;yJ C-d; FWf;Nf cs;s kpd;dOj;jk; ⇒Q = nrYj;jg;gLk; kpd;dOj;jk; Q= 27. A.C. Rw;wpd; jpwd; fhuzp tiuaW. jpwd; fhuzp = cos ,q;F vd;gJ kpd;Ndhl;lj;jpw;Fk;> kpd;dOj;jj;jpw;Fk; cs;s fl;l NtWghL MFk;. ,J ruhrhp jpwDf;Fk;> Njhw;wj;jpwDf;Fk; cs;s jftpw;Fr; rkkhFk;. 28. milg;Gr; RUs; vd;gJ ahJ? A.C. kpd;Rw;wpy; kpd;Ndhl;lj;ijf; fl;Lg;gLj;jg; gad;gLj;jg;gLk; Fiwe;j kpd;jiliaf; nfhz;l fk;gpr; RUs; milg;Gr;RUs; vdg;gLk;. 29. AF milg;Gr;RUs;> RF milg;Gr;RUs; NtWgLj;Jf. t. vz; 1. 2. 3.

AF milg;Gr; RUs;

RF milg;Gr;RUs;

Fiwe;jmjph;ntz; Rw;Wfspy; gad;gLfpwJ. NjdpUk;;Gcs;sfj;ijg; ngw;wpUf;Fk;. jd;kpd;J}z;ly; vz; mjpfk;.

cah; mjph;ntz; Rw;Wfspy; gad;gLfpwJ. fhw;Wcs;sfj;ijg; ngw;wpUf;Fk;.

68

jd;kpd;J}z;ly; vz; FiwT

30.

0.5 m2 gug;gsitAk; 10 Rw;WfisAk; nfhz;l xU fk;gpr; RUspd; jsk; 0.2 Wb/m2 fhe;jg;Gyj;jpw;Ff; Fj;jhf cs;s nghJ fk;gpr; RUspd; topNa ghAk; fhe;jg; ghaj;ijf; fzf;fpLf. jPh;T:- fhe;jg;ghak; Φ = NBAcosθ Φ = NBAcos0o (...θ= 0o) Φ = 10 x 0.2 x 0.5 Φ = 1 Wb

31. thpr;RUs; xd;wpy; 2 As-1vd;w tPjj;jpy; khWk; kpd;Ndhl;lk; 10mV kpd;dpaf;F tpiriaj; J}z;bdhy; thpr;RUspd; jd;kpd; J}z;ly; vz; vd;d? e = -L jPh;T:jd;kpd;J}z;ly; vz; L =

=

L = 5x10-3 H (or) L = 5mH 32. xU RUspy; kpd;Ndhl;lk; 100As-1 vd khWk; NghJ 5V kpd;dpaf;F tpir mjpy; J}z;lg;gLfpwJ mjd; jd;kpd; J}z;ly; vz; vd;d? e = -L jPh;T:jd;kpd;J}z;ly; vz;

L=

=

⇒

L = -0.05H

jd;kpd;J}z;ly; vz; L= 0.05 H

33. 1m ePsKk; 0.05m tpl;lKk; nfhz;l thpr;RUs; 500 Rw;Wfisf; nfhz;Ls;sJ. fk;gpr;RUspd; topNa 2A kpd;Ndhl;lk; gha;fpwJ vdpy; fk;gpr;RUspd; jd;kpd; J}z;ly; vz;izf; fzf;fpLf. jPh;T:-

= 4 x 3.14 x 25 x 3.14 x 625 x 10-7 + 4 - 6 L = 6.16 x 10-3 H (or) L = 6.16mH 34. xU RUspy; 4A kpd;Ndhl;lk; 0.05 s fhyj;jpy; 8A Mf khWk;NghJ kw;nwhU RUspy; 50mV kpd;dpaf;F tpir J}z;lg;gLfpwJ. vdpy; mt;tpU RUs;fSf;F ,ilNa cs;s ghpkhw;W kpd;J}z;ly; vz;izf; fzf;fpLf. e2 = -M( jPh;T:ghpkhw;W kpd;J}z;ly; vz; M = M=

=

=

ghpkhw;W kpd; J}z;ly; vz; M = 6. 25 mH

69

x 10-3 = -6. 25 mH

35. 200 Rw;WfisAk; 0.04 m2 FWf;Fg; gug;igAk; nfhz;Ls;s fk;gpr;RUspd; topNa nry;Yk; fhe;jg;Gyk; 0.2 tpehbapy; 0.1 Wbm-2 ypUe;J 0.04 Wbm-2Mf khWfpwJ vdpy; mjpy; J}z;lg;gLk; kpd;dpaf;F tpiriaf; fzf;fpLf? jPh;T :

200x4x10-2 x3 2x4x3 24V J}z;lg;gl;l kpd;dpaf;F tpirapd; vz;kjpg;G = 24V 36.

xU tpkhdj;jpd; ,wf;ifapd; KidfSf;fpilNa cs;s J}uk; 20.48 m ,J tlf;F Nehf;fp 40 ms-1 vd;w Ntfj;jpy; gwf;fpwJ. Gtpf;fhe;jg; Gyj;jpd; nrq;Fj;Jf; $W mt;tplj;jpy; 2x10-5T vdpy; ,wf;ifapd; KidfSf;F ,ilNa J}z;lg;gLk; kpd;dpaf;F tpiriaf; fhz;f. e=-B v jPh;T:-J}z;lg;gLk; kpd;dpaf;F tpir

e = -2 x 10-5 x 20.48 x 40 = -20.48 x 80 x 10-5 = -1638.4 x10-5 e = -0.0164V 37. xU tpkhdj;jpd; ,wf;ifapd; KidfSf;fpilNa cs;s J}uk; 10m. ,J tlf;F Nehf;fp 720km/hr vd;w jpir Ntfj;jpy; gwf;fpwJ. Gtpf;fhe;jg;Gyr; nrq;Fj;Jf; $W mt;tplj;jpy; 3x10-5T vdpy; ,wf;ifapd; KidfSf;fpilNa J}z;lg;gLk; kpd;dpaf;F tpiriaf; fzf;fpLf J}z;lg;gl;l kpd;dpaf;F tpir e = -B v jPh;T:e = -3 x 10-5 x 10 x 720 x ⇒ e = -3 x 10 x 200 x 10-5 e = -6000 x 10-5⇒e = - 0.06 V 38. jiuAlDk; xd;Wf;nfhd;W kpd;fhg;G nra;ag;gl;l ,uz;L uapy; jz;lthsq;fs; xU kpy;yp Nthy;l; kPl;lUld; ,izf;fg;gLfpd;wd. ,uapyhdJ 180 km/hr Ntfj;jpy; XLtjhfTk; Gtpf;fhe;jg;Gyj;jpd; nrq;Fj;Jf; $wpd; typik 0.2x10-4Wb/m2 vdTk; jz;lthsq;fs; 1m ,ilj;njhiytpy; cs;sd vdTk; nfhz;L Nthy;l;kPl;lhpy; cs;s FwpKs; fhl;Lk; msitf; fzf;fpLf. J}z;lg;gl;l kpd;dpaf;F tpir e = -B v jPh;T :

FwpKs; fhl;Lk; msT = 1m

70

39. ey;ypay;G kpd;khw;wp xd;wpy; kpd;khw;wp tpfpjk; 1:20 mjd; cs;sPL jpwd; kw;Wk; kpd;dOj;jk; KiwNa 600mW, 6V MFk;. Kjd;ik kw;Wk; Jizr;RUspy; ghAk; kpd;Ndhl;lq;fisf; fzf;fpLf. = , Ep Ip = 600 mW; Ep = 6V jPh;T:Ep Ip = 600 mW Ip = Mdhy; Is =

= 100x10-3 = 0.1 A

= = x Ip =

x 0.1 = 2A

Kjd;ikr; RUspy; ghAk; kpd;Ndhl;lk; = 0.1A Jizr;RUspy; ghAk; kpd;Ndhl;lk; = 2A 40. 11 kW kpd;jpwid 22,000V kpd;dOj;jj;jpy; kpd;jil nfhz;l xU fk;gpapd; topahf mDg;gpdhy; Vw;gLk; jpwd; ,og;G ahJ? P = VI jPh;T :- kpd; jpwd; I = I = I = 0.5A = I2R = (0.5)2x 2 = 0.25 x 2 jpwd;,og;G = 0.5 W 41. 25 Row;rpfisf; nfhz;l ird; tbt kpd;Ndhl;lj;jpd; rms kjpg;G 30A vdpy; mjd; rkd;ghl;il vOJf. = sin t jPh;T := jpwd;,og;G

42. 1000 Hz mjph;ntz; nfhz;l khWjpir kpd;Ndhl;l kpd;Rw;wpy; ,izf;fg;gl;Ls;s kpd;Njf;fpapd; kpd;Njf;Fj;jpwd; 2µF nray;gLj;jg;gLk; kpd;dpaf;F tpirapd; rms kjpg;G 10V vdpy; Rw;wpy; ghAk; njhFgad; kpd;Ndhl;lj;jpidf; fzf;fpLf? Xc = = jPh;T:⇒ Xc =

Xc =

=

Ω

njhFgad; kpd;Ndhl;lk; Irms = = Irms =

71

=

= 0.126A

5; kjpg;ngz; tpdh-tpilfs; 1. ePz;l thpr;RUspd; jd;kpd;J}z;ly; vz;. • L ePsk;> A FWf;F ntl;Lg;gug;G kw;Wk; N Rw;WfisAk; nfhz;l thpr;RUisf; fUJNthk;. kpd;Ndhl;lk; I vd;f. • xU Rw;Wf;fhd fhe;jg;ghak; = B×xt;nthU Rw;wpd; gug;G µ NI µ NI   = 0 × A Q B = 0  l l   • thpr;RUNshL njhlh;G nfhz;l µ NIA nkhj;jf; fhe;jg;ghak; φ = 0 ×N l µ N 2 IA φ= 0 ×N → (1) l • fhe;jg;ghak; φ = LI → (2) µ N 2 AI µ N2A ` vdNt L = 0 rkd;ghLfs; 1> 2 ypUe;J> LI = 0 l l 2 µN A cl;GFjpwd; cs;s Clfj;jpy; L = l 2. kpd;J}z;bAld; njhlh;G nfhz;l Mw;wy; • fk;gpr;RUspy; kpd;Ndhl;lj;ij epWt Gw%yq;fshy; Ntiy nra;a Ntz;bAs;sJ. • J}z;L kpd;dpaf;F tpir e = − L dI dt

•

dt fhy ,ilntspapy; nra;ag;gl;l Ntiy dW = e I dt dW = − L

•

dI ⋅ I dt dt

dW = -L I d I kpd;Ndhl;lj;ijg; ngUkkjpg;Gf;F mjpfhpf;fr; nra;Ak; Ntiy I0

W = ∫ dW = ∫ − LIdI 0

1 W = − L I 02 2

•

kpd;J}z;bapy; Nrkpf;fg;gLk; Mw;wypd; vz; kjpg;G U=

1 L I 02 2

3. ,UePz;l thpr;RUs;fSf;fpilNaahd ghpkhw;W kpd;J}z;ly; vz;.

• •

•

S1, S2vd;gd ePsKs;s> A FWf;F ntl;Lg;gug;G l thpr;RUs;fshFk; Rw;Wfspd; vz;zpf;if KiwNa N1, N2. S1y; ghAk; I1 kpd;Ndhl;lj;jhy; S2y; xt;nthU Rw;Wld; njhlh;Gila fhe;jg;ghak; = B1 A N  N  Q B1 = µ0 1 I1  = µ 0 1 I1 A  l  l  N S2 y; njhlh;Gila nkhj;jf; fhe;jg;ghak; φ2 = µ 0 1 I1 A × N 2 l

72

nfhz;l

N1 N 2 I1 A l φ2 = M I1 rkd;ghLfs; 1> 2 ypUe;J>

φ2 = µ 0

• •

MI 1 =

M =

→ (1) → (2)

µ 0 N 1 N 2 AI 1 l

µ0 N1N 2 A

l • µ cl;GFjpwd; nfhz;l Clfj;jpy;> µN1 N 2 A M= l 4. fk;gpr;RUSld; njhlh;Gila gug;ig khw;Wtjhy; kpd;dpaf;F tpir J}z;lg;gLjy;

•

fhe;jg;Gyj;jpw;Ff; Fj;jhf PQRS flj;jp cs;sJ. • L1M1 eOTk; flj;jp ePsk; l vd;f. • njhlf;fg;gug;G L1QRM1 • flj;jp dt fhy ,ilntspapy; dx njhiyT efh;j;jg;gLfpwJ. ,Wjpg; gug;G L2QRM2 • gug;G khWghL dA= l dx • fhe;jgha khWghL dφ= B dA = B l dx − dφ • J}z;L kpd;dpaf;F tpir e= dt dx e = − Bl dt e = − Bl v 5. kpd;khw;wpapy; Vw;gLk; jpwd; ,og;Gfs; - Fiwf;Fk; tpjk; fhuzk; Fiwf;Fk; tpjk; t.vz;. jpwd; ,og;G 1. jaf;f ,og;G jpUk;gj; jpUk;g cs;sfk; kpA+nkl;ly;> fhe;jkhtjhYk; rpypf;fd; ];By; fhe;jj;jd;ikia cs;sfk; ,og;gjhYk; 2. Roy;kpd;Ndhl;l ,og;G fhe;jg;ghak; khWtjhy; ];nly;yha; (,Uk;G ,og;G) Roy; kpd;Ndhl;lk; cUthfp cs;sfk; ntg;g ,og;G Vw;gLtjhy; 3. gha ,og;G Kjd;ikr;Rw;Wld; njhlh;G $Ltif cs;sfk; nfhz;l fhe;jg;ghak; Jizr;Rw;Wld; njhlh;G nfhs;shik 4. jhkpu ,og;G ghAk; kpd;Ndhl;lj;jhy; Fiwe;j kpd;jil [{y; ntg;g ,og;G nfhz;l jbkdhd Vw;gLtjhy; fk;gp gad;gLj;Jjy;

73

6.khWjpir kpd;Ndhl;lj;jpd; RMS kjpg;gpw;fhd Nfhit I Irms = 0 2

•

khWjpir kpd;Ndhl;lk; I = Io sin

(my;yJ )

t

I0 khWjpir kpd;Ndhl;lj;jpd; ngUk kjpg;G •

khWjpir kpd;Ndhl;lk; I MdJ R topahf dt fhyj;jpw;Fg; ghAk;NghJ cUthFk; ntg;g Mw;wy; dH = I 2R dt

•

KORw;Wf;F cUthFk; ntg;gMw;wy; I2Rdt

H=

( sin2

H=

H= •

dt

I02 RT 2

→ (1)

Irms kpd;Ndhl;lk; KORw;Wf;F cUthf;Fk; ntg;gMw;wy; 2 H = I rms RT

•

→ (2)

rkd;ghLfs; 1> 2 ypUe;J

I

2 rms

I 02 = 2

I rms =

I0 2

7. khWjpir kpd;dpaf;F tpir nray;gLj;jg;gLk; kpd;jilahf;fp kl;LNk cila AC Rw;W. *R kpd;jilAila kpd;jilahf;fpAld; xU khWjpir kpd;dpaf;F tpir %yk; ,izf;fg;gl;Ls;sJ.

ve;j xU fzj;jpYk; nray;gLj;jg;gLk; kpd;dpaf;F tpir →

e = E0 sin ω t

(1)

kpd; jilahf;fpapd; FWf;Nf kpd;dOj;j NtWghL> e = iR kpd;dOj;j NtWghL> nrYj;jg;gLk; kpd;dpaf;F tpirf;Fr; rkk;.

74

iR = E0 sin ω t i = E0 sin ω t R → (2)

i = Io sin

kpd;dOj;jKk;> kpd;Ndhl;lKk; xNu fl;lj;jpy; cs;sd. fl;ltiuglk;

fl;lg;glk;

8. A.C kpd;Rw;wpd; ruhrhp jpwd; (cz;ikj;jpwd;) •

ve;jnthU

fzj;jpYk;

kpd;dpaf;F tpir ngUf;fw;gydhFk;. •

AC

kw;Wk;

kpd;dpaf;Ftpir e = E0 sin

kpd;Rw;wpd; Rw;wpy;

jpwd; ghAk;

t

kpd;Ndhl;lk; i = I0 sin( t + φ) •

KOr; Rw;wpy; gad;gLj;jg;gl;l jpwd; Pav =

= Pav = Pav =

cos φ cos φ

= Erms Irmscos φ Pav =

Njhw;wj;jpwd; ×jpwd; fhuzp

75

vd;gJ

mf;fzj;jpy;

kpd;Ndhl;lk;

,tw;wpd;

10 kjpg;ngz; tpdh-tpilfs; 1. fhe;jg;Gyj;jpy;; RUspd; jpiraikg;ig khw;Wtjd; %yk; kpd;dpaf;Ftpiriaj; J}z;Ljy;.

• •

PQRS RUs; rPuhd fhe;jg;Gyj;jpy; nrq;Fj;jhf mike;j mr;irg; gw;wp vd;w Nfhzj;jpir Ntfj;Jld; Roy;tjhff; nfhs;Nthk;. fhe;jg;ghak; khWfpwJ. fhe;jg;ghak;

= NBA cos t

J}z;lg;gl;l kpd;dpaf;F tpir e = e=

-

(NBA cos t )

e = NBA sin e = Eosin ,q;F Eo = NBA

RUspd; jsk;

J}z;L

0o

fhe;jg;Gyj;Jld; nrq;Fj;J

kpd;dpaf;Ftpir o

90o

,iz

Eo

180o

nrq;Fj;J

0

270o

,iz

-Eo

360o

nrq;Fj;J

0

76

2. xUfl;l A.C.

kpd;dpaw;wp (A.C.

ildNkh)

jj;Jtk; : kpd;fhe;jj; J}z;ly;

mikg;G :Kf;fpa ghfq;fs; : Roy; RUs;:- NjdpUk;G cs;sfj;jpy; mjpf vz;zpf;ifapy; Rw;wg;gl;l nrt;tf tbtf; fk;gpr;RUs;. Gyf;fhe;jk;:- jpwd; Fiwe;j ildNkhtpy; epiyf;fhe;jKk;> jpwd; mjpfkhd ildNkhtpy; kpd;fhe;jKk; gad;gLfpwJ. eOT tisaq;fs;:- R1, R2 vd;w cNyhf tisaq;fs; Roy; RUspd; KidfSld; ,izf;fg;gl;L RUSld; Nrh;e;J Roy;fpwJ. J}hpiffs;:- B1, B2 vd;w fhh;gd; J}hpiffs; ntspr;Rw;Wf;F kpd;Ndhl;lj;ijf; flj;Jk;.

i) ii) iii) iv)

nray;ghL:• RUs; fhe;jg; Gyj;jpy; ,lQ;Ropahf Roy;fpwJ. • kpd;dpaf;Ftpir J}z;lg;gLfpwJ • J}z;lg;gl;l kpd;Ndhl;lj;jpd; jpirapid /gpskpq; tyJif tpjp %yk; mwpayhk;. 1) 2) 3)

Kjy; miur;Rw;W AB fPo;Nehf;fp efUk; CD Nky;Nehf;fp efUk; Roy; RUspy; kpd;Ndhl;lk; DCBA topahfg; ghAk;.

,uz;lhtJ miur;Rw;W AB Nky;Nehf;fp efUk; CD fPo;Nehf;fp efUk; Roy; RUspy; kpd;Ndhl;lk; ABCD jpirapy; ghAk;.

4)

ntspr;Rw;wpy; B1 ypUe;J B2 f;F kpd;Ndhl;lk;; ghAk;.

ntspr;Rw;wpy; B2 ypUe;J B1 f;F kpd;Ndhl;lk;; ghAk;.

miytbtk;:

J}z;lg;gl;l kpd;dpaf;Ftpir e = Eo sin t ,q;F Eo = NBA

3. Roy; kpd;Ndhl;lk;> Fiwf;Fk; tpjk;> gad;fs;: Roy; kpd;Ndhl;lk; : cNyhff;fl;b fhe;jg;Gyj;jpy; ,aq;Fk;NghJ my;yJ cNyhff;fl;bAld; njhlh;Gila fhe;jg;ghak; khWk;NghJ mjpy; J}z;lg;gLk; kpd;Ndhl;lk; Roy;kpd;Ndhl;lk; vdg;gLk;. jpir : nyd;]; tpjpapd; %yk; ngwg;gLk; Fiwf;Fk; tpjk;: i) cNyhff;fl;bf;Fg; gjpyhf kpd;fhg;gplg;gl;l nky;ypa jfLfs; gad;gLj;Jtjhy; ii) cNyhfj; jl;by; Jisfis ,Ltjd; %yk;

gad;fs;: 1. miytpyh fhy;tdh kPl;lh;:-

•

fhy;tdh kPl;lh; topahf kpd;Ndhl;lk; ghAk; NghJ fk;gpr;RUs; miyTWk;. 77

• •

cNyhfr; rl;lj;jpy; Roy; kpd;Ndhl;lq;fs; cUthFk; NghJ fk;gpr;RUs; miyTWTij vjph;f;Fk;. RUs; miyTWtJ epd;WtpLtjhy; miytpyh fhy;tdhkPl;lh; vdg;gLk;.

2. J}z;ly; ciy:-

• •

ntg;gg;gLj;j Ntz;ba cNyhfk; mjpf mjph;ntz; nfhz;l khWk; fhe;jg;Gyj;jpy; itf;fg;gl;Ls;sJ. cNyhfj;jpy; Roy; kpd;Ndhl;lk; cUthtjhy; Vw;gLk; mjpf ntg;gj;jhy; cNyhfk; cUFk;.

3. J}z;ly; kpd;Nkhl;lhh;fs;;

:-

• •

Royp xd;W RoYk; fhe;jg;Gyj;jpy; itf;fg;gLfpwJ. Roypapy; Vw;gLk; Roy; kpd;Ndhl;lk; Roypf;Fk; fhe;jg;Gyj;jpw;Fk; cs;s rhh;gpaf;fj;ij Fiwj;J Roypiaj; njhlh;e;J Row;WfpwJ. • ,J kpd;tprpwpapy; gad;gLfpwJ. 4. kpd;fhe;jj; jil :• ,uapy; tz;bapd; rf;fuj;Jld; ,izf;fg;gl;Ls;s cUisAk; Nrh;e;J RoYk;. • jilia nray;gLj;Jk;NghJ cUisapy; khWk; fhe;jg;Gyk; Vw;gl;L Roy;kpd;Ndhl;lk; cUthfpwJ. • Roy;kpd;Ndhl;lk; cUisia Xa;T epiyf;Ff; nfhz;L tUk;. 5. Ntfk; fhl;Lk; fUtp :• thfdj;jpd; Ntfj;jpw;F Vw;g cNyhf cUisapDs; fhe;jk; RoYk;. • cUisapy; Roy;kpd;Ndhl;lk; Vw;gl;L Fwpg;gpl;l Nfhz msT jpUg;Gk;. • cUisapy; ,ize;j FwpKs; msTNfhypy; ,aq;Fk;.

4. kpd;khw;wpapd; jj;Jtk;> mikg;G> nray;ghL> gaDWjpwd;> jpwd; ,og;Gfs;. kpd;khw;wp :Fiwe;j khWjpir kpd;dOj;jj;ij mjpf khWjpir kpd;dOj;jkhfTk; mjpf khWjpir kpd;dOj;jj;ijf; Fiwe;j khWjpir kpd;dOj;jkhfTk; khw;Wk; fUtp. jj;Jtk; :- kpd;fhe;jj;J}z;ly; (ghpkhw;W kpd;J}z;ly;)

mikg;G :• •

nky;ypa jfLfspdhy; Md NjdpUk;G cs;sfk; cs;sJ. cs;sfj;jpd; kPJ Rw;wg;gl;l xd;Wld; xd;W kpd;njhlh;gw;w Kjd;ikr;RUs;> Jizr;RUs; cs;sd.

nray;ghL :• • •

cs;sPL khWjpir kpd;dOj;jk; Kjd;ikr;Rw;Wf;Ff; nfhLf;fg;gLfpwJ. Kjd;ikr;Rw;wpy; fhe;jg;ghak; khWk;. Jizr;Rw;wpYk; fhe;jg;ghak; khWk;. Jizr;Rw;wpy; kpd;dpaf;Ftpir J}z;lg;gLk;. 78

• •

•

Ep, Es - kpd;dpaf;F tpirfs; Np, Ns – Rw;Wfspd; vz;zpf;if> Ip, Is – kpd;Ndhl;lq;fs; vd;f. Kjd;ikr;Rw;W kw;Wk; Jizr;Rw;wpy; fhe;jg;ghak; rkk;. =

ey;ypay;G kpd;khw;wpf;F cs;sPLjpwd; = ntspaPL jpwd; Ep Ip = Es Is mjhtJ =

=

=k

=

kpd;khw;wp tpfpjk; Vw;W kpd;khw;wp Es> Ep Ns>Np Ip>Is K> 1

•

gaDW jpwd;

=

•

jpwd; ,og;Gfs;:

cs;sPL jpwd; jaf;f ,og;G iii) Roy;kpd;Ndhl;l ,og;G

,wf;F kpd;khw;wp Ep > Es Np>Ns Is>Ip K< 1

ntspaPL jpwd; =

i)

ii) iv)

jhkpu ,og;G gha ,og;G

5. kpd;J}z;b kl;Lk; cila A.C.Rw;W

•

Gwf;fzpf;fj;jf;f Fiwe;j kpd;jil cila L jd;kpd;J}z;ly; nfhz;l kpd;J}z;b A.C. %yj;Jld; ,izf;fg;gl;Ls;sJ. kpd;dpaf;Ftpir e = Eo sin t ( 1) J}z;lg;gl;l kpd;dpaf;F tpir e = - L Mdhy; e = - e' Eo sin t = L i=

kpd;Ndhl;lk;

i= i= i=

kpd;Ndhl;lk;

sin t dt

sin t dt sin ( t - )

i = Iosin ( t - )

rkd;ghLfs; 1>2 ypUe;J kpd;Ndhl;lk;> kpd;dOj;jj;ij tpl

79

(2) fl;lk; gpd;jq;fp cs;sJ.

fl;l tiuglk;

fl;lg;glk;

kpd;J}z;bapd; kpd;kWg;G :L = XL D.C. f;F = 0 XL = 0 vdNt J}a kpd;J}z;b D.C. f;F Ropkpd; jiliaf; nfhLf;Fk;. Mdhy; A.C. f;F mjph;ntz;Zf;F Neh;j;jftpy; mikAk;.

6. kpd;Njf;fp kl;Lk; cila A.C.Rw;W :-

•

C kpd;Njf;Fj;jpwd; cila kpd;Njf;fpahdJ khWjpir kpd;dpaf;Ftpir %yj;Jld; ,izf;fg;gl;Ls;sjhff; fUJNthk;.

(1)

e = Eo sin t •

kpd;Njf;fpapd; FWf;Nf cs;s kpd;dOj;j NtWghL nrYj;jg;gLk; kpd;dpaf;F tpirf;Fr; rkk;. e= kpd;Ndhl;lk; i =

= i=

(Ce) (CEo sin

i = E0 C sin i=

sin i = Io sin

) ) )

rkd;ghLfs; 1>2 ypUe;J kpd;Ndhl;lk; kpd;dOj;jj;ij tpl

(2)

fl;lk; Kd;Ndhf;fp

cs;sJ. fl;l tiuglk;

fl;lg;glk;

80

kpd;Njf;fpapd; kpd;kWg;G :• Xc = •

D.C. f;F

•

vdNt kpd;Njf;fp A.C. Rw;wpy; XC

7.

= 0 XC = = d.c. I mDkjpf;fhJ.

R, L, C njhlhpizg;Gr; Rw;W •

kpd;jilahf;fp R, kpd;J}z;b L, njhlhpizg;gpy; cs;sd. • VR = I R •

•

VR, I xj;j fl;lk; VL= I XL VL MdJ I I tpl

fl;lk; Ke;Jk;

Vc= I Xc I I tpl

Vc MdJ

•

kpd;Njf;fp C Mfpad khWjpir kpd;dpaw;wpAld;

fl;lk; gpe;Jk;

Rw;W kpd; epiykj;jd;ikahf fUjpdhy; (i) kpd;dOj;jk;

kpd;dOj;jf; fl;lg;glk;

V2 = VR2 + (VL-VC)2 V= V= V=I

(ii) kpd;ndjph;g;G

(iii) V, I f;F ,ilNa cs;s fl;l NtWghL tan = = tan-1(

)

kpd;Ndhl;lk; I = Io sin (

81

myF 3>5>6>9>10 Mfpa ghlq;fspy; cs;s kpf Kf;fpakhd 3kjpg;ngz; tpdh tpilfs; myF -3 kpd;Ndhl;lj;jpd; tpisTfs; 1. #Nlw;Wk; ,ioahf epf;Nuhk; vd;w cNyhff; fyitapdhy; Md RUs; gad;gLj;jg;gLtJ Vd;? 1. kpd; jil vz; mjpfk;. 2. cUFepiy mjpfk;. 3. tpiutpy; Mf;]pfuzj;jpw;F cs;shfhJ. 2. tiuaW “ngy;bah; Fzfk;” ,jd; myF vd;d? ,uz;L ntt;Ntwhd cNyhfq;fs; nfhz;l re;jpapy; xU Mk;gpah; kpd;Ndhl;lk; xU Mk;gpau; kpd;Ndhl;lk; xU tpdhb Neuj;jpy; ghAk; NghJ ntsptplg;gLk; my;yJ cl;ftug;gLk; Mw;wypd; msT ngy;bah; Fzfk; vd tiuaWf;fg;gLfpwJ. ,jd; myF “Nthy;l;”. 3. gpskpq; ,lJif tpjpiaf; $Wf? ,lJifapd; ngUtpuy; Rl;L tpuy;> eLtpuy; %d;iwAk; xd;Wf;nfhd;W nrq;Fj;jhd jpirfspy; itj;Jf;nfhs;f. Rl;Ltpuy; fhe;jg;Gyj;jpd; jpiriaAk;> eLtpuy; kpd;Ndhl;lj;jpd; jpiriaAk; Fwpj;jhy; ngUtpuy; flj;jp ,aq;Fk; jpiriaf; Fwpf;Fk;. 4. Mk;gpahpd; Rw;W tpjpiaf; $Wf? ve;jnthU %ba tisNfhl;bidr; Rw;wpa fhe;jg;Gyj;jpd; Nfhl;Ltopj; B. dl d; kjpg;ghdJ> cl;GFjpwd; (µ) kw;Wk; tisNfhl;lhy; njhifaPL %lg;gl;l gug;G topNa ghAk; nkhj;j kpd;ndhl;lk; (I0) Mfpatw;wpd; ngUf;fw; gyDf;Fr; rkk;. B.

dl = µ0 I0

5. irf;Nshl;uhdpd; tuk;Gfs; ahit? 1. Bf;fspd; nghpa gug;gpy; rPuhd fhe;jg; Gyk; epWTtJ fbdk;. 2. ngUk jpirNtfq;fspy; Vw;gLk; xg;Gik epiwkhWghL xj;jpiritf; Fiyf;Fk;. 3. cah; mjph;ntz;fspy; vyf;l;uhdpd; xg;Gik epiw khWghL kpf mjpfkhf ,Ug;gjhy;> vyf;l;uhd;fis irf;Ndhl;uhdhy; KLf;f ,ayhJ.

myF – 5 – kpd;fhe;j miyfSk; miy xspapaYk; 1.

bd;lhy; xspr; rpjwy; vd;why; vd;d? $o;kj; Jfs;fshy; xsp rpjwbf;fg;gLk; vdg;gLk;.

epfo;T

bd;lhy;

xspr;

rpjwy;

2.

g;uhd; N`hgh; thpfs; vd;git ahit? #hpa epwkhiyapy; cs;s fUikthpfs; miof;fg;gLfpd;wd.

3.

i`n[d;;]; jj;Jtj;ijf; $Wf? I. miyKfg;gpy; cs;s xt;nthU JfSk; me;j Clfj;jpy; xspapd; jpirNtfj;jpy; nry;yf; $ba ,uz;lhk; epiy miyf;Fl;bfis cUthf;Fk; xsp%q;fshFk;. II. me;j fsj;jpy; ,uz;lhk; epiy miyf; Fl;bfspd; Kd;Gw ciwNa miyKfg;ghFk;.

82

g;uhd;N`hgh;

thpfs;

vd

4.

Ez;Jfs; kw;Wk; /Nghl;lhd; NtWgLj;Jf? Ez;Jfs;

/Nghl;lhd;

1.Ez;zpa epiwaw;w K* kPl;rpj;jd;ikAila Jfs;fs;

1. Mw;wy; jpzpf;fg;gl;l rpW rpW ngl;lfq;fs;.

2. xspapd; Mw;wy; ,jd; ,af;f Mw;wYf;Fr; rkk;

2. Mw;wy; E =h ν

3.xspapd; epwk; Jfs;fspd; gUkidr; hh;e;jJ.

3. spap ; epwk; m y ePsk; my;yJ mjph;ntz;izr; rhh;e;jJ.

5.

K* mf vjph;nuhspg;G eilngwj; Njitahd epge;jidfs; ahit? I. Xsp mlh;kpF Clfj;jpypUe;J mlh;T Fiw Clfj;jpw;Fr; nry;y Ntz;Lk;. II. gLNfhz kjpg;G khWepiyf; Nfhzj;ij tpl mjpfkhf mika Ntz;Lk; (i > C)

6.

epA+l;ld; tisaq;fspd; ikak; fUikahf mikaf; fhuzk; ahJ? I. ikaj;jpy; fhw;Nwl;bd; jbkd; Rop. Ghij NtWghL Ropahtjhy; ikaj;jpy; nghypT Njhd;w Ntz;Lk;. II. mlh;kpF fz;zhbapy; vjpnuhspf;fg;gl;l miyahdJ fl;l NtWghL π milfpwJ. III. Nfhsf nyd;]; gug;gpy; vjpnuhspf;fg;gl;l miyapy; fl;l NtWghL VJk; ,y;iy.

7.

/g;nuney; kw;Wk; /g;uhd;N`hgh; tpspk;G tpidT NtWgLj;Jf? g;nuney; tpspk;G tpisT

/g;uhd;N`hgh; tpspg;G tpisT

1.xsp %yKk; jpiuAk; jilnghUspypUe;J tuk;gpw;Fl;gl;l njhiytpy; Uf;Fk;.

1.xsp %yKk; jpiuAk; jilnghUspypUe;J
2. tpspk;G tpistpw;F cl;gLk; miyKfg;G Nfhsf miyKfg;ghFk;

2. tpspk;G tpistpw;F cl;gLk; miyKfg;G rkjs miyKfg;ghFk;.

3.Ftpnyd;R gad;gLj;jg;gLtjpy;iy

3.Ftpnyd;R gad;gLj;jg;gLfpwJ.

8.

Xspapay; mr;R vd;why; vd;d? gbfk; xd;wpy; rhjhuz fjpUk;. mrhjhuzf;fjpUk; rk jpirNtfj;jpy; nry;Yk; jpir gbfj;jpd; xspapay; mr;R vd;wiof;fg;gLfpwJ.

9.

Xspapay; Row;rpia ghjpf;Fk; fhuzpfs; ahit? I. Gbfj;jpd; jbkd; II. Gofj;jpd; mlh;j;jp III. Gad;gLk; xspapd; miyePsk; IV. fiurypd;b ntg;gepiy. 83

nzG!.7!–!n[-bx
sQvie! lqe
ue
ole
2/!

njzfqtl
njzfqtl
3/!

nkqi
nkqi
4/!

DMVU!kqxe
DMVU!kqxe
!! 5/ zOu!Nb
6/ Oli^
= a ( Z-b)!

7/ Ozsiqe
i) n[k
84

!

nzG!–!:!–!Gjxg
w/gi;!K~b!Si,!K~b!Ge!!! 2.kh#l;ly; vd;why; vd;d? kh#l;Lk; topKiwfs; ahit? Cs;shh;e;j Fiwf;flj;jpapDs; kpfr;rpwpa mstpyhd khR Nrh;f;if epfo;T kh#l;ly;. 1. khR mZf;fis cUfpa epiyapYs;s Fiwf;flj;jpapDs; Nrh;j;jy;. 2. khR mZf;fspd; madpfshy; Fiwf;flj;jpia Nkhjr; nra;jy; 3. khR mZf;ffisf; nfhz;l Fiwf;flj;jp ntg;gg;gbfj;jpDs; tputr;nra;jy;. 4/ kqVk
!!!!!!ii) nkqgiqg
!

iv)-jvs
6/!njzUg
!

!!!ii)olik
i*lqglqgs
!!!!!!ii)lzquie!uqjz! !!!!!!iii)lqgs
!!!!!!v*fl
!

!!!!!!ii) ngUf;fw;gydpd; epug;gpahdJ> epug;gpfspd; $LjYf;Fr; rkkhFk;.

! 85

! 9/ OgOkiM!gkqi mit OR, AND NOT Mfpa mbg;gilNfl;Lfspd; nray;ghLfisr; nra;af; $bait.

10. ngUf;fpapd; gl;il mfyk; tiuaW !!!!!kip
11. nray;ghl;L ngUf;fpapd; Kf;fpa gz;Gfs; ahit? 1. cs;sPL kpd;ndjph;g;G kpf mjpfk; (Kbtpyp) 2. ntspaPL kpd;ndjph;g;G kpf FiwT (Rop) 3. ngUf;fk; kpf mjpfk;. 12.

ilNahLfs; gad;gLj;jg;gl;l OR Nfl; Rw;Wg;glk;.

13. ilNahLfs; gad;gLj;jg;gl;l AND Nfl; Rw;Wg;glk;.

! ! ! ! ! 86

! ! 14. buhd;rp];lh; gad;gLj;jg;gl;l NOT Nfl; Rw;Wg;glk;.

!

myF – 10 – jfty; njhlh;G mikg;Gfs; 1.

jhT njhiyT vd;why; vd;d? thd; miy guTtjpy; Fwpg;gpl;l mjph;ntz;Zf;F gug;Gk; Gs;spapypUe;J Vw;Fk; Gs;sp tiu gug;gpd; topNa cs;s Fiwe;jgl;rj; njhiyT jhT njhiyT vdg;gLk;.

2. gz;Ngw;w vz; tiuaW? gz;Ngw;wj;jpw;Fg; gpd; Ch;jp miyapd; tPr;rpy; Vw;gl;l khw;wj;jpw;Fk;> gz;Ngw;wjpw;F Kd; Ch;jp miyapd; tPr;Rf;Fk; cs;s jfT gz;Ngw;w vz; vdg;gLk;. irif miyapd; tPr;R (Es) M= Ch;jp miyapd; tPr;R (Ec) 3. Nulhhpd; gad;fs; ahit? ghJfhg;ghd thd; kw;Wk; fly;top gazq;fSf;F. I. II. Mfha tpkhdq;fs; ghJfhg;ghf jiuapwq;f. III. thdpiy Muha;r;rpahsh;fs; thdpiy Kd;dwptpg;G nra;a. 4. ,yf;f Kiw jfty; njhlh;gpd; ed;ikfs; ahit? I. mDg;Gifapd; juk; mjpfk;. II. mDg;Gif mikg;gpd; jpwid mjpfg;gLj;jyhk; III. xsp ,iofspy; xspf;fw;iwiag; gad;gLj;JtJ kw;Wk; miytopg;gLjjpfs; Nghd;w GJtif gug;G topfspy; gad;gLfpwJ. 5. Xsp ,ioj; jfty; njhlh;gpd; ed;ikfs; ahit? I. mDg;gPl;bd; NghJ Vw;gLk; ,og;G FiwT. II. NyrhdJ> ,lj;ij milj;Jf;nfhs;shJ. III. Mjpf mstpyhd nra;jpfis mDg;gyhk;. 6. nraw;iff;Nfhs; jfty; njhlh;gpd; ed;ikfs; ahit? I. elkhLk; jfty; njhlh;ig vspjhf Vw;gLj;jyhk;. II. jiutop jfty; njhlh;ig tpl rpf;fdkhdJ. III. mDg;gg;gLk; irifapd; juk;> mDg;Gk; kw;Wk; Vw;Fk; epiyaq;fspd; ,Ug;gplk; Mfpait njhiyitr; rhh;e;jjy;y. 87

7. tPr;Rg;gz;Ngw;wj;jpd; tuk;Gfs; ahit? I. ,iur;rYld; $ba Vw;G. II. Fiwe;j nray;jpwd;. III. Fiwe;j nray;gLk; njhiyT. 8. mjph;ntz; gz;Ngw;wj;jpd; ed;ikfs; ahit? I. ,iur;ryw;w xyp Vw;G. II. Mjpf nray;jpwd;. III. mjpf nray;gLk; njhiyT.

! Lg
!

88

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! 89

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! 90

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91

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92

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93

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94

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96

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100

myF -3 kpd;Ndhl;lj;jpd;

tpisTfs;;

3 kjpg;ngz; tpdhf;fs; 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

[Py; tpjpapidf; $Wf. ngy;bah; Fzfk; tiuaW. tiuaW: jhk;rd; Fzfk; gal;- rhth;l; tpjpapidf; $Wf. Mk;gpah; Rw;W tpjpapidf; $Wf. Mk;gpah; - tiuaW. ntg;g kpd;dpioahf epf;Nuhk; gad;gLj;jg;gLfpwJ. Vd;? rPngf; tpisT vdwhy; vd;d?. ngy;bah; tpisT vdwhy; vd;d?. jpUg;G ntg;gepiy vd;gJ ahJ? Nkf;];nty;ypd; tyf;if jpUF tpjpia vOJf. tyJ cs;sq;if tpjpia vOJf. Kid tpjpiaf; $Wf. iff;Nshl;uhdpd; tuk;Gfs; ahit?. gpskpq;fpd; ,lf;if tpjpia vOJf. fhy;tdhkPl;lhpd; kp;d;Ndhl;l czh;T El;gj;jpid mjpfhpf;Fk; Kiwfis vOJf. fhy;tdhkPl;lhpd; kp;d;Ndhl;l czh;T El;gj;jpid khw;Wk; nghOJ> kpd;dOj;j czh;T El;gj;jpid khw;w KbahJ. Vd;?. 18. kpd;Ndhl;l tisaj;jpd; fhe;j ,UKid jpUg;Gj;jpwd; tiuaW. 5 kjpg;ngz; tpdhf;fs;:-

1. gal; - rhth;l; tpjpia $wp tpsf;Ff. 2. Mk;gpahpd; Rw;W tpjpapidg; gad;gLj;jp thpr;RUspdhy; Vw;gLk; fhe;jjj;Jhz;lypd; kjpg;gpidg; ngWf. 3. fhe;jtpay; nyhud;]; tpirapd; rpwg;gpay;Gfisf; $Wf 4. kpd;Ndhl;lk; ghAk; ,U Neuhd ePz;l ,izf;flj;jpfSf;F ,ilNa Vw;gLk; tpirf;fhd Nfhitiag; ngWf. 5. xU fhy;tdh kPl;liu vt;thW mk;kPl;luhf khw;wyhk;? 6. xU fhy;tdh kPl;liu vt;thW Nthy;l;kPl;luhf khw;wyhk;? 10 kjpg;ngz; tpdhf;fs;:1. [Py; ntg;gtpisT tpjpapidr; rhpghh;f;Fk; Nrhjidapid tpthp. 2. kpd;Ndhl;lk; ghAk; ePz;l mikg;G> ,af;fk; Mfpatw;iw tpthp? 5. rPuhd fhe;jg;Gyj;jp; y; kpd;Dhl;lk; ngw;w Jfspd; ,af;fk; gw;wp tpsf;Ff 6. irf;Nshl;uhdpd; mikg;G> Ntiy nra;Ak; tpjk; Mfpatw;iwg; glj;Jld; tpthp. 7. fhe;jg;Gyj;jpYs;s kpd;Ndhl;lk; ghAk; flj;jpapd; kPJ nray;gLk; tpirapd; Nfhitapidg; ngWf. myF 5 kpd;fhe;j miyfSk;> miy xspapaYk; 3 kjpg;ngz; tpdhf;fs;:-

1. kpd;fhe;j miyfs; vd;why; vd;d? 2. mfr;rptg;Gf; fjph;fspd; gad;fs; ahit? 3. GwCjhf; fjph;fspd; gad;fs; ahit? 4. /g;uhd;N`hgh; thpfs; vd;git ahit? 5. xsph;jy; kw;Wk; epd;nwhsph;jy; vd;why; vd;d? 6. Ez;Jfs; kw;Wk; /Nghl;lhd; NtWgLj;Jf. 7. uhNy xspr;rpjwy; tpjpia vOJf? 8. bd;lhy; xspr;rpjwy; vd;why; vd;d? 9. thdk; ePy epwkhf Njhd;wf; fhuzk; vd;d? 10. ,uhkd; tpistpd; gad;fs; ahit? 11. i`n[d;]; jj;Jtj;ij vOJf. 12. epiy epWj;jg;gl;l FWf;fPl;L tpistpw;fhd epge;jidfs; ahit? 13. epa+l;ld; tisaq;fs; vd;why; vd;d? 14. epa+l;ld; tisaq;fspd; ikak; fUikahfj; Njhd;wf; fhuzk; vd;d? 15. tpspk;G tpisT vd;why; vd;d? 101

16. fPw;wzp %yk; tiuaW. 17. js mjph;Tj;jsk; kw;Wk; js tpisTj;jsk; NtWgLj;Jf. 18. xspapay; mr;R tiuaW. 19. Row;rpj;jpwd; vz; rhh;e;Js;s fhuzpfs; ahit? 20. Row;rpj;jpwd; vz; tiuaW 1. 2. 3. 4. 5. 6. 7.

5 kjpg;ngz; tpdhf;fs;:Ez;Jfs; nfhs;ifia tpsf;Ff. rkjsj;jpy; vjpnuhspf;fg;gl;l rkjs miyKfg;gpdhy; vjpnuhspg;G tpjpfisg; ngWf. epa+l;ld; tisaj;jpd; n tJ fUik tisaj;jpd; Muj;jpw;fhd Nfhitiag; ngWf. jl;lL;f;ifg; glj;Jld; tpthp. GU];lh; tpjpiaf; $wp> ep&gp. ief;fy; gl;lfj;ij tpthp. Nghyuha;Lfs; vd;why; vd;d?. gad;fisf; $Wf. 10 kjpg;ngz; tpdhf;fs;:-

1. 2. 3. 4. 5.

ntsptpL epwkhiy> cl;fth; epwkhiy ,tw;iw tpthp. ,uhkd; xspr;rpjwiy tpsf;Ff. miyf;nfhs;ifiag; gad;gLj;jp KOmf vjpnuhspg;ig tpthp. aq; ,ul;il gpsT Ma;tpy;> gl;il mfyj;jpw;fhd Nfhitiag; ngWf. nky;ypa CLUTk; glyj;jpy; xsp vjpnuhspg;ghy; Vw;gLk; FWf;fPl;L tpistpw;fhd epge;jidia tUtp.

myF 6 – mZ ,aw;gpay; 3 kjpg;ngz; tpdhf;fs; 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

NfNjhL fjph;;fs; vd;why; vd;d? kpy;ypf;fd; Nrhjidapd; jj;Jtj;ijf; $Wf. madpahf;f Mw;wy;-tiuaW. madpahf;f kpd;dOj;jk; tiuaW. td; X- fjph;fs;> nkd; X - fjph;fs; vd;why; vd;d? fpsh;r;rpahf;f kpd;dOj;j Mw;wy; tiuaW. Nkh];Ny tpjpapid vOJf. Nkh];Ny tpjpapd; gad;fis vOJf. jd;dpr;irahd ckpo;T> J}z;L ckpo;T NtWgLj;Jf. ,ay;Gepiy mZj;njhif vd;why; vd;d? mZj;njhif Vw;wk; vd;why; vd;d? Nyrhpd; rpwg;gpay;Gfs; ahit? N`hNyhfpuhgp vd;why; vd;d? Nyrh; nraiyg; ngw Ntz;ba epge;jidfs; ahit? yNt Nrhjidapd; Kf;fpa KbTfs; ahit? 5 kjpg;ngz; tpdhf;fs;:-

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Nfj;NjhL fjph;fspd; gz;Gfisf; $Wf. Giof;fjph;fspd; gz;Gfisf; $Wf. α - Jfs;fspd; mZFk; kPr;rpW njhiytpw;fhd Nfhitapidg; ngWf. rhkh;ngy;L khjphpapd; Fiwfisf; $Wf. i`l;u[dpd; epwkhiy thpfis tpthp X –fjph;fspd; gz;Gfisf; $Wf. gpuhf; tpjpapidf; $wp tUtp. yNt Ma;tpid tpthp. rpwg;G X –fjph; epwkhiyapd; Njhw;wj;jpid tpthp. Nyrhpd; mwptpay; kw;Wk; nghwpapay; gad;ghLfisf; $Wf. 10 kjpg;ngz; tpdhf;fs;:-

1. vyf;l;uhd;pd; kpd;Dhl;l epiwj;jfT fhZk; J.J. jhk;rd; Nrhjidia tpthp. 2. vyf;l;uhdpd; kpd;Dhl;lk; fhZk; kpy;ypf;fd; vz;nza;j;Jsp Ma;tpid tpthp. 3. Nghh; nfhs;ifiaf; $Wf. Nghh;f;nfhs;ifapd; mbg;gilapy; n tJ tl;lg;ghijapd; Muj;jpw;fhd Nfhitiag; ngWf. 4. gpuhf; tpjpiaf; $wpg; ngWf. gpuhf; epwkhiykhdpiag; gad;gLj;jp X-fjphpd; miyePsj;jpidf; fz;lwpAk; Nrhjidapid tpthp. 102

5. &gp Nyrhpd; nray;ghl;bidj; njspthd glj;Jld; tpthp 6. Mw;wy;kl;lg; glj;Jld; He- Ne Nyrhpd; nray;ghl;bid tpthp.

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

myF 9 – Fiwf;flj;jp rhjdq;fs; kw;Wk; mjd; gad;ghLfs; 3 kjpg;ngz; tpdhf;fs;:tpyf;fg;gl;l Mw;wy; ,ilntsp vd;gnjd;d? cs;shh;e;j Fiwf;flj;jpfs; vd;git ahit? Gwtpayhd Fiwf;flj;jpfs; vd;git ahit? khR+l;ly; vd;why; vd;d? khR+l;Lk; Kiwfisf; $Wf. jpUj;Jjy; vd;why; vd;d? xspckpo; ilNahL vd;gnjd;d? gad;fs; ahit? nrdh; KwpT vd;gJ vd;d? buhd;rp];lhpd; cs;sPL kpd;vjph;g;G tiuaW. ,jd; myF vd;d? ngUf;fpapd; gl;il mfyk; tiuaW. gpd;D}l;lk; vd;why; vd;d? mjd; tiffs; ahit? vjph; gpd;D}l;lj;jhy; tpisAk; ew;gad;fs; ahit? miyT xd;wpw;fhd gh;nfsrd; epge;jidfis vOJf. njhFg;Gr; Rw;wpd; ew;gad;fs; ahit? LC miyapaw;wpapd; fl;lg;glj;ij tiuf. ilNahil gad;gLj;jp OR Nfl; Rw;Wg;glk; tiuf. ilNahil gad;gLj;jp AND Nfl; Rw;Wg;glk; tiuf. buhd;rp];liug; gad;gLj;jp NOT Nfl; Rw;Wg;glk; tiuf. B khh;fd; Njw;wq;fisf; $Wf. nghJ Nfl; vd;git ahit? Vd;? nray;ghl;Lg; ngUf;fpapd; Kf;fpag; gz;Gfs; ahit? NfNjhL fjph; miyNehf;fpapd; (CRO) gad;fs; ahit? G+ypad; rkd;ghl;ilg; gad;gLj;jp (A+B) (A+C) = A+BC vd epWTf. 5 kjpg;ngz; tpdhf;fs;:-

1. 2. 3. 4. 5. 6. 7. 8.

ilNahL miu miy jpUj;jpahfr; nray;gLk; tpjj;jpid tpthp. buhd;rp];lhpd; α tpw;Fk;> β tpw;Fk; cs;s njhlh;ig epWTf. buhd;rp];lh; rhtpahfr; nray;gLjiy tpthp: kpd;dOj;jg; gFg;ghd; rhh;ig kpd;Rw;Wld; tpsf;Ff. Bkhh;fd; Njw;wq;fisf; $wp epWTf.. OR kw;Wk; AND Nfl;bd; kpd;Rw;iw tiue;J tpsf;Ff. buhd;rp];lh; ngUf;fpapd; mjph;ntz; czh;jpwd; tiuNfhl;il tpthp. gy; gad;kPl;lh; Xk;kPl;luhfr; nray;gLjiy tpthp.

10 kjpg;ngz; tpdhf;fs;:1. rkdr;Rw;Wj; jpUj;jp nray;gLjiy tpthp. 2. buhd;rp];lh; xd;W ngUf;fpahfr; nray;gLtij tpsf;Ff. 3. gpd;Dhl;lk; vd;why; vd;d? vjph; gpd;Dhl;lk; nfhLf;fg;gl;l ngUf;fpapd; kpd;dOj;jg; ngUf;fj;jpw;fhd Nfhitiag; ngWf. 4. fhy;gpl; miyapaw;wpapd; Rw;Wg;glk; tiue;J mJ nray;gLtij tpthp. 5. nray;ghl;Lg; ngUf;fp> 1. Gul;Lk; ngUf;fp 2. Gul;lyw;w ngUf;fpahfr; nray;gLtij tpthp. 6. nray;ghl;Lg; ngUf;fp> 1. $l;Lk; ngUf;fp 2. NtWghl;Lg; ngUf;fpahfr; nray;gLtij tpthp. 7. gy;gad; kPl;liu kpd;Rw;Wg; glj;Jld; tpsf;Ff. myF 10 – jfty; njhlh;G mikg;Gfs; 3 kjpg;ngz; tpdhf;fs;:1. NubNah miyfs; guTk; Kiwfis vOJf. 2. jhT njhiyT vd;why; vd;d? 3. jhT kz;lyk; tiuaW. 4. gz;Ngw;wk; tiuaW. 5. gz;Ngw;w vz; tiuaW. 6. tPr;R gz;Ngw;wj;jpd; tuk;Gfs; ahit? 7. mjph;ntz; gz;Ngw;wj;jpd; ed;ikfs; ahit? 8. thpf;fz;Nzhl;lk; vd;why; vd;d? 9. ,yf;fKiw jfty; njhlh;gpd; rpwg;Gfs; ahit? 10. Xsp,io jfty; njhlh;gpd; ew;gz;Gfs; ahit? 103

1. 2. 3. 4. 5. 6.

5 kjpg;ngz; tpdhf;fs; tPr;Rg;gz;Ngw;w miygug;gpiaf; fl;lg;glj;Jld; tpthp. fyf;fpg;gphpf;Fk; Vw;gpiaf; fl;lg;glj;Jld; tpthp. Nulhhpd; gad;ghLfisf; $Wf. ,yf;fKiwj; jfty; njhlh;gpd; rpwg;Gfs;> FiwghLfs; ahit? nraw;iff;Nfhs; jfty; njhlh;gpd; ed;ikfs; ahit? tPr;R gz;Ngw;w Vw;gpapd; fl;lg;glk; tiuf. 10 kjpg;ngz; tpdhf;fs;

1. 2. 3. 4. 5. 6.

miytPr;Rg; gz;Ngw;wpapd; gFg;gha;it tpthp. fyf;fpg; gphpf;Fk; AM Vw;gpiaf; fl;lg; glj;Jld; tpthp? tPbf;fhd; epow;glf; fUtpapd; nray;ghl;il tpthp. fUg;G nts;is njhiyf;fhl;rpg; gug;gpapd; ntt;NtW gFjpfspd; nray;ghl;il tpthp. fUg;G nts;is njhiyf;fhl;rp Vw;gpapd; nray;Kiw fl;lg;glk; tiue;J tpsf;F. Nulhhpd; jj;Jtk;> gug;Gif kw;Wk; Vw;G – glj;Jld; tpsf;Ff.

**************************************************************************

“Kaw;rpAk; gapw;rpAk; njhlh;r;rpahf ,Ue;jhy; Njh;;r;rp epr;rak;” ***************************************************************************

104