NatScienceTBM4codex

gIqk76o7kj g7,u0v’c8]j tmkf,6ooaho da[9eo;o vk38,0v’r;d,ao gIqkwfh # V @ = @ V # g-y’j zqo76o9tgmqkj daoF 9kdouhltcf’;kj gIqklhk’l6f Al2O3 4nd8hv’c]h;D 9kd8q;1kj ’ f’ja dkj ;F gIkq lts[5^ wf;h kj grvjn lkh ’lf6 0v’mkf8k,7kj g7,0u v’mkf,o6 gIkq 8vh ’xt8[y fa 8k,0oha 8vof’ja oGhu !? 0Poloa pt]da g7,0u v’mkf,o6 ]’q rvh ,m’a \\kp7kj g7,0u v’r;d,oa f;h p38g]d3ic,’a D @? -vdskmt;u76oI;j ,|hvpl5f0v’7kj g7,umulj tcf’vvdoahoD #? skomt;u76oI;j ,|hvpl5foaho.sh7kj g7,u0v’c8]j tmkf,6oc]h;0Po9eo;omuwj fhIa[ oahoshvp.lgj [nhv’0;kmk’]5,j 0v’laopt]admkf,6omudj Pj ;0hv’D 8k8t]k’ltcf’7jkg7,u0v’[k’mkf,6o 7kj g7,u 3]st vt3]st 7kj g7,u gmqkj ! Na, K, Ag, Cu, Hg H, Cl ສ.ວ.ສສະຫງວນລິຂະສິດ 7kj g7,ugmqkj @ Mg, Ca, Ba, Cu O, S 7kj g7,ugmqkj # N Hg, Fe, Zn, Sn, Pb Al, Cr, Fe 7kj g7,ugmqkj $ Mn C, Si, S 7kj g7,ugmqkj & Mn N,P 7kj g7,ugmqkj * Cr S 7jkg7,u0v’[k’d5j,mkf 7kj g7,u d5,j mkf I NO3- , Cl - ,OH- II III SO32- ,CO32- ,SO42- PO34- 45

lts^5[G 7jkg7,u0v’mkf,6o s^n d5j,mkf,6oc,jo8q;g]dltcf’g4y’7;k,leraomuj,u ສ.ວ.ສສະຫງວນລິຂະສິດ roa mt8+doa 0v’vk38, sn^ d,j5 vk38,F grojy wfdh eofq gvkq 7kj g7,0u v’I3u fic-og-’yj g;]k.fdg= mkjq ! c]t 7kj g7,u0v’vk38,vqd-uc-o g-y’j g;]k.fd=gmkqj @ gxaosq;|;j p;afcmd8k,s^ad7kj g7,uG 4hkI6h x, y c]t a s^n b 9t-vdwfh b s^n a. I6h a c]t b 9t-vdwfh x, y grvnj lhk’gxaol6f3,g]d5o8k, vfa 8kl;j oG x = b = b′ y a a′ .sh x = b sn^ b′ c]t y = a sn^ a′ X4hk a′,b′ c,oj g]drbfltmugj xao9eo;o4h;o,u 7kj 8e]kmP[.lj a, b) &D dko7yfw]j8k,l6fg7,u dD 7;k,\\kp0v’l6fg7,u dyf9tdeG .soh da IPorvh ,doa l’a gdfl’jy mgju Ikq lk,kfIwh6 f9h kdlf6 g7,0u v’oE XH2O? 8w+ xoGU { -lnj f6 g7,uc,oj oED { .ol6fg7,u0v’oE,umkf,6oIu3fic-o c]t vqd-uc-oD { mkf,6oIu3fic-o,u @ vk38,F mkf,6ovqd-uc-o,u ! vk38,D { 7kj g7,u0v’Iu3fic-ogmqkj ! F 7kj g7,u0v’vqd-uc-ogmqkj @D { ,;olko3,g]d5oG (2 x 1) + (1x 16)= 18 g. 9kddyf9tde0kh ’gmy’lf6 g7,u.sgh Ikq Iwh6 fGh { -n0j v’mkfF [aofkmkf,6omuxj tdv[.omkfF mkffPj ; s^n mkfxtlq,D { 9eo;ovk38,0v’c8j]tmkf,6omuj,u.o3,g]d5o0v’mkf X4hkgxaomkfxtlq, 9tlk,kfI6h7kj g7,u.ol6f?D { ,;olko3,g]do5 0v’mkfD vu’8k,0=h,6omluj e7aodPj ;da[l6fg7,u gIqklk,kf7yfw]8j k,l6fg7,ufh;pc[[;ymu8kj ’M 46

0D 7yfw]jlj;oIhvpfhko,;olko0v’c8j]tmkf,6o.ol6f %B= mB ×100% = Y × MB ×100% MAxBy MAxBy %A= mA ×100% = X × MA ×100% M Ax By M Ax By lq,,5f;kj ,ul6fg7,u Ax By gIqklk,kf7yfw]lj ;j oIhvpfhko,;olko Ac]t B. .oooA mA, mB c,oj ,;olko0v’mkf,o6 A c]t mkf,o6 B; MA c]t MB c,oj ,;olko vk38,0v’mkf,6o A c]t mkf,6o B; MAx By c,oj ,;olko3,g]d5o0v’mkfxtlq, AxBy 4hkmkfxtlq,mxuj tdv[fh;ps^kpmkf,6o;ym7uj yfw]dj =9t7hkp7ndaoD 7D vu’.ljvaf8klj;ofhko,;olko0v’mkf,6o.omkfxtlq, 8q;1kj ’G -vdl6f3,g]d5o0v’mkfxtlq,g,vnj I6hvaf8kl;j o,;olkof’aj 8+wxoUG Iu3fic-o [ao95 ! l;j o c]t vqd-uc-o ) l;j oD ສ.ວ.ສສະຫງວນລິຂະສິດ cdhG lq,,5f;kj ,;olkomkfmuoj ewx;yw9c,oj a dik, F ltoAo mH = a → nH = a = a 9 9×1 9 mO = 8a → nO = 8a = a 9 9 ×16 18 nH = 2 l6f3,g]d5oc,oj H2O nO 1 ’D -vd,;olko0v’c8j]tmkf,6o.oxt]y,ko.f|bj’0v’mkfmuj.sh -vd,;olko0v’mkf A .omkfxtlq, AxBy .o MAxBy g 9t,u MA g s^n MA g mkf A ltoAo.o a g 0v’ AxBy 9t,u b g mkf A D 47

b = a mA = a X MA MAxBy MAxBy 8q;1k’G .o !*g CuSO 9t,u Cu 9ad g L 4 ;ymucdhG ; a = 16g M Cu= 64 g; MCuSO4 = MA x By = 160g b = xt]y,ko Cu .o 16 g CuSO4 b = 16g × 64g = 6,4g 160g 8v[G 6,4 g 7e4k,G !D -vdl6f3,g]d5o0v’vqd-ufgs^adI6h;jk,;olko3,g]d5ogmqjk !*W vaf8klj;ofhko ສ.ວ.ສສະຫງວນລິຂະສິດ ,;olkoG M Fe = 7 MO 3 @D -vdl;j oIvh pfkh o,;olko0v’c8]j tmkf,o6 .olf6 D dD HNO3 0 D Al2O3 7D Fe3O4 #D 9qj’0Pol6f3,g]d5o0v’mkfxtlq,I6h;jk.omkfxtlq,,uvaf8klj;ofhko,;olko 8+wxoGU dD Fe = 70; O = 30. 0D Cu = 40% ; S = 20% ; O = 40% $D 9q’j [vd7kj g7,u c]t 9eo;ovk38,0v’c8]j tmkf,6o.ol6fD dD SO3 0D Na2O 7D CO ’D Al2O3 9D MgCl2 lD CO2 &D 9’jq 0Polf6 3,g]do5 0v’mkfxtl,q m[uj oa 9v5 dq -uc-o0v’[oa fkmkf,o6 8+wxoUG dD Fe (III) 0D Na ( I ) 7D N (III) ’D N (V) 9D S. (VI) lD Al (III) -D Mg (II) *D 9’jq 0Polf6 3,g]do5 0v’mkfxtl,q gdnvrvh ,f;h p-vd,;olko3,g]do5 G dD Fe (II) xtdv[da[ NO3 Xou8iaf? 0D Na (I) xtdv[da[ SO4 X-6o2af? 7D Ca (II) xtdv[da[ PO4 X2qflt2af? ’D Cu (II) xtdv[da[ Cl Xd^=iq;? 48

[qfmu ) ສ.ວ.ສສະຫງວນລິຂະສິດ lq,zqog7,u !D 7;k,\\kplq,zqog7,u 8q;1kj ’I6[9e]v’],5j oU oadIPo9tla’gdfwfhco;.fL I6[ )D! lq,zqog7,u grojy .-lh f6 g7,gu rvjn lkh ’gxoa l,q zoq g7,Fu 4kh Ilh6 f6 0v’mkfmgju 0kQ I;j ,.oxt8dy ]y py k c]t mkf mwuj fIh [a s^’a xt8ydy]ypkc];h F groyj lk,kfltcf’xt8ydy]ypkooA f;h pl,q zoq g7,uD !? ;ymu0Polq,zqog7,u .odkolkh ’l,q zoq 0v’xt8dy ]y py kg7,Fu g[vN ’-kh p,gn rojy 0Polf6 g7,0u v’mkfmguj 0kQ I;j , xt8dy ]y py kdoa Xmkfxt8ry oa ? c]t 1gj6 [vN ’0;k,gn rojy 0Polf6 0v’mkfmwju fIh [a s’a^ 9kdxt8dy ]y py k g7,u Xmkfzt]yf8trao?D ]ts;kj ’l6fma’s^kp.oc8]j tg[Nv’.sh.lgj 7nvj ’\\kp[;d (+) 0Ao]t s;jk’mkf X4hk,us^kpl6f?D lj;o16j]ts;jk’dk’0v’mkfxt8yrao c]t mkfzt]yf8trao 0v’xt8dy ]y py k.s.h -]h d6 lvo-wU xmk’g[vN ’0;k X→?D le][a xt8dy ]y py kd’q xoY F g-’jy oda IPo9tgsoa .o-AoIPo8+wx9t.-h]6dlvoma’wx c]t da[ X U ?D ovd9kdoU gryoj pa’[vdrk;t0v’mkfvud fh;pg-aoj G (s) \\kpg4y’mkfc0’F ( l ) \\kpg4y’mkfcs^; c]t (g) \\kpg4y’dklF 8q;1kj ’G 2Cu(s) +O2(g) → 2CuO(s) @? ;ymu-aj’-klq,zqog7,u la’gdf8q;1jk’8+wxoUG { la’gdfg[y’j 9eo;ovk38,0v’c8]j tmkf,6o16gj [Nv’-hkp c]t g[Nv’0;k0v’lq, zoq g7,Du { -a’j -k9eo;ovk38,0v’mkf,6o.o3,g]d5o.splj 5fdvj o c]h;9’bj -’aj -k9eo;ovk 38,.o3,g]do5 ovh p]’q 8k,]ef[a f;h p;ymu8,jn 8;q g]dlextlyf.l|j kh lf6 g7,u.sgh \\kt l,q D 49

{ 4hk.olq,zqog7,u.f,umkffjP;.sh-a’j -kgxaovaofa[ I6[ )D@ 37’Ikj ’lq,zqog7,u lf5 mkh pD { 8hv’gIaf.sh9eo;ovk38,0v’c8]j tmkf,6ogxao g]d9eo;o4;h o8ej lf5 D { c];h o[a 9eo;ovk38,0v’c8]j tmkf,o6 .oc8]j t g[vN ’0v’l,q zoq .sgh mkjq doa \\kp7;k,;kj G l,q zoq oU fo5 fPj ’c];h D 8q;1kj ’G mv’ T vqd-uc-owfhmv’vqd-yf @ D lq,zqog7,uG Cu(s) +O2(g) → CuO(s) !? -aj’lklq,zqo { la’gdfgsao;jkG 9eo;ovk38,0v’vqd-uc-o ສ.ວ.ສສະຫງວນລິຂະສິດ 16gj [Nv’0;k,n,urP’|b’j vk38, l;j o g[Nv’-hkp,n ,lu v’vk38, f’ja ooA gIkq 8vh ’8,jb 8;q g]d Xlextlfy ? @ .l8j +|hkl6f0v’ CuO .og[Nv’0;kF 8q;1kj ’G Cu + O2 → CuO c]h;8b,j 8q;g]d @ 168j + I6[ )D# 0Ao8vo-a’j -klq,zqog7,u |hk Cu g[Nv’-hkp g-aoj G { 9tgsaowfh;kj G 9eo;ovk38,0v’c8j ]tmkf,6oma’lv’g[Nv’0v’lq,zqo oUgmqjkdaog-yj’\\kp7;k,;jkG lq,zqo g7,uoU f5ofPj ’daoc]h;D @? lq,zqog7,uc8d8jk’da[lq,zqo I6[ )D $ -a’j -klq,zqog7,ulq,[6oc]h; rbf-t7toyf .olq,zqorbf-t7toyfF 4hkgIqkxPj o[vj odao ]ts;kj ’rkdl;j og[Nv’-hkp c]t rkdl;j o g[vN ’0;k0v’l,q zoq F 7;k,\\kp0v’,oa d9= t[x+ Pj ocx’ c8.j ol,q zoq g7,u 4kh gIkq xPj o[vj odoa ]ts;kj ’rkdl;j og[Nv’-hkp c]t g[Nv’0;k0v’lq,zqo7;k,\\kp0v’,ao9txPj ocx’1kj ’ loY g-’u D 50

8;q 1kj ’G cmomu9j t0Po 2Al + 3Cl 2→ 2Al Cl3 lq,zqo ! gIqkwx0Po 2Al Cl3 → 2Al + 3Cl2 lq,zqo @ ,oa d=9t\\kpg4y’xt8ydy]ypkxUo grkt;kj l,q zoq muj ! ,oa ltcf’g4y’xt8ydy]ypkxtl,q mkf c8lj q,zqo @ ltcf’g4y’xt8ydy]ypk;yg7ktD lts^5[];,c]h; .odkolhk’lq,zqog7,ugIqk9t8hv’xt8y[aff’aj 8+wxoUG !? 0Pol6f0v’mkfxt8yrao1g6j [Nv’-hkp c]t mkfzt]yf8trao1g6j [Nv’0;kD @? -aj’-klq,zqo fh;pdko8q;g]d Xlextlyf? 16jmk’|hk0v’c8j]tl6fg7,u.olq,zqo gIfa co;.f.s9h eo;ovk38,0v’c8]j tmkf,o6 1.j6 oc8]j tg[vN ’0v’l,q zoq .sgh mkjq dj oa D #? 0Polq,zqo.shlq,[6oc]h;0Po]6dlvo X ? s^n g7nvj ’\\kp X=? .llj q,zqmu-j a’j -kc];h D #?D 7;k,\\kpoe.-h.odko7yfw]j8k,lq,zqog7,u ສ.ວ.ສສະຫງວນລິຂະສິດ .soh da IPo9’jq l’a gdf8k,l,q zoq 8+wxoU 8q;1kj ’G CaCO3(s) ⎯t⎯o→ CaO(s) + CO2 (g) 9eo;o3,]3,g]d5o ! !! 9eo;o3,]vk38, & @# ,;olko Xdik,? !W &* $$ 9eo;o[=]y,kf X{? X{? !V@@F$ 9kd8;q 1kj ’l,q zoq 0kh ’gmy’oU gIkq lk,kfI7h6 ;k,\\kp0v’l,q zoq g7,u7nG !? lq,zqog7,u.shgIqkI6hwfhmkfxt8yrao c]t mkfzt]yf8traomugj duf0BoD @? .shI6hvaf8kl;j oG T Ivh6 fa 8kl;j omk’fkh o9eo;o3,g]do5 F 9eo;o3,]0v’[oa fkmkf.ol,q zoq g7,uD T I6hvaf8kl;j omk’fhko,;olkoF [=]y,kf X0v’mkfvkp?c8]j tmkf.olq,zqog7,uD #D dqfgdocsj’dkoIadlk,;olko .olq,zqog7,uF zqo[;d,;olko0v’[aofkmkfxt8yrao9tgmqkj zqo[;d0v’[aofkmkf zt]fy 8troa g-oja G 51

l,q zoq g7,u A + B = C+ D gIkq ,u 8q;1kj ’ mA + mB = mC+ mD 4 + 32 = 36 $D 7yfw]j8k,lq,zqog7,u !? gIafco;.f9y’j 9t-vdsk,;olko0v’mkfxt8yrao c]t mkfzt]yf8traowfhD 8q;1kj ’G g,nvj gzqksuox6o &W g 4k,;kj 9tgda[wfhx6ofy[9ad gL 0Ao8vodko7yfw]jG { 0Polq,zqoF -’aj -klq,zqoG CaCO3 ⎯t⎯o→ CaO + CO2 { -vd9eo;o3,] CaCO3 muoj ewxgzqkG n CaCO3 = mCaCO3 = 50 = 0,5mol M CaCO3 100 { -vd9eo;o3,] CaO mugj da[wfhg,nvj xt8ydy]ypklYol5fG 8k,lq,zqog7,u9eo;o3,] ສ.ວ.ສສະຫງວນລິຂະສິດ CaCO3 gmqjkda[9eo;o3,] CaO 4hk CaCO3=0,5 mol ltoAo9eo;o3,] CaO= 0,5molS ,;olko mCaO = n x MCaO = 0,5 x 56 = 28 g @? gIfa co;.f9’jy 9t-vdwf[h ]= ,y kfdklmguj 0kQ I;j ,xt8dy ]y py k sn^ dklmwju fIh [a g,vjn xt8dy y ]py kloY lf5 D 8q;1jk’G grojy oegvkq dkd[vo X4kj o? wxgzkq w\\dh [a vdq -cu -o $ g 4k,;kj dkldkd3[ody mugj da[wfh.og’nvj ow0 ,kf8t4ko9t,u9ad]yfL 0Ao8vodko7yfw]j { 0Polq,zqo c]t -a’j -klq,zqoG C+O2 → CO2 { -vd9eo;o3,]vqd-uc-omguj 0QkI;j ,xt8ydy]ypkG nO2 = 4 0,125 3,] 32 { -vd9eo;o3,]0v’ CO mgju dfu 0oB G 8k,l,q zoq ! 3,] O g0kQ I;j ,xt8dy ]y py k9twfh 22 CO2 ! 3,]D ltoAo4hk9eo;o3,] O2 = 0,125 3,] 9eo;o3,] CO2 d=9tgmqkj 0,125 3,]D [=]y,kf0v’ CO2 7yfw]wj fhfa’j oUG lVCO2 = nCO2 × 22, 4 × 0,125 = 2,8 lts^5[0Ao8vo7yfw]j !? 0Pol,q zoq -’ja -kl,q zoq g7,uD 52

@? xPj osq;|;j p,;olko s^n [=]y,kfvvdgxao9eo;o3,]0v’mkfmduj Pj ;0hv’D #? vu’.llj q,zqo-vd9eo;o3,]mkfmugj 0QkI;j ,xt8ydy]ypk s^n mkfmuwj fhIa[8k,[qf39f m’ju kpD $? xPj o9eo;o3,]muwj fhvvdgxao,;olko s^n [=]y,kf XV= 22,4 V n? Xm = n V M ?D [qfg/ydsafG !D 9’jq -’ja -kl,q zoq g7,u8+wxoU dD Al + O2 → Al2O3 0D C+O2 → CO2 7D Al + S → Al2S3 ’D HgO → Hg+O2 @D .ol,q zoq g7,u],j5 oU.sgh Ikq Ish6 p’a cfLj dD 4Fe(s) + 3O2(g) → 2Fe2O3 0D l lC 2(g) + H2(g) → HC (g) #D 9kdlq,zqo Al + O2 → Al2O3 { 9’jq -’ja -kl,q zoq g7,u ສ.ວ.ສສະຫງວນລິຂະສິດ { 4hk.-h Al 2,7g 9twfhIa[ Al2O3 9ad g L { 4hk O ,u 0,16g 4k,;kj 9t.-h Al 9ad gL $D g,nvj oe4kj o XC? wxgzqkw\\hda[vqd-uc-o XO2? 9twfhdkldkd3[oyd (CO2) { 9’jq 0Pol,q zoq 0v’xt8ydy]ypkg7,uf’ja dkj ;L { g,nvj ,u4kj o WF& 3,] 9twfhIa[dkldkd3[oyd9ad3,]L { 4hk,uvqd-uc-o @ 3,] 9twfhIa[dkldkd3[oyd.og’nvj ow0,kf4ko9ad]yfL X I6h;kj G .og’nvj ow0,kf8t4ko ! 3,] m5ddklgmqkj @@F$ ]yf? &D 4hk,u S 10 g 4ndoewxgzqkIhvoda[ Fe 10g grnjv.shwfhgs^ad-6o2q; XFeS? 4k,;jk g,nvj xt8ydy]ypklYol5f9t,umkf.fgs^nv c]t gs^nv9ad3,] { ,;olkogs^ad-6o2q; XFeS? mugj da[wfh,u9ad g L 53

[qfmu _ vqd-uc-o c]t vqd-yffk-q’ !D vqd-uc-o mkf,o6 vdq -cu -o,1u mj6 ;jq wx.ome,t-kfF .ovkdkf,vu dq -cu -oxt,ko !}& fkh o[]= ,y kfD g-’jy loa pt]da 0v’vdq -cu -oc,oj O; 3,g]do5 vdq -cu -oxtdv[,u @ vk38,F lf6 3,g]do5 c,oj O2. !? dkox5’c8j’vqd-uc-o groyj x’5 c8’j vqd-uc-owfhco;.fL dD .oshv’mqf]v’ dyf9tde !G x5’c8j’9kddk]uvv,cxad,a’dkoaf (KMnO4) !D gvkq dk]uvv,cxd,’a dkofa (KMnO4) ສ.ວ.ສສະຫງວນລິຂະສິດ xt,ko ! dik, .lcj dh;dQox5h’F.-hfvo muj,um+lqj’vkpvafxkdcdh;dQox5h’c]h; O2 xvj om+l’jq vkp]’q .lsj ^vfcd;h m[ju oa 9o5 E g8a,.ovkj ’oE XI6[ _D!?D KMnO4 H2O @D 96fs^vfmqf]v’mu,j u KMnO fh;p8t I6[ _D! x5’c8’j vqd-uc-o 4 dP’gs^Qk _WD KMnO4 4nd;yg7ktc]h; wfvh dq -cu -oF vdq -cu -omgju dfu 0oB 9tpoh6 E vvd9kds^vfmqf]v’mu’j ;em+l’qj vkpF g,nvj oE\\qfd=ltcf’;kj vqd-uc-owfhg8a,s^vfmqf]v’ 9kdoAo.-hfvovafxkds^vf mqf]v’ grvnj gda[Iadlkw;hoewx.-hmqf]v’8+MwxD lq,zqog7,uG 2KMnO4 → K2MnO4 +MnO2 +O2 dyf9tde @G x5’c8’j 9kdmkfdk]uvv,d^=]af KClO3 c]t Iu3fic-ocxadvqd-yf H2O2D 8q;1kj ’ !G ;yg7kt KClO3 fh;p7;k,Ihvo3fp,u MnO2 gxaomkfg]a’j D 2KClO3 ⎯M⎯nO⎯2 → 2KCl +3O2 8q;1kj ’ @G ;yg7kt H2O2 54

2H2O2 → 2H2O + O2 ສ.ວ.ສສະຫງວນລິຂະສິດ 0D .ov5flkstde grojy x’5 c8’j O 9kdvkdkf f;h p7;k,foa l’6 c]t vo5 str,6 8O vkdkf9tdkpgxoa mkf 2 cs^;F s^a’9kdoAogIaf.shvkdkfcs^;]tgsupvkp9tgda[ N .ov5ostr6,{!_*OC 8+,k g,njv 2 v5ostr6,{!)#OC 9twfh O2 c]h;gda[vqd-uc-ow;h.o4a’gs^addhkryglfD @? 75o]adltot0v’vqd-uc-o dD 75o]adltotmk’2u-yd dyf9tde #G lbdlk]adltotmk’2u-yd0v’vqd-uc-o !D gvqks^vfmqf]v’[ao95vqd-uc-og8a,m,uj ufvovafg-’yj gda[wfh9kddyf9tde !D @D .shoadIPola’gdfrk;tF lu 0v’vqd-uc-o.os^vfF c]h;[aombdzqoD #D w0fvomvuj afs^vfmqf]v’vvdc]h;fq,doyj F rhv,[aombdzqoD 9kddyf9tde oadIPola’gdfgsao;kj vqd-uc-o gxaodklF [+,ulu c]t g,nvj fq,9t[+,udyoj fa’j oAo9b’j lts^5[wfhG vqd-uc-ogxaodklF [+,udyoj F [+,u]qfF |add;kj vkdkfF ]t]kp.ooehwfh|hvp Xvo5 str,6 20OC oE 100 ml lk,kf]t]kpvdq -cu -owfh 3 ml ?D ltooha vdq -cu -o9’jb lk,kf7’q 8q; c]t Iadlk16j.ooEwfhD v5ostr6, {!!_OC c]t 7;k,fao 50 atm vqd-uc-o16j.ork;t cs^;F ,ulu2hk9nf c]t cs^;d;kj oED vqd-uc-o,uv5ostr6,2qf -183OC, gxaomkf-;j p.odko skp.90v’7qo c]t lafD 0D 75o]adltotmk’g7,u vqd-uc-oxt8ydy]ypkda[vt3]st { dyf9tde $G la’gdfdkogdufxt8ydy]ypk]ts;jk’vqd-uc-oda[4jko XC? c]t ,kf XS? !D oed;fcdh;mu[j ao95vqd-uc-o,k @ d;f @D gvqk4kj ogzqk.shIhvocf’c]h;xvj o]q’d;fcdh;mu!j oadIPola’gdfxkdqfdko c]t [oa mdb zoq D #D gvqk/o5j ,kf.l[j ;j ’96f.shIhvogxvnj p 9kdoAoxvj o]q’d;fcdh;mu@F la’gdfxkdqfdko 55

.og;]k96f.ovkdkf c]t s^a’9kdmuxj vj o]q’.od;fF rhv,ma’[aombdzqoD la’gdfg[yj’I6[c8h, dD96f4jko 0D 96f,kf I6[ _D@D mqflv[]adltotg7,u0v’vqd-uc-o 9kddfy 9tdeoda IPol’a gdfgsoa ;kj G { g,vjn gvkq 4kj omwju \\Ih vh ocf’xvj o]’q .ldj ;fcd;h m!u F 4kj ow29tI’j5 cf’0oB d;kj gdkjq sk^ p ສ.ວ.ສສະຫງວນລິຂະສິດ oahophvo;kj 4kj o X C ? xt8ydy]ypkda[ O2c]h;dkpgxaodkl CO2 faj’lq,zqo C + O2 → CO2 { g,njvgIqk96f,kf.ovkdkf,ao9tw\\hrhv,da[,ucx;w2ohvpMlu,j;’F9kdoahog,njvoe gvkq ,kfmdju e]’a gxvjn p xvj o]’q .ldj ;fcd;h mju @ ,cu x;w2l,u ;j ’I’j5 c9’h d;kj gdkjq ooha d= phvo;kj ,kfw\\h.ovqd-uc-o9twfdh kl-6o26giu s^n ,kf IV vqd-yf fa’j lq,zqoG S + O2 → SO2 { vqd-uc-oxt8ydy]ypkda[3]st X pqdg;aho Pt, Au ? 8;q 1kj ’G { vdq -uc-oxt8ydy]ypkd[a mv’ (Cu) 2Cu + O2 → 2CuO { vdq -uc-oxt8ydy]ypkd[a gs^da (Fe) { vdq -cu 3-Foex+t82dyO]y 2py →kdF[a e,3Okg4p-vu v, (Mg) 2Mg + O2 → 2MgO vqd-uc-oxt8ydy]ypkda[Iu3fic-o.ork;tmkffjP; c]t mkfxtlq, { gdufxt8ydy]ypkd[a Iu3fic-ork;tmkffPj ; 56

2H2 + O2 → 2H2O ສ.ວ.ສສະຫງວນລິຂະສິດ { gdufxt8ydy]ypkd[a Iu3fic-ork;tmkfxtl,q 7nG T gdufxt8ydy]py kgzkq w\\dh [a vkg-8cu ]o (C2H2) 2C2H2(g) + 5O2(g) → 4CO2(g) + 2H2O(l ) T gdufxt8ydy]ypkd[a g,8ko (CH4) CH4(g) + 2O2(g) → CO2(g) + 2H2O(l ) vdq -cu -ogxoa mkffPj ;mgju 7vjn ows;g7,cu I’ X rgy lf.ovo5 str,6 l’6 ? vdq -cu -o gdfu xt8dy y ]ypkg7,uda[s^kpmkffPj ; c]t mkfxtlq, .omkfxtlq,l;j os^kpmkf,6ovqd-uc-o ,u7kj g7,ugmkqj @D #? lj;oxtdv[0v’vqd-uc-o.ovkdkf dyf9tde &G mqflv[xt]y,kovqd-uc-o.ovkdkf !D gvkq cd;h I[6 m+d,q 3]’j m,uj u0uyf\\kp[=]y,kfc];h c[’j 0uf\\kpvvdgxoa * l;j ogmkjq doa D @D gvkq m+d,q ooA 8’A ]’q .ovkj ’cd;h c];h 4vdok.=h l.j srh =furP’0uf\\kpmevyf #D gvkq 2fq lt2.= l[j ;j ’Xm,ju fu vovfa 1dj6 kh o? c];h 9f6 9kdooA xvj o]’q md+ ,q 1.j6 ovkj ’cd;h m,ju u oE c]h;vafm+dq,.shc9[fa’j I6[c8h, la’gdfxt]y,kooE.om+dq, c]t [aombdzqoD 66 55 44 33 22 11 I6[ _D# mqflv[xt]y,kovqd-uc-o.ovkdkf 9kddyf9tde g,nvj 4vdoE.l.j ovkj ’cdh; gsao;kj oE.ovkj ’ws^g0Qk.ocdh;I6[m+dq,rP’ !}* 0v’0uf\\kp Xvkdkf.om+dq,9tgs^nvrP’ & l;j o? c]t rkps^a’muxj vj o[;j ’[ao952qfl2= ]q’wx]=4hk9qow2,vfF gIqkgsao,u7;aolu0k;F 7;aof’aj dkj ;wfhlts^kp8q;.ooE c]t gsao;kj oE.o m+dq,wfhpn’j 0BoIvf0ufmuj @D \\kp7;k,;kj [=]y,kf0v’vkdkf.om+dq,wfhglpwxxt,ko ! l;j o phvo;jkoEwfhg0Qkcmo[=]y,kf0v’dklmujwfhglpwx.odkow\\hF ltoAodklmujglpwxoAoc,jo 57

vdq -uc-o X O2 ? f;h pgsfoU gIkq 9’jb lts[^5 wf;h kj G vdq -uc-o XO2? ,xu t,ko !}& mk’fkh o[]= ,y kf ສ.ວ.ສສະຫງວນລິຂະສິດ 0v’vkdkfD $? dkooe.-h O 2 oadIPo9’qj la’gdfg[y’j I6[ c]h;[vd.shI6h;kj vqd-uc-ogroyj oe.-hgrvnj gIafspa’cfLj I6[ _D$ dkooe.-hvqd-uc-o { vqd-uc-o-;j p.odkoskp.9G .-hgzqkw\\hmkfF -;j ps^+]hP’.oIkj ’dkp0v’7qo c]t lafF -;j p.shoad[yom[uj yol6’F 7qog9a[|adF oadfa[gru’F oadfeoEDDD { vdq -cu -o-;j pdkogzkq w\\Gh .-9h vf sn^ 8fa 3]st gxoa g-vN w2.o3I’’kovf5 lkstdesv^ , 3]stF zt]yf]tg[uf.-h.odkod+lhk’F gxaog-Nvw2g0Qk.opkovk;tdkfD &? dkow\\hc,jospa’L g,vjn 9f6 mPow0gIkq 9tgsoa ;kj ,cu l’w2I’j5 c9’h F ,7u ;k,Ivh oczvj vdF mPo9t7vj pM \\fq wxF ooA c,oj xtdfq dkow\\Dh dkow\\hc,oj xkdqfdkomuj gduf7;k,Ihvo c]t ,ucl’lts;kj ’ g’njvow0mjurk.shgdufdkow\\h { vo5 str,6 l’6 rP’r= { ,vu dq -cu -orP’r= ltooA F grvjn [.+ sdh kow\\gh dfu 0oB 9t8vh ’gIfa .svh o5 str,6 8k+ d;kj vo5 str,6 w\\h c]t 8fa cs’j^ lt|v’vdq -cu -o.sch ddj kow\\Dh 58

.o[k’d]= tovu dq -cu -ogdfu xt8dy ]y py kd[a mkf8kj ’M[c+ ,oj 9tgxoa xt8dy ]y py kgzkq w\\lh tg\\u wxg-oja ;kj 4kh gIkq xtgs^da w;.h ovkdkf-,j5 w]pt|’jb d=9tgsoa ;kj gs^da ooha dkpgxoa lu0\\uh Ph ’D @D vqd-yffk-q’ !? 7;k,\\kp0v’vqd-yffk-q’ 9’jq l’a gdfl,q zoq xt8ydy]ypkmguj duf0Bo]ts;kj ’vdq -uc-od[a mkf8kj ’M mkfxt8yrao mkfzt]yf8trao S + O2 SO2 4Na + O2 2Na 2 O CH4 + O2 CO2 + 2H2O 9kdlq,zqo0hk’gmy’9tgsao;kj xt8ydy]ypkg7,umugj duf0Bo]ts;kj ’vqd-uc-oda[mkf8kj ’Mສ.ວ.ສສະຫງວນລິຂະສິດ c]h;wfhmkfzt]yf8traomugj xaovqd-yf xt8ydy]ypkfa’j dkj ;oahogvuho;kj vqd-yffk-q’D xt8ydy]ypkvqd-yffk-q’,ulv’-toyf7nG { dkogzqkw\\hmkf8kj ’Mfh;pvqd-uc-olqf gduf0Bow;F .shv5ostr6,l6’ c]t ,ucl’lt s;kj ’ 8q;1kj ’G 3Fe + 2O2 ⎯5⎯00oC⎯→ Fe3O4 { dkogzqkw\\hmkf8kj ’M.ovkdkfgduf-hk v5ostr6,8+k c]t [+,ucl’lts;j k’g-aoj G dkogduf\\Ph ’0v’3]stF dkoc]dxPj omkf.oIkj ’dkp0v’7oq F lfa F dko[,qj /oj5 DDD @? vqd-yf vqd-yfc,oj spa’L c[’j vvdgxao9ad-toyfL vqd-yf c,oj mkfxtlq,]ts;kj ’3]st s^n vt3]stda[vqd-uc-ovqd-yfc[’j vvdgxaolv’ -toyf7nG vqd-yf[kg-u c]t vqd-yfvk-yfD { vqd-yf[kg-uc,oj mkfxtlq,]ts;kj ’3]stda[vqd-uc-o g-aoj G K2O, Na2O, CaO... 59

{ vqd-yfvk-yf c,oj mkfxtlq,]ts;kj ’vt3]stda[vqd-uc-o g-aoj G CO2, SO3, P2O5 ສ.ວ.ສສະຫງວນລິຂະສິດ dkovjko-njvqd-yf[kg-uG vjko-nj3]st X4hk3]st,us^kp7jkg7,ud=[vd7jkg7,urhv, c];h ]’q mkh pf;h pvdq -yf? 8q;1kj ’G Na2O ok8iuvv,vdq -yf CaO dko-uvv,vdq -yf FeO gs^ad II vqd-yf Fe2O3 gs^ad III vqd-yf dkovjko-njvqd-yfvk-yf G vkj o-nvj t3]st X4hkvt3]st,us^kp7kj g7,ud=[vd7kj g7,urhv, c];h ]’q mkh pf;h pvdq -yf? CO2 dkd[vo IV vqd-yf SO3 ,kf VI vqd-yf P2O5 2qflt2= V vqd-yf [k’d]= tou grojy vkj o9eo;ovk38,vt3]st8k,rklk]kc8’a F !X3,3o?F @ Xf?u F # X8i?u F $ Xg88ik?F & Xcx’8k?F * XgIad-k?DDDc]h;8+fh;p-njvt3]st 9kdoAo vjko9eo;ovk38, vqd-uc-o 8k,rklk]kc8a’ c]h;]q’mhkpfh;pvqd-yf 8;q 1kj ’G P2O5 vkj o;kj fu2qflt2=cxa’8kvqd-yfD N2O3 vkj o;kj fuou38ic-o8iuvqd-yfD { 4hkvt3]st,u|b’j vk38,9t[+vkj o9eo;ovk38, c8vj kj o9eo;ovk38,0v’vqd-u c-oD CO2 vkj o;kj dkd[vofuvqd-yfD SO3 vkj o;kj ,kf8iuvqd-yfD CO vkj o;kj dkd[vo3,3ovqd-yfD NO vkj o;kj ou38ic-o3,3ovqd-yfD [k’d]= tou vdq -fy vk-fy [k’-tofy mmju P,7vj6 k-fy lk,kfvkj o0oB 8oQ f;h pvkoIfu ify 8f+ ;h p 60

-nj vt3]st c]h;]q’mhkp XgVu? s^n XVyd?D SO2 vkj o;kj vkoIufiyf-5o26giu SO3 vkj o;kj vkoIufiyf-5o26iyd CO2 vkj o;kj vkoIufiyfdkd3[oydD P2O5 vkj o;kj vkoIufiyf2ql2=iydD [qfg/ydsafG !D g,nvj 96fdkd[vo WF@$ g mu,j umkfvnoj [+w\\hxqo16j @ : 4k,;kj dkldkd3[oydmugj duf0Bo ,u9ad g L @D 9q’j -vd[=]y,kfvqd-uc-o c]t vkdkfmu8j hv’.-hgzqkw\\hmkfxqo !Wg .ooAo,u,kf @W: c]t 2ql2= )W:L #D 9’qj 9af[aofkl6f0v’vqd-yf8+wxoU.l8j k8t]k’.sh4nd8hv’ Na2O, MgO, CaO, ZnO, Al2O3, K2O, CO2, Mn2O7, CrO3, SO3, CO ສ.ວ.ສສະຫງວນລິຂະສິດ l6f3,g]d5o -nmj kf vdq -yf[kg-u vdq -yfvk-yf $D mkf.f8+wxoU.-hx5’c8’j vqd-uc-owfhG Fe3O4, KMnO4, KClO3, H2O,CuSO4, CaCO3 &D .oshv’mqf]v’gryjox5’c8j’ Fe O fh;p;ymugvqkgs^adxt8ydy]ypkda[vqd-uc-o.o 34 v5ostr6,l6’ dD 9q’j 0Polq,zqo c]t -a’j -k 0D 4hk1kdwfh Fe3O4 13,5g 9t.-hvqd-uc-o.og’nvj ow0,kf8t4ko9ad]yfL 7D 4hk,uvqd-uc-o !* g 9twfh Fe3O4 9ad gL *D g,vjn l’jy c;f]vh ,gxgy xvN o9t,zu oq glpskpsp’a cfgj dfu 0oB L 1kdgIfa .svh kdkfxvf.l c]t ,uvqd-uc-orP’r=9t,u;ymuxhv’daoco;.fL 61

[qfmu !W Iu3fic-o !D mkf,6oIu3fic-o mkf,6oIu3fic-o.ome,t-kf16j.ork;tgl]u,uxt]y,ko|hvpc8j.omkfxtlq,,us^kp g-oja G.ooEF [+oE,oa f[y F [+4kj osou FDDD mkf,o6 I3u fic-o,lu oa pt]da c,oj H , 3,g]do5 xtdv[f;h p lv’vk38, l6f3,g]d5oc,oj H2 .om5dM mkfxtlq,Iu3fic-o,u7kj g7,ugmqkj ! @D dkox5’c8j’Iu3fic-o groyj x5’c8’j Iu3fic-owfhco;.fL dD .oshv’mqf]v’ dyf9tde!G x5’c8j’9kd Zn xt8ydy]ypkda[ HCl ສ.ວ.ສສະຫງວນລິຂະສິດ !? xtdv[g7vnj ’mfq ]v’f’ja I[6 c8,h HCl @? 1vfvk-yf HCl xt,ko & ml ]q’.o H2 davd 9kdoAod=gxufdavd.shvk-uf]q’.lj d;fcdh;mu,j ula’dtluxt,ko ${& g,afD xtw;hw]pt|b’j .shdkl]tgsupvvd grnvj Zn gIaf.shvkdkf.od;fcdh;\\qfwxF .-h s^vfmqf]v’gda[gvqkdklmujwfhc]h; vaffh;pfvoD I6[ !WD! dkox5’c8’j Iu3fic-o #? oes^vfmqf]v’[ao95dklmujxyjoxkd]q’ ],5j vaffh;pfvom,uj um+l’qj dkl $? 9kdoAo.shxyoj xkds^vfmqf]v’0Bogmy’F H2 .-hw,h0ufw2muj,ucx;w2]5dw\\h96fdkl I3u fic-omxju kpml+ ’qj dklF l’a gdfxkdfq dko c]t [oa mdb zoq D I6[ !WD@ dkomqflv[7;k,lqfdklIu3fic-o 62

zqo0v’dkomqf]v’ ສ.ວ.ສສະຫງວນລິຂະສິດ gsao,u/vfdkl8yf16jzy;|hk0v’g,afla’dtlu c]h;d=,udkl]tgsupvvdF g,afla’dtlu 9tovh p]’q wxg]vN pMD lq,zqog7,umujgduf0Bo Zn + 2HCl → ZnCl2 + H2 g,vnj .-hw,h0ufw2m,uj ucx;w2]5dw\\h96fxkpm+l’qj dkl9t,ucx;w2lu,;j ’gduf0Bo lts^5[ 9kdzoq dkomfq ]v’1’A 1on wf;h kj dklmgju dfu 0oB ooA c,oj I3u fic-o grojy gd[a dkl I3u fic-ozkj ooEpvh o;kj I3u fic-o[+]t]kp.ooED \\kpgsfG .odkox5’c8j’dklIu3fic-ovkf9txjPocmo HCl gxao H2SO49k’F xPj ocmo Zn gxao3]stvnoj g-aoj G Al, Fe d=wfhD 0D .ov5flkstde .ovf5 lkstdegrojy lk,kfx’5 c8’j dklI3u fic-owf9h kddko;gy 7ktoEf;h pdtclw22kh 3fp.-h NaOH s^n H2SO4 gxaomkfg]a’j D 2H2O ⎯;yg7⎯kt⎯w2⎯2hk⎯→ 2H2 +O2 ovd9kdoAopa’.-hdkd[vo16.j om+lq’j vkp4kj oIhvof6fvqd-uc-ovvd9kdoE s^n x5’c8’j Iu3fic-o 9kdvkpme,t-kfF vkp[+oE,aofy[ fa’j I6[c8h,D H2 O2 H2O H2O dD 9kd[+oE,aofy[ 0D 9kdoE 7D 9kdvkp4kj o I6[ !WD# zt]yfdklIu3fic-o.ov5flkde 63

#D 75o]adltot0v’Iu3fic-o ສ.ວ.ສສະຫງວນລິຂະສິດ !? ]adltotmk’2u-yd dyf9tde @G lbdlk]adltotmk’2u-yd0v’dklIu3fic-o !D gvkq s^vfmfq ]v’[oa 9d5 klIu3fic-og8,a m,uj ufvovfa c9[ g-’yj wf9h kddkox’5 c8’j D @D .shoadIPo la’gdfrk;tF lu0v’dklIu3fic-o c]t [aombdzqoD #D w0fvomvuj afs^vfmqf]v’ c]h;fq,dyoj F rhv,[aombdzqoD 9kddyf9tde @ gsao;kj dklIu3fic-ogxaodkl [+,uluF [+,udyoj D dyf9tde #G lbdlk]adltotmk’2u-yd0v’Iu3fic-o gvqkx6,gxQk ! |;j p mulj 6[fh;pdklIu3fic-o c]t vud ! |;j p l6[fh;p[A’l6[,afxkdx6, gxQk c8]j t|;j p fh;plkp1k’c]h;xvj p0Bolv6j kdkfrhv,daoF la’gdf c]t [aombdzqoD 9kddfy 9tde # gsoa ;kj x,5 gxkhq m[ju oa 9d5 klI3u fic-ox;y 0oB wfFh l;j o|;pj mlju [6 f;h p[’A l[6 9t[+xy;D oAoltcf’;kj dklIu3fic-og[qkd;kj vkdkfD I3u fic-o ovd9kd,]u da ltotmdju kj ;,kocU ];h p’a ,]u da ltotvojn Mvdu g-oja G []+ t]kp.ooEF ,uv5ostr6,gxnvj p{@&_F#$OCF 2qf {@&@F)(OCD @? ]adltotg7,u dD Iu3fic-oxt8ydy]ypkda[vqd-uc-o !D [oa 9v5 dq -uc-o.lcj d;h mfq ]v’xkdd;kh ’m,uj u[=]yu,kf!WW ml @D oegvkq I3u fic-ox’5 c8’j wfch ];h ,k9f6 9kdooA xvj oml+ ’jq dkl]’q d;fm[ju oa 9v5 dq -cu -o f’ja I[6 !WD$ l’jy m7ju ;ogvkq .9.lGj g;]kx’5 c8’j dklI3u fic-o8vh ’gvkq .9 .lrj ly f6 .swh fh 7;k,lqf0v’dklIu3fic-oglpdvj o9’bj oewx96fgrnvj xhv’daodko]tg[ufD dkomqf ]v’gsao;jk dklIu3fic-o9tln[8+w\\h.ovqd-uc-ocI’0BoF g[Nv’.o0v’d;f cd;h ,ug,fa oEovh pM8yf1Dj6 lq,zqog7,u 2H2 +O2 ⎯t⎯o→ 2H2O 64

HCl ສ.ວ.ສສະຫງວນລິຂະສິດ H2 O2 HCl H2O Zn I6[ !WD$ mqflv[]adltotg7,u0v’3fic-o 0D Iu3fic-oxt8ydy]ypkda[ CuO xtdv[dkomfq ]v’f’ja I[6 H2 CuO H2O I6[ !WD& dklIu3fic-oxt8ydy]ypkda[mv’lv’vqd-yf oegvqkdklIu3fic-olqfzkj og0Qkwx.os^vfmu[j ao95 CuO lufemudj e]a’gzqkIvhoF zqodko mfq ]v’ gsoa ;kj .ovo5 str,6 me,tfkxt8ydy]ypk[+gduf0Bo c8gj ,vnj ,vu o5 str,6 l’6 xt,ko $WW°C /5oj CuO lufe9tdkpgxao Cu lugs^nv’ c]t ,uoEgduf0BoD lq,zqog7,uG H2 +CuO ⎯t⎯o→ H2O + Cu #? dkooe.-hdklIu3fic-o 9’qj la’gdfI6[],5j oU c]h;[vd;kj dklIu3fic-ogroyj oe.-hgIafspa’cfLj 65

l6[[k]6o c]t x6,gxQk zt]yfg-Nvw2 9vfF 8af3]st x5’c8j’3]stlqf 9kdvqd-yf3]st x5’c8’j HCl zt]yf NH3 zt]yfxJ5p I6[ !WD* xt3spf.odkooe.-hIu3fic-o 9kddkola’gdfI6[ gsao;kj gryoj oe.-hdklIu3fic-o l6[[k]6oF x6,gxQkF zt]yfg-Nvw2 Xoelq’j ]6dlvow2F cmooE,aocvaf-a’FDDD?F x5’c8’j 3]stlqfF vk-yfd^=IufiydD zt]yfvk3,oypadF xJ5pD .-h.odko9vf c]t 8af3]stD ovd9kdoAo pa’zt]yfmkfvq’7tmkf8kj ’MD ສ.ວ.ສສະຫງວນລິຂະສິດ [qfg/ydsafG !D 9q’j 0Po c]t -a’j -k lq,zqo8+wxoU.sh7q[4h;o dD Fe2O3 + H2 ⎯t⎯o→ 0D HgO+ H2 ⎯t⎯o→ 7D Cl2 + H2 → @D g,vnj oegvqkdklIu3fic-owxzkj omv’ II vqd-yf $)g c]h;gzqkIhvo dD 9q’j 7yfw],j ;olkomv’muwj fhIa[,u9ad gL 0D -vdsk[]= ,y kf0v’dklI3u fic-o.og’vjn ow0,kf8t4kom9ju t8vh ’.-,h gu mkjq .f]fy L #D 9’jq -vdsk,;olko0v’oEmwuj fIh [a g,vnj groyj .sdh klIu3fic-o )F$ ]yfxt8ydy]ypkd[a dklvqd-uc-o @F) ]yf Xdklm5d-toyf]h;oc8;j afcmd.og’nvj ow0 ,kf8t4ko?D $D 9’jq pdq 8;q 1kj ’dkooe.-dh klIu3fic-omIuj 9h6 da L &D 9’jq 7fy w]lj ;j oIvh pfkh o,;olko0v’dklI3u fic-o.omkfxtl,q 8w+ xoGU C2H2, H2SO4 66

rkdmu III dtclw22hkdq’ ສ.ວ.ສສະຫງວນລິຂະສິດ [qfmu !! dkorq;rao]ts;jk’dtclw22hkF zqo]q[]tfa[w22hk c]t 7;k,8hkow22hkS dqfgdo3v, !D dtclw22hk c]t myf0v’dtclw22hk oda IPowfIh Po,kc];h ;kj 4kh [oa fkgvg]da 8i’q gl]gu 7vjn omwju x8k,mfy fP;doa .o;fa 4o5 ew2 2hk grjyo4n;jk .o;af45oew22hkoAo,udtclw22hkc]jozjkoD dtclw22hk9tgduf0Bowfh.o;af45 oew22kh wf8h vh ’,]u tf[a w22kh mcju 8d8kj ’doa sn^ g;kQ vdu 1kj ’|’jb ;kj 8vh ’,zu oq ][q ]tf[a w22kh D l’jy mrju k.sgh dfu ,zu oq ][q ]tf[a w22kh grvnj .s,h du tclw22kh gdfu 0oB ooA ,lu v’-tofy 7Gn -tofy m|u ’jb wfch dxj oy c]t vda dp5 g-y’j vkwlxt8ydy]ypkmk’g7,Fu -tofy mulv’ wfch dfj ou k3, g-’yj vkwl rt]a’’kodqo9ad c]t c,gj s^adD dyf9tde !G lbdlkmyf0v’dtclw22hk !? 8+g7vnj ’cmdw22kh .lxj yo ! dvh o f’ja I[6 !!D!D l’a gdfdkog|’a 8u’0v’g0,a g7vnj ’cmd w22hk c]t [aombdzqoD @? gIfa dkomfq ]v’7n !? c8xj Pj ogvkq lkpw22kh m8ju d+ [a loQ [;d0v’g7vjn ’cmdw22kh wx8d+ [a lQo]q[0v’xyo c]t dq’dao0hk,D oda IPol’a gdf gsoa dkog|’a 8’u 0v’g0,a g7vjn ’cmdw22kh .odkomfq ]v’ !? c]t @? 8kj ’ daoco;.fL 9tlts^5[wfhco;.fL I6[ !!D! I6[ !!D@ 67

zqodkomqf]v’ !? c]t @? g0a,g7nvj ’cmdw22hkg|a’8u’wxmk’dq’0hk,dao XmP[da[ 0uf W?D oAoltcf’;kj dtclw22hkvvd9kdxyo s^n vadd5p ,urP’myffP;7n 9kd0Q;[;dwxsk 0Q;]q[ g-y’j gryjogvUo;kj dtclw22hkdq’ sn^ dtclw22hk DC. .o]ts;kj ’xu 7Dl !)#W mkj ovecx X!((&{!)#*? oad;ymtpklkf-k;/i’aj wfhdeoqf;kj G 16j;q’9vorkpovd[+w22hkF dtclw22hkdq’c,oj dtclw22hkmugj 7nvj omuvj vd9kd0Q;[;dwxsk 0Q;]q[0v’[+w22hk Xxyo sn^ vadd5p? faj’I6[ !!D@ @D dkorq;rao]ts;jk’7;k,g0A,dtclw22hkda[zqo]q[]tfa[w22hk dyf9tde @G 7;k,g0A,dtclw22hk0Boda[zqo]q[]tfa[w22hk !? 8+xyo ! dhvoF g7nvj ’cmdvecx(A) ! g7nvj ’F g7nvj ’cmd3;o(V) ! g7nvj ’ c]t sq;mPo *V ! fvdD .shgxao;q’9vow22hkXfaj’I6[!!D#?D la’gdf7;k,I5j’0v’sq;mPoF vjko7jk0v’ 7;k,g0A,dtclw22hk(I) c]t zqo]q[]tfa[w22hk(U). [aombdzqoD ສ.ວ.ສສະຫງວນລິຂະສິດ VA V A I6[ !!D# @? gIafdkomqf]v’7nda[ 0=h !? c8.j -hxyo @ dhvo8+]PodaoD #? gIafdkomqf]v’7nda[ 0=h !? c8.j -hxyo # dhvo8+]PodaoD { 7;k,I5’j 0v’sq;mPo.og;]k.-hxyo ! dhvoF @ dhvo c]t # dhvo 8kj ’daoco;.fL { 7kj 7;k,g0,A dtclw22kh (I) c]t zoq ][q ]tf[a w22kh (U) g;]k.-xh yo ! dvh oF @ dvh o c]t # dhvo xPj ocx’co;.fL { oadIPo9tlts^5[zqodyf9tde 7nco;.fL 9kdzqodyf9tdeoadIPogsao;jk g,njvgruj,9eo;oxyomuj8+]Podao0BoXgruj,zqo]q[]tfa[ w22hk0Bo? 7;k,Ij5’0v’sq;mPo c]t 7jk7;k,g0A,0v’dtclw22hkgruj,0Bo8k,]efa[D oAoltcf’;kj .o;q’9vow22hkF ovd9kddkoxPj ocx’0v’[+w22hkc]h; 4hkl;j oxtdv[vnoj [+xPj ocx’ sn^ g;Qk;kj 4hk7;k,8hkow22hk[+xPj ocx’ c,oj 7;k,g0A,dtclw22hkgru,j 0Bo8k, dkogruj,0Bo 0v’zqo]q[]tfa[w22hkD 8k,dkomqf]v’0v’oad;ymtpklkf16j.oshv’mqf]v’ 68

.-hg7nvj ’cmd,u7;k,-afg9ol6’ lk,kflts^5[;kj G .o;q’9vow22hk|’bj 4hk7;k,8hkow22hk R [+xPj ocx’F 7;k,g0,A dtclw22kh I 9txPj ocx’8k,zoq ][q ]tf[a w22kh U 8k,dkor;q roa vfa 8kl;j odq’dao I ~ U #D dkorq;rao]ts;jk’7;k,g0A,dtclw22hkda[7;k,8hkow22hk dfy 9tde #G ldb lkdkor;q roa ]ts;kj ’7;k,g0,A dtclw22kh c]t 7;k,8kh ow22kh !? 8+xyo # dhvo 8+]PodaoF g7nvj ’cmdvecx(A) ! g7nvj ’F g7nvj ’cmd3;o(V) ! g7nvj ’F sq;mPo ! fvd c]t g7nvj ’8hkow22hk(R) ! vao .shgxao;q’9vow22hk Xf’aj I6[ !!D$?D la’gdf7;k,I5j’0v’sq;mPoF vkj o7kj 7;k,g0A,dtclw22hk c]t zqo]q[]tfa[ w22kh D [oa mdb zoq D RR V ສ.ວ.ສສະຫງວນລິຂະສິດ I6[ !!D$ A @? gIafdkomqf]v’7n 0=h !? c8.j -hg7nvj ’8hkow22hk(R) @ vao 8+]PodaoD #? gIafdkomqf]v’7n 0=h !? c8.j -hg7nvj ’8hkow22hk(R) # vao 8+]PodaoD { 7;k,I5’j 0v’sq;mPo.og;]k8+g7nvj ’8hkow22hk(R) .lj ! vaoF @ vaoF # vao 8kj ’dao co;.fL { g,nvj 8+g7nvj ’8hkow22hk.l;j q’9vo ! vaoF @ vao c]t # vao 7kj 7;k,g0A,dtclw22hk c]t zqo]q[]tfa[w22hkxPj ocx’co;.fL { 9kdzoq dfy 9tde oda IPo9tlts[5^ dPj ;d[a dkor;q roa ]ts;kj ’7;k,g0,A dtclw22kh da[7;k,8hkow22hkco;.fL zoq dfy 9tde [w+ 22kh [x+ Pj ocx’F 7;k,I’j5 0v’s;q mPo s^n 7kj 7;k,g0,A dtclw22kh sf5^ ]’q g,njvgruj,9eo;og7njv’8hkow22hk0BoD oAoltcf’;jk .o;q’9vow22hkF g,njvzqo]q[]tfa[ w22hk[+xjPocx’7;k,g0A,dtclw22hks^5f]q’8k,dkogruj,0Bo0v’7;k,8hkow22hkD 8k, dkomfq ]v’0v’oda ;my tpklkf1.6j osvh ’mfq ]v’m.ju -gh 7vjn ’cmd,7u ;k,-fa g9ol’6 lk,kflts[5^ ;kj G .o;’q 9vow22kh |’jb 4kh zoq ][q ]tf[a w22kh (U) [+xPj ocx’F 7;k,g0,A dtclw22kh (I) xPj o cx’8k,7;k,8hkow22hk (R) 8k,dkorq;raovaf8kl;j oxUodao I ~ 1 D R 69

$D dqfgdo3v, dko7Qo7;hkmqf]v’dPj ;da[ dkorq;rao]ts;kj ’ 7;k,g0A,dtclw22hkF zqo]q[]tfa[ w22kh c]t 7;k,8kh ow22kh .o;’q 9vow22kh |’jb mkj o 9va f-u,vo3v, (George Simon Ohm) wfhlts^5[gxaodqfgdo c]t 0Pogxaol6f0v’dkorq;raof’aj oU G 7;k,g0A,dtclw22hk (I) mucj ]oj .o8vo|b’j 0v’;q’9vow22hkF gxaovaf8kl;j odq’da[ zqo]q[]tfa[w22hk (U) c]t gxaovaf8kl;j oxYoda[7;k,8hkow22hk (R). 9kd X!? 4vowfh I =U X!? s^n R X@? X#? R=U I U = IR 8k,l6f X@? zqo]q[]tfa[w22hk(U) ,usq;|j;p ສ.ວ.ສສະຫງວນລິຂະສິດ gxoa 3;o(V), 7;k,g0,A dtclw22kh (I) ,su ;q |;j pgxoa vecx (A), 7;k,8hkow22hkXR?9t,usq;|j;pcmdgxao mkj o George Simon Ohm 3;o}vecx (V/A) c8gj rnjv]tobdg4y’zqo’ko0v’ mjko 3v,DXoad2u-yd-k;g1p]t,aomuj,u-njlP’g-jy’gxaoz6h7Qo (1789-1854) 7;hkmqf]v’ c]t lhk’gxaodqfgdodkorq;rao]ts;jk’ 7;k,g0,A dtclw22kh F zoq ][q ]tf[a w22kh c]t 7;k,8kh o w22kh g-’yj 4;n kj gxoa dfq gdoroN 4komlju e7oa 0v’w22kh dtcl d’q ? gryoj 9’jb deofq s;q |;j pcmd7;k,8kh ow22kh gxoa 3v, 3fp.-vh da lvo3vg,dk(Ω ) .orklkgdida gxoa loa pt]da D fa’j oAo 1Ω = 1 V A 7e4k, !D 9’qj .soh ypk,dtclw22hkdq’ rhv,ma’vtmy[kplkgsfdkodegouf0v’,aoD @D 4kh 1l6j v’9f5 0v’lkpw22kh ,]u tf[a w22kh gmkjq doa D 4k,;kj 9t,du tclw22kh c]oj zkj o 8volkpoAo[+L phvospa’L #D 9’jq g]kjq govN .odfq gdo3v,D 70

[qfmu !@ 8volkp8+]Podao c]t 8+0t|kodao !D 8volkp8+]Podao dyf9tde !G lbdlkdko8+g7nvj ’.-hw22hk s^n g7njv’8hkow22hkc[[]PodaoD !? 8+sq;mPo ! fvdF xyo @ dhvo I6[ !@D ! .sgh xoa ;’q 9voxyf f’a I[6 !@D!D la’gdf7;k,I5j’0v’sq;mPoD [oa mdb zoq D @? 8+sq;mPo @ fvdF xyo @ dhvo ສ.ວ.ສສະຫງວນລິຂະສິດ .shgxao;q’9voxyffaj’I6[ !@D@ la’gdf7;k,I5’j 0v’sq;mPoD [oa mdb zoq D I6[ !@D @ #? 8+sq;mPo # fvdF xyo @ dhvo.shgxao;q’9voxyf fa’j I6[!@D#D la’gdf7;k,I5’j 0v’ s;q mPoD [oa mdb zoq D I6[ !@D # 71

{ .odkomqf]v’ !?F @? c]t #? 7;k,I5j’0v’sq;mPo8kj ’daoco;.fL { dko8+sq;mPo]Podao XI6[ !@D@? c]t XI6[ !@D#? c[[.f,udtclw22hk c]oj zkj owlh 0v’sq;mPos^kpd;kj L I6hwfhco;.fL { dko8s+ ;q mPo sn^ 8g+ 7vjn ’.-wh 22kh vojn c[[]Podoa XI[6 !@D@? c]t XI[6 !@D#? c[[.f9t ,u7;k,8hkow22hk];,s^kpd;kj L I6hwfhco;.fL .odkomqf]v’ !?F @? c]t #? mju.-hsq;mPo7ndao8+da[[+w22hkXxyo? vaofP;dao Xxyolv’dhvo7ndao?D ltoAoF zqo]q[]tfa[w22hk1j6lv’0Q;0v’sq;mPoma’\\qfgmqjkda[zqo]q[ ]tfa[w22hk16lj v’0Q;0v’[+w22hk Xlv’0Q;0v’xyo @ dhvo 8+]Podao?D g,nvj mP[zqodkomqf]v’ !?F @? c]t #? gsao;kj @? 7;k,I’5j 0v’sq;mPos^5f]q’ mP[da[ !? c]t X#? 7;k,I’j5 0v’s;q mPosf5^ ]’q vdu mP[d[a X@?D ltcf’;kj g,vjn s;q mPo8]+ Podoa sk^ p0oB F 7;k,8kh ow22kh ];,0v’;’q 9vogr,uj s^kp0BoD dkomqf]v’0v’oad;ymtpklkf mu.j -hv5xtdvo,u7;k,-afg9ol6’ lk,kflts^5[wfhf’aj oUສ.ວ.ສສະຫງວນລິຂະສິດ Xlts^5[8k,8volkp8+]Podao f’aj I6[ !@D$?D { 7;k,g0,A dtclw22kh I mcju ]oj zkj omd5 9f5 .o;’q 9vogmkjq doa X7;k,g0,A dtclw22kh [+xPj o? \\kp;kj I zkj o;q’9voma’\\qfgmqkj I1 zkj o R1 gmqkj I2 zkj o R2 . I = I1 = I2 (1) { zqo]q[]tfa[w22hk16lj v’0Q;0v’g7vnj ’ I R1 R2 .-wh 22kh m’a \\fq gmkjq zoq [;d0v’[oa fk I1 I2 zqo]q[]tfa[w22hk16lj v’0Q;0v’g7vnj ’ .-wh 22kh md5 voa m8ju ]+ Podoa .o8volkpD V1 V2 U = U1 +U2 (2) V I6[ !@D $ { 7;k,8hkow22hkma’\\qf gmqjkzqo[;d[aofk7;k,8hkow22hk0v’g7nvj ’8hkow22hk ;’q 9vo m8uj +]Podoa D R = R1 + R2 (3) 72

[qfg]d8q;1jk’G 7;k,g0A,dtclw22hkc]oj zkj o8volkpmu8j +]Podaovao|b’j ,u7kj gmqkj ! AD .o;q’9vooU,ug7nvj ’.-hw22hklv’vao g-yj’r;d,ao,u7;k,8hko w22hk @ Ω c]t # Ω D 9q’j -vdskG d? 7;k,8kh ow22kh m’a \\fq .o;’q 9vo 0? zoq ][q ]tf[a w22kh 0v’g7vnj ’.-wh 22kh gskj^q ooA D cdhG d? .-hl6f R = R1 + R2 ⇒ R = 2 + 3 = 5Ω 0? .-hl6f U = U1 +U2 c]t U = IR U = IR1 + IR2 = I (R1 + R2) = 1(2 + 3 ) = 5 V. s^n U = IR = 1 x 5 = 5 V. @D 8volkp8+0t|kodao dfy 9tde @G ldb lkdko8g+ 7vjn ’.-wh 22kh sn^ 8g+ 7vnj ’8kh ow22kh c[[0t|kodoa D ສ.ວ.ສສະຫງວນລິຂະສິດ !? 8+sq;mPo ! fvdF xyo @ dhvoD .sh gxao;q’9voxyffa’I6[ !@D& la’gdf 7;k,I’5j 0v’s;q mPoD [oa mdb zoq D I6[ !@D& @? 8s+ ;q mPo @ fvdF xoy @ dvh o .sgh xoa ;q’9voxyf faj’I6[ !@D*D la’gdf 7;k,I’j5 0v’s;q mPoD [oa mdb zoq D I6[ !@D* 73

#? 8s+ ;q mPo # fvdF xoy @ dvh o .sgh xoa ;q’9voxyffa’I6[ !@D(D la’gdf 7;k,I’j5 0v’s;q mPoD [oa mdb zoq D I6[ !@D( { dkomqf]v’ !?F @? c]t #? 7;k,I5j’0v’sq;mPo8kj ’dao[+L gxaophvospa’L dko8+sq;mPo0t|kodao XI6[ !@D*? c]t XI6[ !@D(? sq;mPoc8]j tfvdI5j’gmqjkdaoD oAoltcf’;kj zqo]q[]tfa[w22hk16lj v’0Q;0v’ sq;mPoc8]j tvao gmqkj zqo]q[]tfa[w22hk16jlv’ 0;Q 0v’[+w22kh D dkomqf]v’0v’oad;ymtpklkfmuj.-hv5xtdvo,u7;k,-afg9ol6’ lk,kflts^5[wfh fa’j oU G .o8volkp8+0t|kodoa G ສ.ວ.ສສະຫງວນລິຂະສິດ { 7;k,g0,A dtclw22kh mcju ]oj .olkp8oQ gmkjq zoq [;d7;k,g0,A dtclw22kh mcju ]oj .o [aofklkpxud I = I1 + I2 X!? { zoq ][q ]tf[a w22kh 1l6j v’0;Q 0v’g7vnj ’.-wh 22kh m’a \\fq gmkjq zoq ][q ]tf[a w22kh 1l6j v’ 0Q; 0v’g7vnj ’.-hw22hkc8]j tvaoD U = U1 = U2 X@? R1 { 7;k,8hkow22hkma’\\qf (R) 7yfw]8j k,l6fG I1 V1 1=1+ 1 X#? I R2 I R R1 R2 I2 V2 9kd X#? 4vowfhG 1 = R1 + R2 V R R1R2 sn^ R = R1R2 X$? I6[ !@D) R1 + R2 [qfg]d8q;1jk’G g7nvj ’.-hw22hkmu,j u7;k,8hkow22hk @Ω c]t #Ω 8+.ldj ao c[[0t|kodoa .o;’q 9vow22kh voa |’jb D d? 9’jq -vdsk7;k,8kh ow22kh ];,0v’r;d,oa D 74

0? g,nvj I6h;kj dtclw22hkwxzkj og7nvj ’.-hw22hkmu,j u7;k,8hkow22hk @ Ω gmqkj !F@ A. 9q’j -vdsk7;k,g0A,dtclw22hkmucj ]oj zkj og7nvj ’.-hw22hk mu,j u7;k,8hkow22hk #Ω c]t 7;k,g0,A dtclw22kh ];,m’a \\fq D ;ymucdhG d? -vdsk7;k,8kh ow22kh ];,G oe.-lh f6 R = R1R2 R1 + R2 ⇒ R = 2× 3 = 1, 2Ω 2+3 0? deofq .s h I1=!F@ A c,oj 7;k,g0,A dtclw22kh mwju xzkj og7vjn ’.-wh 22kh m,ju 7u ;k,8kh o w22hk @ Ω c]t .sh I2 c,jo7;k,g0A,dtclw22hkmujwxzjkog7njv’.-hw22hkmuj,u 7;k,8hkow22hk # Ω D fa’j oAoG U = U1 = U2 I1R1 = I2R2 ສ.ວ.ສສະຫງວນລິຂະສິດ ⇒ I2 = I1R1 = 1, 2× 2 = 0, 8A R2 3 -vdsk I ];,ma’\\qfG 9kdl6f I = I1 + I2 cmo7kj wfhG I = 1,2 + 0,8 = 2 A #D dko8+g7njv’.-hw22hkc[[xtlq, ovd9kddko8+fh;p;ymu8+]Po c]t 8+0t|koc]h; .o8q;9y’gryjolk,kfgvqkdko8yf8A’ g7nvj ’.-hw22hkma’lv’;ymu,k];,.ldj ao Xc[[xtlq,? 16j.o;q’9vovaofP;daowfh fa’j I6[ !@D_D R1 R2 I2 I3 R4 I4 R3 I1 R5 I6[ !@D _ 75

7e4k, ສ.ວ.ສສະຫງວນລິຂະສິດ !D dko8yf8A’g7njv’.-hw22hk.o;q’9vow22hk,uc[[.fcfjL 9qj’vtmy[kp95fryglfc8j ]tc[[D @D groyj 8s+ ;q mPolv’fvdF fvdm|u ’jb ,7u ;k,8kh ow22kh !W Ω F fvdmlu v’,7u ;k,8kh o w22hk @WΩ g-y’j 8+gxao8volkpfa’j oUG Xd? 8+c[[]Podao X0? 8+c[[0t|kodaoD 9’jq -vdsk7;k,8kh ow22kh m’a \\fq 0v’8volkpc8]j tc[[ooA D #D .sh;q’9vow22hk fa’j I6[ !@D( c]t .sh R1 = R2 = R3 = 6 Ω c]t xyo @ dhvo g-y’j c8]j tdhvo,uzqo]q[]tfa[w22hk16j !F& 3;oD 9q’j -vdsk7;k,8hkow22hk];, c]t 7;k,g0,A dtclw22kh ];,0v’;’q 9vow22kh oUD $D .sh;q’9vow22hk fa’j I6[ !@D) c]t .sh R1 = $ Ω F R2 = * Ω F g7nvj ’cmd3;o V1 vkj o7kj wfh @F$ 3;oD 9q’j -vdskG dD 7;k,8hkow22hk];, 0v’;q’9vow22hkoUD 0D 7;k,g0A,dtclw22hkmuwj xzkj og7nvj ’8hkoc8]j tvaoD 7D g7nvj ’cmd3;o V2 -U9ad3;oL &D .sh;q’9vow22hk fa’j I6[ !@D_ c]t .sh R1 = ! Ω F R2 = @ Ω F R3 = @ Ω F R4 = ! Ω c]t R5= #Ω D 9q’j -vdsk7;k,8hkow22hk];, 0v’;q’9vow22hkoUD 76

[qfmu !# 7;k,8hkow22hk0Boda[7;k,pk;F goNvmuj|hk8af c]t mkfmujgIaflkpw22hk !D 7;k,8hkow22hk0Boda[7;k,pk;0v’lkpw22hk dyf9tde !G dkorq;rao]ts;kj ’7;k,8hkow22hkda[7;k,pk;0v’lkpw22hk d0 7’ 9l I6[ !#D! I6[ !#D@ I6[ !#D#ສ.ວ.ສສະຫງວນລິຂະສິດ !? 8+sq;mPo ! fvdF xyo @ dhvo c]t ];foy3di, d0D .shgxao;q’9vow22hkf’aj I6[ !#D!D la’gdf7;k,I5’j 0v’sq;mPoD [aombdzqoD @? gIafdkomqf]v’7nda[!? c8.j -h];foy3di, 7’ ,u0t|kf.spgj mqkj d0 c8pj k;d;kj d0 fa’j I6[ !#D@D la’gdf7;k,I5j’0v’sq;mPoD [aombdzqoD #? gIafdkomqf]v’7nda[ !? c]t @? c8.j -h];foy3di, 9l ,u0t|kf.spgj mkqj d0 c]t 7’ c8pj k;d;kj 7’ fa’j I6[ !#D#D la’gdf7;k,I5j’0v’sq;mPoD [aombdzqoD .odkomqf]v’ !?F @? c]t #? 7;k,I5’j 0v’sq;mPo8kj ’daoco;.fL oadIPo9tlts^5[ zoq dkomfq ]v’.odyf9tdeoUco;.fL zqodkomqf]v’!?F @? c]t #? gsao;kj G .odkomqf]v’ @? 7;k,I5j’0v’sq;mPos^5f]q’ d;kj dkomqf]v’!? c]t .odkomqf]v’ #? 7;k,I5j’0v’sq;mPos^5f]q’d;kj dkomqf]v’ @?D oAoltcf’;kj dkomqf]v’ @? ,u7;k,g0A,dtclw22hk c]oj zkj owlhsq;mPoohvpd;kj !?S #? ,u7;k,g0A,dtclw22hk c]oj zkj owlhsq;mPoohvpd;kj @?D zqodkomqf]v’dyf9tdeoU.shIh6;kj G 7;k,g0A,dtclw22hk I, gxaovaf8kl;j orq;raoxUo da[7;k,pk; 0v’lkpoew22hk.o;q’9vow22hkoAo s^n ;kj I ∼ 1 D 77

.o[fq mu !! wf.h sIh c6h ];h ;kj G .o;’q 9vow22kh |’jb 7;k,g0,A dtclw22kh I, gxoa vfa 8kl;j o rq;raoxUoda[7;k,8hkow22hk R X I ∼ 1 ?D dkorq;rao]ts;kj ’7;k,pk; c]t 7;k,8hkow22hk R gxaofa’j oUG 1 ∼1 sn^ R∼ X!? R fa’j oAoF lk,kflts^5[wfhfa’j oUG 7;k,8hkow22hk R, gxaovaf8kl;j orq;raodq’da[7;k, pk; 0v’lkpoew22hkoAoD @D 7;k,8hkow22hk0Boda[0tsokf.spj0v’lkpw22hk dyf9tde @G dkorq;rao]ts;kj ’7;k,8hkow22hkda[7;k,.sp0j v’lkpw22hk ສ.ວ.ສສະຫງວນລິຂະສິດ d0 7’ 9l I6[ !#D$ I6[ !#D& I6[ !#D* !? 8+sq;mPo ! fvdF xyo @ dhvo c]t ];foy3di, d0 .shgxao;q’9vow22hkfa’I6[ !#D$D la’gdf7;k,I5j’0v’sq;mPoD [aombdzqoD @? gIafdkomqf]v’7nda[ !? c8.j -h];foy3di, 7’ pk;gmkqj d0 c8,j u0t|kf.spdj ;kj d0 fa’j I6[ !#D&D la’gdf7;k,I5j’0v’sq;mPoD [aombdzqoD #? gIafdkomqf]v’7nda[!? c]t X@? c8.j -h];foy3di, 9l pk;gmqkj 7’ c8,j u0t|kf .spdj ;kj 7’ fa’j I6[ !#D*D la’gdf7;k,I5j’0v’sq;mPoD [aombdzqoD .odkomqf]v’ !?F @? c]t #? 7;k,I5j’0v’sq;mPo8jk’daoco;.fL oadIPo9t lts^5[zqodkomqf]v’.odyf9tdeoUco;.fL 78

zqodkomqf]v’ @? mP[da[ !? c]t #? mP[da[ @? gsao;kj G .odkomqf]v’ @? sq;mPoI5’j d;kj dkomqf]v’ !? c]t dkomqf]v’ #? sq;mPoI5’j d;kj d;kj dkomqf]v’ @?D oAoltcf’;kj .odkomqf]v’ @? ,u7;k,g0A,dtclw22hkc]oj zkj owlh s;q mPo.spdj ;kj !? c]t dkomfq ]v’ #? ,7u ;k,g0,A dtclw22kh c]oj zkj owlsh ;q mPo.spdj ;kj @? s^n g;kQ vud1kj ’|’bj goNvmu|j kh 8fa 0v’lkpoew22kh .spj ,7u ;k,8kh ow22kh |vh p c]t d’q doa 0hk,D fa’j oAoF 7;k,g0A,dtclw22hk I gxaovaf8kl;j orq;raodq’da[goNvmu|j hk8af A 0v’lkp oew22hkoAo s^n I ~ A [qfmu !! wfh.shIh6c]h;;kj .o;q’9vow22hk|b’j 7;k,g0A,dtclw22hk I gxaovaf8l;j o rq;raoxUoda[7;k,8hkow22hk R s^n R ∼ R D fa’j oAoF dkorq;rao]ts;kj ’goNvmu|j hk8af A c]t 7;k,8kh ow22kh 9’bj gxoa G R∼ X@? ສ.ວ.ສສະຫງວນລິຂະສິດ R 9kd[aoskmudj kj ;,k0hk’gmy’lk,kflts^5[wfhf’ja oUG 7;k,8kh ow22kh R gxoa vfa 8kl;j o rq;raoxUoda[goNvm|uj hk8af A 0v’lkpoew22hkD #D 7;k,8hkow22hk 0Boda[mkfmujgIaf];flkpoew22hk dyf9tde #G dkorq;rao]ts;kj ’7;k,8hkow22hkda[mkfmugj Iaf];flkpoew22hk ou3di, gs^ad mv’cf’ d0 7’ 9l I6[ !#D( I6[ !#D) I6[ !#D_ !? 8+sq;mPo ! fvdF xuo @ dhvo c]t ];foy3di, d0 .shgxao;q’9vow22hk fa’j I6[ !#D(D la’gdf7;k,I5’j 0v’sq;mPoD [aombdzqoD 79

@? gIafdkomqf]v’7nda[ !? c8.j -h];fgs^ad 7’ .spdj ;kj pk;gmqkj da[];fou3di, d0 fa’j I6[ !#D)D la’gdf7;k,I5’j 0v’sq;mPoD [aombdzqoD #? gIafdkomqf]v’7nda[ !? c]t @? c8.j -h];fmv’cf’ 9l .spdj ;kj pk;gmqkj ];fou 3di, d0 fa’j I6[ !#D_D la’gdf7;k,I5j’0v’sq;mPoD [aombdzqoD .odkomqf]v’!?F @? c]t #? 7;k,I5j’0v’sq;mPo8jk’daoco;.fL oadIPo9t lts^5[zqodkomqf]v’ dyf9tdeoUco;.fL zqodkomqf]v’ @? da[ !? c]t #? da[ @? gsao;kj G .odkomqf]v’ @? sq;mPoI5j’s^kp d;kj dkomqf]v’!? c]t dkomqf]v’ #? sq;mPoI5j’s^kpd;kj dkomqf]v’ @?D oAo ltcf’;kj ,du tclw22kh m,uj 7u ;k,g0,A c]oj zkj owlsh ;q mPo.odkomfq ]v’ #? .spdj ;kj dkomfq ]v’ @? c]t dkomqf]v’ @? .spdj ;kj dkomqf]v’ !?D zqodkomqf]v’dyf9tdeoU.shIh6;kj 7;k,g0A,dtclw22hkmucj ]oj zkj o];flkpoew22hk 9txPj ocx’8k,-toyf0v’mkfmguj Ifa ];flkpoew22kh ooA D dko7Qo7;hk0v’oad;ymtpklkfrq[;jk 7;k,8hkow22hk0v’lkpw22hk gxaovaf8kສ.ວ.ສສະຫງວນລິຂະສິດ l;j orq;raodq’da[ ltrk[7;k,8hkow22hk ρ Xvkj o;kj 3i? 0v’mkfmugj Iaflkpw22hkoAoD R ∼ ρ X#? ltrk[7;k,8hkow22hk ρ 0v’mkfmugj Iaflkpw22hkgxao9eo;o7q’7kj le]a[ c8]j t mkfgryoj 9’bj gvUo;kj 7;k,8hkow22hk9egrkt0v’c8]j tmkfD ,usq;|;j pgxaoΩm X3v,c,af?D 7;k,8hkow22hk9egrkt0v’mkf9eo;o|’bj 16j @W C -jnmkf 7;k,8hko9egrkt X Ωm ? g’yo !F*V!W{) Ωm mv’cf’ !F(V!W{) Ωm vk]6,uouvv, @F(V!W{) Ωm gsa^d )F*V!W{) Ωm -no @@V!W{) Ωm oycdo $@V!W{) Ωm 80

9kd X!?F X@? c]t X#? gryjolk,kf0Pol6fdkorq;rao]ts;kj ’ R, , A c]t ρ wfhf’aj oUG R=ρ X$? A [qfg/ydsaf !D g,vjn groyj l[a xPj o];foew22kh @ gloA m,uj 0u t|kfgmkjq doa F xkdfq ;kj fvdw22kh m8uj .+ l;j ’q 9vof’ja dkj ;I’5j [+gmkjq doa D 9’jq vtmy[kplkgsf0v’7;k,c8d8kj ’ooA D @D 9qj’lq,mP[7;k,8hkow22hk0v’];fmujgIaffh;pvk]6,uouvv,da[];fmujgIaffh;p mv’cf’mu,j u7;k,pk; c]t goNvm|uj hk8afgmkqj daoD #D g7njv’8hkow22hk # vao,u7;k,8hkow22hk !WΩ S @WΩ c]t #WΩ 8k,]efa[D 4k,;kj 4hkgvqkg7nvj ’8hkow22hkma’lk,vaooU,k8+.ldj ao 8k,I6[]5,j oU 9twfh7;k, 8hkow22hk];,gmkqj .fL R1 R2 ສ.ວ.ສສະຫງວນລິຂະສິດ R 3 $D g7nvj ’8hkow22hk # vaoF c8]j tvao,u7;k,8hko !Ω gmqkj dao\\qfD 4hkgvqkg7nvj ’8hko w22hkma’lk,vao,k8+daoc[[G d? ]PodaoF 0? 0t|kodao 9twfh7;k,8hkow22hk ];,.oc8]j tc[[gmkqj .fL &D g7vnj ’8hkow22hk $ vaoF c8]j tvao,u7;k,8hko !W Ω gmkqj dao\\qfD 9t8hv’oer;d,ao ,k8+daoco;.f 9b’j 9twfh7;k,8hkow22hk];, @F& Ω c]t @&Ω D *D gryjomqf]v’8+sq;mPofvd|bj’da[\\=hw22hk|j;p|bj’ fh;plkpw22hk0t|kf.spj gmqkj daofa’j 8+wxoUG gmnvj mu ! .-hlkpw2pk; !mF gmnvj mu @ .-hlkpw22hkpk; !WmD zqodkomqf]v’gryoj gsao;kj gmnvj mu ! sq;mPoI’5j d;kj D 9’qj vtmy[kpphvospa’9’bj gxao co;ooA L (D gxaospa’gryjo[+.-hlt;yfme,tfkmuj.-hda[fvdw22hkmqj;wx g0Qkda[g7njv’.-hw22hk m.uj -hdtclw22hk.spgj -oaj G g8qkw22hkF g8qk]ufF g7vnj ’xa[vkdkfDDD 81

[qfmu !$ g7njv’8hkow22hkxjPo7jk c]t g7njv’8hkow22hk.og8adoyd .o;q’9vow22hk c]t ;q’9vogvg]ad38ioydmq;j wx ,ad.-hg7nvj ’8hkow22hkmugj Iaffh;p /5jo dkd[vovafc|hogxaoI6[m+dq,D g7nvj ’8hkow22hkc[[faj’dkj ;oU,u7kj 7;k,8hkow22hk7q’7kj 9b’j gvUo;kj g7vnj ’8kh ow22kh 7’q 7kj c]t loa pt]da f;h p 3fp7kj 7;k,8kh ow22kh 9t[vd fh;pc4[lu mu0j ufIv[g7nvj ’8hkow22hkoAo fa’j I6[ !$D!D laopt]ad c4[mu ! c4[mu @ c4[mu # c4[mu $ I6[ !$D! D I6[g7njv’8hkow22hk7q’7kj c4[lumu0j ufvhv, Iv[g7vnj ’8hkow22hkc8]j tvao,u7;k,\\kpf’aj oUG c4[mu ! [vd7kj 38g]dmevfy D ສ.ວ.ສສະຫງວນລິຂະສິດ c4[mu @ [vd7kj 38g]dmlu v’D c4[mu # [vd7kj 38g]dde]’a m8ju vh ’gvkq wx7o6 d[a lv’38g]dmevfy D c4[mu $ [vd7kj 7;k,zyffPj ’ 0v’7kj 7;k,8hkow22hk mvuj kj owfh9kdlk,c4[oAo 3fp[vdgxoa l;j oIvh p Xgxug-oa ?D lu c4[ c4[mu ! c4[mu @ c4[mu # c4[mu $ fe W W V! Ω W oEvvh pdvh o ! ! V!W! Ω !: cf’ @ oE\\kddPh ’ @ V!W@ Ω @: # # V!W# Ω gsv^n ’ $ $ V!W$ Ω 0P; & & V!W& Ω oEg’oy * * V!W* Ω vyf ( ( V!W( Ω 0gU mkjq ) ) V!W) Ω 0k; _ _ VWF!Ω 7e g’oy &: !W: 82

8q;1jk’G g7nvj ’8hkow22hkvao|b’j ,uc4[lu0ufvhv,Iv[fa’j oUG gIqkvkj o7kj 7;k,8hkow22hkfa’j oU G { c4[lumevyf lucf’ { c4[lumulv’ 0P; { c4[lumulk, luoE\\kddhP’ { c4[lumuluj lu7e cf’ 0P; luoE\\kddhP’ 7e ສ.ວ.ສສະຫງວນລິຂະສິດ f’aj oAoF g7vnj ’8hkow22hkoU,u7kj 7;k,8hkow22hk s^n R = 25×103 ± 25×103 × 5 100 = (25 000 1250) = 23750 Ω s^n 26250Ω !D g7njv’8hkow22hkxjPo7jk g7njv’8hkow22hkxjPo7jkmuj.-h3fpmqj;wxxtdv[fh;p c4[7;k,8hkow22hk g-yj’vkf gIfa f;h pdkd[vo sn^ gloA ];froa .lmj x+ k^ l8dy sn^ foy 4;h p0k; 8d+ [a 0k ! c]t #F l;j o|kh lezfa 8+ da[0k @F fa’j I6[!$D@ 13 13 2 2 A dD g7nvj ’8hkow22hkxPj o7kj laopt]ad 0D ;q’9vow22hk8+da[g7nvj ’8hkow22hkxPj o7kj I6[ !$D@ 83

dkox[a xPj o7;k,8kh ow22kh F xt8[y fa wf3h fpdkog]vjn of,5 lezfa gm’y |kh lezfa c4[g7vnj ’ ສ.ວ.ສສະຫງວນລິຂະສິດ 8kh ow22kh sn^ |kh d]h= ;fD dkooegvkq g7vjn ’8kh ow22kh xPj o7kj wx.-7h ;[7,5 dtclw22kh .o;’q 9vo w22hk xt8y[afwfh3fpdko8+ 0k ! s^n 0k # c]t 0k @ g0Qkda[;q’9vow22hk7nfa’j I6[ !$D@ 0?D g,vnj g]vnj of5,lezafgmy’|hklezaf0v’g7vnj ’8hkow22hkxPj o7kj .o;q’9vo 9kdmu8j A’lQo ! wxsk lQo # 7;k,8hkow22hk9tgru,j 0BoD fa’j oAoF 4hkg]nvj of5,lezafwxgmy’|hklezaf0v’g7njv’8hko w22hkwx.omyfdq’0hk,9tgIaf.sh7;k,8hkow22hks^5f]q’ gIaf.shdtclw22kh .sp0j oB D g7vjn ’8kh o w22kh xPj o7kj mgju Ifa |kh m7ju ;[7,5 dtclw22kh .o;’q 9vow22kh gvoU ;kj g7vjn ’7;[7,5 dtclw22kh D @D dkog7njv’8hkow22hkxjPo7jk.-h.og8adoyd g7njv’8hkow22hkxjPo7jk,adoypq,.-h7;[75,dtclw22hk.o;q’9vow22hkD I6[ !$D# c,oj czo;kfltcf’dko.-gh 7vjn ’8kh ow22kh xPj o7kj 7;[7,5 7;k,I’5j 0v’fvdw2 c]t .-xh [a 7;k,fa’7jvp{fa’cI’0v’lP’.og7njv’lP’8jk’MD I6[ !$D$ dkogIaf;Pd0v’g7njv’cmd xt]y,kooE,ao.o4a’oE,ao]qf9ad c]t ]qf.spDj fvdw2 8q;g]nvj o g7nvj ’8hkow22hk I6[ !$D$ g7nvj ’8hkow22hkxPj o7kj .-h I6[ !$D# g7nvj ’8hkow22hkxPj o7kj .-h7;[75,7;k,Ij5’0v’fvdw2D .og7nvj ’cmdo=hk,ao.o4a’o=hk,ao]qfD ovd9kdoUpa’.-hgxaol;j oxtdv[le7ao0v’g7nvj ’cmd[k’-toyfg-oaj G g7nvj ’cmd7;k, 8hkow22hk X3v,,ug8u?D #D fu3vf (Diode) fu3vf gIaf9kd;af45g7yj’oew22hk,u0Q; I6[ !$D* laopt]ad0v’ w22hk[;d c]t 0Q;]q[ fa’j I6[ !$D*D fu3vf I6[ !$D& fu3vf 84

dyf9tde !G lbdlkdkogIaf;Pd0v’fu3vf !? 8+fu3vfF \\=hw2 c]t g7nvj ’cmdvecx gxao;q’9vow22hk 3fpgvqk0Q;[;d0v’fu3vf 8+da[0Q;[;d0v’\\=hw2 c]t gvqk0Q;]q[0v’fu3vf 8+da[0Q;]q[0v’\\=hw2 fa’j I6[ !$D(D l’a gdfg0,a 0v’g7vnj ’cmdvecxD [oa mdb zoq D I6[ !$D( I6[ !$D) @? gIafdkomqf]v’7nda[ !? c8jltsa^[0Q;0v’fu3vf 3fpgvqk0Q;]q[0v’fu3vf 8+da[ ສ.ວ.ສສະຫງວນລິຂະສິດ 0;Q [;d0v’\\=wh 2 c]t 0;Q [;d0v’fu3vf 8+d[a 0;Q ][q 0v’\\=wh 2 f’aj I[6 !$D)D l’a gdf g0,a 0v’g7vnj ’cmdvecxD [oa mdb zoq D .odkomfq ]v’ !? c]t @? g0,a 0v’g7vjn ’cmdvecx-U8kj ’doa co;.fL oda IPo9tlts^[5 zoq dkomfq ]v’0v’dyf9tdeoUco;.fL zqodkomqf]v’ !? c]t @? gsao;kj .odkomqf]v’ !? g0a,0v’g7nvj ’cmdvecx[Pj ’ vvd9kd0uf WF oAoltcf’;kj ,udtclw22hkc]oj .o;q’9voS l;j o.odkomqf]v’ @? g0a,0v’ g7vnj ’cmdvecx [+g|a’8u’F oAoltcf’;kj [+,udtclw22hkc]oj .o;q’9voD 9kddkomqf]v’.odyf9tdeoU lk,kflts^5[wfh;kj fu3vf,u[qf[kf.shdtclw22hkc]oj zkj o s^n [+.shzkj o s^n g;Qk1kj ’|bj’c,oj g,njv.shdtclw22hkc]oj zkj owx.omyf|bj’ ,ao,u7;k, 8kh ow22kh |vh p c8.j omfy d’q doa 0kh ,,oa ,7u ;k,8kh ow22kh s^kpmluj f5 9oq gIfa .s7h ;k,g0,A dtcl w22hkgxao WD faj’oAoF fu3vf gxaov5xtdvow22hkmjupv,.shdtclw22hkzjkowfhrP’myffP;D pvh oco;ooA gryoj 9’jb .-fh u3vfxPj odtclw22kh lts^a[wxgxoa dtclw22kh d’q D 85

[qfg/ydsaf ສ.ວ.ສສະຫງວນລິຂະສິດ !D g,vjn ,du tclw22kh m,ju 7u ;k,g0,A @A c]oj zkj ogloA I’5j Xwl?h fvdw2fvd|’bj gIfa .sgh dfu ,uzoq ][q ]tf[a w22kh 1l6j v’loQ 0v’gloA I’5j ooA gmkjq !WW V. dD 9’jq -vdsk7;k,8kh ow22kh 0v’fvdw22kh oUD 0D 4kh dtclw22kh c]oj zkj ofvdw2oU ,u7;k,g0,A gmkjq WF&A. 9’jq -vdskzoq ][q ]tf[a w22kh 1l6j v’loQ 0v’fvdw22kh oDU @D g7vjn ’8kh ow22kh ,u dD c4[luG oE\\kddhP’F feF cf’ c]t lu7eD 0D c4[luG oEvhvpdhvoF 0Ugmqkj F oE\\kddhP’ c]t luoEg’yoD 7D c4[lu 0P;F 2hkg0,A F gs^vn ’ c]t l7u eD 4k,;kj g7vjn ’8kh ow22kh dF 0 c]t 7 c8]j tvoa ,7u ;k,8kh ow22kh gmkjq .fL 86

[qfmu !& de]a’w22hkF rt]a’’kow22hk c]t cI’’kodtclw22hk !D de]a’w22hk 4kh l’a gdfg[’yj g7vjn ’.-wh 22kh c8]j t-tofy g-oja G fvdw22kh F g8kq w22kh F rfa ],q F g8kq ]fu w22kh D 9tgsao;jk g7jnv’.-hw22hkc8j]tvao,u8q;g]ddeda[8yf1j6da[g7njv’.-hw22hkoAog-ajoG fvdw22hk fvd|bj’ ,ug]ddeda[ @@WV-60WS raf]q,|j;p|jb’ ,u8q;g]ddeda[ @@WV{#&W; \\=hs5’ g0Qk|j;p|jb’ ,u8q;g]ddeda[ @@WV{)WWW;DDD 8q;g]d @@WV [vd.shIh6;jk g7jnv’.-hw22hk c8j]tvao8hv’.-hda[w22hkmuj,uzqo]q[]tfa[w22hk @@WVD lj;o8q;g]d *WW; 35W; 800W... [vd.sIh d6h e]’a 0v’g7nvj ’.-wh 22kh c8]j tg7nvj ’ooA D .odko.-h8q;9y’F fvdw22hk !WWW I5’j d;kj fvdw22hk $WW; lts;kj ow22hkmuj,ude]a’ ສ.ວ.ສສະຫງວນລິຂະສິດ !&WWW, .-hda[fvdlts;kj o.spj c]t lk,kf g9ktg[8q’F w,hc0’ c]t |kwfhS l;j olts;kj o ohvpmju,ude]a’ #WWW .-hwfhrP’c8jda[fvdlts;jkoohvp c]t lk,kfg9ktwfhc8jw,h[k’ me,tfkS 8Q,oExt]y,kogmqkj daofh;p\\h=|;j pfP;daogmy’g8qkw22hkmuj,ude]a’ !&WWW 2qfw; d;kj 8Q,.og8qkmuj,ude]a’ !WWWWDDD oAoltcf’.shIh6;kj g7njv’.-hw22hk-toyffP;daoF g7njv’.f,u de]a’.spdj ;kj c,oj ,ao,ucI’s^kpd;kj s^n vvdcI’’kowfhs^kpd;kj D dko7Qo7;hkmqf]v’dPj ;da[de]a’w22hk fh;pg7njv’,nmuj,u7;k,-afg9ol6’ gryjolk,kf lts[5^ wf;h kj de]’a w22kh 0v’g7vnj ’.-wh 22kh gmkjq d[a zoq 7o6 ]ts;kj ’ zoq ][q ]tf[a w22kh 1l6j v’0;Q 0v’g7nvj ’.-wh 22kh d[a 7;k,g0,A dtclw22kh mucj ]oj zkj og7nvj ’.-wh 22kh ooA D P = UI U ,usq;|;j pgxao3;o XV? I ,usq;|;j pgxaovecx XA? P ,usq;|;j pgxao;af XW? →1W = 1A V 1V 87

gonjv’9kd U = IR. fa’j oAoF l6f P = IU lk,kf0PovudI6[|bj’fa’j oUG P = I2R = U2 R sq;|;j pde]a’w22hkc,oj ;af (W) F ovd9kdgxao;af (W) c]h; pa’.-h G dy3];af (kW) c]tg,dk;af (MW) vudfh;pG 1kW = 1000 W = 103 W c]t 1 MW = 1000 000 W = 106 W @D rt]a’’kow22hk c]t cI’’kodtclw22hk dD rt]a’’kow22hk ສ.ວ.ສສະຫງວນລິຂະສິດ g,vnj .sdh tclw22kh c]oj zkj ofvdw22kh F fvdw22kh I’5j 0oB S g,vnj .sdh tclw22kh c]oj zkj o wlgh 8kq w22kh ,oa cf’I’5j 0Borvh ,m’a .s7h ;k,Ivh oS g,nvj .sdh tclw22kh zkj orfa ],q w22kh F rfa ],q xjyoSDDDD 8q;1jk’mjudjk;,koU ltcf’.shIh6;jk dtclw22hk,urt]a’’ko c]t rt]a’’kow22hk lk,kfxPj ogxaort]a’’koI6[vnoj M8k,-toyf0v’g7nvj ’.-hw22hkoAo g-oaj ;kj G raf]q,F lts;kj o w22hkF dq[w22hkF ]qfw22hkDDD xPj ort]a’’kow22hkgxaort]a’’kodqo9adS dt8yd8Q,oEw22hkF \\h=s5’g0QkDDD xjPort]a’’kow22hkgxaort]a’’ko7;k,IhvoDDD rt]a’’ko0v’dtclw22hk gryoj gvUo;kj rt]’a ’kow22kh D 0D cI’’kow22hk .o;q’9vow22hkmuxj tdv[fh;p [+w22hk8+da[g7nvj ’.-hw22hk f’aj I6[!&D! R .sh I c,oj 7;k,g0,A dtclw22kh mcuj ]oj U .o;’q 9voD I6[ !&D! Q c,oj xt]y,kow22kh [oa 95 c]oj zkj o g7vjn ’.-wh 22kh D U c,oj zqo]q[]tfa[w22hk16lj v’0Q;0v’ g7vnj ’.-wh 22kh D W c,oj cI’’’kow22kh mgju 7vjn ’.-wh 22kh zt]yfvvd.ow]ptg;]k t ;yokmuD 88

dkorq;rao]ts;j k’ W, U, Q c]t I gxaowx8k,l6ffa’j oUG ສ.ວ.ສສະຫງວນລິຂະສິດ W = QU c8j Q = It fa’j oAo W = UIt le]a[g7nvj ’.-hw22hk8kj ’M mu,j u7;k,8hkow22hk R c,oj U = IR fa’j oAoF 0PowfhG W = I 2Rt sn^ W = U 2t R fhko|bj’ 9kdl6f W = UIt c]t P = UI lk,kf4vowfhG W = Pt sq;|;j pcI’’kow22hk gryjod=.-h16oXJ? sn^ dk]=]uXCal? 7ndaoda[ cI’’kodqo9ad c]t cI’’ko7;k,Ivh oD cI’’ko0v’dtclw22hkmuzj t]yfvvd.o8volkp|b’j gmkqj da[ xt]y,ko rt]’a ’kow22kh m8uj volkpooA .-gh rvnj xPj ogxoa rt]’a ’koI[6 vonj D 8q;1jk’ !G g8kq w22kh |;j p|’jb ,du e]’a w22kh !WWWW. 4.h -hg8kq w22kh oU ! -;jq 3,’ ,ao9t.-hrt]a’’kow22hkgmkqj .fL ;ymucdhG .shIh6 P = 1000W , t = 1 h = 3 600 s -vdsk W =? oe.-hl6f W = Pt cI’’kow22kh mguj 8kq w22kh zt]fy vvdc,oj G W = Pt = 1000 V 3600 = 3 600 000 (J) 9kdzqo8v[0v’[qfg]d8q;1kj ’oU .shI6h;kj cI’’kow22hkF 4hk7yfgxao J X16o? 9tgxao 9eo;o.spjs^kpD faj’oAoF grjyo9bj’.-hsq;|j;pmju.spjd;jk16o sq;|j;pfaj’djk; gryjogvUo;jk dy3];af3,’ laopt]ad kWh. dy3];af3,’ c,jocI’’kow22hkmujzt]yfvvd g,njvg7njv’.-h w22hkmu,j ude]a’ 1 kW gIaf;Pd.og;]k ! h (-q;j 3,’). 89

g7vjn ’.-wh 22kh m.ju -.h oc8]j tgInvo s^n vk7ko l;j os^kp9tgxoa g7vjn ’.-wh 22kh m.ju -dh [a w22khສ.ວ.ສສະຫງວນລິຂະສິດ @@W V. rt]’a ’kow22kh m.uj -.h oc8]j tgfnvo0Bod[a 9eo;og7vnj ’.-wh 22kh F de]’a w22kh 0v’g7vjn ’ .-hw22hkc8j]t-toyf c]t g;]kmu.j -hg7nvj ’.-hw22hkc8]j tvaomuj,uoAoD cI’’kow22hkmuj.-hma’ \\qf9t4ndoa[fh;p\\=hoa[w22hk c]t dko9kj pg’yo7kj cI’’kow22hk c,oj 9kj p8k,cI’’ko w22kh m\\ju oh= [a w22kh [oa mdb w;Dh 8q;1jk’ @G fvdw22hkfvd|’bj ,ude]a’w22hk $WW 4hkw8hfvdw22hkfvdoU !W -q;j 3,’ 9t.-hcI’’kow22hk9addy3];af3,’L c]t 9tglp7kj cI’’kow22hkgmqkj .fL 4hkvaf8k7kj w22hk ! dy3];af3,’ gmqkj #!W du[L ;ymucdh G .shIh6G P = 40W = 0,04 kW; t =10 h -vdG cI’’kow22hk (W = ?) cI’’kow22hkmufj vdw22hkzt]yfvvdc,oj G W = Pt = 0,04 V 10 = 0,4 kWh. 8hv’glp7kj w22hkgmkqj c,oj G WF$ V #!W du[ = 124 du[D #D dkocmdcI’’kow22hk 8k,lf6 W = UIt gsoa ;kj grvnj cmdcI’’kodtclw22kh 8vh ’.-gh 7vnj ’cmdg4’y # 1kj ’7Gn g7njv’cmdvecxF g7njv’cmd3;o c]t 3,’9a[g;]kD .o8q;9y’ cI’’kodtclw22hk 4ndcmd fh;pg7nvj ’cmdw22hk-toyf|b’j g-y’j gvUo;kj \\h=oa[w22hk Xdq’g8u s^n Meter? f’aj I6[ !&D @ g,vnj ,du tclw22kh c]oj zkj o;’q 9voF \\o=h [a w22kh 9toa[xt]y,kocI’’ko muj[aofkg7njv’.-hw22hk 8jk’M 1j6.o;q’9vozt]yfvvdgxaody3];af 3,’. I6[ !&D@ dq’g8uw22hk 90

8;q 1kj ’dkoo[a xt]y,kocI’’kow22kh g;]km.uj -h cI’’kow22kh ]efa[ ]kpdko de]’a 0v’g7nvj ’.-h X-q;j 3,’ sn^ h? X kWh ? ! fvdw22kh 1000W= 0,1 kW # -q;j 3,’ 0,3 @ \\s=h ’5 g0kQ ! -q;j 3,’ 0,5 # g8kq ]fu 500W= 0,5 kW WF& -qj;3,’ 0,5 1000W = 1 kW $ ];, $D dkooe.-hrt]a’’kow22hk ສ.ວ.ສສະຫງວນລິຂະສິດ rt]a’’kow22hkgxaort]a’’komulj tvkfF [+gxaoryfgxaowr8+ly’j c;f]hv,F ltf;d8+dko .-h c]t lk,kfxPj ort]’a ’kow22kh gxoa rt]’a ’koI[6 vojn MD f’ja ooA F .o3]dxt9[5 oa zz6h t]fy g7vjn ’ .-wh 22kh 9’jb zt]yfg7vnj ’.-wh 22kh okM-toyfvvd.-h o[a c8gj 7vnj ’.-wh 22kh ’kj pfkpmluj f5 Xw2lkp? g4y’l[a loq mluj f5 Xg7vnj ’7v,ry;g8u?D g7njv’.-hw22hkxtgrf8jk’M,uG { g7vnj ’.-hw22hk.shrt]a’’kocl’lts;kj ’g-oaj G fvdw22hkF s^vfw22hkDDD { g7vjn ’.-wh 22kh .srh t]’a ’ko7;k,Ivh og-oja G g8kq ]fu w22kh F g8kq w22kh F \\sh= ’5 g0kQ w22kh F dt8yd8Q,oEw22hkF g8qkvq[w22hkF 7hvo9vfw22hkDDD { g7nvj ’.-hw22hk.shrt]a’’kodqo9adg-aoj G 3,g8uw22hkF raf]q,F g7nvj ’gxqkj zq,F g7nvj ’xaoj \\kdw,Fh g7vnj ’-da zkh DDD { g7vnj ’.-hw22hk.shrt]a’’kolP’g-oaj G dtfy’w22hkF ;ymtp5F 3m]tla[DDD [qfg/ydsafG !D vu’.lgj sfzqovao.f9bj’g;Qkwfh;kj dtclw22hk,urt]a’’koL @D 4hkw8hsq;mPo 6V- 0,45 A fh;p\\=hw2 6V gxaog;]k !F& -q;j 3,’ ,ao9tzt]yf cI’’kow22kh vvdgmkqj .fL #D g8qkw22hkvao|b’j g,nvj 8+da[]t[q[w22hkmu,j uzqo]q[]tfa[w22hk @@W V c]h;,udtcl w22hkc]oj zkj o 5A. 4k,;kj g8qkw22hkoAo ,ude]’a gmqkj .f;afD 91

[qfmu !* dqfgdo16o{c]ol !D dqfgdo16o{c]ol g,vjn .sdh tclw22kh c]oj zkj o;fa 4o5 ew22kh m,ju 7u ;k,8kh ow22kh ,oa gIfa .s;h fa 4o5 oA Ivh o0oB c]t dt9kp7;k,Ivh ovvd,k 8;q 1kj ’G .sdh tclw22kh c]oj zkj owlgh 8kq w22kh F wlgh 8kq ]fu w22kh sn^ wlh0v’g7vnj ’gxkqj zq,DDD ,ao,u7;k,Ihvogduf0BoD .odko7oQ 7;kh dkoxPj ort]’a ’kow22kh gxaort]a’’ko7;k,Ihvo grjyowfhgIafdkomqf ]v’fh;pv5xtdvofa’j oUG g7nvj ’cmd7;k,IhvoF \\=hw22hkxt,ko *{!@V, g7vnj ’cmd3;o lk,kf cmdwfh.o0v[g0f W{!& V. g7njv’cmdvecx ສ.ວ.ສສະຫງວນລິຂະສິດ mluj k,kfcmdwfh.o0v[g0f W{!WA, g7vnj ’8hko w22hkxPj o7kj wfhF g7nvj ’cmdv5ostr6, c]t lt I6[ !*D! ;yfw22hkma’\\qf8+gxao;q’9vow22hkD zqodko mfq ]v’s^’a 9kdxvj p.sdh tclw22kh c]oj zkj o;’q 9vo.og;]k t ;yokmuF grjyogsao;jk oE1j6.og7njv’cmd7;k,IhvooAoIhvo0Bo g-yj’la’gdfwfh 9kddkoxPj ocx’vo5 str,6 .og7vjn ’cmdvo5 str,6 D xkdfq dkof’ja dkj ;ltcf’;kj g,vnj dtclw22kh c]oj zkj o];foew22kh m,uj 7u ;k,8kh ow22kh R, ,aogIaf.shgduf7;k,IhvoD oAoltcf’;kj rt]a’’kow22hkwfhxPj ogxaort]a’’ko7;k,IhvoD g,vnj gvkq xt],y ko8kj ’Mmduj Pj ;0vh ’ ,k7fy w]j groyj gsoa ;kj cI’’kow22kh W mduj tclw22kh zt]fy vvdgmkqj da[xt]y,ko7;k,Ihvo Q mcuj z.j shcdoj ED f’aj oAoG W = Q 9kdl6f W = I2Rt = UIt = Pt lk,kf0Powfh Q = I2Rt = UIt = Pt Q ,usq;|;j pgxao Joule 0Posph=fh;p J 1 J = 0,24 Cal 92

fa’j oAoF l6f7yfw]7j ;k,Ihvomuj.-hsq;|;j p Cal 9bj’gxaoG ສ.ວ.ສສະຫງວນລິຂະສິດ Q = 0,24 I2Rt = 0,24 UIt = 0,24 Pt .odkoxPj ocx’rt]’a ’kow22kh ,kgxoa rt]’a ’ko7;k,Ivh o .odkomfq ]v’oU [+0oB d[a g’vjn ow0mk’ovd \\kp;kj rt]’a ’kow22kh rP’c8xj Pj oI[6 ,kgxoa rt]’a ’ko7;k,Ivh ogmkjq ooA D oad2u-yd-k;va’dyf-nj;jk 16o (Joule) c]t -k;]afg-p-nj;jk c]ol (Lenz) wfhgIaf dkomqf]v’ c]t wfhIa[zqo7hkp7ndao;kj g,nvj dtclw22hkwxzkj o;af45oew22hkmuj,u7;k,8hko w22hkrkp.o w]ptg;]k.f|b’j ,aowfhgIaf.shv5ostr6,;af45oAoxPj ocx’ g-yj’cI’’kow22hk mduj tclw22kh zt]fy vvd gmkjq d[a xt],y ko7;k,Ivh omguj dfu 0oB D ltooA F dfq gdoo9U ’bj wf4h dn gvoU ;kj dqfgdo16o{c]olD 8q;1jk’ !G g8qk]ufw22hkg7njv’|bj’,u7;k,8hkow22hk @WΩ F g,njv.shdtclw22hk & A c]oj zkj og8qk]ufoU #Ws. 9q’j 7yfw]7j ;k,Ihvomugj duf0Bo9kdg8qk]ufw22hkoU .osq;|j;p J c]t Cal. ;ymucdhG .osq;|;j p J. oe.-hl6fG Q = I2Rt ⇒ Q = (5 )2 X 20 X 30 = 15.000 J sn^ = 15 kJ .osq;|;j p cal oe.-h7kj xP[mP[G 1 J = 0,24 cal ⇒ Q = 0,24 X 1500 = 3600 Cal sn^ = 3,6 k Cal 8q;1jk’ @G g8qkw22hkg7njv’|bj’ ,u7;k,8hkow22hk )Ω F g,njv.shdtclw22hk 15A c]oj zkj o g8qkzy’fa’j dkj ;gxaog;]k $ -q;j 3,’D 9q’j -vdskde]a’0v’g8qkgxao W c]t cI’’ko w22hkmujg8qkoAozt]yfvvd.ow]ptg;]kfa’j dkj ; c]t 4k,;kj 9t8hv’glp7kj w22hk 9addu[ 4hk;kj vaf8k7kj w22hk #!W du[}kWh?D 93

;ymucdhG ສ.ວ.ສສະຫງວນລິຂະສິດ 7yfw]dj e]’a 0v’g8kq G oe.-hl6fG P = I2 R ⇒ P = (15 )2 × 8 Ω = 1 800 W = 1,8 kW. 7fy w]cj I’’kow22kh G oe.-hl6fG W = Pt ⇒ W = 1,8 × 4 = 7,2 kwh 8hv’9kj p7kj w22hkG 7,2 × 310 du[ = 2 232du[. @D dko.-hg7njv’.-hw22hkmuj.sh7;k,Ihvo I6[ !*D@ g7vnj ’.-hw22hkm.uj sh7;k,Ihvo c,oj g7vnj ’.-hw22hkmxju Pj ort]a’’kow22hkgxaort]a’’ko 7;k,Ivh o g-’jy ,su k^ p-tofy g-oja G g8kq ]fu w22kh F g8kq w22kh F \\sh= ’5 g0kQ w22kh F dt8dy 8,Q oEw22kh F g8kq v[q w22kh F 7vh o9vfw22kh DDD l;j oxtdv[mluj e7ao0v’g7vnj ’.-hw22hkm.uj sh7;k,Ihvo c,oj ]=-= sn^ czoj 3]stmguj Iaffh;p 3]stxtlq, ]ts;kj ’oygdyoda[3di, g-y’j gxao3]stxtlq,mu,j u7;k,8hkow22hks^kp c]t ,u95f Ihvogxnvj pl6’D ]=-= sn^ czoj 3]st0v’g7nvj ’.-hw22hk.sh7;k,Ihvol;j os^kp9t3v[fh;pmkfdao w22kh moju el’jq 7;k,Ivh owffh u c];h 3v[f;h p3]stmoq 7;k,Ivh ol’6 D g7vjn ’.-wh 22kh .s7h ;k,Ivh o 94