GUsIuy:UsáÚb ¬emeronTI 6 CMBUkTI 2 emeronfñak;TI 10¦

edIm,IeGay)anyl;c,as; BIdMeNIrkarrbs;GUsIuy:UsáÚb eKRtUvdwgfabMlas;TIrbs;s,:t ¬cMnucPøW¦ enAelIeGRkg;smamaRt nwg tg;süúgEdleKeRbI . dMeNIrkarmanBIr ³ dMeNIrkareday XY nig dMeNIrkaredayekos . 1- dMeNIrkareday XY

eKGacGnuvtþtg;süúg • rvagbnÞH Y nig Y' tamRck Y nigma:s M tageday UY

• rvagbnÞH X nig X' tamKnøg X nigma:s M tageday UX

edIm,IBnül;)atuPUtenH eKeRbIKMnUstagGUsIuy:UsáÚbgaymYy . enHCa]TahrN_xøH rbs;tg;süúgEdleRbI nig TItaMgEdlRtUvnwgs,:t . ]bmafaenAelIKnøgTaMgBIeKRbImaRtdæan K = 1V/div

Y XX Y • XY' X'X' Y'

UY = 3V UX = 0 UY = 0 UX = 2V

•

UY = 3V UX = 2V UY = -3V UX = 2V

µX = 0

x'

x y

y'

x'

x

t

-3

µY(v) 3

t

-3

µY(v) 3

t

-3

-3

t

µY(v) 3

3 µX(v)

x'

x

y'

y

y'yt

-3

µX(v) 3

t

-3

3 µY(v)

x'

x y

y'

2- dMeNIrkaredayekos • edIm,IeGaygayyl; eKRtUveRbIrUbd¾saMjaMénGUsIuy:UsáÚb ³ GUsIuy:UsáÚbBitR)akdmanbnÞH 2

sMrab;lMgakbBaÄr Y1Y'1 nig Y2Y'2 ehIynigKUb XX'

kaNugeGLicRtug YB Ux

eKalcUl Cnitaéntg;süúgekos

Y

Y'1

Y1 Y2 X

M

X' Y'2

ma:s

O

Y

X

• tg;süúgekosenAcenøaHbnÞH XX' enAkñúgGUsIuy:UsáÚbmanCnitamYyeTotEdlbeBa©jtg;süúg CaeFµjrNa Ux manxYb T . tg;süúgenHGnuvtþeday sV½yRbvtþenAcenøaHbnÞH X nig X' ehAfatg;süúgekos .

t

T

Ux

+5V

-5V

]TahrN_ ³ Ux EdltMélERbRbYlBI -5V eTA +5V

P

kalNa Ux ERbRbYlBI -5V eTA +5V cMnuctUcpøas;TI BI P (-5cm) eTA Q (+5cm) kñúgry³eBl T . Q

kalNa Ux mantMélBI +5V eTA -5V cMnuctUc RtLb;ya:gelOnmkcMnuc P vij ehIyman clnadEdleLIgvijkñúgxYb T. eKemIleXIjelIeGRkg;nUvKMnUsedk KWCael,ÓnéncMnuctUcenaH BI P mk Q manTisedAEtmYy . bMlas;TIrbs;vasmamaRt nigry³eBl . PQ tagG½kSeBl .

• tg;süúgbBaÄr tg;süúgEdlRtUvsikSa RtUv)anGnuvtþn_elIbnÞH Y1Y'1 tamry³Rck YA nigmanma:s M

b¤elIbnÞH Y2Y'2 tamry³Rck YB nigmanma:s M

]TahrN_ ³ tamRck YA eKeFVIeGaymantg;süúg sIunuysUGIut UY manxYb T dUctg;süúg Ux

Ux(V)

;dfg

eK)antMéléntg;süúgkñúgtarag xageRkamCatMélERbRbYléntg;süúg Ux nig UY tameBl .

t 0 4T

2T

43T T

ux(v) -5 -2,5 0 2,5 5 uy(v) 0 2 0 -2 0 b¤eKGac)antarag kUGredaenén cMnuctUc ¬s,:t¦ elIeGRkg;tamtMél

t 0 4T

2T

43T T

Xcm -5 -2,5 0 2,5 5 Ycm 0 2 0 -2 0 cMnuctUc ¬s,:t¦ elIeGRkg;pøas;TI ragCasIunuysUGIut kñúgxYb T ehIy RtLb;mkvijya:gelOnCabnÞat;BIcMnuc Q mk P . bnÞab;mkvacab;epþImeFVIclnadEdl edaypøas;TICafµIkñúgkEnøgdEdl .

ehtudUcenHehIy)anCaeKeXIjelIeGRkg;nUvrUbnwg tagedayGnuKmn_ UY = f(t) .

y

xP

PaBrYsQr 1V/div

43T

4T

t

t

T

T

0

-5

0

UY

Q

+5

2T

kalNamantg;süúgekos ¬manbMlas;TIéncMnucPøWelI XX' ¦ eKGaceRbIGUsIuy:UsáÚb tamRckEtmYy YA b¤YB nigGaceRbIRckTaMgBIrRBmKña YA nig YB . kñúgkrNIenHeKGacsikSabMErbMrYltg;süúgEtmYy b¤tg;süúgBIrkñúgeBlCamYyKñaCaGnuKmn_éneBl.

3- lMhat; eKeFVIeGaymantg;süúgtamRck YA b¤YB EdlmanrUbemIleXIjelIeGRkg; ¬PaBrYsQr 1V/div

ry³eBlekos 1ms/div ¦ . XY BAL

1 U = 3V

(YA)

XY BAL

-3

+3

10 ms

t

u(t)(YA) 2

XY BAL

-3V

+3V

10 ms

t

u(t)(YB) 3

krNI 1 & 2 tg;süúg U & U(t) RtUv)anbBa¢ÚntamRck YA . Rtg; XY b¤ Rtg;kMeNos (BAL)

tg;süúgenAEtGnuvtþcenøaHbnÞHlMgakQr Y1Y'1 . krNI 3 tg;süúg U(t) RtUv)anbBa¢ÚntamRck YB . Rtg; XY tg;süúgGnuvtþedaysV½yRbvtþcenøaHbnÞHlMgakedk XX' . Rtg;kMeNos (BAL) tg;süúgGnuvtþcenøaH bnÞaHlMgakQr Y2Y'2 .

4- etIeKeRbIR)as;GUsIuy:UsáÚbya:gdUcemþcedIm,InwgsikSaGaMgtg;sIuetcrnþ? eKeRbIGUsIuy:UsáÚbkñúgdMeNIrkaredayekos . eKGnuvtþ tamRck YA b¤ YB nUvtg;süúgrvageKalrbs;GgÁFatucMlgGUmEdlmanersIusþg; R Edl eKsÁal;tMél . tamc,ab;GUm uR = Ri

edayGaMgtg;sIueténcrnþsmamaRteTAnwgtg;süúg eKsegáteXIjtg;süúgmanRkabragdUcKñanwgRkab rbs;GaMgtg;sIuetCaBiessmanxYb T dUcKña .

karbgðajeGayeXIjnUvcrnþkñúgesoKVI UR = Ri YA

i Im

-Im

T t

Rui R=

]TahrN_CaelxkñúgesoKVIxagelIenH eKGacrkeXIjGMBøITutEdlmanGaMgtg;sIuet Im = Um / R ebI Um = 6,0V

R = 100 eKGacTaj)an Ω mA0,6A0060,0100

0,6Im ===

rgVas;éntg;süúg GUsIuy:UsáÚb - v:ulEm:t

lMhat;TI 1 ³ tg;süúgkMBUl - kMBUl tg;süúgqøas;sIunuysUGIuténbNþajmYykMnt;sMKal;eday f = 50Hz

nigtg;süúgRbsiT§ U = 220V

a- kMnt;xYbrbs;va . b- kMnt;tg;süúgkMBUl - kMBUl . dMeNaHRsay a- kMnt;xYb tamrUbmnþ ³

fT 1= ; eday f = 50Hz

sT 020,0501==

dUcenH

b- kMnt;tg;süúgkMBUl - kMBUl tamrUbmnþ 2UUm = ; eday U = 220V

eyIg)an V310414,12202220Um =×== tg;süúgkMBUl - kMBUlKW ³ V6203102U2 m =×= dUcenH tg;süúgkMBUl - kMBUlesµI 630V

lMhat;TI 2 ³ Gal;ETNaT½réneTacRkyan

T = 0,020s

GUsIuy:URkabénrUbxageRkamenHpþl;edayGal;ETNaT½reTacRkyanmYy ¬CYnkaleKehAtamTMlab;fa DINam:U¦ k- tg;süúgEdlemIleXIjCatg;süúgCab; b¤ ERbRbYl? x- etIvaCatg;süúgxYbrWeT? K- RbsinebItg;süúgxYb KUsGUsIuy:URkabenHeLIgvij ehIydak;sMKal;edayKMnUsExVgBIrenAxagedIm nig xagcugvdþ .

X- etIxYbmantMélb:unµan ebIel,ÓnekosesµI 2s.div-1. etIeKeFVIeGayDINam:Uviledayel,Ón b:unµanCMukñúg

1 naTI ?

dMeNaHRsay k- tg;süúgEdlemIleXIjCatg;süúgERbRbYl. x- vaCatg;süúgxYb . K- tg;süúgenHCatg;süúgEdlmanrUbdUcxageRkamenH

X- kMnt;xYb T = vb x x eday vb = 2s.cm-1 x = 3RkLa = 3cm

naMeGay sT 632 =×=

dUcenH T = 6s

- kMnt;el,ÓnCaCMukñúg 1naTI (tr.mn-1)

DINam:UeFVI)anmYyxYb KWmYyCMu ebIvaeFVIkñúg 1mn eyIg)an

660

=N = 10tr.mn-1

lMhat;TI 3 ³ KMnUsRkiténv:ulEm:t edIm,Ivas;tg;süúgqøas;sIunuysUGIutrvagcMnucBIr eKP¢ab;v:ulEm:tCaExñgeTAnwgcMnucenaH . k- etIv:ulEm:tvas;tg;süúgRbsiT§ rW tg;süúgGtibrma? x- v:ulEm:tmanRbelaHRkit 100 ehIyRTnicrbs;vacg¥úlKMnUsRkitTI 80 . KNnatMéltg;süúgRbsiT§ nig tg;süúgGtibrma ebIv:ulEm:tenaHmankalIb 30V .

dMeNaHRsay k- v:ulEm:tvas;tg;süúgRbsiT§ x- tMéltg;süúgRbsiT§ ³ tamTMnak;TMng

onn

CalU

=

naMeGay on

nCalU =

eday Cal = 30V

n = 80 RbelaHRkit no = 100 RbelaHRkit dUcenH

10080.30

=U = 24V

tMéltg;süúgGtibrma tamTMnak;TMng

2mUU =

eyIg)an 2UUm = V34414,124 =×= dUcenH Um = 34V

lMhat;TI 4 ³ rgVas;tg;süúgedayGUsIuy:UsáÚb kñúgesoKVIénrUbxageRkamenH G CaCnitatg;süúgCab;mYy . eKP¢ab;cMnuc B eTAnwgeKalcUl Y én GUsIuy:UsáÚb cMnuc C eTAnwgma:s . PaBrYsQresµInwg 5V.div-1 . k- etIGUsIuy:UsáÚbvas;tg;süúg UBC

rW UCB ? x- enAeBlEdlbgÁMdMeNIrkar cMnucPøWpøas;TIeLIgelI)an 2,4cm . cUlkMNt;tMéltg;süúgEdl)anvas; K- \LÚvenHeKEktMrUvel,ÓnekosmktMél Vb = 0,1ms/div cUrKUstamTMhMBitTidæPaBelIeGRkg; .

N

ma:s eKalcUlY

B C

G P

A

dMeNaHRsay k- GUsIuy:UsáÚbvas;tg;süúg UBC N

C B A

ma:s YB YA

UBC

UAC

G P

x- kMnt;tMéltg;süúgEdl)anvas; tamTMnak;TMng UBC = Sv.Y

eday Sv = 5V/div ; Y = 2,4div

eK)an UBC = 5.2,4 = 12V

K- KUstamTMhMBitTidæPaBelIeGRkg; cMeBaHel,Ónekos Vb = 0,1ms/cm

cMnucPøWKUselIeGRkg;)anbnÞat;edkmYy BIeqVgeTAsþaMya:gelOn kalNaeKGnuvtþtg;süúgCab;mYy

eKeXIjbnÞat;edkmYy . cMeBaHtg;süúg U = 12V nigPaBrYsQr Sv = 5V/div eKeXIjbnÞat;mYykat;G½kS Gredaenr 2,4div ehIyRsbnwgG½kSGab;sIus

Y = 2,4cmUBC = 12V

• sMKal; ebIeKeRbIeKalcUlTI 2 YA eKP¢ab;cMnuc A énesoKVIeTAnwg YA dUcenHeKeXIj UAC ¬rvag YA nig ma:s¦ ehIymineXIj UAB eT . lMhat;TI 5 ³ karP¢ab;énGUsIuy:UsáÚb eKP¢ab;bNþajdUcrUbxageRkam ³

Q R

N eKal Y P

CnitaeRbkg;Tab

eK)anTTYlGUsIuy:URkabdUcrUbxageRkam . karéltMrUvGUsIuy:UsáÚbKW - el,Ónekos ³ 2ms.div-1

- PaBrYsQr ³ 5V.div-1

k- etItg;süúgEdleyIgeXIjCatg;süúgGVI? x- kMnt;tMéleRbkg; nig tg;süúgGtibrma . K- eFVIKMnUstageLIgvij edIm,Ivas;tg;süúg UNP ; URN enAelIeGRkg;GUsIuy:UsáÚb . X- eKpþac;dMeNIrkarekos . KUsrUbGUsIuy:URkabeLIgvij tamTMrg;edIm . dMeNaHRsay k- tg;süúgEdlemIleXIjCatg;süúg qøas;sIunuysUGIut UPQ

x- eRbkg;éntg;süúg

Tf 1= (1)

(2) xvT b ×=

tam (1) nig (2) eyIg)an ³

xvf

b ×=

1 eday vb = 2ms/div = 2.10-3 s/div ; x = 8div

Hzf 5,6216

10008.10.2

13 === −

dUcenH Hz63~f − kMnt;tg;süúgGtibrma Um

Um = Sv.Y eday Sv = 5V/div ; Y = 3div

naMeGay Um = 5 x 3 = 15V

dUcenH Um = 15V K- eFVIKMnUstageLIgvijedIm,Ivas; UNP

CnitaeRbkg;Tab

eKalcUl Y

UNP

N P R Q

- eFVIKMnUstageLIgvijedIm,Ivas;tg;süúg URN

CnitaeRbkg;Tab

eKalcUl Y

URN

R Q

P N X- eKpþac;dMeNIrkarekos . rUbGUsIuy:URkabKW ³

-15V

+15V lMhat;TI 6 ³ karéltMrUvenAelIGUsIuy:UsáÚb rUbxageRkam KWCaGUsIuy:URkabéntg;süúgmYyEdlmanragCaeFµjrNa . kMEntMrUvénGUsIuy:UsáÚbman ³ - el,Ónekos 2ms/div

- PaBrYstamExSQr 5V/div

k- etItg;süúgenHCatg;süúgxYbb¤eT? ebIEmnetIeyIgeXIjelIeGRkg;b:unµanxYb ? x- kMnt;tMélénxYb nig eRbkg;rbs;va ? K- etItg;süúgGtibrma Um mantMélb:unµan ? X- eKeFVIkaréltMrUv ehIyeK)antMélfµI - el,Ónekos 5ms/div

- PaBrYstamExSQr 10V/div

KUrrUbTidæPaBfµIelIeGRkg;énGUsIuy:UsáÚbtamTMhMBit .

dMeNaHRsay

k- tg;süúgenHCatg;süúgxYb . eyIgeXIjelIeGRkg; 2 xYb . x- KNnaxYbéntg;süúg T

tamrUbmnþ T = Vb x x

eday Vb = 2ms/div ; x = 5div

naMeGay T = 2 x 5 = 10ms

dUcenH T = 10ms

kMnt;eRbkg;éntg;süúg ³ f tamrUbmnþ

Tf 1= eday T = 10ms = 10.10-3s = 10-2s

eyIg)an Hzf 10010

12 == −

dUcenH f = 100Hz

K- KNnatg;süúgGtibrma Um

tamrUbmnþ Um = Sb x Y eday Sb = 5V/div ; Y = 3div Um = 5 x 3 = 15V dUcenH Um = 15V

X- tamtMélfµIeyIg)an

bb v

TxxvT =⇒×=

eday vb = 5ms/div ; T = 10ms x = 2,0div ⇒

Um = Sv.Y naMeGay v

m

SUY =

(V) (V/div)(div) eday Um = 15V ; Sv = 10V/div

eyIg)an divY 5,11015

== dUcenH Y = 1,5div

KUrrUbTidæPaBfµIelIeGRkg;énGUsIuy:UsáÚbtamTMhMBit

lMhat;TI 7 ³ tg;süúgeRkNU eK)aneXIgtg;süúgeRkNU mYyenAelIeGRkg;énGUsIuy:UsáÚbmYy . eKéltMrUvmantMél ³ - PaBrYsedk 0,2ms/div

- PaBrYsQr 5V/div

k- etItg;süúgenHCatg;süúgxYbb¤eT ? ebIEmnkMnt;tMélxYb nig eRbkg;rbs;va x- etItg;süúgGtibrma Um mantMélb:unµan ? K- etIeKRtUveGaytMélel,Ónekosb:unµan edIm,IeGayeXIjmanEtmYyxYbKt;elIeGRkg; ?

tg;süúgeRkNU

dMeNaHRsay k- tg;süúgenHCatg;süúgxYb tg;süúgeRkNU kMnt;xYb (T)

tamrUbmnþ T = vb x x

eday vb = 0,2ms/div = 2.10-4s/div x = 2,5div = 25.10-1div eyIg)an T = 2.10-4.25.10-1 = 5.10-4s

dUcenH T = 5.10-4s

kMnt;eRbkg; (f) Hz

Tf 3

4 10.210.511

=== −

dUcenH f = 2.103 Hz

x- KNnatg;süúgGtibrma Um

tamrUbmnþ Um = Sv.Y

eday Sv = 5V/div ; Y = 3div

naMeGay Um = 5 x 3 = 15V

dUcenH Um = 15V

K- KNnael,Ónekos edIm,IeGayeKemIleXIjenAelIeGRkg;manEtmYyxYb tamrUbmnþ T = vb . x

naMeGay xTvb =

eday T = 5.10-4s = 0,5ms ; x = 10div

` eyIg)an divmsvb /05,010

5,0==

dUcenH vb = 0,05ms/div lMhat;TI 8 ³ tg;süúgsIunuysUGIutEdlERbkøayeTACatg;süúgEdlmanTisEtmYy GUsIuy:URkabdUcrUbxageRkamCarbs;tg;süúgqøas;sIunuysUGIutEkTisedayDIy:UtmYy . - el,Ónekos 0,1ms.div-1

- PaBrYsQr 0,2V . div-1

k- etItg;süúgenHCatg;süúgCab; rW ERbRbYl? x- etIehtuGI)anCacrnþenHmaneQµaHfacrnþEkTis ? K- etItg;süúgenHCatg;süúgxYb b¤eT? ebIEmnkMnt;tMélxYb nig eRbkg;rbs;va . X-etItg;süúgGtibrmamantMélb:unµan ?

dMeNaHRsay k- tg;süúgenHCatg;süúgERbRbYl x- bBa¢ak;eQµaHcrnþEkTis )anCamaneQµaHcrnþEkTis eRBaHkaledImeLIyvaCacrnþqøas;sIunuysUGIut b:uEnþeKEktMrUvbM)at;tg;süúg GviC¢manecj ykRtwmEtKMnUs 0 rYceLIgeTAtg;süúgviC¢manvij . K- tg;süúgenHCatg;süúgxYb - tMélxYb T = vb x x eday vb = 0,1ms . div-1 ; x = BIrkar:U = 2div

naMeGay T = 0,1 x 2 = 0,2ms

- tMéleRbkg;

Tf 1=

eday T = 0,2ms = 0,2.10-3s = 2.10-4s

naMeGay Hzf 500010.21

4 == − dUcenH f = 5.103Hz

X- kMnt;tMéltg;süúgGtibrma Um

Um = Sv .Y

⎪⎪⎩

⎪⎪⎨

⎧

−

KitCa KitCa KitCa

divYdiv.VS

VU1

v

m

eday Sv = 0,2V.div-1 ; Y = 3kar:U = 3div

naMeGay Um = 0,2 x 3 = 0,6V