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