amocana №1 - ieeetsu

ieeetsu.ge

amocana №1 - ieeetsu

a m o c a n a # 1

O

omis kanonis Semowmeba cvladi denisaTvis,

TviTinduqciisa da tevadobis gansazRvra.

g a f r T x i l e b a

nebismieri eleqtruli sqemis CarTvis win yvela mravalskaliani

gamzomi xelsawyo gadaiyvaneT udides zRvarze. reostatebi CarTeT

mTlianad, potenciometrebi _ gamorTeT.

xelmZRvanelis mier sqemis Semowmebis Semdeg gamzomi xelsawyoebi

gadaiyvaneT iseT nominalur zRvarze, rom gazomvebi awarmooT xelsawyos

nominaluri Cvenebis maxloblobaSi.

xelmZRvanelis mier sqemis Semowmebamde wredi ar CarToT!

samuSaosTvis saWiroa:

1. denis wyaro - mudmivi da cvladi;

2. induqciuri koWa;

3. kondensatori;

4. voltmetri (mudmivi da cvladi denisTvis);

5. ampermetri (mudmivi da cvladi denisTvis);

6. reostati;

7. CamrTveli;

8. SemaerTebeli mavTulebi.

- 1 -


cvladi denis generatoris gamomyvanebze Zabva icvleba sinusoiduri

kanoniT:

U U

m

sint

(1)

sadac U - Zabvis myisieri mniSvnelobaa,

U

m - Zabvis amplituduri

mniSvneloba, - denisa da Zabvis cikluri sixSire, t - dro

Tu cvladi denis wyaros gamomyvanebs CavketavT gare wrediT, maSin

wredSi aRiZvreba cvladi deni, romelic agreTve icvleba sinusoiduri

kanoniT:

i I

m

sint

(2)

sadac i - cvladi denis myisieri mniSvnelobaa, I m ki - amplituduri.

cvladi denis SemTxvevaSi (2) tolobas yovelTvis ara aqvs adgili,

radgan denis faza damokidebulia gare wredSi CarTuli R

winaaRmdegobis, L induqciurobis da C tevadobis sidideebze.

am sakiTxis Sesaswavlad ganvixiloT cvladi denis wredis ramdenime

SemTxveva:

I. gare wredi Seicavs mxolod omur (anu aqtiur) winaaRmdegobas R .

aseT SemTxvevaSi cvladi denis wredis pirobebi ar gansxvavdeba mudmivi

denis wredis pirobebisagan. Ddenis Zalis gansazRvrisaTvis SeiZleba

gamoviyenoT omis kanoni wredis ubnisTvis:

I U

denisa da Zabvis myisieri mniSvnelobisTvis formula miiRebs Semdeg saxes :

(1) tolobidan U -s mniSvneloba CavsvaT (3)-Si:L

i


U

m

sint


R

R

i U

R

(3)

U

m

R

sint


I

m

sint

I

m iqneba denis amplituduri

mniSvneloba. advili SesamCnevia, rom

Zabva da deni, am SemTxvevaSi, erTnairi

faziT irxevian. (ixileT Zabvisa da denis

diagrama nax.1-ze).

II. gare wredi Seicavs mxolod

induqtivobas L


induqtivobis SemTxvevaSi cvladi denis

i, U

I m

U

m

0 t

nax. 1

- 2 -


wredSi aRiZvreba induqciis e.m.Z.

formuliT:


L , romlis sidide ganisazRvreba

di

dt


L

L

(4)

sadac L gare wredis TviTinduqciis koeficientia.

induqtivobis koWa SeiZleba ganvixiloT, rogorc wredis ubani, romelic

Seicavs emZ-s. aseTi ubnisTvis omis kanons eqneba saxe:

vinaidan R 0 , amitom

sadac

U

L

U iR

L



L

di

L dt

L

5,


U

L aris Zabva induqciuri koWas boloebze.

Tu (5)-Si CavsvamT i -s mniSvnelobas (2)-dan da gavawarmoebT, miviRebT:

an

sadac

U

m


I

m

L

U I Lcos

t

U

L

U

m


sint




2

L m

(6)

Aaris Zabvis amplituduri mniSvneloba. aqedan

I

m

U

m

.

L

L

sidides winaaRmdegobis ganzomileba aqvs da mas wredis induqtiuri

winaaRmdegoba ewodeba. SemovitanoT aRniSvna:

2

U

m

I

m


(7)

xL

L xL

maSin:

1

i

U Lm

I m

0

1

1 2 3 4 5 6

t

Lm

lurji - i

wiTeli - U L

yviTeli - e L

2

u L

e L

nax. 2

- 3 -


(7) Fformula gvaZlevs kavSirs denis Zalis da Zabvis amplitudur

mniSvnelobebs Soris, igi omis kanonis analogiuria.

(2) da (6) formulebis SedarebiT SegviZlia davaskvnaT, rom gare wredSi

mxolod induqtivobis CarTvis dros, denis Zala meoTxedi periodiT

CamorCeba Zabvas. grafikulad es gamosaxulia nax. 2-ze.

III. cvladi denis gare wredi Sedgeba mxolod C


kondensatorisgan.

tevadobis

muxti kondensatoris firfitebze ganisazRvreba Semdegi formuliT:

q CU C

, SevitanoT U -s mniSvneloba (1)-dan, miviRebT:

q CU

m

sint

(8)

(8)-s diferencirebiT miviRebT

dq

dt


i CU

m

cos t

an

I sint


2

U

m

sadac I

m

denis amplituduri mniSvnelobaa.

1

C

SemovitanoT aRniSvna:

1

C


i

m (9)

x

C sidides uwodeben gare wredis tevadur winaaRmdegobas.

U

I

(10)

m

m

xC

(10) formula omis kanonis analogiuria. (1) da (9) formulebis SedarebiT

SegviZlia davaskvnaT, rom Tu gare wredSi CarTulia mxolod

kondensatori, denis Zalis faza Zabvas uswrebs periodis meoTxediT.

grafikulad es gamosaxulia nax.3-ze.

x C

;

2

U C

I m

1

i

U m

1

0

1 2 3 4 5 6

t

lurji - U C

wiTeli - i

nax. 3

2

- 4 -


IV. gare wredi Sedgeba mimdevrobiT SeerTebuli aqtiuri

L da tevaduri

C winaaRmdegobebisagan.

gamoviyvanoT damokidebuleba Zabvis da denis

amplitudur mniSvnelobebs Soris.

Zabvis vardna wredis calkeul ubanze da

wyaros gamomyvanebze SeiZleba warmovadginoT

veqtoruli diagramiT (ix. nax. 4-a). m iyos

denis amplituduri mniSvnelobis veqtori.

radganac Zabva omuri winaaRmdegobis boloebze

faziT emTxveva dens, SegviZlia Zabvis veqtori

I

gadavzomoT m veqtoris mimarTulebiT. viciT,

rom Zabva induqtiuri winaaRmdegobis boloebze

periodis meoTxediT



2

I

nax.4a.

R , induqciuri

nax.4a.

uswrebs dens, amitom I m L sigrZis veqtori

gadavzomoT 0 wertilidan I m -is perpendikularulad zeviT, xolo

tevadobis SemTxvevaSi, radgan Zabva CamorCeba dens periodis meoTxediT,

I m

C

1

sigrZis veqtori gadavzomoT m

nax.4-a

I -is perpendikularulad qveviT,

I m

L

-is sawinaaRmdegod. nax.4.a-dan Cans, rom

OA

U L m UCm

.

4

2

I

U c

0

2

4

1 2 3 4 5 6

U L

U m

U R

t

iisferi- I

wiTeli- U R

mwvane - U C

yviTeli -U L

lurji – U m

nax. 4-b

nax. 4-b-ze mocemulia am sami veqtoris geometriuli jami, romelic iZleva

gare wredis jamuri Zabvis amplitudur mniSvnelobas.

gamoisaxeba Semdegnairad:

- 5 -

U

m

veqtoris sidide


U

m


2 1

I

m

L I

m


( I

mR)


C


am formulidan gamovsaxoT denis Zalis amplituduri mniSvneloba:

I

m


U

m

2 1

R L


C

(11) formulis mniSvnelSi mdgomi sidide avRniSnoT Z -iT :

2 1

Z R L (12)

C

Z aris cvladi denis ganuStoebeli wredis sruli (an moCvenebiTi)

winaaRmdegoba. igi damokidebulia R , L , C parametrebze da agreTve

cvladi denis sixSireze 2f

.

1

sidides L ewodeba ganuStoebeli wredis reaqtiuli

C

winaaRmdegoba. (12)-is gaTvaliswinebiT (11) formula ase Caiwereba:

U

I m

m

Z

isev miviReT omis kanonis analogiuri gamosaxuleba wredis ubnisaTvis. is

iZleva damokidebulebas denis Zalis da Zabvis amplitudur mniSvnelobebs

Soris zogad SemTxvevaSi, rodesac wredi Seicavs R , L da C -s, xolo

denis Zalis da Zabvis fazebi wanacvlebulia -iT, romelic

gansxvavebulia 2


-sagan (ix. nax. 4b). amitom (1) da (2) gantolebebi zogad

SemTxvevaSi miiRebs saxes:


2

2


2

(11)

U U sin m

t


(13)

i I

m

sint

(14)

SeiZleba iyos rogorc dadebiTi ise uaryofiTi, imis mixedviT, Tu

romeli winaaRmdegobaa meti: x

L Tu x C .

ganisazRvreba Semdegi formuliT


L

1

arctg C

R


(15)

- 6 -


samuSaos Sesruleba

1. koWis L TviTinduqciis koeficientis da fazaTa sxvaobis

gansazRvra.

omis kanoni, roca cvladi denis wredi Seicavs induqciur koWas omuri

winaaRmdegobiT, ase Caiwereba:

I

U


Z

R

2

U


2 2 2

( L)

R xL

I da U denisa da Zabvis efeqturi mniSvnelobebia. cvladi denis

efeqturi mniSvneloba tolia mudmivi denis im mniSvnelobisa, romelic

imave R winaaRmdegobis gamtarSi, imave droSi siTbos imave raodenobas

gamoyofs, rasac cvladi deni.

denisa da Zabvis efeqtur da amplitudur mniSvnelobebs Soris arsebobs

Semdegi damokidebuleba:

I

I m

,

2

- 7 -


U

U m

2

cvladi denis wredSi CarTuli eleqtro gamzomi xelsawyoebi aCveneben

gasazomi sidideebis moqmed anu efeqtur mniSvnelobas.

induqciuri koWas moCvenebiTi winaaRmdegoba

Z


aqedan SeiZleba ganvsazRvroT

L

1

R

2

( L)


2

U

(16)

2 2

Z R

(17)

koWas omuri winaaRmdegobis gansasazRvravad vawyobT wreds #1 sqemis

mixedviT da vaerTebT mudmivi denis wyarosTan. denis da Zabvis

regulirebas vaxdenT potenciometris saSualebiT. omis kanonis gamoyenebiT

U

( R ) viTvliT winaaRmdegobas sami sxvadasxva reJimisaTvis da

I

vpoulobT R -is saSualo mniSvnelobas R .

Z -is gansasazRvravad induqciuri koWa unda CavrToT cvladi denis

wredSi, amisaTvis vawyobT analogiur sqemas, mudmivi denis xelsawyoebs

vcvliT cvladi denis xelsawyoebiT.

moCvenebiTi winaaRmdegobis saSualo mniSvneloba Z

R -is analogiurad:

U

Z

I

ganisazRvreba

R da Z -is saSualebiT gamoiTvleba TviTinduqciis koeficienti L

henrebSi da fazaTa sxvaoba

R

arctg L

gamoTvlili sidideebisTvis ganisazRvreba absoluturi da fardobiTi

cdomilebebi (calkeuli gazomvebisaTvis cal-calke).


2. kondensatoris tevadobis gansazRvra.

wreds vawyobT #2 sqemis mixedviT. omis kanons aseTi wredisaTvis eqneba

saxe:

radganac

1

x C

C

U

I aqedan

x C

, miviRebT

1

C x C

U

x C


I

gazomvebis Tanmimdevroba iseTivea, rogorc R -is da L -is gazomvebis

dros.

3. omis kanonis Semowmeba cvladi denis wredisaTvis roca CarTulia R , L

da C .

wreds vawyobT #3 sqemis mixedviT. omis kanonis Semowmeba daiyvaneba (12)

formuliT gamoTvlili moCvenebiTi winaaRmdegobis Sedarebamde

eqsperimentulad miRebul winaaRmdegobasTan, romelic gamoiTvleba omis

kanonis gamoyenebiT wredis ubnisaTvis.

cdomilebaTa mxedvelobaSi miRebiT unda dakmayofildes toloba:

Z

gam

Z

gam


Z

eqsp

Z

amis garda, (15) formuliT gamoiTvleba fazaTa wanacvlebis kuTxe - .

gazomvebis Tanmimdevroba iseTivea, rogorc 1 da 2 nawilSi.

eqsp

literatura:

1. T. xazaraZe. zogadi fizikis kursi eleqtroba. § 12.4. Tsu 1991.

2. C. Г. Калашников. Электричество. § 217-220. М. Наука 1977.

3. А.Н. Матвеев. Электричество и магнетизм. § 48ю М. Высшая школа 1983.

4. D. Halliday, R. Resnick, J. Walker. Fundamentals of Physics. § 36.3, 36.4. John Wiley

&. Sons. Inc. 1993.

- 8 -


A

A

V

V

U

sqema #1 sqema #2

A

V

sqema #3

- 9 -

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