Электротехника и электроника

71

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

ìàãíèòíîé íàïðÿæåííîñòüþ, ïîëíîñòüþ ðàçìàãíè÷èâàþùåé ìàòåðèàë.

Äëÿ ìàãíèòíî-ìÿãêèõ ìàòåðèàëîâ îáû÷íî íå ó÷èòûâàþò ìàãíèòíûé

ãèñòåðåçèñ è èñïîëüçóþò îñíîâíóþ êðèâóþ íàìàãíè÷èâàíèÿ Â(Í)

(çàâèñèìîñòü ìàãíèòíîé èíäóêöèè îò íàïðÿæåííîñòè ìàãíèòíîãî ïîëÿ),

ïîêàçàííóþ ïóíêòèðîì íà ðèñ.6.7.

Äëÿ ìàãíèòíî-òâåðäûõ ìàòåðèàëîâ íåîáõîäèìî ó÷èòûâàòü íå òîëüêî

îñíîâíóþ øèðîêóþ ïåòëþ ãèñòåðåçèñà, íî è ëîêàëüíûå ïåòëè ãèñòåðåçèñà.

Ëîêàëüíûå ïåòëè óçêèå è â ïåðâîì ïðèáëèæåíèè ìîãóò áûòü çàìåíåíû ñðåäíåé

ëèíèåé, íà êîòîðîé íàõîäÿòñÿ èõ âåðøèíû. Ýòà ëèíèÿ áëèçêà ê ïðÿìîé è

íàçûâàåòñÿ ëèíèåé âîçâðàòà (ËÂ).

6.4.3. Êîýðöèòèâíàÿ ñèëà

Êîýðöèòèâíàÿ ñèëà õàðàêòåðèçóåòñÿ çíà÷åíèåì âíåøíåé îòðèöàòåëüíîé

ìàãíèòíîé íàïðÿæåííîñòè, êîòîðàÿ ïîëíîñòüþ ðàçìàãíè÷èâàåò ìàòåðèàë.

Äëÿ ìàãíèòíî-ìÿãêèõ ìàòåðèàëîâ õàðàêòåðíî íèçêîå çíà÷åíèå

êîýðöèòèâíîé ñèëû. Äëÿ ýòèõ ìàòåðèàëîâ çíà÷åíèå Í

Ñ

ëåæèò â ïðåäåëàõ

10  100 À/Ì.

Ìàãíèòíî-òâåðäûå ìàòåðèàëû èìåþò âûñîêèå çíà÷åíèÿ Í

Ñ

, ïîðÿäêà

10000-1000000 À/Ì, ÷òî ïîçâîëÿåò èì ñîçäàâàòü ìàãíèòíûé ïîòîê çà ñ÷åò ñâîåé

íàìàãíè÷åííîñòè â îòñóòñòâèå îáìîòîê âîçáóæäåíèÿ. Èç ìàãíèòíî-òâåðäûõ

ìàòåðèàëîâ èçãîòàâëèâàþò ïîñòîÿííûå ìàãíèòû.

72

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

ÇÀÄÀÍÈß ÄËß ÑÀÌÎÑÒÎßÒÅËÜÍÎÉ ÐÀÁÎÒÛ

1. Ñîñòàâüòå ëîãè÷åñêóþ ñõåìó áàçû çíàíèé ïî òåìå þíèòû.

73

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

ÒÐÅÍÈÍÃ ÓÌÅÍÈÉ

1. Ïðèìåð âûïîëíåíèÿ óïðàæíåíèÿ òðåíèíãà íà óìåíèå ¹1

Çàäàíèå

Îïðåäåëèòü òîê â âåòâè ñ ñîïðîòèâëåíèåì r = 10 Îì, åñëè ñîïðîòèâëåíèå

r

1

= 20 Îì, r

2

= 15 Îì, r

3

= 5 Îì, ÝÄÑ = 30 Â.

¹

ï/ï

Àëãîðèòìû Êîíêðåòíîå ñîîòâåòñòâèå çàäàíèÿ

ïðåäëîæåííîìó àëãîðèòìó

1 Ðàçìûêàíèå èññëåäóåìîé

öåïè

Îòêëþ÷àåì âåòâü ñ ñîïðîòèâëåíèåì r

2 Îïðåäåëåíèå íàïðÿæåíèÿ íà

êîíöàõ ðàçîìêíóòîé âåòâè

öåïè

A86,0

1520

30

rr

E

rr

öö

I

2121

21

1x

=

+

=

+

=

+

−

=

A2

15

30

rr

E

rr

öö

I

4343

21

2x

==

+

=

+

−

=

Ïîòåíöèàëû òî÷åê:

2x4âõ2x

Iröö

⋅−=

;

1x22x4âõ1x22õàõ

IrIröIröö

⋅+⋅−=⋅+=

.

Ðàçíîñòü ïîòåíöèàëîâ âûâîäîâ à è b èëè

íàïðÿæåíèå íà êîíöàõ ðàçîìêíóòîé âåòâè

öåïè:

=⋅+⋅−=−=

1x22x4bxaxx

IrIrU

ϕϕ

= -10

⋅

2 + 15

⋅

0,86 = -7,1Â

Ðåøåíèå

74

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

3 Îïðåäåëåíèå âõîäíîãî

ñîïðîòèâëåíèÿ âñåé ñõåìû

îòíîñèòåëüíî ðàçîìêíóòîé

âåòâè ïðè çàêîðî÷åííûõ

èñòî÷íèêàõ

Ïðè îïðåäåëåíèè âíóòðåííåãî

ñîïðîòèâëåíèÿ äâóõïîëþñíèêà ñ÷èòàåì,

÷òî ÝÄÑ Å íå äåéñòâóåò, à âíóòðåííåå

ñîïðîòèâëåíèå ýòîãî èñòî÷íèêà ðàâíî

íóëþ.

Ïàññèâíûé äâóõïîëþñíèê ïîëó÷àåòñÿ èç

àêòèâíîãî ïîñëå ñîåäèíåíèÿ óçëîâ 1 è 2:

Ñîïðîòèâëåíèÿ r

1

è

r

2

ñîåäèíåíû

ïàðàëëåëüíî. Èõ îáùåå ñîïðîòèâëåíèå:

8,57Oì

1520

rr

r

21

12

=

+

⋅

=

+

⋅

=

.

Äëÿ ñîïðîòèâëåíèé r

3

è

r

4

:

3,33Oì

105

rr

r

43

34

=

+

⋅

=

+

⋅

=

.

Ýêâèâàëåíòíàÿ ñõåìà ñ ñîïðîòèâëåíèÿìè

r

12

è

r

34

:

Âõîäíîå ñîïðîòèâëåíèå ïàññèâíîãî

äâóõïîëþñíèêà:

9,1133,357,8rrr

3412âõ

=+=+=

.

4 Îïðåäåëåíèå òîêà â

ðàññìàòðèâàåìîé âåòâè

0,32À

11,910

7,1

rr

U

I

âõ

x

−=

+

−

=

+

=

75

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

Ðåøèòå ñàìîñòîÿòåëüíî ñëåäóþùèå çàäàíèÿ

Çàäàíèå 1

Îïðåäåëèòü òîê â âåòâè ñ ñîïðîòèâëåíèåì r

7

= 20 Îì, åñëè ñîïðîòèâëåíèÿ:

r

1

= 5 Îì; r

2

= 12 Îì; r

3

= 7 Îì; r

4

= 15 Îì; r

5

= 9 Îì; r

6

= 13 Îì; ÝÄÑ Å = 40 Â.

_________________________________________________________________________________________________

Çàäàíèå 2

Îïðåäåëèòü òîê â äèàãîíàëè àb ñõåìû, åñëè: r

1

= 10 Îì; r

2

= 15 Îì; r

3

= 7

Îì; r

4

= 5 Îì; r

5

= 12 Îì; Å

1

= 10 Â; Å

2

= 20 Â.

76

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

_________________________________________________________________________________________________

2. Ïðèìåð âûïîëíåíèÿ óïðàæíåíèÿ òðåíèíãà íà óìåíèå ¹2

Çàäàíèå

Îïðåäåëèòü çíà÷åíèå òîêîâ â âåòâÿõ öåïè ñî ñìåøàííûì ñîåäèíåíèåì

ýëåìåíòîâ è îïðåäåëèòü íàïðÿæåíèÿ íà åå ýëåìåíòàõ.

Ðåøåíèå

¹

ï/ï

Àëãîðèòìû Êîíêðåòíîå ñîîòâåòñòâèå çàäàíèÿ

ïðåäëîæåííîìó àëãîðèòìó

12 3

1Ïðåäñòàâëåíèå èñõîäíûõ äàííûõ î

ïàðàìåòðàõ âñåõ ýëåìåíòîâ

àíàëèçèðóåìîé öåïè â êîìïëåêñíîé

ôîðìå

Ïåðâûé ýëåìåíò èìååò ðåçèñòèâíîå

ñîïðîòèâëåíèå : r

1

= 2 Îì è

èíäóêòèâíîå jx

1

= j 0,1 Îì.

Âòîðîé ýëåìåíò èìååò ðåçèñòèâíîå

ñîïðîòèâëåíèå : r

2

= 5 Îì è

èíäóêòèâíîå jx

2

= j 0,3 Îì.

Òðåòèé ýëåìåíò èìååò ðåçèñòèâíîå

ñîïðîòèâëåíèå : r

3

= 4 Îì è

èíäóêòèâíîå jx

3

= j 0,5 Îì.

Íàïðÿæåíèå U = 120 B.

77

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

12 3

2Âûáîð ïîëîæèòåëüíûõ

íàïðàâëåíèé äëÿ òîêîâ âî âñåõ

âåòâÿõ

Âûáåðåì ïîëîæèòåëüíîå

íàïðàâëåíèå òîêà I â

íåðàçâåòâëåííîé ÷àñòè öåïè îò À ê

Ñ. Ïîëîæèòåëüíûå íàïðàâëåíèÿ

òîêîâ â ïåðâîé I

1

è âî âòîðîé I

2

âåòâÿõ âûáåðåì îò Ñ ê D.

3 Ñîñòàâëåíèå ñ ïîìîùüþ çàêîíîâ

Îìà è Êèðõãîôà â êîìïëåêñíîé

ôîðìå, óðàâíåíèé, îïðåäåëÿþùåé

ðåæèì ðàáîòû öåïè

Ñîãëàñíî ïåðâîìó çàêîíó

Êèðõãîôà:

0III

21

=++−

èëè

21

III

+=

.

Ñîãëàñíî çàêîíó Îìà:

1

Z

U

I

=

;

2

Z

U

I

=

;

IZUU

1221

⋅==

, ãäå Z

12

-

ñîïðîòèâëåíèå ðàçâåòâëåííîé

÷àñòè öåïè.

IZU

33

⋅=

;

()

21

12

ZZ

Z

+

⋅

=

4 Îïðåäåëåíèå êîìïëåêñíûõ

çíà÷åíèé òîêîâ â âåòâÿõ öåïè è

êîìïëåêñíûõ çíà÷åíèé íàïðÿæåíèé

íà åå ýëåìåíòàõ

j0,12Z

1

+=

;

j0,35Z

2

+=

;

j0,54Z

3

+=

;

()()

j0,35j0,12

Z

12

+++

+⋅+

=

()()

j0,47

j0,35j0,12

+

+⋅+

=

j0,47

j1,19,97

+

=

j0,47

0,47

j0,47

j1,19,97

−

⋅

+

=

22

4,07

4,01,1797,9

+

⋅+⋅

+

22

4,07

0,49,97-71,1

j

+

⋅⋅

=

j0,5761,429

+

;

j0,5765,429

120

Z

U

I

+

==

=

−

⋅

+

j0,5765,429

120

=

()

=

+

⋅

+

⋅

2222

576,05,429

0,576120-

j

576,0429,5

429,5120

=21,857-j2,319;

()

⋅+=⋅==

j0,0761,429IZUU

1221

()

j1,65331,41j2,31921,857

−=−⋅

;

()( )

j2,31921,857j0,54IZU

33

−⋅+=⋅=

;

j1,65388,588U

3

+=

;

j1,60815,625

j0,12

j1,65331,41

1

−=

+

−

==

Z

U

I

;

j0,7056,24

j0,35

j1,65331,41

Z

U

I

2

−=

+

−

==

.

78

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

Ðåøèòå ñàìîñòîÿòåëüíî ñëåäóþùèå çàäàíèÿ

Çàäàíèå 1

Îïðåäåëèòü çíà÷åíèÿ òîêîâ â âåòâÿõ öåïè è íàïðÿæåíèé íà åå ýëåìåíòàõ

êîìïëåêñíûì ìåòîäîì.

r

1

= 5 Îì; r

2

= 10 Îì; r

3

= 3 Îì;

1

L

X

=1,5 Îì;

2L

X

=2 Îì;

3

C

X =2,5 Îì;

127BU =

_________________________________________________________________________________________________

Çàäàíèå 2

Îïðåäåëèòü òîêè âî âñåõ ó÷àñòêàõ öåïè, åñëè ÝÄÑ l

1

= 280 sinωt, l

2

= 290

sinωt. Âíóòðåííèå ñîïðîòèâëåíèÿ èñòî÷íèêîâ ïèòàíèÿ èíäóêòèâíûå Õ

1L

= Õ

2L

=

0,1 Îì. Ñîïðîòèâëåíèå íàãðóçêè

j0,51Z += Îì.

79

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

_________________________________________________________________________________________________

3. Ïðèìåð âûïîëíåíèÿ óïðàæíåíèÿ òðåíèíãà íà óìåíèå ¹3

Çàäàíèå

Îïðåäåëèòü ôàçíûå è ëèíåéíûå òîêè, åñëè ê ñåòè ñ ñèììåòðè÷íûìè

ëèíåéíûìè íàïðÿæåíèÿìè U

ë

= 220 Â ïîäêëþ÷åí ïðèåìíèê, ôàçû êîòîðîãî

ñîåäèíåíû òðåóãîëüíèêîì. Ñîïðîòèâëåíèå ôàç òðåóãîëüíèêà â Îìàõ:

j4

3Z

ab

+=

;

10Z

bc

=

;

j68Z

ca

+=

.

Ðåøåíèå

¹

ï/ï

Àëãîðèòìû Êîíêðåòíîå ñîîòâåòñòâèå çàäàíèÿ

ïðåäëîæåííîìó àëãîðèòìó

1 Ïðåäñòàâëåíèå ëèíåéíûõ

íàïðÿæåíèé â

êîìïëåêñíûõ ÷èñëàõ

Òàê êàê íà÷àëüíóþ ôàçó îäíîé èç

ñèíóñîèäàëüíûõ âåëè÷èí ìîæíî âûáðàòü

ïðîèçâîëüíî, òî áóäåì ñ÷èòàòü âåêòîð

ab

U

íàïðàâëåííûì ïî äåéñòâèòåëüíîé îñè,

ò.å. ïðèìåì

220BUU

abab

==

.

Â ýòîì ñëó÷àå íàïðÿæåíèÿ (â âîëüòàõ) áóäóò

ðàâíû:

00

0

j120

bc

sin120j220cos120220l220U

⋅−⋅=⋅=

−

=

1j19110

−−

;

j191110l220U

0

j120

ca

+−=⋅=

.

2 Îïðåäåëåíèå ôàçíûõ

òîêîâ

Ôàçíûå òîêè (â àìïåðàõ), ñîãëàñíî çàêîíó

Îìà:

()

=

+

==

j43

220

Z

U

I

ab

()

=

−

⋅

+

j43

220

=

j32,526,4

25

j880660

43

4j2203220

22

−=

−

=

+

⋅−⋅

;

4432,526,4I

22

ab

=+=

;

()

j1911

10

j191110

Z

U

I

bc

−−=

−−

==

;

221911I

22

bc

=+=

;

=

−

⋅

+

+−

=

+

+−

==

j68

j191110

j68

j191110

Z

U

I

ca

=

j21,82,6

+

;

2221,82,6I

2

ca

=+=

.

80

Ñîâðåìåííûé Ãóìàíèòàðíûé Óíèâåðñèòåò

Ðåøèòå ñàìîñòîÿòåëüíî ñëåäóþùèå çàäàíèÿ

Çàäàíèå 1

Îïðåäåëèòü ôàçíûå è ëèíåéíûå òîêè, åñëè ê ñåòè ñ ñèììåòðè÷íûìè

ëèíåéíûìè íàïðÿæåíèÿìè U

ë

= 127 Â ïîäêëþ÷åí ïðèåìíèê ôàçû, êîòîðîãî

ñîåäèíåíû òðåóãîëüíèêîì. Ñîïðîòèâëåíèÿ ôàç ïðèåìíèêà â Îìàõ:

j75Z

ab

+=

;

51Z

bc

=

;

j89Z

ca

+=

.

_________________________________________________________________________________________________

Çàäàíèå 2

Ê ñèììåòðè÷íîìó ãåíåðàòîðó, ôàçû êîòîðîãî ñîåäèíåíû çâåçäîé ñ ôàçàìè

ÝÄÑ Å

À

= Å

Â

= Å

ñ

=120 Â, ïðèñîåäèíåí ïðèåìíèê, ôàçû êîòîðîãî ñîåäèíåíû

çâåçäîé. Ñîïðîòèâëåíèÿ ôàç ïðèåìíèêà Z

a

=2a =10 Îì; Z

b

=2b =0,4 Îì;

Z

c

=2c =2,5 Îì. Ñîïðîòèâëåíèå íåéòðàëüíîãî ïðîâîäà

j0,40,3Z

N

+=

Îì.

Îïðåäåëèòå ôàçíûå òîêè è òîê â íåéòðàëè.

_________________________________________________________________________________________________

4. Ïðèìåð âûïîëíåíèÿ óïðàæíåíèÿ òðåíèíãà íà óìåíèå ¹4

3 Îïðåäåëåíèå ëèíåéíûõ

òîêîâ ñ ïîìîùüþ ïåðâîãî

çàêîíà Êèðõãîôà

=−−−=−=

j21,82,6j35,226,4III

caabA

=

()

j57,023,821,835,2j2,626,4

−=+−−

;

61,85723,8I

22

A

=+=

;

()

j40,813,6j1911j21,82,6III

bccaC

+=−−−+=−=

;

4340,813,6I

22

C

=+=

;

Àíàëîãè÷íî íàõîäèì

B

I

:

j13,537,4III

abbcB

+−=−=

;

40I

B

=

.

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