elect magnet 16

8/2/2019 Elect Magnet 16

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16 16


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22

12. 12.

12.1. 12.1.

12.2. 12.2.

12.3. 12.3.

12.4. 12.4. RLCRLC

12.5. 12.5.


3/27

33

12.1. 12.1.

-- ww

V=V=EE

mmsinsinwwtt EEmm--

, , ff--

, , TT--

22 f

T

w


4/27

44

, ,

, ,

V=vV=vRR==EE

mmsinsinwwtt vvRR--

IImm--

vvRR=I=ImmRsinRsinwwt,t, IImmR=R=EE

mm iiRR vvRR

R

R m

vi sin t I sin t

R Rw w

Em

mIR

Em

V=Emsinwt

vR

R

iR,ImEm

t

iR

vR

vR


5/27

55

1 1

, ,

-- ,,

ImIR

Em

vR

wt


6/27

66

2 2

, ,

Im

Im

iR

wt

wt

Im

t

Em

Em Im


7/27 77

12.2. 12.2.

coscoswwt=t= -- sin(sin(wwtt--/2)/2)

(1)(1)-- , ,

/2/2 9090

--

vvLL

L

V=Emsinwt

vL

L

diV v L sin t ( 1 )dt w E

m

Li sin tdt cos t ( 2 )L L

w ww

Em Em

Li sin( t )L 2

w

w

Em


8/27 88

, , 9090--

di/dtdi/dt-- ~~ vv

LL

ii tt-- di/dtdi/dt(()) iiLL(t)(t)

i=0i=0 vvLL

, ,

Im

iL

vL

iL

t

vL,

Em

Em

Im


9/27 99

XXLL==wwLL (())

ii vv--

9090--

vvLL==EEmmsinsinwwt=It=ImmXXLLsinsinwwtt

XXLL

m

L

IL Xw

Em Em


10/27

1010

12.1 12.1

L=25L=25,,EEmm=150 B=150 B .. a)a) 50 50

..

ww=2=2f=2f=2(50)=314 c(50)=314 c--11

XXLL==wwL=(314 cL=(314 c--11)(25)(251010--33)=7,85)=7,85

)) 5 5 (a)(a)

.. 5 5 ww=3,14=3,14101044 cc--11

XXLL==wwL=785L=785 IImm=0,191 A=0,191 A

m

L

150 B I 19,1 A

X 7,85 Em


11/27

1111

12.3. 12.3.

vvCC

=Q/C=Q/C Q=CQ=CEEmmsinsinwwtt : : i=dQ/dti=dQ/dt

coscoswwt=sin(t=sin(wwt+t+/2)/2) iiCC==wwCCEEmmsin(sin(wwt+t+/2)/2)

, , 9090

V=vV=vCC==EEmmsinsinwwtt vvCC

C

V=Emsinwt

vC

C

dQi C cos t

dtw w Em


12/27

1212

,, 90 90--

XXCC

Im iC vC

iC

t

vC,

Em

Em

Im

m

C

I CX

w EmE

m

C

1X

Cw


13/27

1313

vvCC=I=ImmXXCCsinsinwwtt

XXCC--

EEmm

ww 00


14/27

1414

12.2 12.2 8 8

. . 150 150 , , 50 50 . . . .

:: ww== 22ff == 314 c314 c--11

2 2 XXCC 2 2 2 2

C 1 6

1 1 X 398C ( 314 c )( 8 10 )w

m

C

150 B I 0,377 A

X 398 Em


15/27

1515

12.4. 12.4. RLCRLC

i=Ii=Immsinsinwwtt ff

ff IImm--

R, L, C,R, L, C, 4 4--

:: V=V=EEmmsin(sin(wwt+t+ff))

L

V=Emsinwt

R C


16/27

1616

: :

9090-- 9090--

w

VR Im

90

wwVL

Im ImVC

90


17/27

1717

3 3

vvRR=I=ImmR sinR sinwwt=Vt=VRRsinsinwwtt vvLL=I=ImmXXLLsin(sin(wwt+t+/2)=V/2)=VLL coscoswwtt

vvCC=I=ImmXXCCsin(sin(wwtt--/2)=/2)= -- VVCCcoscoswwtt

VVRR, V, VLL, V, VCC

VVRR=I=Imm R , V R , VLL=I=ImmXXLL, V, VCC=I=ImmXXCC 3 3

V=vV=vRR+v+vLL+v+vCC

IImm

w ImVC

VR

Em

VL


18/27

1818

VVLL--VVCC.... , , VVRR VVRR, V, VLL, V, VCC 33--

EEmm -- IImm ff (( DD))

XXLL==ww L, X L, XCC=1/=1/wwCC

3 3

VVLL VVCC

w ImVC

VR

Em

VLVL-VC

VR

Em

f

2 2 2 2

R L C m m L m C V (V V ) ( I R ) ( I X I X ) Em2 2

m L CI R ( X X ) Em


19/27

1919

EEmm=I=ImmZZ.. EE=IZ=IZ

XXLL XXCC (RL, RC, LC)(RL, RC, LC)-- !!

IImm--

m2 2

L C

IR ( X X )

Em

VL-VC

VR

Em

f

2 2 2 2

L C

1Z R ( X X ) R ( L )

Cw

w


20/27

2020

RLCRLC

,,

: :

: : XXLL>X>XCC(( )) , ,

XXLL


21/27

2121

12.3 12.3 R=250R=250 ,,L=0,6L=0,6,, C=3,5C=3,5,, ww=377=377--11 EEmm=150=150

RLCRLC . .

:: XXLL==wwL=226L=226,, XXCC=1/=1/wwC=758C=758 ..

, ,

, , ff

2 2 2 2

L C Z R ( X X ) ( 250 ) ( 226 758 ) 588 m

150 B I 0,255 A

Z 588 Em

1 1L CX X 226 758tan tan 64,8 R 250

f


22/27

2222

VVRR=I=ImmR=0,255 AR=0,255 A 250250 =63,8 B=63,8 B

VVLL=I=ImmXXLL=0,255 A=0,255 A 226226=57,6 B=57,6 B VVCC=I=ImmXXCC=0,255 A=0,255 A 758758 =193 B=193 B

V=150sinV=150sinwwtt 3 3

vvRR=63,8sin377t B,=63,8sin377t B, vvLL=57,6cos377t B,=57,6cos377t B, vvCC== --193cos377t B193cos377t B

3 3 VVRR+V+VLL+V+VCC=314 B=314 B 150 150

, ,

12 5 12 5


23/27

2323

12.5. 12.5.

--

RLCRLC p=iv=Ip=iv=Immsinsinwwt[Et[Emmsin(sin(wwt+t+ff)]=I)]=ImmEEmmsinsinwwttsin(sin(wwt+t+ff))

sin(sin(wwt+t+ff)=sin)=sinwwtt coscosff+cos+coswwttsinsinff

p=Ip=ImmEEmmsinsin

22wwtt coscosff+I+ImmEEmmsinsinwwtt coscoswwttsinsinff


24/27

2424

p=Ip=ImmEEmmsinsin

22wwttcoscosff+I+ImmEEmmsinsinwwttcoscoswwttsinsinff

IImm

, E, Emm

,, f, wf, w pp--

sinsin22wwtt--

2 2

sinsinwwt cost coswwt=1/2t=1/2 cos2cos2wwtt

1av m2

P I cosf Em

wt

sin

2

wt

0 2

1/2

1


25/27

2525

(root(rootmean squaremean square rms)rms)

vv ii

--

2 2 2

mv sin ( t )w f

2

E

2 2 2 2

av m av m

1( v ) [sin ( t )]

2w f E E

2

rms avV ( v )

2

Em


26/27

2626

220 220 220220=311 B=311 B

PPavav=I=IrmsrmsVVrmsrmscoscosjj coscosjj RLCRLCRR

(( DD)) VVRR=I=ImmR=R=EEmmcoscosff coscosff=V=VRR//EEmm=I=ImmR/ER/Emm

,, LL CC ff=0, cos=0, cosff=1=1 PPavav=I=IrmsrmsVVrmsrms

2

2 mrms av I I ( I )

2

2m mav rms rms rms rms av rms

I R I R P I V cos I I P I R

2 2f

Em

Em


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elect magnet 16

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