Реднo RLC колo

: :

O RLC O

UNIVERSITY OF KRAGUJEVAC FACULTY OF TEHNICAL

SCIENCE

1. ................................................................................................................................ 1

2. RLC ............................................................................. 4

2.1 ................................................... 10

2.2 RLC ............................................................................................................ 11

2.3 RLC ................................................................................ 14

2.4 RLC ............................................................................................. 16

3. .................................................................................................................... 17

RLC -

FIZIKI OSNOVI ELEKTROTEHNIKE 1

1.

- , ( , , ). . , . , , . .

, :

, . . ( 1.) .

RLC -


1 -

2 -

3 -

RLC -


. . , , . .

. . (t) (t). ( 4.)

4 - (t) (t)

RLC -


2. RLC

RLC : , . (eng. R-Resistor, L-Inductor, C-Capacitor). RLC ( 5.). , , , .

5 RLC

(. resistor) , ( 6.). . O . .

6

, .

RLC -


ZR = l

S (1)

. ().

ZR = u(t)

i(t) ZR =[

V

A ] = [ ] (2)

7

iR(t) = Im cos t = 2 I cos t (1) uR(t) = R i(t) = 2 R I cos t (2) ( 7.) :

= (3) = = 0

( = 0 )

(4) :

R ( -)

jXR , ( y-)

ZR = R ( ) (5)

uR = ZR iR (6)

RLC -


( 8.) ( 9.) . :

p = uR(t) iR(t) (7) :

uR = ZR iR iR = uR

ZR (8)

:

p = ZR iR 2

(9)

: p = u

2

ZR (10)

p = [w] = [V A] = [ A2] = [ V2

]

8 9

() . ( 10.). .

10

RLC -


:

L = 0 N2 S

l (11)

:

L = 0 r N2 S

l (12)

:

0 = 4 107 [H

m] ( ) ,

r , N ,

l S . (H).

11 k

uL(t) = L di

dt = - L Im sin t = 2 XL I cos(t +

2) (13)

( 11. ) :

= +

2 (14)

= = +

2 =

2

RLC -


2

(15) :

RL ( )

XL = L ZL = j XL (16)

uL = ZL iL (17)

, ( 12.). ( ) .

12

. ()

q

u .

C =

(18)

(F). , .

:

C = 0 r

(19)

:

RLC -


C = 0 r 2

2

1

(20)

:

C = 0 r 1 2

21 (21)

= 0 r ,

0 = 8,85 10-12 [F

m]

13 k

uL(t) = q(t)

C =

1

C ()

0 =

Im

C sint (22)

uL(t) = 2 cos(t

2 ) (23)

( 13. ) :

= -

2 (24)

= = -

2 = -

2

(25)

RLC -


:

RC

XC = 1

C = - j

1

C

ZL = j XC (26)

uC = ZC iC (27)

2.1

I , :

I = 1

2()

0 (28)

:

I 2 = 1

2()

0 =

1

2() sin2( + 0)

0 (29)

:

I = Im

2 = 0,707 Im (30)

:

U = Um

2 (31)

:

i = 2 I sin( + ) (32)

, . , , , .

RLC -


2.2 RLC

, :

i(t) = Im sin t (33) iR(t) = iL(t) = iC(t) = i(t) (34)

uR ,

uL uC , ( 14.):

14 RLC

u(t) = uR(t) + uL(t) + uC(t) (35)

uR = R i (36)

uL = L di

dt (37)

uC = 1

C

0 (38)

u(t) = R i + L di

dt +

1

C

0 (39)

u(t) = R Im sin t + L Im cos t - 1

C Im cos t (40)

:

u(t) = Um sin (t + ) (41) :

Um sin (t + ) = Um sin t + (ULm UCm) cos t (42)

RLC -


(43)

Um :

a sin ( ) = a sin cos a cos sin (43) Um cos sint+Um sin cost=URm sint+(ULmUCm)cost

:

Um sin = ULm UCm = (L - 1

C) Im (44)

Um cos = R Im (45)

:

Um2 = URm

2 + (ULm UCm)2 (46) (44 45) :

u(t) = R i(t) (47)

(44) , :

(L - )

:

X = XL XC = L - (48) . .

(45) R .

Z . :

15

RLC -


1 RLC

Z = ZR + ZL + ZC (49)

Z = R + jXL - jXC (50)

Z = R + j(XL - XC)

X = XL - XC = L - 1

C - ( )

R

RLC ( 15.) :

(51)

.

: X > 0

;

RLC -


X < 0 .; X = 0,

. . 900 + 900. , .

2.3 RLC

16 RLC

.

(52)

(53)

(54)

(55)

(56)

RLC -


(57)

(58)

(59)

(60)

(61)

(62)

RLC

(63)

(64)

(65)

(66)

RLC -


(67)

2.4 RLC

17 RLC

RLC ( 17.), :

R = R1 + R2 (68)

X = X1 + X2 (69)

Z Z1 + Z2 (70)

1 + 2 (71)

.

RLC -


3.

. ,

. , , 2006.

,

http://en.wikipedia.org/wiki/RLC_circuit

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