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RCDipole RC

I Condensateur .

1

1: .

.

.:

1

UAB UAB=E.

2 2 . qAqB AB

. B A

A qAB qB

3 qAqB

qA=- qB qA+qB=0 :qAqB :qA=- qB.:

. Q

(C)Q=+qA=-qB. 2

A: i>0

i

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(V)u2 4 6 8 10

q (mC)

5

10

15

20

25

i(t) A:

qA(C)t(s)i(t)(A).: :

(I=Cte)

:Aq I. t=

3 :. 2

. I=100A

.

. .

10 :

1086420uAB(V)21,417,112,98,64,30t(s)

0,02140,01710,01290,00860,00430qA(C):

1 qA t .qA=I.t qA.

2 qA=f(uAB) .3 .

O :

qA=K.uABK :K=2,14mF

C

:qA=C.uAB

C :F

: mF=10-3FF=10-6FnF=10-9F

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II . 1

A B 1 2

1 AB 2 AB

AB

1 2

q q q i i i

q C U C Uq C.U

C C C

= + = +

= +=

= +

:n

ii 1

C C=

=

. : .

2 A

BAB AD DB

1 2AB

1 2

1 2

U U U

Q QQU

C C C

1 1 1C C C

= +

= = +

= +

:n

i 1 i

1 1C C=

=

: .III RC .

1 RC R C.

u(t) : :

t0:u(t)=0 t>0:u(t)=E1 :

2t>0:u(t)=-E t0:u(t)=0

2 :

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3.Y1Y2 . 1. 2.

.:

I 1

1 Y1 .

Y1 uDB=E

: 2 Y2

Y2 uC

. t=0 4

2 1 :

CC

duRC u E

dt+ = uC(t) t

RC . :

uR+uC=u u=E.

uR(t)=Ri(t) :dqi(t)dt

=(Cq(t C.u (t)=

Cdu (t)i(t) Cdt

= :

CC C

duRi(t) u (t) E RC u E

dt+ = + =

22 :

xtCu (t) Ae B= + ABx .

xB. :

xt xtCC

duRC u E RC.( Axe ) Ae B E

dt1 1

RC.x 1 xRC

E B 0 B E

+ = + + =

= = =

= =

:

t

Cu (t) Ae E

= +

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uC(0)=0 A. uC(t) t. uC(0)=0 t t=0.uC(t=0+)=uC(t=0-)=0

C

t

C

u (0) A E 0 A E

u (t) E(1 e )

= + = =

=

3 )4(

: .t

Cu (t) E(1 e )

= 3 1 :

: uC(t)

: . .3 2uC(0)uC()uC(t) t4 RC

.= R.C 4 1

. =RC

:

I tdu

i C Cdt V

= =

:

Uu Ri R

i = =

I t U

R.C . tU i

= =

.s : RC .

4 2 R.C.

.=33s RC=33s5 uC(t).5 1 uC(t=)E.

1Cu ( ) E(1 e ) 0,63E

= =

5 2 ..0,63E

5 3 Cdudt

t=0E

.

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c

t 0

dudt

=

uC(t) t=0ct 0

du Et

dt=

=

uC(t) t=ouC=E t=.6 .

RC :

RC

Cdudqi C.dt dt

: = =t

Cu (t) E(1 e )

= RC =:

t tCdudq 1 Ei C. CE(0 e e

dt dt RC R

= = = =

II 21 Y1

. :Ru Ri=

2 Y2 Y2 uC

2(t=0) 5

(uC(0)=E).

2 1 :C

C

duu 0

dt + =

uC(t) t RC RC.

:

R C C

C

CC

u u 0 Ri u 0

dudqi i C

dt dt

duRC u 0dt

+ = + =

= =

+ =

22

:xtCu (t) Ae BxB A+ =

. xB.

:

tEi(t) e

R

=

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xt xtCC

duRC u 0 RC.( Axe ) Ae B 0

dt1 1

RC.x 1 xRC

B 0

+ = + + =

= = =

=

:t

Cu (t) Ae

= uC(0)=E A. uC(t) t.

uC(0)=0 t t=0.uC(t=0+)=uC(t=0-)=E

C

t

C

u (0) A E A E

u (t) Ee

= = =

=

:t

Cu (t) k e

= k.

3 .

:uC(0)-uC()uC(t) t

.uC(0)=E t uC

k.k=E

4 5 .

t=0 .0,37E

6 uC(t) t=5

C

C

u (5 )

u (0)

.

3C

C

u (5 )6,73.10 0,67%

u (0) = =

t=5 .

7 1

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8

:tE

i(t) eR

=

Cdudqi C.

dt dt: = =

t

Cu (t) Ee

=

RC =:t

Cdudq Ei C. edt dt R

= = =

:tE

i(t) eR

=

IV .1

: .

:2 K

.

.

.

2 .

:P Cu .i= Cdudqi C

dt dt: = =

P2c

C C

du d 1C.u Cu

dt dt 2

= =

P2e

e C

d 1Cu K

dt 2

= = +(e(0 0 = Cu (0) K=0=0

:

2e C

1Cu

2 =

RAM

.