[Www.devoir.tn] Circuit Rc Rl Rlc Libre 2012 2013(Fethi Affi)

8/17/2019 [Www.devoir.tn] Circuit Rc Rl Rlc Libre 2012 2013(Fethi Affi)

1/42

E C

C ?

i(t)

R1

K

E C uC(t)

2


2/42

E

i(t)

R

C uC(t)

1 2

K

1 C

=0 : 1

C(=0)=0

( ) ( ) R C E u t u t = +

τ τ . ()

C

( )( )C C

du t R C u t E

dt ⋅ ⋅ + =

( ) ( )C C du t u t E

dt τ τ + =


3/42

1 C

( ) ( )C C du t u t E dt τ τ

+ =

=0 : 1

C(=0)=0 E

i(t)

R

C uC(t)

1 2

K

: ( ) ( )expC H t u t K τ = ⋅ −

:

( )C P u t E =

: ( ) ( )expC t u t K E τ

= ⋅ − +

( ) ( )1 expC t u t E τ = − −


4/42


5/42

1 C

C()E0,95.E

=0 : 1

C(=0)=0 E

i(t)

R

C uC(t)

1 2

K

ττττ 3.τ3.τ3.τ3.τ 5.τ5.τ5.τ5.τ

0,63.E

( ) ( )1 expC t u t E τ = − −


6/42

1 C

C()E

ττττ ?

τ=τ=τ=τ=.C

( ) ( )1 expC t u t E τ

= − −


7/42

2 D

=0 : 2

C(=0)=E

( ) ( ) ( ) ( )0 R C C u t u t R i t u t = + = ⋅ +

E

i(t)

R

C uC(t)

1 2

K

( ) ( )0

C C du t u t

dt τ + =

( ) ( )expC t u t E τ

= ⋅ −


8/42

2 D

C()E

i(t)

R

C uC(t)

12

K

E

1

2


9/42


10/42

3 E

E ? E ?

C :

E

i(t)

R

C uC(t)

1

2

K

2

fournie C E = ⋅

21

2 stockée C E = ⋅ ⋅

21

2dissipée E C E = ⋅ ⋅


11/42

3 E

E ? E ?

D :

E

i(t)

R

C uC(t)

1

2

K

21

2 stockée C E = ⋅ ⋅

21

2dissipée C E = ⋅ ⋅


12/42


13/42

A :

100 000 . 24 24 , 60 80 ,

: .

, ' '

( )

' .

'

30


14/42


15/42


16/42

A :

1 : (τ1=.C)

2 :

(τ2=.C >> τ1)

3 : C ,

.

4 :

C


17/42


18/42

A :

//../.11&


19/42

A ?

http://www.psychoweb.fr/news/actualites-de-la-recherche/454-tocs-et-depressions-le-pace-maker-

cerebral-a-foncti.html

http://revue.medhyg.ch/print.php3?sid=30031


20/42

A ?

http://www.lexpress.fr/actualite/sciences/sante/le-pacemaker-du-cerveau_491581.html

http://www.uwhealth.org/news/setting-the-pace-neuropace-pacemaker-for-epilepsy/12893


21/42

A ?


22/42

:

, .

:

( ) )C du t

i t C dt

= ⋅

E , :C=

=0


23/42

E

D ( ) () ( ) ()

E

CuC(t)

R1

R2

Cu t

R2

)

)

1

E

C2u2 (t)

R1 R2

C1u1 (t)

EC2

R2

R1

C1

u2 (t)

u1 (t)

)

)


24/42

E

1, C(C=47 µF) E=4,5 .

2,

.

C

=0 : C=4,5

=200 : C= 3


25/42

E

C

C=47 µF

=0 : C=4,5

=200 : C= 3


26/42


27/42

1 E

( ) ( ) R L E u t u t = + ( ) ( )di t

E R i t Ldt

= ⋅ + ⋅

=0 : 1(=0)=0 A

( )( )

di t R E i t

dt L L+ ⋅ =

ττττ

i t i t E dt Lτ + =

: ( ) ( )exp E t i t K Rτ

= ⋅ − +

( ) ( )1 exp E

t i t R τ = − −

2


28/42

2 A

( ) ( )0 R Lu t u t = + ( ) ( )

0di t

R i t Ldt

= ⋅ + ⋅

=0 : 2(=0)=E/

( )( ) 0

di t Ri t

dt L+ ⋅ =

ττττ

0i t i t dt τ + =

: ( ) ( )exp t i t K τ

= ⋅ −

( ) ( )exp E

t i t R τ = ⋅ −

3 E


29/42

3 E

()

E/ E t

Rτ

−

( ) ( )1 exp E t i t R τ

= − −

3 E


30/42

3 E

() ?

1 : E

( ) ( )

L

di t u t L

dt = ⋅

( ) ( )1 exp t

i t R τ = − −

( )

( )

1 exp 1 exp

1exp exp

L

L

E t t d d

R L E u t L

dt R dt

L E t L E t u t

R R

τ τ

τ τ τ τ

− − − − ⋅ = ⋅ = ⋅

⋅ ⋅ = − ⋅ − ⋅ − = ⋅ −

⋅

( ).

( ) exp Lt

u t E τ

= ⋅ −


31/42

3 E


32/42

3 E

() ?

()

E/

()

E

E


33/42

E C


34/42

E C

C ?

i(t)

RK

E uL(t)

L

C

uC(t)


35/42

E C


36/42

E C

( ( ( )2

2

C C C

d u t du t C RC u t E dt dt

⋅ + ⋅ + =

0 < < 100 ΩΩΩΩ

=100

C=1

E C


37/42

E C

= 100 ΩΩΩΩ ( ) ( )

( )

2

2

C C

C

d u t du t

LC RC u t E dt dt ⋅ + ⋅ + =


38/42

E C


39/42

E C

= 1 ΩΩΩΩ ( ) ( )

( )

2

2

C C

C

d u t du t


E C


40/42

C

= 0 ΩΩΩΩ ( ) ( )

( )

2

2

C C

C

d u t du t



41/42

A E /


42/42

/

( ) ( ) ( )2

2

d q t dq t q t

L R E dt dt C + ⋅ + =

( ) ( )

( )

2

2 0

d x t dx t

m f k x t dt dt ⋅ + ⋅ = ⋅ =

:

:

:

:

: C

: E=1/2..

: E=1/2.C

: =.

:

:

: 1/

: E=1/2..

: E=1/2..

: F=.

[Www.devoir.tn] Circuit Rc Rl Rlc Libre 2012 2013(Fethi Affi)

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