circuit_rlc.py

Created by famille-bvc

Created on May 19, 2022

917 Bytes


R = 10 Ω, E = 1Vet C = 10μF

   ___.     
   |   \__R__>__.____
   |  .         | ^
  ^|  |         | |
Ve|O  |         C | V
   |  |         | |
   |  |         | 
   -------------.----

La tension appliquée à t=0 est 
un échelon de tension Ve = 0 
si t<0 et Ve = E si t0

La résistance interne du 
générateur est nulle. La tension 
aux bornes du condensateur est
nulle : V = V0 = 0

Ecrire la loi dOhm, et déterminer
léquation différentielle en V, 
tension aux bornes du condensateur.

1) Ri + V = Ve      i=dQ/dt
et Q = CU donc i=c* dv/dt
=> RC*(dv/dt) + (1/RC)*V = Ve = E

2)(E) dv/dt + (1/RC)V = E/RC

(E0) dv/dt + (1/RC)V = 0

Vh = ke(-t/RC)

Vp = ERC/RC = E
              _
Donc V = Vh + V = ke(-t/RC) +E
or v(0) = 0 donc k+E=0 et k=-E

d'où v(t)=E*(1-e(-t/RC))

application numérique :
  
v(t) = 1(1-e(-t/10*10*10^-6))
     = 1-e(-10^4)
     
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