e1.py

Created by fatoundira

Created on March 18, 2025

1.46 KB


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intensite : 
  i=q/delta T i en ampere
  i=dq/dt
  q=uc xC
 1) demonstration :
    I=dq/dt =d(Cxuc)/dt
    =dc/dt(=0) xuc+Cxduc/dt
    I=cxduc/dt
    Cas de charge
    dapres loi mailles:
      Ur+Uc-E=0
      =Ur+uc=E or ur=Rxi (loidhom)
      et i=cxduc/dt
      on a alors 
      RxCxduc/dt+uc=E equation diff de la tension uc
2)solution:
  duc/dt=-1/rc xuc +E/rc
  les solutions de lequation diff sont donc 
  uc(t)=Kxexp(-1/rc x t)+E
3)le condensat est initialmt decharche donc uc(o)=0V
uc(0)=Kxexp(-1/rcxt)+E=0
donc K =-E
la solution de lequa diff est uc(t)=-Exexp(-1/rcx0)+E
donc Uc=E(1-exp-1/rcxt)
Decharge
dapres maille 
Ur+uc=0 ur =rxI et I=cxduc/dt
donc RxCxduc/dt+Uc=0
2) duc:dt=-1/rc xuc
lesq sol de lequation diff st 
uc(t)=kxexp(-1/rcxt)
3 dapres les conditions initiale
cas de charge ,le cond est charge
donc U(0)=E
on a alors 
uc(0)=k exp(_1/rcxt)
temp caract:PERMET de detrminer la duree de la charge ou dech dun condensateur
taux t=rxc
delt t=5xtaux (ecart de 1pourcent)
dans le dipole rc initialmt decharge
uc(taux)=E(1-exp(-1/rcxrc))
=E(1-exp(-1))=0,63E
cas decharge
uctaux=Eexp(-1/r'c)
=Eexp-1=0,37E
analyse dimentionnelle:
  ur =rxI dapres ohm u=ur/i
  [R]=v.A-1
  i=cxduc/dt
  [c]=[i]x[dt]/[duc]=A.s.v-1
  donc [taux]=[r]x[c]=v.a-1xsxv-1=S donc homogene
  intensite =debir de charges electriques que ce soit en regome permenant ou var
  iable
  capacité=aptitude dun condensateur a accumuler sur ses armatures un gd nbr de
  charges elec

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