poly_circuit_rc

# poly_circuit_rc - Montage Montage Original EC3 – C ircuit...

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Unformatted text preview: Montage Montage Original : EC3 – C ircuit RC soumis à un échelon de tension Evolution de La tension e(t) d’alimentation : i(t) e(t) Modification du circuit e(t) Modification du circuit GBF E TRANSITOIRE t = 0- Régime PERMANENT t = t0- t=0 Régime TRANSITOIRE R C C uC(t) Ainsi :  i(0-) = 0  uC(0-) = 0 τ RC t = t0 Régime TRANSITOIRE = Régime LIBRE R e(t)=0 C E du C (t ) + u C (t ) = E dt C uC(t) Equation : Ainsi :  i(t0-) = 0  uC(t0-) = E τ RC Régime PERMANENT Schéma équivalent : i(t) i(t) Schéma : Résolution : uC(t) R e(t)=0 du C (t ) + u C (t ) = 0 dt C duC (t ) + uC (t ) = 0 avec τ = RC dt uC(t) Ainsi :  i(+∞) = 0  uC(+∞) = 0 Résolution : SSM C (t ) + u PART C (t ) = E + λe −t uC (t ) = uCSSM (t ) + uCPART (t ) = 0 + λ ′e τ CI : u C ( 0 + ) = u C ( 0 − ) = 0 = E + λ CI : u C ( 0 + ) = u C ( 0 − ) = Ee (car la tension est continue dans un C) Evolution des tensions t R uC(t) duC (t ) + uC (t ) = E avec τ = RC dt uC ( t ) = u uC(t) t = t0+ Schéma équivalent : i(t) R E Equation : Régime PERMANENT i(t) Schéma : C TRANSITOIRE t = 0+ Schéma équivalent : i(t) e(t)=0 R ( ⇒ ∀t ∈ 0,t 0 , uC (t ) = E 1 − e −t τ ) −t 0 τ −t τ = λ′ (car la tension est continue dans un C) −(t −t 0 ) ⇒ ∀t ∈ t 0 , +∞ , uC (t ) = Ee E τ 95% 95%E e(t) 63%E 63%E 0 Evolution du courant E/R 0 i (t ) = C t 5 %E τ i(t)  TENSION CONTINUE 37% 37%E uC(t) 2τ 37%× 37%×E/R duC (t ) CE −t τ E −t = e = i (t ) = e τ dt τ R 3τ t0 t0+τ t0+2τ 5%×E/R t0+3τ  COURANT DISCONTINU -E/R i (t ) = C duC (t ) −E −(t −t = i (t ) = e dt R 0 ) τ t ...
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