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Diffstat (limited to 'annexe')
| -rw-r--r-- | annexe/main.tex | 24 |
1 files changed, 12 insertions, 12 deletions
diff --git a/annexe/main.tex b/annexe/main.tex index 072e927..b094801 100644 --- a/annexe/main.tex +++ b/annexe/main.tex @@ -163,21 +163,21 @@ \subsection{Décharge} \begin{gather*} \begin{align} - 0 & = \vlt + V_C(t) + V_R(t) \\ + 0 & = \vlt + V_C(t) + V_R(t) \\ \label{eq:rlc_decharge_initial} - 0 & = \vlt+\frac{1}{C}\int I_(t)\dt + R_I(t) \\ - 0 & = \ddt{2}\left[ \vlt + \frac{1}{LC}\iint\vlt\dt^2 + \frac{R}{L}\ddt{} \vlt \right] \\ - 0 & = \ddt{2}\vlt+ \frac{R}{L}\ddt{}\vlt +\frac{1}{LC}\vlt \\ - 0 & = \ddt{2}+\vlt+2\al\ddt{}\vlt+\ws \\ - \nonumber\text{Posons que: } + 0 & = \vlt+\frac{1}{C}\int I_(t)\dt + R_I(t) \\ + 0 & = \ddt{2}\left[ \vlt + \frac{1}{LC}\iint\vlt\dt^2 + \frac{R}{L}\ddt{} \vlt \right] \\ + 0 & = \ddt{2}\vlt+ \frac{R}{L}\ddt{}\vlt +\frac{1}{LC}\vlt \\ + 0 & = \ddt{2}+\vlt+2\al\ddt{}\vlt+\ws \\ + \nonumber \text{Posons que: } & \vlt=Ae^{\la t} \Rightarrow \ddt{}\vlt=\la Ae^{\la t} \Rightarrow - \ddt{2}\vlt=\la^{2}Ae^{\la t} \\ - 0 & = \la^2Ae^{\la t} +2\al Ae^{\la t} + \ws Ae^{\la t} \\ - 0 & = Ae^{\la t} \left(\la^2 +2\al\la+\ws \right) \\ - 0 & = \la^2 +2\al\la+\ws \\ - \la_{1,2} & = \frac{-2\al\pm\sqrt{(-2\al)^2-4\ws}}{2(-2\al)} \\ - \la_{1,2} & = -\al\pm\sqrt{\al^2-\ws} + \ddt{2}\vlt=\la^{2}Ae^{\la t} \\ + 0 & = \la^2Ae^{\la t} +2\al Ae^{\la t} + \ws Ae^{\la t} \\ + 0 & = Ae^{\la t} \left(\la^2 +2\al\la+\ws \right) \\ + 0 & = \la^2 +2\al\la+\ws \\ + \la_{1,2} & = \frac{-2\al\pm\sqrt{(-2\al)^2-4\ws}}{2(-2\al)} \\ + \la_{1,2} & = -\al\pm\sqrt{\al^2-\ws} \end{align} \end{gather*} Puisque $R$ est de l'ordre des \si{\kohm} et $L$ de l'ordre des \SI{}{\mH}, on peut déterminer |