diff options
Diffstat (limited to 'presentation/01-rlc.tex')
| -rw-r--r-- | presentation/01-rlc.tex | 29 |
1 files changed, 22 insertions, 7 deletions
diff --git a/presentation/01-rlc.tex b/presentation/01-rlc.tex index 4854494..106f8b7 100644 --- a/presentation/01-rlc.tex +++ b/presentation/01-rlc.tex @@ -17,7 +17,6 @@ \end{tabular} \end{table} \end{column} - \begin{column}{.5\textwidth} \begin{figure} \includegraphics[width=.7\textwidth]{figure/screenshot-rlc.jpg} @@ -32,7 +31,17 @@ \subsection{À la charge} \begin{frame} \frametitle{Mises en équation de la charge} - \todo{Meth charge RLC} + \begin{align} + V_\mathrm{in}(t) & = V_C(t) + V_R(t) + V_L(t) + \Rightarrow + V_\mathrm{in}^{\prime\prime}(t) = V_L^{\prime\prime}(t) + \frac{R}{L}V_L^{\prime}(t) + \frac{1}{LC}V_L(t) \\ + V_C(0) & = 0;\quad + V_R(0) = 0;\quad + V_L(0) = 12;\quad + I(0) = 0; \\ + V_L(t) & = \e^{-1000t} \left( 12\cos(8516.42t) - 1.41\sin(8516.42t) \right) + \end{align} + \todo{Finish charge RLC} \end{frame} \begin{frame} @@ -63,7 +72,16 @@ \subsection{À la décharge} \begin{frame} \frametitle{Mises en équation de la décharge} - \todo{Meth décharge RLC} + \begin{align} + V_\mathrm{in}(t) & = V_C(t) + V_R(t) + V_L(t) \\ + V_\mathrm{in}(0) & = 0 ;\quad + V_C(0) = 12;\quad + V_R(0) = 0;\quad + I(0) = 0; \\ + V_L^\prime(t) & = -\frac{R}{L}V_L(t) = -\frac{R}{L}12 = + 60\times10^{6} \\ + V_L(t) & = -12 \e^{5\times10^{6}t} + \end{align} \end{frame} \begin{frame} @@ -72,7 +90,7 @@ \begin{column}{0.5\textwidth} \begin{figure} - \includegraphics[width=.9\textwidth]{figure/vl_t_charge.png} + \includegraphics[width=.9\textwidth]{figure/vl_t_decharge.png} \caption{M.E.É. du circuit RLC en décharge} \label{graph:mee-decharge-rlc} \end{figure} @@ -85,10 +103,7 @@ \label{graph:lts-decharge-rlc} \end{figure} \end{column} - - \end{columns} - \todo{Graph Desmos decharge RLC} \todo{Graph LTspice decharge RLC} \end{frame} |