From b0a101640711d281082ebc92c30fe030a1f7820a Mon Sep 17 00:00:00 2001
From: Benjamin Chausse <benjamin@chausse.xyz>
Date: Tue, 3 Dec 2024 03:00:33 -0500
Subject: More stuff done

---
 presentation/01-rlc.tex | 29 ++++++++++++++++++++++-------
 1 file changed, 22 insertions(+), 7 deletions(-)

(limited to 'presentation/01-rlc.tex')

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}
 
-- 
cgit v1.2.3

