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weird mathscr P_R full 2

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Vincent
2024-10-28 17:02:41 +01:00
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Physique1A/Physique_1A_04_C_RT.markdown
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@@ -604,6 +604,7 @@ $\Leftrightarrow \mathscr{P}_L(t) = L\left(\dfrac{E}{L}e^{-\frac{Rt}{L}}\right)\
$\Leftrightarrow \mathscr{P}_L(t) = \dfrac{E^2}{R}\left(e^{-\frac{Rt}{L}} - e^{-\frac{2Rt}{L}}\right)$
Donc $\mathscr{P}_{out}(t) =\mathscr{P}_R(t) + \mathscr{P}_L(t)$
$\Leftrightarrow \mathscr{P}_{out}(t) = \dfrac{E^2}{R}\left(1 - 2e^{-\frac{Rt}{L}} + e^{-\frac{2Rt}{L}}\right) + \dfrac{E^2}{R}\left(e^{-\frac{Rt}{L}} - e^{-\frac{2Rt}{L}}\right)$
$\Leftrightarrow \mathscr{P}_{out}(t) = \dfrac{E^2}{R}\left(1 - e^{-\frac{Rt}{L}}\right) = \mathscr{P}_{in}(t)$