diff --git a/06_cicruits_electriques.md b/06_cicruits_electriques.md index 2855d6791e406f139e7244fa6d8066ccb1536448..405f7a4e88bf38eaa46801401de7dcdf43be7673 100644 --- a/06_cicruits_electriques.md +++ b/06_cicruits_electriques.md @@ -5,4 +5,52 @@ allons décrire les circuits les plus simples ici sans aller dans des cas trop a ## Les résistances en série et en parallèle -Quand deux ou plus \ No newline at end of file +Quand deux résistances ou plus sont connectées bouts à bouts sur un seul chemin +comme sur la @fig:three_res on dit qu'elles sont branchées **en série**. + +{#fig:three_res width=50%} + +Toutes les charges passant par $R_1$ passera aussi par $R_2$ et $R_3$. On +sait donc que le courant sera le même au travers de chaque résistance, +sinon cela impliquerait que les résistances créeraient ou stockeraient des charges +ce qui n'est pas observé dans les circuits +(ou que la conservation de la charge ne serait pas respectée). +Le voltage $V$ (également appelée tension) et on suppose que les fils ont une résistance négligeable (nulle). On a que $V_1$, $V_2$, et $V_3$ sont les différences +de potentiels au travers de chaque résistance. On sait de la loi d'Ohm que +\begin{equation*} +V=RI, +\end{equation*} +et donc +\begin{equation*} +V_1=R_1 I,\quad +V_2=R_2 I,\quad +V_3=R_3 I. +\end{equation*} + +--- + +Question (Conservation) # + +Quelle est la relation entre $V$ et $V_1$, $V_2$, $V_3$? + +--- + +--- + +Réponse (Conservation) # + +L'énergie étant conservée, on a naturellement que +$$ +V=V_1+V_2+V_3. +$$ + +--- + +On déduit de cette relation que +$$ +V=R_1I+R_2I+R_3I=(R_1+R_2+R_3)I, +$$ +et donc qu'on peut remplacer les trois résistances par une résistance équivalente (ou nette), où +$$ +R_\mathrm{eq}=R_1+R_2+R_3. +$$ \ No newline at end of file diff --git a/figs/three_res.svg b/figs/three_res.svg new file mode 100644 index 0000000000000000000000000000000000000000..cb00eb32b470d560f539d2d548047075e95f26c6 --- /dev/null +++ b/figs/three_res.svg @@ -0,0 +1,402 @@ +<?xml version="1.0" encoding="UTF-8" standalone="no"?> +<!-- Created with Inkscape (http://www.inkscape.org/) --> + +<svg + width="146.36209mm" + 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