diff --git a/06_cicruits_electriques.md b/06_cicruits_electriques.md index 405f7a4e88bf38eaa46801401de7dcdf43be7673..4fa21d7adef233b1ec5f610b3e34bfd422733941 100644 --- a/06_cicruits_electriques.md +++ b/06_cicruits_electriques.md @@ -53,4 +53,64 @@ $$ et donc qu'on peut remplacer les trois résistances par une résistance équivalente (ou nette), où $$ R_\mathrm{eq}=R_1+R_2+R_3. -$$ \ No newline at end of file +$$ + +--- + +Exemple (Trois résistances) # + +Soit une source de tension qui produit un courant continu de $12\V$ et trois +résistances en série de $3\Omega$ chacune connectées au circuit comme sur la @fig:three_res. Quelle est le courant total dans le circuit? + +--- + +--- + +Solution (Trois résistances) # + +Les trois résistances étant connectées en série, ce circuit est équivalent à +un circuit avec une seule résistance de $R=R_1+R_2+R_3=9\Omega$. En utilisant ensuite +la loi d'Ohm on obtient +$$ +I=V/R=12 / 9=4\A. +$$ + +--- + +Une autre façon simple de connecter eds résistances sur un circuit est en **parallèle** (voir @fig:three_res_par). Les charges dans ce circuit suivent +trois chemins différents et donc le courant total, $I$, est séparé en trois parties (pas forcément égales), $I_1$, $I_2$, et $I_3$. +$$ +I=I_1+I_2+I_3. +$${#eq:isum} +Dans ce type de circuit le courant n'est pas interrompu si une des résistances est +déconnectée (dans le cas où un des appareils que la dite résistance représente arrête de fonctionner par exemple). + +{#fig:three_res_par width=50%} + +Quand les résistances sont en parallèle, le voltage qui les traverse doit être le même. +En effet, étant donné qu'on néglige la résistance des fils, deux points connectés +directement entre eux ont le même voltage. Ainsi, on a pour les courants +$$ +I_1=\frac{V}{R_1},\quad +I_2=\frac{V}{R_2},\quad +I_3=\frac{V}{R_3}. +$${#eq:i3} +De plus on sait de la loi d'Ohm, qu'on doit pouvoir remplacer les trois résistances +par une unique résistance équivalent, $R_\mathrm{eq}$, avec +$$ +I=\frac{V}{R_\mathrm{eq}}. +$${#eq:ipar} +En mélangeant les 3 équations ci-dessus (voir @eq:isum, @eq:i3, et @eq:ipar), on obtient +$$ +\frac{V}{R_\mathrm{eq}}= +\frac{V}{R_1}+ +\frac{V}{R_2}+ +\frac{V}{R_3}, +$$ +et on déduit +$$ +\frac{1}{R_\mathrm{eq}}= +\frac{1}{R_1}+ +\frac{1}{R_2}+ +\frac{1}{R_3}. +$$ diff --git a/figs/three_res_par.svg b/figs/three_res_par.svg new file mode 100644 index 0000000000000000000000000000000000000000..87b5916f54e8570c8ca549a876ea6fa6b0dc74dc --- /dev/null +++ b/figs/three_res_par.svg @@ -0,0 +1,457 @@ +<?xml version="1.0" encoding="UTF-8" standalone="no"?> +<!-- Created with Inkscape (http://www.inkscape.org/) --> + +<svg + width="154.19136mm" + height="125.97395mm" + viewBox="0 0 154.19136 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