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......@@ -178,4 +178,35 @@ Exercice (Résistances multiples) #
Deux résistances de $100\Omega$ sont connectées en parallèle ou en série sur une batterie de $24\V$. Quel est le courant total dans chaque circuit? Et la résistance équivalente?
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Pour des circuits beaucoup plus compliqués que ceux vus ici, il faut noter qu'il y a un ensemble
de règles qu'on peut appliquer pour déterminer le courant dans un circuit: les **lois de Kirchoff**. On ne va pas les lister ou les étudier ici.
## Les circuits contenant des capacités en parallèle ou en série
Comme les résistances, les capacités peuvent être placée en série ou en parallèle.
Pour le cas parallèle (voir @fig:three_cap_par) chaque capacité est soumise à la même
différence de potentiel $V$. Ainsi les 3 capacités ont les charges
$$
Q_1=C_1 V,\quad Q_2=C_2 V,\quad Q_3=C_3 V.
$$
La conservation de la charge impose que la charge totale sortant de la source de tension
est donnée par
$$
Q=Q_1+Q_2+Q_3.
$$
![Les résistances $C_1$, $C_2$, $C_3$ sont connectées en parallèle à la source $V$ et accumulent les charges $Q_1$, $Q_2$, $Q_3$.](figs/three_cap_par.svg){#fig:three_cap_par width=50%}
Si nous essayons de décrire ce circuit sous forme de circuit équivalent avec une seule capacité,
$$
Q=C_\mathrm{eq}V,
$$
on voit que
\begin{align}
C_\mathrm{eq}V&=Q_1+Q_2+Q_3,\nonumber
C_\mathrm{eq}V&=(C_1+C_2+C_3)V,\nonumber
C_\mathrm{eq}&=C_1+C_2+C_3.
\end{align}
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