From 16252c9aee130d6e224eb89f4bf1c5daef5f89e7 Mon Sep 17 00:00:00 2001
From: Orestis <orestis.malaspinas@pm.me>
Date: Thu, 27 Apr 2023 11:27:55 +0200
Subject: [PATCH] added some exercises
---
exercices/circuits.md | 127 +++++++++++++++++++++
exercices/figs/rc.svg | 205 ++++++++++++++++++++++++++++++++++
exercices/figs/three_cap.svg | 206 +++++++++++++++++++++++++++++++++++
exercices/figs/three_res.svg | 186 +++++++++++++++++++++++++++++++
4 files changed, 724 insertions(+)
create mode 100644 exercices/figs/rc.svg
create mode 100644 exercices/figs/three_cap.svg
create mode 100644 exercices/figs/three_res.svg
diff --git a/exercices/circuits.md b/exercices/circuits.md
index 63027d1..9de6412 100644
--- a/exercices/circuits.md
+++ b/exercices/circuits.md
@@ -46,3 +46,130 @@ Corrigé (Luminosité d'ampoules) #
1. Quand l'interrupteur est fermé, le courant passant dans $C$ est séparé en deux parties égales pour passer dans $A$ et $B$, car leurs résistances sont égales. Ainsi, $A$ et $B$ auront la même luminosité, mais brilleront moins que $C$ qui a un courant plus important.
2. Quand on ouvre l'interrupteur, l'ampoule $A$ ne sera plus alimentée en courant. On a donc que le courant passera uniquement par $B$ et le circuit sera équivalent à avoir uniquement deux ampoules en série. La résistance équivalente de ce circuit ($=2R$) sera plus grande que celle du circuit avec l'interrupteur fermé ($=3R/2$). Ainsi en fermant l'interrupteur on diminue le courant sortant de la batterie passant par $C$ qui sera moins lumineuse. En revanche, $B$ va recevoir plus de courant que dans le cas où l'interrupteur est fermé. Elle brillera donc plus. Aussi comme $C$ et $B$ ont la même résistance, elles auront la même luminosité.
+---
+
+Exercice (Résistances équivalentes) #
+
+Soit le circuit de la @fig:three_res. Quel est le courant sortant de la batterie?
+
+{#fig:three_res width=50%}
+
+Corrigé (Résistances équivalentes) #
+
+Les résistances de $8\Omega$ et $4\Omega$ sont en parallèle et donc leur résistance équivalente se calcule comme
+$$
+\frac{1}{R_\mathrm{eq1}}=\frac{1}{8}+\frac{1}{4}=\frac{3}{8},\Leftrightarrow R_\mathrm{eq1}=\frac{8}{3}\Omega.
+$$
+Ensuite il nous reste deux résistances en série, et il vient
+$$
+R_\mathrm{eq}=6+\frac{8}{3}=\frac{26}{3}\Omega.
+$$
+Finalement, on utilise la loi d'Ohm
+$$
+V=R_\mathrm{eq}I\Leftrightarrow I=\frac{V}{R_\mathrm{eq}}=3\mathrm{A}.
+$$
+
+---
+
+Exercice (Capacités équivalentes) #
+
+1. Déterminer la capacité d'un condensateur unique qui aurait le même effet que la combinaison de la @fig:three_cap. Prendre $C_1=C_2=C_3=C$.
+2. Si on suppose $V$ et $C$ connus. Que vaut la charge dans chaque condensateur?
+3. Si on suppose $V$ et $C$ connus. Que vaut le voltage dans chaque condensateur?
+
+{#fig:three_cap width=50%}
+
+Corrigé (Capacités équivalentes) #
+
+1. On commence par calculer la capacité équivalente de $C_2$ et $C_3$ qui sont en parallèle et on obtient
+$$
+C_{23}=C_2+C_3=2C.
+$$
+Ensuite $C_{23}$ est en série avec $C_1$ en on as
+$$
+\frac{1}{C_\mathrm{eq}}=\frac{1}{C_1}+\frac{1}{C_{23}}=\frac{3}{2C},\Leftrightarrow C_\mathrm{eq}=\frac{2}{3}C.
+$$
+2. La charge totale quittant la batterie est donnée par la relation
+$$
+Q=C_\mathrm{eq}V=\frac{2CV}{3}.
+$$
+Les capacités $C_2$, et $C_3$ étant les mêmes, on a que $Q_2=Q_3$ et que ces charges sont la moitié de $Q$ (la charge est séparée de manière égale entre les deux condensateurs car ils ont la même capacité). La conservation de la charge fait que la charge dans $C_1$ est $Q$. On a donc à la fin que $Q_1=Q$, et $Q_2=Q_3=Q/2$.
+
+En utilisant l'équaiton $Q=C\cdot V$ sur chacune des charges on a donc
+\begin{align}
+V_1&=\frac{Q_1}{C_1}=\frac{Q}{C}=\frac{2V}{3},\\
+V_2&=\frac{Q_2}{C_2}=\frac{Q}{2C}=\frac{V}{3},\\
+V_3&=\frac{Q_3}{C_3}=\frac{Q}{2C}=\frac{V}{3}.
+\end{align}
+
+---
+
+Exercice (Décharge de circuit RC) #
+
+Soit un condensateur a une capacité $C$ chargée et est connecté à une résistance $R$ comme dans la @fig:rc qui a une tension $V_0$.
+
+{#fig:rc width=50%}
+
+Quelle est la durée $t$ nécessaire pour que le condensateur voit sa tension baisser à $10\%$ de la tension initiale?
+
+Corrigé (Décharge de circuit RC) #
+
+La décroissance de la tension dans le condensateur est donnée par
+$$
+V_C(t)=V_0e^{-\frac{t}{RC}}.
+$$
+On cherche $t$ tel que
+$$
+V_C(t)=0.1V_0.
+$$
+On obtient
+\begin{align}
+&V_0e^{-\frac{t}{RC}}=0.1V_0,\nonumber\\
+&e^{-\frac{t}{RC}}=0.1,\nonumber\\
+&-\frac{t}{RC}=\ln{0.1}=-2.3,\nonumber\\
+&t=-2.3RC.
+\end{align}
+
+---
+
+Exercice (Sèche-linge) #
+
+Soit un sèche linge dont le la résistance est de $10\Omega$.
+
+1. Quel est le courant passant dans la résistance, si la machine à laver est branchée à une tension de $230\mathrm{V}$?
+2. Combien de charges passent en $60\mathrm{min}$?
+
+Corrigé (Sèche-linge) #
+
+De la loi d'Ohm on a que
+$$
+I=\frac{V}{R}=\frac{230}{10}=23\mathrm{A}.
+$$
+On sait que $I=\Delta Q/\Delta t$, avec $\Delta t=3600\mathrm{s}$. On a donc
+$$
+\Delta Q=23\cdot 3600\mathrm{C}.
+$$
+
+---
+
+Exercice (Chauffage) #
+
+Un chauffage est connecté à une source de tension alternative de $V_\mathrm{rms}=240\mathrm{V}$. Sa résistance est de $60\Omega$.
+
+1. Quelle est la puissance moyenne utilisée?
+2. Quelles sont les valeurs de puissance minimale et maximale?
+
+Corrigé (Chauffage) #
+
+En utilisant les différentes formules du cours, on a
+
+1. La moyenne de la puissance est donnée par
+$$
+\overline{P}=\frac{V_\mathrm{rms}^2}{R}=\frac{240^2}{60}\mathrm{W}.
+$$
+2. La puissance minimale est nulle (en effet il y a des moments où la tension est nulle). La puissance maximale étant donnée par
+$$
+P_\mathrm{max}=\frac{V_0^2}{R}=\frac{(\sqrt{2}V_\mathrm{rms})^2}{R}=2\frac{V_\mathrm{rms}^2}{R}=2\overline{P}.
+$$
+
+---
diff --git a/exercices/figs/rc.svg b/exercices/figs/rc.svg
new file mode 100644
index 0000000..7330ff9
--- /dev/null
+++ b/exercices/figs/rc.svg
@@ -0,0 +1,205 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+ width="146.36209mm"
+ height="83.975021mm"
+ viewBox="0 0 146.36209 83.975021"
+ version="1.1"
+ id="svg626"
+ inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+ sodipodi:docname="rc.svg"
+ xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+ xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+ xmlns="http://www.w3.org/2000/svg"
+ xmlns:svg="http://www.w3.org/2000/svg">
+ <sodipodi:namedview
+ id="namedview628"
+ pagecolor="#ffffff"
+ bordercolor="#666666"
+ borderopacity="1.0"
+ inkscape:showpageshadow="2"
+ inkscape:pageopacity="0.0"
+ inkscape:pagecheckerboard="0"
+ inkscape:deskcolor="#d1d1d1"
+ inkscape:document-units="mm"
+ showgrid="false"
+ inkscape:zoom="1.551655"
+ inkscape:cx="426.64123"
+ inkscape:cy="135.98384"
+ inkscape:window-width="1920"
+ inkscape:window-height="1007"
+ inkscape:window-x="0"
+ inkscape:window-y="0"
+ inkscape:window-maximized="1"
+ inkscape:current-layer="layer1" />
+ <defs
+ id="defs623" />
+ <g
+ inkscape:label="Layer 1"
+ inkscape:groupmode="layer"
+ id="layer1"
+ transform="translate(-34.725612,-104.02868)">
+ <g
+ id="g2402">
+ <g
+ id="g745"
+ style="stroke-width:4.44992;stroke-dasharray:none"
+ transform="matrix(0.22472321,0,0,0.22472321,85.284846,83.474005)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:4.44992;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 41.58549,162.58447 9.950702,-17.17818"
+ id="path649"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:4.44992;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 71.25275,179.69249 51.38999,145.28918"
+ id="path649-6" />
+ </g>
+ <g
+ id="g745-7"
+ transform="matrix(0.22472321,0,0,0.22472321,94.180614,83.474005)"
+ style="stroke-width:4.44992;stroke-dasharray:none">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:4.44992;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 31.673432,179.8096 19.86276,-34.40331"
+ id="path649-5" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:4.44992;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 71.25275,179.69249 51.38999,145.28918"
+ id="path649-6-3" />
+ </g>
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 119.03967,123.85006 2.24069,-3.85159"
+ id="path649-5-3"
+ sodipodi:nodetypes="cc" />
+ <g
+ id="g745-5"
+ transform="matrix(0.22472321,0,0,0.22472321,103.04972,83.474005)"
+ style="stroke-width:4.44992;stroke-dasharray:none">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:4.44992;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 31.673432,179.8096 19.86276,-34.40331"
+ id="path649-62" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:4.44992;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 71.25275,179.69249 51.38999,145.28918"
+ id="path649-6-9" />
+ </g>
+ </g>
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 121.26207,120.00262 h 27.77826"
+ id="path835-0"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 155.78208,120.00262 h 25.14204"
+ id="path835-0-29"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 34.928773,120.00262 h 5.392054"
+ id="path835-9" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 66.923999,120.00262 H 94.643317"
+ id="path835-0-2"
+ sodipodi:nodetypes="cc" />
+ <g
+ id="g2379"
+ transform="translate(36.328673,-7.7638427)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 68.182175,195.76755 V 178.29166"
+ id="path297" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 75.070441,191.47103 v -8.88285"
+ id="path297-3"
+ sodipodi:nodetypes="cc" />
+ </g>
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 111.75628,179.26576 H 181.0877"
+ id="path2406"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 34.999453,179.26576 H 104.33087"
+ id="path2406-1"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 180.58094,179.58366 V 119.59291"
+ id="path2406-9"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 35.225612,179.53023 V 119.53948"
+ id="path2406-9-3"
+ sodipodi:nodetypes="cc" />
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="113.56507"
+ y="175.52403"
+ id="text2558-3-4"><tspan
+ sodipodi:role="line"
+ id="tspan2556-6-7"
+ style="stroke-width:0.264583"
+ x="113.56507"
+ y="175.52403">V<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2560-1-4" /></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="101.9148"
+ y="111.79266"
+ id="text2558-9"><tspan
+ sodipodi:role="line"
+ id="tspan2556-4"
+ style="stroke-width:0.264583"
+ x="101.9148"
+ y="111.79266">R<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2679" /></tspan></text>
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 39.879896,119.99876 67.4,112.62477"
+ id="path630" />
+ <circle
+ style="fill:#ffffff;stroke:#000000;stroke-width:1;stroke-linecap:square;stroke-dasharray:none"
+ id="path1244"
+ cx="67.314163"
+ cy="112.58821"
+ r="1.1891615" />
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="139.82135"
+ y="116.10652"
+ id="text2558-9-3"><tspan
+ sodipodi:role="line"
+ id="tspan2556-4-67"
+ style="stroke-width:0.264583"
+ x="139.82135"
+ y="116.10652">C<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2679-5" /></tspan></text>
+ <g
+ id="g926-7"
+ transform="translate(65.095003,61.442884)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 84.167369,67.297681 V 49.821791"
+ id="path297-36-3" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 91.055635,67.297681 V 49.821791"
+ id="path297-7-6" />
+ </g>
+ </g>
+</svg>
diff --git a/exercices/figs/three_cap.svg b/exercices/figs/three_cap.svg
new file mode 100644
index 0000000..af41b8e
--- /dev/null
+++ b/exercices/figs/three_cap.svg
@@ -0,0 +1,206 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+ width="146.36209mm"
+ height="121.28944mm"
+ viewBox="0 0 146.36209 121.28944"
+ version="1.1"
+ id="svg7057"
+ inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+ sodipodi:docname="three_cap.svg"
+ xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+ xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+ xmlns="http://www.w3.org/2000/svg"
+ xmlns:svg="http://www.w3.org/2000/svg">
+ <sodipodi:namedview
+ id="namedview7059"
+ pagecolor="#ffffff"
+ bordercolor="#666666"
+ borderopacity="1.0"
+ inkscape:showpageshadow="2"
+ inkscape:pageopacity="0.0"
+ inkscape:pagecheckerboard="0"
+ inkscape:deskcolor="#d1d1d1"
+ inkscape:document-units="mm"
+ showgrid="false"
+ inkscape:zoom="0.83812363"
+ inkscape:cx="119.31414"
+ inkscape:cy="95.451312"
+ inkscape:window-width="1920"
+ inkscape:window-height="1007"
+ inkscape:window-x="0"
+ inkscape:window-y="0"
+ inkscape:window-maximized="1"
+ inkscape:current-layer="layer1" />
+ <defs
+ id="defs7054" />
+ <g
+ inkscape:label="Layer 1"
+ inkscape:groupmode="layer"
+ id="layer1"
+ transform="translate(-14.382133,-47.217929)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 77.567021,111.44339 H 122.98959"
+ id="path835-0"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 154.84771,85.501417 h 5.17978"
+ id="path835-0-4"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 28.317521,58.559736 H 72.04454"
+ id="path835-0-0"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 79.221531,58.559736 H 122.94854"
+ id="path835-0-0-7"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 15.156308,85.501417 H 29.104763"
+ id="path835-0-7"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 122.33163,85.501417 h 25.35133"
+ id="path835-0-7-7"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 28.286946,111.44339 H 70.057228"
+ id="path835-0-2"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 84.167369,168.50737 V 151.03148"
+ id="path297" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 91.055635,164.21085 V 155.328"
+ id="path297-3"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 91.412801,159.76942 H 160.74422"
+ id="path2406"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 14.655974,159.76942 H 83.987391"
+ id="path2406-1"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 160.23746,160.08732 V 85.003268"
+ id="path2406-9"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 14.882133,160.03389 V 85.004231"
+ id="path2406-9-3"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 28.779108,111.61159 V 58.207933"
+ id="path2406-9-3-3"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 122.5045,111.57761 V 58.173952"
+ id="path2406-9-3-3-5"
+ sodipodi:nodetypes="cc" />
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="135.96272"
+ y="81.811836"
+ id="text2558"><tspan
+ sodipodi:role="line"
+ id="tspan2556"
+ style="stroke-width:0.264583"
+ x="135.96272"
+ y="81.811836">C<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2560">1</tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="93.221596"
+ y="156.02769"
+ id="text2558-3-4"><tspan
+ sodipodi:role="line"
+ id="tspan2556-6-7"
+ style="stroke-width:0.264583"
+ x="93.221596"
+ y="156.02769">V<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2560-1-4" /></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="57.93293"
+ y="107.69395"
+ id="text2558-9"><tspan
+ sodipodi:role="line"
+ id="tspan2556-4"
+ style="stroke-width:0.264583"
+ x="57.93293"
+ y="107.69395">C<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2679">2</tspan></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="57.93293"
+ y="54.880238"
+ id="text2558-8"><tspan
+ sodipodi:role="line"
+ id="tspan2556-45"
+ style="stroke-width:0.264583"
+ x="57.93293"
+ y="54.880238">C<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2681">3</tspan></tspan></text>
+ <g
+ id="g926"
+ transform="translate(-11.944105)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 84.167369,67.297681 V 49.821791"
+ id="path297-36" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 91.055635,67.297681 V 49.821791"
+ id="path297-7" />
+ </g>
+ <g
+ id="g926-9"
+ transform="translate(63.528075,26.941681)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 84.167369,67.297681 V 49.821791"
+ id="path297-36-1" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 91.055635,67.297681 V 49.821791"
+ id="path297-7-2" />
+ </g>
+ <g
+ id="g926-7"
+ transform="translate(-13.758489,52.883654)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 84.167369,67.297681 V 49.821791"
+ id="path297-36-0" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 91.055635,67.297681 V 49.821791"
+ id="path297-7-9" />
+ </g>
+ </g>
+</svg>
diff --git a/exercices/figs/three_res.svg b/exercices/figs/three_res.svg
new file mode 100644
index 0000000..c6b2ed2
--- /dev/null
+++ b/exercices/figs/three_res.svg
@@ -0,0 +1,186 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+ width="146.39714mm"
+ height="122.70409mm"
+ viewBox="0 0 146.39714 122.70409"
+ version="1.1"
+ id="svg626"
+ inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+ sodipodi:docname="three_res.svg"
+ xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+ xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+ xmlns="http://www.w3.org/2000/svg"
+ xmlns:svg="http://www.w3.org/2000/svg">
+ <sodipodi:namedview
+ id="namedview628"
+ pagecolor="#ffffff"
+ bordercolor="#666666"
+ borderopacity="1.0"
+ inkscape:showpageshadow="2"
+ inkscape:pageopacity="0.0"
+ inkscape:pagecheckerboard="0"
+ inkscape:deskcolor="#d1d1d1"
+ inkscape:document-units="mm"
+ showgrid="true"
+ inkscape:zoom="1.0971858"
+ inkscape:cx="272.51538"
+ inkscape:cy="268.86968"
+ inkscape:window-width="1920"
+ inkscape:window-height="1007"
+ inkscape:window-x="0"
+ inkscape:window-y="0"
+ inkscape:window-maximized="1"
+ inkscape:current-layer="layer1">
+ <inkscape:grid
+ type="xygrid"
+ id="grid667"
+ originx="0.001054"
+ originy="38.729068" />
+ </sodipodi:namedview>
+ <defs
+ id="defs623" />
+ <g
+ inkscape:label="Layer 1"
+ inkscape:groupmode="layer"
+ id="layer1"
+ transform="translate(-34.724558,-65.29961)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 108.69524,107.42845 V 79.650194"
+ id="path835-0"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 108.21659,107.01906 h 13.85549"
+ id="path835-0-9-3"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 147.96102,107.01906 h 13.85549"
+ id="path835-0-9-3-6"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 148.05052,80.089454 h 13.85549"
+ id="path835-0-9-3-1"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 161.45466,107.42845 V 79.650194"
+ id="path835-0-28"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 94.010276,93.539324 H 108.6853"
+ id="path835-0-02"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 161.12156,93.539324 h 19.99542"
+ id="path835-0-02-2"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 34.724558,93.539324 H 68.124627"
+ id="path835-0-2"
+ sodipodi:nodetypes="cc" />
+ <g
+ id="g2379"
+ transform="translate(36.328673,-7.7638427)">
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 68.182175,195.76755 V 178.29166"
+ id="path297" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 75.070441,191.47103 v -8.88285"
+ id="path297-3"
+ sodipodi:nodetypes="cc" />
+ </g>
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 111.75628,179.26576 H 181.0877"
+ id="path2406"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 34.999453,179.26576 H 104.53744"
+ id="path2406-1"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 35.225612,179.53023 V 93.212858"
+ id="path2406-9-3"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 180.6217,179.70109 V 93.090897"
+ id="path2406-9-3-7"
+ sodipodi:nodetypes="cc" />
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+ x="113.56507"
+ y="175.52403"
+ id="text2558-3-4"><tspan
+ sodipodi:role="line"
+ id="tspan2556-6-7"
+ style="stroke-width:0.264583"
+ x="113.56507"
+ y="175.52403">26 V<tspan
+ style="font-size:65%;baseline-shift:sub"
+ id="tspan2560-1-4" /></tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;line-height:0;font-family:'Standard Symbols PS';-inkscape-font-specification:'Standard Symbols PS, Normal';font-variant-ligatures:normal;font-variant-caps:normal;font-variant-numeric:normal;font-variant-east-asian:normal;letter-spacing:0px;stroke-width:0.264583"
+ x="74.207596"
+ y="85.178001"
+ id="text1070-1"><tspan
+ sodipodi:role="line"
+ id="tspan1068-0"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;font-family:'Standard Symbols PS';-inkscape-font-specification:'Standard Symbols PS, Normal';font-variant-ligatures:normal;font-variant-caps:normal;font-variant-numeric:normal;font-variant-east-asian:normal;stroke-width:0.264583"
+ x="74.207596"
+ y="85.178001">6W</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;line-height:0;font-family:'Standard Symbols PS';-inkscape-font-specification:'Standard Symbols PS, Normal';font-variant-ligatures:normal;font-variant-caps:normal;font-variant-numeric:normal;font-variant-east-asian:normal;letter-spacing:0px;stroke-width:0.264583"
+ x="128.2363"
+ y="72.559753"
+ id="text1070-2"><tspan
+ sodipodi:role="line"
+ id="tspan1068-06"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;font-family:'Standard Symbols PS';-inkscape-font-specification:'Standard Symbols PS, Normal';font-variant-ligatures:normal;font-variant-caps:normal;font-variant-numeric:normal;font-variant-east-asian:normal;stroke-width:0.264583"
+ x="128.2363"
+ y="72.559753">8W</tspan></text>
+ <text
+ xml:space="preserve"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;line-height:0;font-family:'Standard Symbols PS';-inkscape-font-specification:'Standard Symbols PS, Normal';font-variant-ligatures:normal;font-variant-caps:normal;font-variant-numeric:normal;font-variant-east-asian:normal;letter-spacing:0px;stroke-width:0.264583"
+ x="128.4498"
+ y="120.36523"
+ id="text1070-15"><tspan
+ sodipodi:role="line"
+ id="tspan1068-5"
+ style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:10.5833px;font-family:'Standard Symbols PS';-inkscape-font-specification:'Standard Symbols PS, Normal';font-variant-ligatures:normal;font-variant-caps:normal;font-variant-numeric:normal;font-variant-east-asian:normal;stroke-width:0.264583"
+ x="128.4498"
+ y="120.36523">4W</tspan></text>
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 108.25653,80.089454 h 13.85549"
+ id="path835-0-9-3-2"
+ sodipodi:nodetypes="cc" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="M 67.826791,97.497549 V 89.392648 H 94.31333 v 8.013885 H 67.910402"
+ id="path3873" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 121.83207,84.187412 v -8.104901 h 26.48654 v 8.013885 h -26.40293"
+ id="path3873-1" />
+ <path
+ style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1"
+ d="m 121.93377,111.11702 v -8.1049 h 26.48654 v 8.01388 h -26.40293"
+ id="path3873-2" />
+ </g>
+</svg>
--
GitLab