electricite-2nde.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Prog officiel : Représenter et exploiter la caractéristique d’un dipôle \n",
    "## Représenter un nuage de points associé à la caractéristique d’un dipôle et modéliser la caractéristique de ce dipôle à l’aide d’un langage de programmation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lire ma doc : [modelisation graphique](modelisation-graphique.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On exploite les mesures de tension aux bornes d'un conducteur ohmique de résistance R = 470 ohms, en fonction de l'intensité I qui le traverse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# tension en V\n",
    "U = np.array([0.5, 0.9, 1.4, 1.9, 2.4, 2.8, 3.3, 3.8, 4.2]) \n",
    "# intensité en mA\n",
    "I = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
    "I = I / 1000 # conversion en A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### La loi d'Ohm nous dit que U est proportionnelle à I : U = R I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R = 470.87719302743864 ohms\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# définition de la fonction modèle\n",
    "def loi_ohm(I, R):\n",
    "    \"\"\" Loi d'Ohm \"\"\"\n",
    "    U = R * I\n",
    "    return U\n",
    "\n",
    "# modélisation : recherche des paramètres optimisés du modèle (cf ma doc sur python scientifique)\n",
    "parametres = curve_fit(loi_ohm, I, U)[0]\n",
    "\n",
    "R = parametres[0] # il n'y a qu'un seul paramètre dans la modélisation ici\n",
    "print(f'R = {R} ohms')\n",
    "\n",
    "# calcul des ordonnées avec la fonction du modèle et les paramètres optimisés\n",
    "U_model = loi_ohm(I, R)\n",
    "\n",
    "# tracé des graphes des données à modéliser et de la fonction modèle optimisée\n",
    "plt.plot(I, U, 'rp') # valeurs expérimentales : points rouges\n",
    "plt.plot(I, U_model, 'b') # courbe modélisée en bleu\n",
    "\n",
    "plt.title(\"Caractéristique tension-courant \\nd'un conducteur ohmique\")\n",
    "plt.xlabel('I (A)')\n",
    "plt.ylabel('U (V)')\n",
    "plt.text(.001, 3.75, f'R = {R:.0f} ohms')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### On exploite les mesures de tension aux bornes d'une pile de fem E = 4,5 V et de résistance interne r = 4,8 ohms, en fonction de l'intensité I qu'elle débite."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# tension en V\n",
    "U = np.array([4.5, 4.3, 4, 3.8, 3.5, 3.3, 3, 2.8, 2.6]) \n",
    "# intensité en mA\n",
    "I = np.array([i for i in range(0, 401, 50)])\n",
    "I = I / 1000 # conversion en A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### La caractéristique de la pile est une fonction affine décroissante : U = E - r I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "E = 4.506666667129351 volts ; r = 4.8666666689800895 ohms\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# définition de la fonction caractéristique\n",
    "def caracteristique_pile(I, E, r):\n",
    "    \"\"\" caractéristique d'une pile : U = E - r.I \"\"\"\n",
    "    U = E - r * I\n",
    "    return U\n",
    "\n",
    "# modélisation : recherche des paramètres optimisés du modèle\n",
    "parametres = curve_fit(caracteristique_pile, I, U)[0]\n",
    "\n",
    "E, r = parametres # il y a deux paramètres dans la modélisation ici\n",
    "print(f'E = {E} volts ; r = {r} ohms')\n",
    "\n",
    "# calcul des ordonnées avec la fonction du modèle et les paramètres optimisés\n",
    "U_model = caracteristique_pile(I, E, r)\n",
    "\n",
    "# tracé des graphes des données à modéliser et de la fonction modèle optimisée\n",
    "plt.plot(I, U, 'rp')\n",
    "plt.plot(I, U_model, color=\"blue\")\n",
    "\n",
    "plt.title(\"Caractéristique tension-courant \\nd'une pile\")\n",
    "plt.xlabel('I (A)')\n",
    "plt.ylabel('U (V)')\n",
    "plt.axis(ymin=0, ymax=5)\n",
    "plt.text(.31, 3.8, f'E = {E:.1f} volts \\nr = {r:.1f} ohms')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}