AKarbas · November 2, 2019 12:01
diff --git a/PhysLab2_4.ipynb b/PhysLab2_4.ipynb
 {
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Capacitator Charge/Decharge\n",
    "\n",
    "Physics Lab 2 (Sat 10.30-12.30) week 3 homework assignment (Experiment 4)\n",
    "\n",
    "By M. Karbasforushan (951200207) and A.H. Fashamiha (94108306)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "import math"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1: Capacitator Charge\n",
    "\n",
    "$$\n",
    "V = V_0 \\times e^{- \\frac{t}{R_1 C}}\n",
    "\\rightarrow\n",
    "\\frac{V}{V_0} = e^{- \\frac{t}{R_1 C}}\n",
    "\\rightarrow\n",
    "ln(\\frac{V}{V_0}) = - \\frac{t}{R_1 C} \\\\\n",
    "\\rightarrow\n",
    "\\tau = R_1 C = \\frac{-1}{slope} \\\\\n",
    "\\rightarrow\n",
    "R_1 = \\frac{\\tau}{C}\n",
    "$$\n",
    "\n",
    "$\n",
    "V_0 = 10 ~ (V)\\\\\n",
    "C = 18.4 ~ (\\mu F)\n",
    "$\n",
    "\n",
    "| t (s) || 0 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 |\n",
    "| --- || --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n",
    "| V (V) || 10 | 9.25 | 8.51 | 7.82 | 7.20 | 6.64 | 6.11 | 5.64 | 5.19 | 4.77 |\n",
    "| $\\frac{V}{V_0}$ || 1.0 | 0.925 | 0.851 | 0.782 | 0.720 | 0.664 | 0.611 | 0.564 | 0.519 | 0.477 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope: -0.005489\n",
      "RC: 182.180738\n",
      "R: 9.901127e+06\n"
     ]
    }
   ],
   "source": [
    "t = [x * 15 for x in range(10)]\n",
    "v = [10., 9.25, 8.51, 7.82, 7.20, 6.64, 6.11, 5.64, 5.19, 4.77]\n",
    "v0 = 10.\n",
    "v_v0 = [x / v0 for x in v]\n",
    "v_v0_log = [math.log(x) for x in v_v0]\n",
    "slope, intercept, _, _, _ = stats.linregress(t, v_v0_log)\n",
    "fitted_v_v0_log = [slope * x + intercept for x in t]\n",
    "\n",
    "plt.plot(t, v_v0_log, 'b+')\n",
    "plt.plot(t, fitted_v_v0_log)\n",
    "plt.title('Voltage Fraction vs. Time')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel(r'ln($\\frac{V}{V_0}$)')\n",
    "plt.show()\n",
    "\n",
    "print(f'Slope: {slope:f}')\n",
    "print(f'RC: {-1/slope:f}')\n",
    "c = 18.4E-6\n",
    "print(f'R: {-1/slope/c:e}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "Slope = -0.005489 ~ (\\frac{1}{s}) \\\\\n",
    "\\rightarrow\n",
    "\\tau = -\\frac{1}{Slope} = 182.180738 ~ (s) \\\\\n",
    "\\rightarrow\n",
    "R_1 = \\frac{\\tau}{C} = \\frac{182.180738}{18.4 \\times 10^{-6}} = 9.901127E6 ~ (\\Omega)\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2: Capacitator Decharge\n",
    "\n",
    "$$\n",
    "V = V_0 \\times e^{- \\frac{t}{R_2 C}}\n",
    "\\rightarrow\n",
    "\\frac{V}{V_0} = e^{- \\frac{t}{R_2 C}}\n",
    "\\rightarrow\n",
    "ln(\\frac{V}{V_0}) = - \\frac{t}{R_2 C} \\\\\n",
    "\\rightarrow\n",
    "\\tau = R_2 C = \\frac{-1}{slope} \\\\\n",
    "\\rightarrow\n",
    "R_2 = \\frac{\\tau}{C} \\\\\n",
    "$$\n",
    "\n",
    "$\n",
    "V_0 = 10 ~ (V)\\\\\n",
    "C = 5 ~ (\\mu F)\n",
    "$\n",
    "\n",
    "| t (s) || 0 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 |\n",
    "| --- || --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n",
    "| V (V) || 10 | 7.37 | 5.43 | 4.61 | 2.94 | 2.19 | 1.61 | 1.18 | 0.87 | 0.64 |\n",
    "| $\\frac{V}{V_0}$ || 1.0 | 0.737 | 0.543 | 0.461 | 0.294 | 0.219 | 0.161 | 0.118 | 0.087 | 0.064 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope: -0.020517\n",
      "RC: 48.740409\n",
      "R: 9.748082e+06\n"
     ]
    }
   ],
   "source": [
    "t = [x * 15 for x in range(10)]\n",
    "v = [10., 7.37, 5.43, 4.61, 2.94, 2.19, 1.61, 1.18, 0.87, 0.64]\n",
    "v0 = 10.\n",
    "v_v0 = [x / v0 for x in v]\n",
    "v_v0_log = [math.log(x) for x in v_v0]\n",
    "slope, intercept, _, _, _ = stats.linregress(t, v_v0_log)\n",
    "fitted_v_v0_log = [slope * x + intercept for x in t]\n",
    "\n",
    "plt.plot(t, v_v0_log, 'b+')\n",
    "plt.plot(t, fitted_v_v0_log)\n",
    "plt.title('Voltage Fraction vs. Time')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel(r'ln($\\frac{V}{V_0}$)')\n",
    "plt.show()\n",
    "\n",
    "print(f'Slope: {slope:f}')\n",
    "print(f'RC: {-1/slope:f}')\n",
    "c = 5E-6\n",
    "print(f'R: {-1/slope/c:e}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "Slope = -0.020517 ~ (\\frac{1}{s}) \\\\\n",
    "\\rightarrow\n",
    "\\tau = -\\frac{1}{Slope} = 48.740409 ~ (s) \\\\\n",
    "\\rightarrow\n",
    "R_2 = \\frac{\\tau}{C} = \\frac{48.740409}{5 \\times 10^{-6}} = 9.748082E6 ~ (\\Omega) \\\\\n",
    "\\rightarrow\n",
    "\\overline{R} = \\frac{ R_1 + R_2 }{2} = \\frac{ 9.901127E6 + 9.748082E6 }{2} = 9.824604E6 ~ (\\Omega) \\\\\n",
    "\\rightarrow\n",
    "e(R_1) = \\frac{ R_1 - \\overline{R} }{R_1} = 0.773 \\% \\\\\n",
    "\\rightarrow\n",
    "e(R_2) = \\frac{ R_2 - \\overline{R} }{R_2} = -0.785 \\%\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3: Capacitators In Series\n",
    "\n",
    "$$\n",
    "V = V_0 \\times e^{- \\frac{t}{\\overline{R} C}}\n",
    "\\rightarrow\n",
    "\\frac{V}{V_0} = e^{- \\frac{t}{\\overline{R} C}}\n",
    "\\rightarrow\n",
    "ln(\\frac{V}{V_0}) = - \\frac{t}{\\overline{R} C} \\\\\n",
    "\\rightarrow\n",
    "\\tau = \\overline{R} C = \\frac{-1}{slope} \\\\\n",
    "\\rightarrow\n",
    "C = \\frac{\\tau}{ \\overline{R} }\n",
    "$$\n",
    "\n",
    "$\n",
    "V_0 = 10 ~ (V)\n",
    "$\n",
    "\n",
    "| t (s) || 0 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 |\n",
    "| --- || --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n",
    "| V (V) || 10 | 6.78 | 4.67 | 3.15 | 2.11 | 1.45 | 0.98 | 0.67 | 0.45 | 0.31 |\n",
    "| $\\frac{V}{V_0}$ || 1.0 | 0.678 | 0.467 | 0.315 | 0.211 | 0.145 | 0.098 | 0.067 | 0.045 | 0.031 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IJDAVGfmFsiWK8dgFzXm3TzuSDK56aTL3DZ3F1l0acFNE8k5FRnLU7sTj+Pzuzvyuy4n8Z+pqug8ax5h5G8KOJSIJRkVGclWiWDL3n3MSH93RgYqlinPLG1O58+3p/KABN0XkCKnIyGG1qFWB4Xd25J5ujRg9dwPdBo7jo+/+N+Cmbv0sIrnR92QkTxZv2M69Q2fx3aotnNWkKo9d0IyaFUtSRP8biRQ5+p6MxFTDamX54Nb2PHxuGt8s/ZHugzIo03Il2RqaRkRyoCIjeZacZKwaW48l/+xM5sIKHNdjDsdfM4lilXaq60xEfkFFRo5Kejrs21KK7985lR9GtqBKo22ceHsG1c9cyv6s7LDjiUicUJGRY2Jm7Jxdm7H9u9ClURWe+GwBF/7ra+at2xZ2NBGJAyoycswGDIBq5UrwwrWt+dfVrVi/dRfnPzOBv49eyJ79WWHHE5EQ6eoyyXebd+7l0RHz+HD6WhpULcOTF7eg9Qm/uqGpiCQgXV0moatYujgDL2vJaze2ZdfeLC55/mse+WQuO/dowE2RokZFRmLmjMZVGdWvM9e1O4FXJ66gx9MZjF+cGXYsESlAKjISU2VSU3ikdzPev/V0iqckce3L33LvBzPZ+pMG3BQpClRkpEC0rVuJkX07cfsZ9Rk6fS1dB43j8znfhx1LRGJMRUYKTIliydzbswkf39GBKmVSufWtadw+ZBobt+8OO5qIxEhcFxkzu9TM5ppZtpnlejWDmfU0s4VmtsTM7ivIjJJ3zWqW5+M7O/DHHo0ZO38j3QZmMHTaGorqlY4ihVlcFxlgDnARkJFbAzNLBp4FzgHSgCvNLK1g4snRKpacxB1nNmBk3040rFqGe96fyfWvTmHN5p/CjiYi+Siui4y7z3f3hYdpdiqwxN2Xufte4F2gd+zTSX5oULUM//nd6TxyflOmrthE90EZvP71Cg24KVJIxHWROUI1gdVR82uCZb9iZn3MbKqZTc3M1KW08SIpybi+fV1G9+tMm7qVGDB8Lpe98A1LM3eEHU1EjlHoRcbMxprZnBwe+X404u4vunsbd29TpUqV/N68HKNaFUvx+o1teerSk1m8cQfnDB7Ps18uYZ8G3BRJWClhB3D3rse4ibVA7aj5WsEySUBmxiWta9G5UWXSh8/lb6MWMmLWev56SQua1SwfdjwRyaPQj2TywRSgoZnVM7PiwBXA8JAzyTGqWrYE/7q6Nc9f04rMHXvo/exEnvx8Abv3acBNkUQS10XGzC40szXA6cAIMxsVLD/ezEYCuPt+4E5gFDAf+I+7zw0rs+Svns1qMLZfFy46pSbPfbWUXoPHM2XFprBjicgR0ijMkjDGL87k/g9ns2bzLq47/QTu7dmEMqmh9/iKFCkahVkKrU4NqzDq7s7c2KEub05aSY9BGXy1cOPP63XrZ5H4oyMZSUjTVm7mT0NnsWTjDi5qVZM//yaNSmWKU0T/O4sUmLweyaivQRJS6xMqMqJvR5757xKe+2opGYsyKdW4Ge7VMbOw44lIQN1lkrBSU5LZ/nVjVr3UkbWLS1LlgulUu2gaKWV2q+tMJE6oyEhCS0+HvRvLsfqV9mz+sgkVm2aS9odxpJ27WgNuisQBFRkpFFKSk9j2bX0+u6sTTWqU494PZnHty9+yepMG3BQJk4qMFBoDBsCJVcrw7i3teOyCZsxYvYXugzJ4ZcJysjTgpkgodHWZFFrrtuzigWGz+WphJq3qVODJi1vQsFrZsGOJJDR9T0YkcHyFkrx6Q1uevrwly3/YyW/+MYF/frFYA26KFCAVGSnUzIwLTqnJmP5d6N60Gn8fs4jz/jmB2Wu2hh1NpEhQkZEioXKZVJ65qhUvXtuaTTv30vvZCfy/z+ZrwE2RGFORkSKle9PqjOnfhcva1OaFccs4Z/B4Ji/7MexYIoWWiowUOeVLFuOJi1sw5ObTyMp2Ln9xEg99NJvtu/eFHU2k0FGRkSKrQ4PKfH53J27uWI+3J6+ix6AMvlyw8fBPFJEjpiIjRVqp4ik8dG4aQ29rT+nUFG58bQr93pvBpp17w44mUiioyIgAp9SpyKd9O3LX2Q35ZOY6ug0cxycz12loGpFjpCIjEkhNSaZft0Z82rcjNSuW5PfvfMctb0xjw7bdYUcTSVgqMiIHaVK9HB/e1p4He53E+MWZdB04jne/XaWjGpGjoCIjkoOU5CRu6Xwio+7uTFqNctz34Wyufmkyq37UgJsieRHXRcbMLjWzuWaWbWa5jpVjZivMbLaZzTAzDUgm+aZu5dK8c0s7/nJhc2at2Ur3p8fx0vhlGnBT5AjFdZEB5gAXARlH0PZMd2+Zl4HbRI5EUpJx1Wl1GNO/Mx3qV+axEfO5+LmvWbRhe9jRROJeXBcZd5/v7gvDziECUKN8SV66vg2Dr2jJqk0/8Zt/jGfw2MXs3a8BN0VyE9dFJg8cGG1m08ysT26NzKyPmU01s6mZmZkFGE8KCzOjd8uajOnXmV7NazBobGTAzZmrt4QdTSQuhV5kzGysmc3J4dE7D5vp6O6tgHOAO8ysc06N3P1Fd2/j7m2qVKmSL/mlaDquTCqDrziFl65rw9Zd+7jwXxN5fMQ8du3NIj097HQi8SMl7ADu3jUftrE2+LnRzIYBp3Jk53FEjknXtGqcemIlnvhsAf8ev5zR8zYw+ZUWpKcfF3Y0kbhw1EcyZlbazJLzM8wx5Ch7YBroTuSCAZECUa5EMf5yYXPeuaUdANWvmsT9H85mmwbcFDnyImNmSWZ2lZmNMLONwALgezObZ2Z/M7MG+R3OzC40szXA6cAIMxsVLD/ezEYGzaoBE8xsJvAtMMLdP8/vLCKHkp4O7Rscx/gHOrN18om8PWkVafdk8Ns/bwg7mkio7Ei/xWxm44CxwMfAHHfPDpZXAs4ErgKGuftbMcqar9q0aeNTp+orNZL/zGDGqi38aegsFny/nfNPPp4B56VxXJnUsKOJHDMzm5aXr4rkpcgUc/d9By3LcvfkQ7WJVyoyEitm4A5792fz3FdLeebLxZQtUYwB56Vx/snHY2ZhRxQ5anktMkfcXZZL8bAjaCNSpAwYEPlZPCWJu7o2ZETfTtSpVIq73p3Bza9PZf3WXeEGFClAhz2SMbPi7p7jzTUOPpJJJDqSkYKUle28OnE5T41eSEpSEvf3asKVbeuQlKSjGkkssTiSGWpm5x/hi19jZvcGj6uPNIRIYZecZNzc6URG392FFrXK8+CwOVz10iRW/LAz7GgiMXUkReYCoI6ZDTGzRjk1MLPiwWRNd/+ru/8VqJVfIUUKizrHlWLIzafx5MXNmbtuGz2ezuDFjKXsz9LQNFI45eXEf0XgAWCvuz8YLMty92Qz+wT4N7AJaA9kA5PdfXxsYh87dZdJ2DZs281DH81hzLwNnFyrPE9e0oIm1cuFHUvkkPL96jIzOw9oCpwEpAJ73P36YN2BIpMM3Ebk+yyPuPuio30DBUVFRuKBuzNi9noGfDyXrbv2cfuZDbjjzPqkpiTkqU4pAmJRZK4BZgPzjuAS5l8d7cQrFRmJJ5t37uX/Pp3HsO/W0rBqGZ68pAWt6lQMO5bIr8TsezK5vNiBI5mDj3Z2u/sNR73hAqAiI/HoywUbeWDYbL7ftpubOtTjnu6NKFU89CEGRX5W0EUm292TDnW0E69UZCRebd+9jyc/X8Bbk1ZRu1JJnrioBR0aVA47lggQwy9jWg5fU3b3pODnW+4+E9h/pNsTkZyVLVGMxy5oznt92pGSlMTVL03mvqGz2LorIT6/ifxCXkZh/tLMfm9mdaIXmllxMzvLzF4Hrs/feCJF12knHsdnd3Xi1i71eX/aGroNHMfoud+HHUskT/JSZHoCWcA7ZrYuGH15ObAYuBJ42t1fi0FGkSKrRLFk7junCR/d3oHjyqTS581p3PH2dDK37wk7msgROapzMmZWDKgM7HL3hLzvrM7JSKLZl5XNC+OW8o8vllAqNZkB56VxQcuaGnBTClTMzslEc/d97r4+UQuMSCIqlpzEnWc1ZORdHTmxcmn6vTeTG1+bwtotGnBT4leej2TMLBW4GKhL1O2b3f3/8jVZjOlIRhJZVrbzxjcr+OvnC0kyuK/XSVx9qgbclNgriCOZj4HeRK4k2xn1EJECkpxk3NihHqP7dabVCRX580dzuOLFSSzL3AFE7tQpEg+O5khmjrs3i1GeAqMjGSks3J0Ppq3h0U/nsWd/Nv26NeK2M+vh2UfVGy5ySAVxJPO1mTU/iueJSAyYGZe2qc3Y/l04o3EVnvhsAdWvm8i8ddvCjiZyVEWmIzDdzBaa2Swzm21ms/I7mIjkzb8GluDF69qQOawVKWV3c86gCVTsvJCHBmSFHU2KsKMpMj2BBkA34FzgN8HPfGdmfzOzBUExG2ZmFXJp1zMoekvM7L5YZBGJd+np4A47F9Zg3UtduKRtTcq3X8I35cYzbeWmsONJEZWXYWW2m9k2YA6RccrmBI+5wc9YGAM0c/cWwCLg/hxyJQPPAucAacCVZpYWozwiCSF7d3H+ftnJvH7Tqezel80lz39D+vC57NyjkZ+kYB1xkXH3su5eLodHWXePyZ2W3H20ux/4rZhEznfbPBVY4u7L3H0v8C6Rq99EiqwBAyI/uzSqwqh+nbmu3Qm8/s0KejydwfjFmaFmk6IlkS4/uQn4LIflNYHVUfNrgmW/YmZ9zGyqmU3NzNQvmhRe0Zcwl0lN4ZHezfjP706neEoS1778LX98fyZbf9KAmxJ7oRcZMxtrZnNyePSOavMgke/lDDmW13L3F929jbu3qVKlyrFGF0kobetWYmTfTtx+Rn0+/G4tXQeN4/M568OOJYVc6HdDcveuh1pvZjcQubDgbM/5Sz1rgdpR87WCZSJykBLFkrm3ZxN6Na/BvR/M4ta3pnNOs+o80rspVcuWCDueFEKhH8kcipn1BO4Fznf3n3JpNgVoaGb1zKw4cAUwvKAyiiSiZjXL8/GdHfhjj8Z8sWAj3QZm8MG0NRzLTQxFchLXRQZ4BigLjDGzGWb2PICZHW9mIwGCCwPuBEYB84H/uPvcsAKLJIpiyUnccWYDRvbtRMOqZfjD+zO5/tUprNmc2+c5kbw7ptsvJzINKyPyP9nZzluTV/LkZwtw4E89m3BtuxM04Kb8SoEM9S8ihUtSknHd6XUZ1a8zbepWYsDwuVz2wjcsDQbcFDlaKjIi8rNaFUvx+o1t+fulJ7N44w7OGTyeZ79cwr6s7LCjSYJSkRGRXzAzLm5di7H9u9D1pKr8bdRCej8zkTlrt4YdTRKQioyI5KhK2VT+dXVrnr+mFZk79tD72Yk8+fkCdu/TgJty5FRkROSQejarwdh+XbjolJo899VSeg0ez5QVGnBTjoyKjIgcVvlSxfjbpSfz5m9PZW9WNpc+/w0PfzyHHRpwUw5DRUZEjlinhlUYdXdnbuxQlzcnraTHoAzGLdI4gJI7FRkRyZPSqSkMOK8pH9zanpLFk7n+lW/p/58ZbPlpb9jRJA6pyIjIUWl9QkVG9O3I789qwPAZ6+g6cBwjZ6/X0DTyCyoyInLUUlOSuad7Y4bf2ZEa5Uty+5Dp3PrWNDZu2w388pYDUjRpWBkRyRf7s7J5acJyBo1ZRGpKEg+dm8blbWvhrqFpChMNKyMioUhJTuLWLvX57K5ONKlejns/mEXVy79l9SYNuFmUqciISL5649kyvH9bO34c1YzUGlvo8FgG5dos5+EBRbPXpKhTkRGRfJWeDu7G9u9OYN3LnTmreSUqdZ3HnGpfs2Tj9rDjSQFTkRGRmMnaXpJXb2jL05e3ZPkPO+k1eALP/HexBtwsQlRkRCRmBgyIDLh5wSk1GdO/C92bVuOp0Ys4758TmL1GA24WBbq6TEQK1Oi53/PQR3P4Yccebul8Iv26NqJEseSwY8kR0tVlIhLXujetzpj+XbisTW1eGLeMcwaPZ/KyH8OOJTGiIiMiBa58yWI8cXELhtx8GlnZzuUvTuKhj2azffe+sKNJPovrImNmfzOzBWY2y8yGmVmFXNqtMLPZZjbDzNQHJpIgOjSozOd3d+LmjvV4e/IqegzK4MsFG8OOJfkorosMMAZo5u4tgEXA/Ydoe6a7t5bFTkgAABF4SURBVMxLX6GIhK9U8RQeOjeNobe1p3RqCje+NoV+781g004NuFkYxHWRcffR7n7ghhWTgFph5hGR2DmlTkU+7duRu85uyCcz19Ft4Dg+nbVOA24muLguMge5Cfgsl3UOjDazaWbWJ7cNmFkfM5tqZlMzM3UPDJF4k5qSTL9ujfi0b0dqVizJnW9/R583p7EhGHBTEk/olzCb2Vigeg6rHnT3j4M2DwJtgIs8h8BmVtPd15pZVSJdbL9394xDva4uYRaJb/uzsnl14gqeGr2Q4ilJPNjrJC5vWxszDbgZprxewhx6kTkcM7sB+B1wtrsfdqQ9M0sHdrj7U4dqpyIjkhhW/LCT+z6cxaRlm2hf/zieuKgFdY4rFXasIqtQfU/GzHoC9wLn51ZgzKy0mZU9MA10B+YUXEoRiaW6lUvz9s3t+MuFzZm9Zivdnx7HS+OXkZUd3x+QJSKuiwzwDFAWGBNcnvw8gJkdb2YjgzbVgAlmNhP4Fhjh7p+HE1dEYiEpybjqtDqM7t+ZDvUr89iI+Vz83Ncs2qABN+Nd3HeXxYq6y0QSk7szfOY6HvlkHtt37+POMxty2xn1KZ4S75+ZC4dC1V0mInIwM6N3y5qM6deZXs1rMGjsIs5/ZgIzV28JO5rkQEVGRBLScWVSGXzFKbx8fRu2/LSPC/81kb+MnM+uvVlhR5MoKjIiktDOPqkao/t35opT6/BixjJ6Ds7gm6UacDNeqMiISMIrV6IYf7mwOe/c0g6AK/89ifs/nM22YMDN9PQQwxVxOvEvIoXKrr1ZDBq7iJfGL6Nq2RI8fmEzuqZVo4j+qct3OvEvIkVayeLJPNDrJIbd3oEKpYrx29enUvm87/hxx56woxVJKjIiUigNe7kCo+7pyJbxjSjVeD0tH8igdNpaBgzQIU1BUpERkUIpPR08K4ktExuy/rVOtG5ciirnz2BNvams37or7HhFhoqMiBR6+34oy9Db2vPnc9P4eumPdBuYwZDJK8nW0DQxpyIjIoXegAGQnGT8tmM9Rt3dmZNrl+fBYXO46qVJrPhhZ9jxCjVdXSYiRY6785+pq3lsxHz27s/mnu6NuKlDPVKS9bn7cHR1mYjIYZgZl7etw9j+XejcqAp/GbmAi5/7mgXfbws7WqGjIiMiRVa1ciV48drWPHtVK9Zu2cW5/5jAwDGL2LNfQ9PkFxUZESnSzIzftKjBmH5dOP/k4/nHF4s59x8TmL5qc9jRCgUVGRERoGLp4gy8vCWv3tiWnXv2c/FzX/Pop/P4ae/+sKMlNBUZEZEoZzauyqh+nbnmtBN4ecJyejydwcQlP4QdK2GpyIiIHKRsiWI8ekEz/vO700lJSuLqlyZz39BZbN21L+xoCUdFRkQkF6fWq8Rnd3XitjPq8/60NXQbOI7Rc78PO1ZCUZERETmEEsWS+VPPJnx0eweOK5NKnzenccfb08ncrgE3j0RcFxkze9TMZpnZDDMbbWbH59LuejNbHDyuL+icIlL4Na9VnuF3duCPPRozZu4Gug0ax7Dv1lBUv9B+pOL6G/9mVs7dtwXTfYE0d7/1oDaVgKlAG8CBaUBrdz/k9Yf6xr+IHK0lG7dz7wezmL5qC2c0rsLjFzanZoWSYccqEIXqG/8HCkygNJEicrAewBh33xQUljFAz4LIJyJFU4OqZXn/1vakn5fGt8s30X3gON78ZoUG3MxBXBcZADN73MxWA1cDD+fQpCawOmp+TbBMRCRmkpOMGzpEBtxsdUJF/vzxXK54cRLLMneEHS2uhF5kzGysmc3J4dEbwN0fdPfawBDgzmN8rT5mNtXMpmZmZuZHfBEp4mpXKsUbN53K3y5pwYLvt9Fz8Hie+2op+7Oyw44WF+L6nEw0M6sDjHT3ZgctvxI4w91/F8y/AHzl7u8cans6JyMi+W3j9t08/NFcPp/7Pc1qluOvF59M2vHlwo6VrwrVORkzaxg12xtYkEOzUUB3M6toZhWB7sEyEZECVbVsCZ6/tjXPXd2K77fu4fxnJvDUqIXs3hcZcDM9Pdx8YYjrIxkzGwo0BrKBlcCt7r7WzNoE0zcH7W4CHgie9ri7v3q4betIRkRiactPe3n00/kMnb6G+lVK89dLWtCmbiXi+E/uEcnrkUxcF5lYUpERkYIwblEmD3w4m3Vbd7F1Sl1Wj2hM6dSUsGMdtULVXSYikui+fLsK3wzozNapJ1C29Qoa351ByXqZRabrTEVGRCSG0tMhe08Km8Y0Y8OQ02nUIIlql3/LjqYz2fpT4R9wU0VGRKSA7FlbiZF9O3HHmfUZ9t1aug4ax+dz1ocdK6ZUZERECsiAAZEBN//YownD7+xA1bKp3PrWdG57axobt+8OO15M6MS/iEhI9mVl8+/xy3h67GJKFkvmod+cxCWta2FmYUfLlU78i4gkiGLJSdx+RgM+u6sTjaqV4Y8fzOK6V75l9aafwo6Wb1RkRERCVr9KGd7rczr/17sp01dupsfTGbw2cXmhGHBTRUZEJA4kJRnXnV6XUf0606ZuJdI/mcdlL3zDko2JPeCmioyISBypVbEUr9/Ylr9fejJLMnfQa/B4nv1yCfsSdMBNFRkRkThjZlzcuhZj+nWhW1o1/jZqIb2fmcictVvDjpZnKjIiInGqStlUnr26Fc9f05rMHXvo/exEnvx8wc8DbiYCFRkRkTjXs1l1xvbrwsWtavLcV0vpNXg8U1ZsCjvWEVGRERFJAOVLFeOvl5zMW789jb1Z2Vz6/Dc8/PEcduzZH3a0Q1KRERFJIB0bVmbU3Z25sUNd3py0ku4Dx/Hlwo1hx8qVioyISIIpnZrCgPOa8sGt7SmVmsKNr06h/3sz2Lxzb9jRfkVFRkQkQbU+oSIj+nak71kNGD5zHd0GjWPErPXE03BhKjIiIgksNSWZ/t0bM/zOjtQoX5I73p7O796cxoZt8THgpoqMiEghkHZ8OYbd3p77z2nCuEWZdB04jvemrAr9qEZFRkSkkEhJTuJ3Xerz2V2dOKlGOf40dDbXvDyZVT+GN+CmioyISCFzYpUyvHtLOx67oBkzV2+lx9MZvDxhOVnBgJsFeevnuL6fjJk9CvQGsoGNwA3uvi6HdlnA7GB2lbuff7ht634yIlIUrNuyiweHzebLhZmcUqcCf724BY2ql+Vo//Tn9X4y8V5kyrn7tmC6L5Dm7rfm0G6Hu5fJy7ZVZESkqHB3Pp6xjkc+mcvOPVmsH5nG9u9OOKptFaqblh0oMIHSQPxWRBGROGVmzPi4JrOe7MLm2dXZv7k0ZmAW+66zuD6SATCzx4HrgK3Ame6emUOb/cAMYD/whLt/lMu2+gB9AOrUqdN65cqVMcstIhKvzCg63WVmNhaonsOqB93946h29wMl3H1ADtuo6e5rzexE4L/A2e6+9FCvq+4yESmqCrLIpBzdy+Qfd+96hE2HACOBXxUZd18b/FxmZl8BpwCHLDIiIkXVgF/9FY2duD4nY2YNo2Z7AwtyaFPRzFKD6cpAB2BewSQUEUk8BXkJc+hHMofxhJk1JnIJ80rgVgAzawPc6u43AycBL5hZNpGi+YS7q8iIiMSBuC4y7n5xLsunAjcH018DzQsyl4iIHJm47i4TEZHEpiIjIiIxoyIjIiIxE/r3ZMJiZplELiY4GpWBH/IxTkFIxMyQmLmVuWAoc8E4OPMJ7l7lSJ9cZIvMsTCzqXn5MlI8SMTMkJi5lblgKHPBONbM6i4TEZGYUZEREZGYUZE5Oi+GHeAoJGJmSMzcylwwlLlgHFNmnZMREZGY0ZGMiIjEjIqMiIjEjIpMHplZTzNbaGZLzOy+sPPkxMxqm9mXZjbPzOaa2V3B8kpmNsbMFgc/K4ad9WBmlmxm35nZp8F8PTObHOzv98yseNgZo5lZBTP7wMwWmNl8Mzs93vezmfUL/l/MMbN3zKxEPO5nM3vFzDaa2ZyoZTnuW4v4R5B/lpm1iqPMfwv+f8wys2FmViFq3f1B5oVm1iNeMketu8fMPBjh/qj2s4pMHphZMvAscA6QBlxpZmnhpsrRfuAed08D2gF3BDnvA75w94bAF8F8vLkLmB81/yQwyN0bAJuB34aSKneDgc/dvQlwMpHscbufzawm0Bdo4+7NgGTgCuJzP78G9DxoWW779hygYfDoAzxXQBkP9hq/zjwGaObuLYBFwP0Awe/kFUDT4Dn/Cv7GFLTX+HVmzKw20B1YFbU4z/tZRSZvTgWWuPsyd98LvEvkPjdxxd3Xu/v0YHo7kT98NYlkfT1o9jpwQTgJc2ZmtYDfAC8F8wacBXwQNImrzGZWHugMvAzg7nvdfQtxvp+JjL5e0sxSgFLAeuJwP7t7BrDpoMW57dvewBseMQmoYGY1Cibp/+SU2d1Hu/v+YHYSUCuY7g286+573H05sITI35gClct+BhgE3AtEXx2W5/2sIpM3NYHVUfNrgmVxy8zqErlT6GSgmruvD1Z9D1QLKVZunibynzo7mD8O2BL1Cxpv+7sekAm8GnTxvWRmpYnj/RzcRfYpIp9O1wNbgWnE936Oltu+TZTfzZuAz4LpuM1sZr2Bte4+86BVec6sIlOImVkZYChwt7tvi17nkWvX4+b6dTM7F9jo7tPCzpIHKUAr4Dl3PwXYyUFdY3G4nysS+TRaDzgeKE0OXSWJIN727eGY2YNEurKHhJ3lUMysFPAA8HB+bE9FJm/WArWj5msFy+KOmRUjUmCGuPuHweINBw5tg58bw8qXgw7A+Wa2gkg35FlEzndUCLp1IP729xpgjbtPDuY/IFJ04nk/dwWWu3umu+8DPiSy7+N5P0fLbd/G9e+mmd0AnAtc7f/7cmK8Zq5P5EPIzOD3sRYw3cyqcxSZVWTyZgrQMLgSpziRk3bDQ870K8G5jJeB+e4+MGrVcOD6YPp64OOCzpYbd7/f3Wu5e10i+/W/7n418CVwSdAs3jJ/D6y2yC3CAc4G5hHH+5lIN1k7MysV/D85kDlu9/NBctu3w4Hrgquf2gFbo7rVQmVmPYl0A5/v7j9FrRoOXGFmqWZWj8jJ9G/DyBjN3We7e1V3rxv8Pq4BWgX/3/O+n91djzw8gF5ErhBZCjwYdp5cMnYk0o0wC5gRPHoROcfxBbAYGAtUCjtrLvnPAD4Npk8k8ou3BHgfSA0730FZWwJTg339EVAx3vcz8AiwAJgDvAmkxuN+Bt4hct5oX/CH7re57VvAiFz5uRSYTeTquXjJvITIeYwDv4vPR7V/MMi8EDgnXjIftH4FUPlo97OGlRERkZhRd5mIiMSMioyIiMSMioyIiMSMioyIiMSMioyIiMSMiozIMTKz48xsRvD43szWRs1/HaPXPMXMXj7E+ipm9nksXlskL1IO30REDsXdfyTyfRnMLB3Y4e5PxfhlHwAeO0SmTDNbb2Yd3H1ijLOI5EpHMiIxZGY7gp9nmNk4M/vYzJaZ2RNmdrWZfWtms82sftCuipkNNbMpwaNDDtssC7TwYPBCM+sSdeT0XbAeIl8OvbqA3qpIjlRkRArOycCtwEnAtUAjdz+VyK0Nfh+0GUzkvi5tgYuDdQdrQ+Tb+gf8AbjD3VsCnYBdwfKpwbxIaNRdJlJwpngwzpOZLQVGB8tnA2cG012BtMiwYgCUM7My7r4jajs1iNxi4ICJwEAzGwJ86O5rguUbiYy0LBIaFRmRgrMnajo7aj6b//0uJgHt3H33IbazCyhxYMbdnzCzEUTGp5toZj3cfUHQZlcu2xApEOouE4kvo/lf1xlm1jKHNvOBBlFt6ntk5NwniYwU3iRY1YhfdquJFDgVGZH40hdoY2azzGwekXM4vxAcpZSPOsF/t5nNMbNZREbSPXDnxTOBEQURWiQ3GoVZJAGZWT9gu7vndGHAgTYZQG9331xwyUR+SUcyIonpOX55jucXzKwKMFAFRsKmIxkREYkZHcmIiEjMqMiIiEjMqMiIiEjMqMiIiEjMqMiIiEjM/H/+cHc9LjkPhAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope: -0.025793\n",
      "RC: 38.770358\n",
      "C: 3.946251e-06\n"
     ]
    }
   ],
   "source": [
    "t = [x * 15 for x in range(10)]\n",
    "v = [10., 6.78, 4.67, 3.15, 2.11, 1.45, 0.98, 0.67, 0.45, 0.31]\n",
    "v0 = 10.\n",
    "v_v0 = [x / v0 for x in v]\n",
    "v_v0_log = [math.log(x) for x in v_v0]\n",
    "slope, intercept, _, _, _ = stats.linregress(t, v_v0_log)\n",
    "fitted_v_v0_log = [slope * x + intercept for x in t]\n",
    "\n",
    "plt.plot(t, v_v0_log, 'b+')\n",
    "plt.plot(t, fitted_v_v0_log)\n",
    "plt.title('Voltage Fraction vs. Time')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel(r'ln($\\frac{V}{V_0}$)')\n",
    "plt.show()\n",
    "\n",
    "print(f'Slope: {slope:f}')\n",
    "print(f'RC: {-1/slope:f}')\n",
    "r = 9.824604E6\n",
    "print(f'C: {-1/slope/r:e}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "Slope = -0.025793 ~ (\\frac{1}{s}) \\\\\n",
    "\\rightarrow\n",
    "\\tau = -\\frac{1}{Slope} = 38.770358 ~ (s) \\\\\n",
    "\\rightarrow\n",
    "C = \\frac{\\tau}{ \\overline{R} } = 3.946251E-6 ~ (F)\n",
    "$\n",
    "\n",
    "Also, from the values of $C_1$ and $C_2$:\n",
    "\n",
    "$\n",
    "C' = ( \\frac{1}{C_1} + \\frac{1}{C_2} ) ^{-1}\n",
    "   = ( \\frac{1}{18.4E-6} + \\frac{1}{5E-6} ) ^{-1}\n",
    "   = 3.932 ~ (\\mu F)\n",
    "$\n",
    "\n",
    "$\n",
    "\\rightarrow\n",
    "e(C) = \\frac{ C ~ - ~ C' }{C} = \\frac{ 3.946251E-6 ~ - ~ 3.932E-6 }{3.946251E-6} = 3.611 \\%\n",
    "$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 4: Capacitators In Parallel\n",
    "\n",
    "$$\n",
    "V = V_0 \\times e^{- \\frac{t}{\\overline{R} C}}\n",
    "\\rightarrow\n",
    "\\frac{V}{V_0} = e^{- \\frac{t}{\\overline{R} C}}\n",
    "\\rightarrow\n",
    "ln(\\frac{V}{V_0}) = - \\frac{t}{\\overline{R} C} \\\\\n",
    "\\rightarrow\n",
    "\\tau = \\overline{R} C = \\frac{-1}{slope} \\\\\n",
    "\\rightarrow\n",
    "C = \\frac{\\tau}{ \\overline{R} }\n",
    "$$\n",
    "\n",
    "$\n",
    "V_0 = 10 ~ (V)\n",
    "$\n",
    "\n",
    "| t (s) || 0 | 15 | 30 | 45 | 60 | 75 | 90 | 105 | 120 | 135 | 150 | 165 | 180 | 195 | 210 | 225 | 240 | 255 | 270 | 285 |\n",
    "| --- || --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n",
    "| V (V) || 10 | 9.41 | 8.80 | 8.25 | 7.73 | 7.21 | 6.77 | 6.35 | 5.96 | 5.57 | 5.21 | 4.89 | 4.57 | 4.28 | 4.01 | 3.76 | 3.52 | 3.30 | 3.09 | 2.89 |\n",
    "| $\\frac{V}{V_0}$ || 1.0 | 0.941 | 0.880 | 0.825 | 0.773 | 0.721 | 0.677 | 0.635 | 0.596 | 0.557 | 0.521 | 0.489 | 0.457 | 0.428 | 0.401 | 0.376 | 0.352 | 0.330 | 0.309 | 0.289 |"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope: -0.004362\n",
      "RC: 229.246116\n",
      "C: 2.333388e-05\n"
     ]
    }
   ],
   "source": [
    "t = [x * 15 for x in range(20)]\n",
    "v = [10., 9.41, 8.80, 8.25, 7.73, 7.21, 6.77, 6.35, 5.96, 5.57, 5.21, 4.89, 4.57, 4.28, 4.01, 3.76, 3.52, 3.30, 3.09, 2.89]\n",
    "v0 = 10.\n",
    "v_v0 = [x / v0 for x in v]\n",
    "v_v0_log = [math.log(x) for x in v_v0]\n",
    "slope, intercept, _, _, _ = stats.linregress(t, v_v0_log)\n",
    "fitted_v_v0_log = [slope * x + intercept for x in t]\n",
    "\n",
    "plt.plot(t, v_v0_log, 'b+')\n",
    "plt.plot(t, fitted_v_v0_log)\n",
    "plt.title('Voltage Fraction vs. Time')\n",
    "plt.xlabel('Time (s)')\n",
    "plt.ylabel(r'ln($\\frac{V}{V_0}$)')\n",
    "plt.show()\n",
    "\n",
    "print(f'Slope: {slope:f}')\n",
    "print(f'RC: {-1/slope:f}')\n",
    "r = 9.824604E6\n",
    "print(f'C: {-1/slope/r:e}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$\n",
    "Slope = -0.004362 ~ (\\frac{1}{s}) \\\\\n",
    "\\rightarrow\n",
    "\\tau = -\\frac{1}{Slope} = 229.246116 ~ (s) \\\\\n",
    "\\rightarrow\n",
    "C = \\frac{\\tau}{ \\overline{R} } = 2.333388E-5 ~ (F)\n",
    "$\n",
    "\n",
    "Also, from the values of $C_1$ and $C_2$:\n",
    "\n",
    "$\n",
    "C' = C_1 + C_2\n",
    "   = 18.4E-6 + 5E-6\n",
    "   = 23.4 ~ (\\mu F)\n",
    "$\n",
    "\n",
    "$\n",
    "\\rightarrow\n",
    "e(C) = \\frac{ C ~ - ~ C' }{C} = \\frac{ 2.333388E-5 ~ - ~ 23.4E-6 }{2.333388E-5} = -2.834 \\%\n",
    "$"
   ]
  }
 ],
 "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
 }
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