{
 "cells": [
  {
   "attachments": {
    "image.png": {
     "image/png": "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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# INVESTIGATION OF THE ENERGY STORED IN A CAPACITOR\n",
    "\n",
    "## Theory\n",
    "The energy stored by a capacitor is given by the equation: $𝑈= 1/2QV$ Given that $𝑄=𝐶V$ then the equation for the energy stored can be written in the form: $𝑈=1/2 CV_{2}$. The capacitor can be charged to various values of $V$ and then the energy stored can be determined by using a Joule meter. \n",
    "\n",
    "The energy stored can be measured as the capacitor discharges. A graph of energy stored against $V^{2}$ should be linear and the value of the capacitance can then be measured.\n",
    "\n",
    "\n",
    "## Apparatus:\n",
    "* d.c. power supply\n",
    "* Voltmeter (multimeter set on d.c. voltage range or CRO) – resolution ± 0.01V\n",
    "* Digital joule meter\n",
    "* 4mm leads\n",
    "* Suitable switches\n",
    "* Electrolytic capacitors e.g. a 1 000 μF or 2 200 μF\n",
    "* Resistors e.g. 100 kΩ or other values\n",
    "\n",
    "## Experimental Method:\n",
    "\n",
    "![image.png](attachment:image.png)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The parameters of the line: [[ 0.13452381]\n",
      " [-0.01035714]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Importing the necessary libraries\n",
    "from matplotlib import pyplot as plt\n",
    "import numpy as np\n",
    "#from prettytable import PrettyTable\n",
    "\n",
    "# Preparing the data to be computed and plotted\n",
    "dt = np.array([\n",
    "          \n",
    "    [1.0, 0.15],\n",
    "    [2.0, 0.29],\n",
    "    [3.0, 0.38],\n",
    "    [4.0, 0.50],\n",
    "    [5.0, 0.60],\n",
    "    [6.0, 0.81],\n",
    "    [7.0, 0.90],\n",
    "    [8.0, 1.13]\n",
    "])\n",
    "\n",
    "# Preparing X and y data from the given data\n",
    "x = dt[:, 0].reshape(dt.shape[0], 1)\n",
    "X = np.append(x, np.ones((dt.shape[0], 1)), axis=1)\n",
    "y = dt[:, 1].reshape(dt.shape[0], 1)\n",
    "\n",
    "# Calculating the parameters using the least square method\n",
    "theta = np.linalg.inv(X.T.dot(X)).dot(X.T).dot(y)\n",
    "\n",
    "print(f'The parameters of the line: {theta}')\n",
    "\n",
    "# Now, calculating the y-axis values against x-values according to\n",
    "# the parameters theta0 and theta1\n",
    "y_line = X.dot(theta)\n",
    "\n",
    "# Plotting the data points and the best fit line\n",
    "plt.scatter(x, y)\n",
    "plt.plot(x, y_line, 'r')\n",
    "plt.title('Best fit line using regression method')\n",
    "plt.xlabel('Length in cm')\n",
    "plt.ylabel('Resistance')\n",
    "\n",
    "plt.show()\n",
    "\n",
    "\n",
    "\n",
    "#def makePrettyTable(table_col1, table_col2):\n",
    " #   table = PrettyTable()\n",
    "  #  table.add_column(\"Column-1\", x)\n",
    "   # table.add_column(\"Column-2\", Y)\n",
    "    #return table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "In comparison....\n"
   ]
  },
  {
   "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}