{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "23d56895",
   "metadata": {},
   "source": [
    "# PHYS 216 — Assignment 6, Question 4\n",
    "## Beginner Python: RC charging and discharging\n",
    "\n",
    "**Goal:** Use Python to draw simple graphs. Work out the assignment's numerical answers on paper. Python will help you see **how voltage and current change with time**.\n",
    "\n",
    "Run each code cell from top to bottom using **Shift + Enter**. Only two libraries are needed: `numpy` (numbers) and `matplotlib` (plots)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5767453",
   "metadata": {},
   "source": [
    "### 1. Import the plotting tools\n",
    "`np` and `plt` are just short names we use for the libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "23db4ac2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T18:33:26.912087Z",
     "iopub.status.busy": "2026-11-03T18:33:26.911960Z",
     "iopub.status.idle": "2026-11-03T18:33:27.423103Z",
     "shell.execute_reply": "2026-11-03T18:33:27.422026Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbb116fb",
   "metadata": {},
   "source": [
    "### 2. Enter the values from the question\n",
    "`47000` means 47.0 kΩ, and `220e-6` means 220 µF. The variable `tau` is the time constant in seconds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ad826a87",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T18:33:27.424852Z",
     "iopub.status.busy": "2026-11-03T18:33:27.424599Z",
     "iopub.status.idle": "2026-11-03T18:33:27.428776Z",
     "shell.execute_reply": "2026-11-03T18:33:27.427723Z"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Charging time constant = 10.34 s\n"
     ]
    }
   ],
   "source": [
    "R = 47000           # resistance in ohms\n",
    "C = 220e-6          # capacitance in farads\n",
    "V_battery = 9.0     # battery voltage in volts\n",
    "\n",
    "tau = R * C\n",
    "print(\"Charging time constant =\", round(tau, 2), \"s\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fa72e5d3",
   "metadata": {},
   "source": [
    "### 3. Plot the capacitor voltage while charging\n",
    "`np.linspace(0, 5*tau, 100)` creates 100 times between 0 and 5 time constants. `np.exp(...)` means the exponential function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cd542d41",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T18:33:27.430964Z",
     "iopub.status.busy": "2026-11-03T18:33:27.430192Z",
     "iopub.status.idle": "2026-11-03T18:33:27.608938Z",
     "shell.execute_reply": "2026-11-03T18:33:27.607649Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "time = np.linspace(0, 5*tau, 100)\n",
    "V_cap = V_battery * (1 - np.exp(-time/tau))\n",
    "\n",
    "plt.plot(time, V_cap)\n",
    "plt.xlabel(\"Time (s)\")\n",
    "plt.ylabel(\"Capacitor voltage (V)\")\n",
    "plt.title(\"Charging capacitor\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52c2273d",
   "metadata": {},
   "source": [
    "**Check the graph:** What voltage does the capacitor start at? What voltage does it approach? What fraction of the final voltage is reached after one `tau`?"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a71dd110",
   "metadata": {},
   "source": [
    "### 4. Plot the charging current\n",
    "The current is largest at first. Multiplying by `1000` changes amperes to milliamperes (mA)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "4093f03f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T18:33:27.612331Z",
     "iopub.status.busy": "2026-11-03T18:33:27.611943Z",
     "iopub.status.idle": "2026-11-03T18:33:27.724267Z",
     "shell.execute_reply": "2026-11-03T18:33:27.723265Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "I_charge = (V_battery / R) * np.exp(-time/tau)\n",
    "\n",
    "plt.plot(time, I_charge * 1000)\n",
    "plt.xlabel(\"Time (s)\")\n",
    "plt.ylabel(\"Current (mA)\")\n",
    "plt.title(\"Charging current\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81dbbd57",
   "metadata": {},
   "source": [
    "### 5. Discharge through the 10.0 kΩ resistor — part (f)\n",
    "When the battery is removed, the charged capacitor acts as the source. Use the **new resistor** but keep the same capacitor. This plot uses the voltage at full charge as its starting value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "46fbcde4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T18:33:27.726719Z",
     "iopub.status.busy": "2026-11-03T18:33:27.726557Z",
     "iopub.status.idle": "2026-11-03T18:33:27.818216Z",
     "shell.execute_reply": "2026-11-03T18:33:27.817072Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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tW7dufej8EZkCvtcPERlEVlYWHB0dsWjRogqrqxraihUrMGPGDCQkJMDb29toz/NvBw8eRLdu3bB161YMGzasRp6TiMrwWCAR6a2q5eDLr3P595Luhn6eoqIifPnllwgJCamxkkJE4uI1KkSkty1btuDbb79F//79YWNjg6NHj2LTpk3o3bs3OnbsaLDneeqpp+Dn54fmzZsjOzsb69evR1RUFDZs2GCw5yAi08aiQkR6a9q0KSwsLLBs2TLk5OToLrBdtGiRQZ+nT58++Oqrr7BhwwZoNBo0atQImzdvxrPPPmvQ5yEi08VrVIiIiMhk8RoVIiIiMlksKkRERGSyavU1KlqtFklJSbC1tTXYIlNERERkXIIgIDc3F15eXg9djLBWF5WkpCT4+vqKHYOIiIgewe3bt+Hj4/PAbWp1UbG1tQVQ9kLt7OwMum+1Wo09e/agd+/ej/1GcOaM82gYnEfD4DwaBufRMMx5HnNycuDr66v7Pf4gtbqolJ/usbOzM0pRsbKygp2dndn9BTIkzqNhcB4Ng/NoGJxHw+A8Pvw9uwBeTEtEREQmjEWFiIiITBaLChEREZksFhUiIiIyWSwqREREZLJYVIiIiMhksagQERGRyWJRISIiIpPFokJEREQmi0WFiIiITBaLChEREZksFhUiIiIyWSwq93EnuwiphWKnICIiMm8sKlVY9/dNdP7oMP64zekhIiISE38TV6Gpjz0AIDpbAo1WEDkNERGR+WJRqUIzHwfYKC1QUCrB5aQcseMQERGZLRaVKljIpGgf5AQAOHrjrshpiIiIzBeLyn10CnYGAByNYVEhIiISC4vKfZQXlfPxWcgrLhU5DRERkXliUbkPPycruCgFlGoFnOBRFSIiIlGwqDxAqEPZHT9HrqeJnISIiMg8sag8QANdUUkXOQkREZF5YlF5gBA7ATKpBLHp+bidUSB2HCIiIrPDovIAlhZA83uLvx29waMqRERENY1F5SE63rv7h9epEBER1TwWlYfQradyPZ3L6RMREdUwFpWHaOJlBzuVBXKKSnExIUvsOERERGaFReUhLGRSdAx2AcC7f4iIiGoai0o1PBHiCoDXqRAREdU0FpVqeCKk7IjKufgs5BapRU5DRERkPlhUqsHXyQqBLtbQaAX8zXdTJiIiqjEsKtXUpX7Z6Z9D11JFTkJERGQ+WFSqqWtoWVE5GJ0GQeBtykRERDWBRaWa2gU5Q2khxZ3sIkSn5Iodh4iIyCywqFSTSi5Dh3pli78diOLdP0RERDWBRUUP3Rq4AQAORvM6FSIioprAoqKHrvXLisqZuEzk8DZlIiIio2NR0YOfsxWCXO/dpsxVaomIiIyORUVP5UdVDvD0DxERkdGxqOipWwPepkxERFRTWFT01CbQCZZyGVJzi3HlTo7YcYiIiOo0FhU9KS1k6BhcdpvywWjepkxERGRMLCqPoGsob1MmIiKqCSwqj6B8Of1z8VnILuBtykRERMbCovIIfBytEOJmA41WwJEbPP1DRERkLCwqj+ifVWpZVIiIiIyFReURda1ffptyKrRa3qZMRERkDKIWFY1Ggzlz5iAwMBCWlpaoV68eFi5cWCvWJ2kd6ARblQXS80oQkZAldhwiIqI6yULMJ//ggw+watUqfPfdd2jcuDHOnDmDcePGwd7eHlOnThUz2kPJZVJ0qe+K3y7ewb6rKWjh5yh2JCIiojpH1CMqx44dw5NPPokBAwYgICAAw4YNQ+/evXHq1CkxY1Vbr0buAIC/rvA2ZSIiImMQtah06NAB+/btw7Vr1wAAFy5cwNGjR9GvXz8xY1Vb1/pukEkliE7Jxe2MArHjEBER1Tminvp56623kJOTgwYNGkAmk0Gj0WDx4sUYNWpUldsXFxejuLhY931OTtkS9mq1Gmq1YdczKd/fg/ZrJQda+jng1K1M/BmZhDHt/Q2aoS6ozjzSw3EeDYPzaBicR8Mw53nU5zVLBBGvXN28eTPeeOMNfPjhh2jcuDEiIiIwffp0LF++HGPGjKm0/fz587FgwYJK4xs3boSVlVVNRK7kQJIEO+JkqG+vxeRGWlEyEBER1SYFBQV47rnnkJ2dDTs7uwduK2pR8fX1xVtvvYXJkyfrxhYtWoT169cjKiqq0vZVHVHx9fVFenr6Q1+ovtRqNfbu3YtevXpBLpffd7tbd/PRa8XfkMskOPlWV9iq7r+tOaruPNKDcR4Ng/NoGJxHwzDneczJyYGLi0u1ioqop34KCgoglVa8TEYmk0GrrfrIhFKphFKprDQul8uN9of8sH2HeDignqs1YtLycexmFgY29TJKjtrOmH9G5oTzaBicR8PgPBqGOc6jPq9X1ItpBw0ahMWLF+P333/HrVu3sH37dixfvhxDhw4VM5beejYsu/tn31Xe/UNERGRIohaVlStXYtiwYXj11VfRsGFDzJo1Cy+//DIWLlwoZiy99bhXVPZHpaJUw+tUiIiIDEXUUz+2trZYsWIFVqxYIWaMx9bCzwGOVnJkFqhxNi4TbYOcxY5ERERUJ/C9fgzAQiZFt9CyNyn862qKyGmIiIjqDhYVA+nZiNepEBERGRqLioE8EeICuUyC2PR8xKTliR2HiIioTmBRMRBblRzt7l2bsvcKT/8QEREZAouKAfVu7AEA+PNysshJiIiI6gYWFQPqfe86lfPxWUjJKRI5DRERUe3HomJA7nYqtPBzAADs4VEVIiKix8aiYmB9dKd/eJ0KERHR42JRMbDyonI89i6yCkpETkNERFS7sagYWICLNRp42EKjFbimChER0WNiUTEC3v1DRERkGCwqRtD3XlE5dC0NBSWlIqchIiKqvVhUjKChpy18nSxRXKrF4WtpYschIiKqtVhUjEAikeiOquyO5OkfIiKiR8WiYiTld//si0pFSalW5DRERES1E4uKkbTwc4SLjRK5RaU4HntX7DhERES1EouKkUilEvRuXLakPu/+ISIiejQsKkZUfvpnz+UUaLSCyGmIiIhqHxYVI2of5Aw7lQXS84px+laG2HGIiIhqHRYVI1JYSHVHVX6/eEfkNERERLUPi4qRDWjqCQDYFZnM0z9ERER6YlExso7BLrC3lCM9rxinbvL0DxERkT5YVIxMLpOiz727f36/lCRyGiIiotqFRaUGDGjqBaBslVqe/iEiIqo+FpUa0KGeMxys5EjPK8HJm1z8jYiIqLpYVGqAXCZFn0a8+4eIiEhfLCo1pP+9u392RyajVMP3/iEiIqoOFpUaUn76525+Ce/+ISIiqiYWlRoil0nR997ib79d4ukfIiKi6mBRqUH9m/D0DxERkT5YVGpQ+3rOcLSSIyO/BCd5+oeIiOihWFRqkFwmRd+wstM/v0Zw8TciIqKHYVGpYYOalS3+tivyDopLNSKnISIiMm0sKjWsbaAz3O2UyCkqxaHoNLHjEBERmTQWlRomk0ow6N6S+r9c4OkfIiKiB2FREcGTzb0BAH9dSUFecanIaYiIiEwXi4oIwrztEORijeJSLfZcThY7DhERkcliURGBRCLB4OZlp3928O4fIiKi+2JREUn56Z+/b6QjLbdY5DRERESmiUVFJIEu1mjmYw+NVsAfXFKfiIioSiwqIhp876jKLxGJIichIiIyTSwqIhrU1BMSCXAuPgvxdwvEjkNERGRyWFRE5GanQod6zgCAnRd5US0REdF/saiI7MlmZad/dpxPhCAIIqchIiIyLSwqIusT5gGFhRTXU/NwOSlH7DhEREQmhUVFZPaWcvRq6A4A+PlcgshpiIiITAuLigl4umXZ6Z9fI5Kg1mhFTkNERGQ6WFRMwBMhrnCxUeBufgnfUZmIiOhfWFRMgFwm1a1Uy9M/RERE/2BRMRFPt/ABAOy7moqsghKR0xAREZkGFhUT0cjLDg08bFGi0WLnRS6pT0REBDxiUVGr1bh9+zaio6ORkZFh6Exma1jLsqMqP5/l6R8iIiJAj6KSm5uLVatWoUuXLrCzs0NAQAAaNmwIV1dX+Pv7Y8KECTh9+rQxs9Z5Tzb3hkwqQcTtLMSk5Ykdh4iISHTVKirLly9HQEAA1q1bh549e2LHjh2IiIjAtWvXcPz4ccybNw+lpaXo3bs3+vbti+vXrxs7d53kaqtEl/quAIBtvKiWiIgIFtXZ6PTp0zh8+DAaN25c5eNt2rTB+PHjsXr1aqxbtw5HjhxBSEiIQYOai6daeGN/VCq2n0vE671CIZVKxI5EREQkmmoVlU2bNlVrZ0qlEpMmTXqsQOauZ0N32KkskJRdhOOxd9Ex2EXsSERERKKp9jUqw4YNw+7du/nGeUamksswsJkXAOAnXlRLRERmrtpFJTMzEwMGDICfnx/mzp2L2NhYY+Yya8Pv3f3zx6U7yC5Ui5yGiIhIPNUuKvv27UNsbCxefPFFrF+/HiEhIejevTs2btyI4uJiY2Y0O819HRDqboviUi1+jUgUOw4REZFo9FpHxd/fH/Pnz0dsbCz27t0LLy8vTJgwAZ6enpg8eTLOnj1rrJxmRSKR4JnWvgCALWdui5yGiIhIPI+8Mm337t2xfv16JCcnY+nSpdi8eTPatm1ryGxmbWi4NxQyKSITcxCZmC12HCIiIlE81hL6N2/exEcffYQlS5YgOzsbPXv2NFQus+dkrUDvxu4AgC2neVSFiIjMk95FpaioCOvXr0f37t0REhKC77//Hi+++CJu3ryJ3bt3GyOj2RrR2g8AsCMiEUVqjchpiIiIal611lEBgFOnTuGbb77Bli1bUFRUhKFDh2L37t3o0aMHJBIuSmYMHeo5w8fREgmZhdgVeQdDw33EjkRERFSjqn1EpV27djh58iQWLlyIpKQkbNy4ET179nzskpKYmIjnn38ezs7OsLS0RJMmTXDmzJnH2mddIZVK8EyrsotqN5/i6R8iIjI/1T6icubMGbRo0cKgT56ZmYmOHTuiW7du2LVrF1xdXXH9+nU4Ojoa9Hlqs2EtfbDir2s4eTMDN9PzEehiLXYkIiKiGlOtohIfH69XSUlMTIS3t/dDt/vggw/g6+uLdevW6cYCAwOr/TzmwMvBEp3ru+JgdBp+PHMbb/ZtIHYkIiKiGlOtUz+tW7fGyy+/jNOnT993m+zsbKxduxZhYWH4+eefq/Xkv/76K1q1aoXhw4fDzc0N4eHhWLt2bfWSm5ER99ZU+elsAtQarchpiIiIak61jqhcuXIFixcvRq9evaBSqdCyZUt4eXlBpVIhMzMTV65cweXLl9GiRQssW7YM/fv3r9aTx8bGYtWqVZg5cybefvttnD59GlOnToVCocCYMWMqbV9cXFxhFdycnBwAgFqthlpt2KXmy/dn6P0+iifqOcHZWoG03GLsiUxC70buYkeqNlOax9qM82gYnEfD4DwahjnPoz6vWSLo8S6DhYWF+P3333H06FHExcWhsLAQLi4uCA8PR58+fRAWFqZXUIVCgVatWuHYsWO6salTp+L06dM4fvx4pe3nz5+PBQsWVBrfuHEjrKys9Hru2mZnnBR/JUkRaq/Fq414VIWIiGqvgoICPPfcc8jOzoadnd0Dt9WrqBiav78/evXqha+++ko3tmrVKixatAiJiZXf46aqIyq+vr5IT09/6AvVl1qtxt69e9GrVy/I5XKD7vtRJGQWovv/jkAQgL3TOyLAuXZcVGtq81hbcR4Ng/NoGJxHwzDneczJyYGLi0u1ikq17/oxho4dOyI6OrrC2LVr1+Dv71/l9kqlEkqlstK4XC432h+yMfetj0A3ObrWd8WB6DT8eDYJ7wxoJHYkvZjKPNZ2nEfD4DwaBufRMMxxHvV5vY+1hP7jmjFjBk6cOIElS5bgxo0b2LhxI9asWYPJkyeLGctkPd+urMBtPZvAlWqJiMgsiFpUWrduje3bt2PTpk0ICwvDwoULsWLFCowaNUrMWCara6gbvB0skVWgxh+X7ogdh4iIyOhELSoAMHDgQFy6dAlFRUW4evUqJkyYIHYkkyWTSjCyTdmtyutPxImchoiIyPhELyqkn2da+8JCKsG5+CxcScoROw4REZFRPVJR+eGHH9CxY0d4eXkhLq7sX/YrVqzAL7/8YtBwVJmbrQp9wjwAAOtP8qgKERHVbXoXlfIF2vr374+srCxoNGUXdTo4OGDFihWGzkdVeL5t2UW1v5xPRF5xqchpiIiIjEfvorJy5UqsXbsW77zzDmQymW68VatWuHTpkkHDUdXaBTkh2M0G+SUabD9feb0ZIiKiukLvonLz5k2Eh4dXGlcqlcjPzzdIKHowiUSCUW39AAA/HL8FEdfsIyIiMiq9i0pgYCAiIiIqje/evRsNGzY0RCaqhqdb+sBKIcO1lDwci7krdhwiIiKj0Htl2pkzZ2Ly5MkoKiqCIAg4deoUNm3ahKVLl1ZYCp+My04lx7CWPvj+eBzW/X0LHYNdxI5ERERkcHoXlZdeegmWlpZ49913dW8q5OXlhU8++QQjRowwRka6jzEdAvD98Tjsi0pB/N0C+DnX7TdmJCIi8/NItyePGjUK169fR15eHpKTk5GQkIAXX3zR0NnoIeq52qBLfVcIAvDd8VtixyEiIjK4x1rwzcrKCm5ubobKQo9gbMcAAMCPp28jn7cqExFRHaP3qZ/w8HBIJJJK4xKJBCqVCsHBwRg7diy6detmkID0YF1CXBHkYo3Y9HxsO5eAF9oHiB2JiIjIYPQ+otK3b1/ExsbC2toa3bp1Q7du3WBjY4OYmBi0bt0ad+7cQc+ePblKbQ2RSiUY0yEAALDu2C1otbxVmYiI6g69j6ikp6fj9ddfx5w5cyqML1q0CHFxcdizZw/mzZuHhQsX4sknnzRYULq/p1v64MM/oxGblo8jN9LRpb6r2JGIiIgMQu8jKj/++CNGjhxZaXzEiBH48ccfAQAjR45EdHT046ejarFRWmB4Kx8AwLd/3xQ5DRERkeHoXVRUKhWOHTtWafzYsWNQqVQAAK1Wq/uaasaY9gGQSIAD0WmITcsTOw4REZFB6H3q57XXXsOkSZNw9uxZtG7dGgBw+vRpfPXVV3j77bcBAH/++SeaN29u0KD0YAEu1uge6oZ9Uan4+uhNLB7aROxIREREj03vovLuu+8iMDAQn332GX744QcAQGhoKNauXYvnnnsOADBp0iS88sorhk1KDzWhcxD2RaXip7MJmNmrPpxtlGJHIiIieix6FxWgbMG3UaNG3fdxS0vLRw5Ej65toBOa+tjjYkI21p+Ix7SeIWJHIiIieiyPteAbmRaJRIIJTwQBAL4/fgtFao3IiYiIiB6P3kVFo9Hgo48+Qps2beDh4QEnJ6cKHySufmEe8HawxN38Emw7lyh2HCIioseid1FZsGABli9fjmeffRbZ2dmYOXMmnnrqKUilUsyfP98IEUkfFjIpXuwUCAD46kgsF4AjIqJaTe+ismHDBqxduxavv/46LCwsMHLkSHz11VeYO3cuTpw4YYyMpKdnWvvCTmWB2PR87ItKFTsOERHRI9O7qCQnJ6NJk7JbX21sbJCdnQ0AGDhwIH7//XfDpqNHYqO0wKh2/gCAtYdjRU5DRET06PQuKj4+Prhz5w4AoF69etizZw+AsrVUlEreDmsqxnYIgFwmwalbGTgfnyl2HCIiokeid1EZOnQo9u3bB6Bs8bc5c+YgJCQEo0ePxvjx4w0ekB6Nu50KTzb3BgCsPcKjKkREVDvpvY7K+++/r/v62Wefhb+/P44dO4aQkBAMGjTIoOHo8Ux4Igg/nU3ArshkxKblIcjVRuxIREREetH7iMrhw4dRWlqq+75du3aYOXMm+vXrh8OHDxs0HD2eUA9b9GzoBkEAvjzEoypERFT76F1UunXrhoyMjErj2dnZ6Natm0FCkeG82i0YALDtfAKSsgpFTkNERKQfvYuKIAiQSCSVxu/evQtra2uDhCLDaeHniPZBzlBrBF6rQkREtU61r1F56qmnAJQt0z527NgKd/hoNBpcvHgRHTp0MHxCemyTuwXjeOxdbDoVjyndgvlmhUREVGtUu6jY29sDKDuiYmtrW+GNBxUKBdq1a4cJEyYYPiE9to7BzmjmY48LCdlY9/ctzOoTKnYkIiKiaql2UVm3bh0AICAgALNmzeJpnlpEIpHg1W7BePmHs/ju+C1M7BIEO5Vc7FhEREQPpfc1KvPmzWNJqYV6NXRHiJsNcotKsf5EnNhxiIiIqqVaR1TCw8OrvIC2KufOnXusQGQcUqkEr3arhxlbLuDrIzcxrkMgLBUysWMRERE9ULWKypAhQ4wcg2rCoKZe+HjPNSRkFmLTqXiMv/cuy0RERKaqWkVl3rx5xs5BNcBCJsWrXYPx9vZLWHUoBs+19YNKzqMqRERkuvS+RqXc2bNnsX79eqxfvx7nz583ZCYyomEtfeDtYIm03GJsPBkvdhwiIqIH0ruopKamonv37mjdujWmTp2KqVOnomXLlujRowfS0tKMkZEMSGEhxZTuZavVrjoUgyK1RuRERERE96d3UXnttdeQm5uLy5cvIyMjAxkZGYiMjEROTg6mTp1qjIxkYE+3+OeoygYeVSEiIhOmd1HZvXs3vvjiCzRs2FA31qhRI3z++efYtWuXQcORcfz7qMpqHlUhIiITpndR0Wq1kMsrLxYml8uh1WoNEoqMj0dViIioNtC7qHTv3h3Tpk1DUlKSbiwxMREzZsxAjx49DBqOjEdhIcVr5deqHIxBYQmPqhARkenRu6h89tlnyMnJQUBAAOrVq4d69eohMDAQOTk5WLlypTEykpE81cIHPo6WSM8rxoaTXK2WiIhMT7Xf66ecr68vzp07h7/++gtRUVEAgIYNG6Jnz54GD0fGpbCQYkq3YLy17RJW31tXxUqh918JIiIio9H7t9Lt27fh6+uLXr16oVevXsbIRDXo6ZY++OJgDOIzCrDu71uY3C1Y7EhEREQ6ep/6CQgIQJcuXbB27VpkZmYaIxPVILlMipm96gMouwMoq6BE5ERERET/0LuonDlzBm3atMF7770HT09PDBkyBD/99BOKi4uNkY9qwOBmXmjgYYvcolKsPhQrdhwiIiIdvYtKeHg4PvzwQ8THx2PXrl1wdXXFxIkT4e7ujvHjxxsjIxmZVCrBrN6hAIBvj91Eak6RyImIiIjKPPJ7/UgkEnTr1g1r167FX3/9hcDAQHz33XeGzEY1qEdDN7Twc0CRWouV+2+IHYeIiAjAYxSVhIQELFu2DM2bN0ebNm1gY2ODzz//3JDZqAZJJBL8X98GAIBNp+IRf7dA5ERERESPUFS+/PJLdOnSBQEBAfj+++/x7LPPIiYmBkeOHMGkSZOMkZFqSLsgZ3Su74pSrYD//XVN7DhERET6F5VFixahbdu2OHv2LCIjIzF79mz4+/sbIxuJ4P/6lF2rsiMiEVHJOSKnISIic6f3Oirx8fGQSCTGyEImIMzbHgOaeOL3S3fwwa4orBvXRuxIRERkxvQ+osKSUvfN6hMKC6kEB6LTcPR6uthxiIjIjD3yxbRUdwW6WOP5dmWn8xb/cRUarSByIiIiMlcsKlSlqT1CYKuywNU7Odh+PlHsOEREZKb0KiqCICA+Ph5FRVwQrK5zslZgyr33/fl4TzQKSzQiJyIiInOkd1EJDg7G7du3jZWHTMiYDgHwdrDEnewifPP3TbHjEBGRGdKrqEilUoSEhODu3bvGykMmRCWX4f/6lt2u/MWBG0jL5fs5ERFRzdL7GpX3338fb7zxBiIjI42Rh0zMoKZeaOZjj/wSDT7Zx0XgiIioZuldVEaPHo1Tp06hWbNmsLS0hJOTU4UPqlukUgne7t8QALDp1G1EJ+eKnIiIiMyJ3gu+rVixwggxyJS1DXJGvzAP7IpMxoKdl7HhpbZcT4eIiGqE3kVlzJgxxshBJu7t/g2xPyoVx2Lu4s/Lyegb5il2JCIiMgN6FxUA0Gg02LFjB65evQoAaNy4MQYPHgyZTGbQcGQ6fJ2s8HLnIHy6/wYW/X4VXUPdoJLzz5uIiIxL72tUbty4gYYNG2L06NHYtm0btm3bhueffx6NGzdGTEyMMTKSiZjUtR487VVIyCzEmsOxYschIiIzoHdRmTp1KurVq4fbt2/j3LlzOHfuHOLj4xEYGIipU6c+cpD3338fEokE06dPf+R9kHFZKSx0F9Z+cfAGkrIKRU5ERER1nd5F5dChQ1i2bFmFO3ycnZ3x/vvv49ChQ48U4vTp0/jyyy/RtGnTR/p5qjkDm3qiTaATitRaLN0VJXYcIiKq4/QuKkqlErm5lW9RzcvLg0Kh0DtAXl4eRo0ahbVr18LR0VHvn6eaJZFIMG9QI0glwM4LSTgZy8X/iIjIePS+mHbgwIGYOHEivv76a7Rp0wYAcPLkSUyaNAmDBw/WO8DkyZMxYMAA9OzZE4sWLXrgtsXFxSgu/md11JycHACAWq2GWq3W+7kfpHx/ht5vXVDf1QrPtPLB5tMJmLMjEjtebQe5rOrOy3k0DM6jYXAeDYPzaBjmPI/6vGaJIAiCPjvPysrCmDFjsHPnTsjlcgBAaWkpBg8ejHXr1sHBwaHa+9q8eTMWL16M06dPQ6VSoWvXrmjevPl912qZP38+FixYUGl848aNsLKy0udl0GPKVwOLI2TIL5XgSX8Nunvp9deIiIjMWEFBAZ577jlkZ2fDzs7ugdvqXVTK3bhxQ3d7csOGDREcHKzXz9++fRutWrXC3r17ddemPKyoVHVExdfXF+np6Q99ofpSq9XYu3cvevXqpStkVNFP5xIxe/tlWClk2D21IzztVZW24TwaBufRMDiPhsF5NAxznsecnBy4uLhUq6jofernvffew6xZsxAcHFyhnBQWFuLDDz/E3Llzq7Wfs2fPIjU1FS1atNCNaTQaHD58GJ999hmKi4srrcuiVCqhVCor7UsulxvtD9mY+67tnm3tj23nk3D6ViYW74rGly+0uu+2nEfD4DwaBufRMDiPhmGO86jP69X7YtoFCxYgLy+v0nhBQUGVp2Xup0ePHrh06RIiIiJ0H61atcKoUaMQERHBxeNqAalUgkVDmsBCKsGfl1OwPypF7EhERFTH6H1ERRCEKt/n5cKFC3q9KaGtrS3CwsIqjFlbW8PZ2bnSOJmuUA9bvNgpEF8ejsXcXy6jfZALLBUsmUREZBjVLiqOjo6QSCSQSCSoX79+hbKi0WiQl5eHSZMmGSUkmbapPUKw80ISEjIL8dmB63ijTwOxIxERUR1R7aKyYsUKCIKA8ePHY8GCBbC3t9c9plAoEBAQgPbt2z9WmIMHDz7Wz5M4rJUWmDe4MV7+4SzWHI7Fk829Ud/dVuxYRERUB1S7qJS/a3JgYCA6dOhgdhf+0IP1buSOng3d8dfVFLz580X8NKkDZNLKpwiJiIj0Ua2LacsXVgOA8PBwFBYWIicnp8oPMk8SiQQLhzSGjdIC5+Oz8P3xW2JHIiKiOqBaRcXR0RGpqakAAAcHBzg6Olb6KB8n8+Vpb4m3+pVdn/Lhn9FIyCwQOREREdV21Tr1s3//ft0dPfv376/yrh8iAHiujR9+vZCEUzcz8Pb2SHz1fHOxIxERUS1WraLSpUsX3dddu3Y1VhaqA6RSCd5/qgn6fnIEh6+lYUfEHVReoo+IiKh69F7wbd26ddi6dWul8a1bt+K7774zSCiq3YJcbTCtRwgAYMmuaOSa3/ttERGRgehdVJYuXQoXF5dK425ubliyZIlBQlHtN7FzEBp52iGrUI2fbur914yIiAjAIxSV+Ph4BAYGVhr39/dHfHy8QUJR7SeXSbFsWFPIpBJE3JXi90vJYkciIqJaSO+i4ubmhosXL1Yav3DhApydnQ0SiuqGMG97vNK5rNTO33kVqblFIiciIqLaRu+iMnLkSEydOhUHDhyARqOBRqPB/v37MW3aNIwYMcIYGakWe6VLEHysBWQVqvH2tksQBEHsSEREVIvoXVQWLlyItm3bokePHrC0tISlpSV69+6N7t278xoVqkRhIcWoehrIZRL8dTUVP59LFDsSERHVInoXFYVCgS1btiAqKgobNmzAtm3bEBMTg2+++QYKhcIYGamW87IGpnUPBgAs+PUykrIKRU5ERES1RbXf6+e/6tevj/r16xsyC9VhL3UKwL7oNJyPz8KbP1/E9+PbcOFAIiJ6qEcqKgkJCfj1118RHx+PkpKSCo8tX77cIMGobpFJJfh4eDP0//QIjlxPx3fHbmFsx8p3jxEREf2b3kVl3759GDx4MIKCghAVFYWwsDDcunULgiCgRYsWxshIdUSQqw3e7t8Qc3+5jCW7otCunjMaeNiJHYuIiEyY3teozJ49G7NmzcKlS5egUqnw888/4/bt2+jSpQuGDx9ujIxUh7zQzh/dG7ihpFSLaZsiUKTWiB2JiIhMmN5F5erVqxg9ejQAwMLCAoWFhbCxscF7772HDz74wOABqW6RSCRYNqwpXGwUiE7Jxfu7osSOREREJkzvomJtba27LsXT0xMxMTG6x9LT0w2XjOosFxslPhzeDADw7bFbOBCdKnIiIiIyVXoXlXbt2uHo0aMAgP79++P111/H4sWLMX78eLRr187gAalu6hbqhrEdAgAAb2y9gLTcYnEDERGRSdK7qCxfvhxt27YFACxYsAA9evTAli1bEBAQgK+//trgAanueqtfA4S62yI9rwSztl6AVstVa4mIqCK97/oJCgrSfW1tbY3Vq1cbNBCZD5Vchk9HhmPwZ0dx6Foavjwci1e61hM7FhERmRC9j6iUO3PmDH744Qf88MMPOHv2rCEzkRkJ9bDF/MGNAQAf7YnG6VsZIiciIiJTovcRlYSEBIwcORJ///03HBwcAABZWVno0KEDNm/eDB8fH0NnpDpuRGtfnIi9i18ikvDaxvP4Y9oTcLLm2zEQEdEjHFF56aWXoFarcfXqVWRkZCAjIwNXr16FVqvFSy+9ZIyMVMdJJBIsGdoEQa7WSM4pwswfI3i9ChERAXiEonLo0CGsWrUKoaGhurHQ0FCsXLkShw8fNmg4Mh/WSgt8/lwLKC2kOBhddr0KERGR3kXF19cXarW60rhGo4GXl5dBQpF5auhphwX/ul7lZOxdkRMREZHY9C4qH374IV577TWcOXNGN3bmzBlMmzYNH330kUHDkfl5trUvhjT3gkYrYPLG80jOLhI7EhERiUjvojJ27FhERESgbdu2UCqVUCqVaNu2Lc6dO4fx48fDyclJ90GkL4lEgiVPNUEDD1uk5xXjlQ1nUVzK9wMiIjJXet/1s2LFCiPEIPqHlcICX77QEoNWHsX5+Cws/O0KFg1pInYsIiISgd5FZcyYMcbIQVSBv7M1PhkRjvHfncb6E/Fo6uOAZ1r5ih2LiIhq2CMv+AYARUVFyMnJqfBBZCjdGrhhRs/6AIB3d0TiYkKWuIGIiKjG6V1U8vPzMWXKFLi5ucHa2hqOjo4VPogMaUq3YPRs6IaSUi0m/XCWb15IRGRm9C4q//d//4f9+/dj1apVUCqV+Oqrr7BgwQJ4eXnh+++/N0ZGMmNSqQTLn22OIBdrJGUX4eUfzqBIzYtriYjMhd5FZefOnfjiiy/w9NNPw8LCAk888QTeffddLFmyBBs2bDBGRjJzdio5vhrTCnYqC5yLz8Lb2y9BELhyLRGROdC7qGRkZOjeQdnOzg4ZGWVvItepUyeuTEtGE+Rqg89HtYBMKsG2c4lYw5VriYjMgt5FJSgoCDdv3gQANGjQAD/++COAsiMt5W9SSGQMT4S4Yu7ARgCA93dH4a8rKSInIiIiY9O7qIwbNw4XLlwAALz11lv4/PPPoVKpMGPGDLzxxhsGD0j0b6Pb+2NUWz8IAjBt83lEJfNOMyKiukzvdVRmzJih+7pnz56IiorC2bNnERwcjKZNmxo0HNF/SSQSzB/cGLFp+Tgeexfj1p3G9lc7wsNeJXY0IiIygsdaRwUA/P398dRTT7GkUI2Ry6RY9XwL1HO1xp3sIoz79jTyikvFjkVEREZQ7aKyf/9+NGrUqMpF3bKzs9G4cWMcOXLEoOGI7sfBSoFvx7WBi40CV+/k4NUN56DWaMWORUREBlbtorJixQpMmDABdnZ2lR6zt7fHyy+/jOXLlxs0HNGD+DpZ4ZuxrWEpl+HwtTTM2RHJ25aJiOqYaheVCxcuoG/fvvd9vHfv3jh79qxBQhFVV1MfB6wcGQ6pBNh8+jY+239D7EhERGRA1S4qKSkpkMvl933cwsICaWlpBglFpI+ejdwxf3BjAMDHe69h86l4kRMREZGhVLuoeHt7IzIy8r6PX7x4EZ6engYJRaSv0e0D8ErXegCAt7dfwu7IOyInIiIiQ6h2Uenfvz/mzJmDoqKiSo8VFhZi3rx5GDhwoEHDEenj//qEYkRrX2gFYOqmCByLSRc7EhERPaZqr6Py7rvvYtu2bahfvz6mTJmC0NBQAEBUVBQ+//xzaDQavPPOO0YLSvQwEokEi4aEIbOgBH9eTsHE789i04R2aOJjL3Y0IiJ6RNU+ouLu7o5jx44hLCwMs2fPxtChQzF06FC8/fbbCAsLw9GjR+Hu7m7MrEQPZSGT4pMR4Wgf5Iy84lKMWXcKMWl5YsciIqJHpNeCb/7+/vjjjz+Qnp6OkydP4sSJE0hPT8cff/yBwMBAY2Uk0otKLsOa0S0R5m2HjPwSPP/VSdzOKBA7FhERPYJHWpnW0dERrVu3Rps2beDo6GjoTESPzVYlx7fj2iDYzQZ3soswcu0JJGUVih2LiIj09NhL6BOZKhcbJTa81Bb+zlZIyCzEqK9OIjWn8sXgRERkulhUqE5zt1Nh44R28HawxM30fIz66iTu5hWLHYuIiKqJRYXqPG8HS2ya0A4edipcT83D81+fQmZ+idixiIioGlhUyCz4OVthw4S2cLFR4uqdHIxce4JHVoiIagEWFTIb9VxtsHliW7jaKhGVnIuRa08gLZdlhYjIlLGokFkJdrPF5ont4G6nxLWUPIxcewKpubzAlojIVLGokNmp52qDLRPbw9NehRupeRix5gRSeDcQEZFJYlEhsxTgYo0tE9vD28ESsWn5GL76OBeFIyIyQSwqZLb8nK2weWI7+DlZIT6jAE+vOoZrKblixyIion9hUSGz5utkhZ8mtUeouy1Sc4vxzJfHceF2ltixiIjoHhYVMntudipsebkdmvs6IKtAjefWnsCxmHSxYxEREVhUiAAADlYKbHipLToGOyO/RIOx605jd+QdsWMREZk9FhWie6yVFvh6TGv0buSOklItXtlwDt8duyV2LCIis8aiQvQvKrkMX4xqgVFt/SAIwLxfL+P9XVHQagWxoxERmSUWFaL/sJBJsWhIGN7oEwoAWH0oBq9vvYCSUq3IyYiIzI+oRWXp0qVo3bo1bG1t4ebmhiFDhiA6OlrMSEQAAIlEgsndgvHhsKaQSSXYfj4RY9edQnaBWuxoRERmRdSicujQIUyePBknTpzA3r17oVar0bt3b+Tn54sZi0hneCtffDO2NawVMhyLuYuhq/7GrXT+/SQiqimiFpXdu3dj7NixaNy4MZo1a4Zvv/0W8fHxOHv2rJixiCroUt8VWyd1gJe9CrFp+Rjyxd84GXtX7FhERGbBQuwA/5adnQ0AcHJyqvLx4uJiFBf/8263OTk5AAC1Wg212rCH5Mv3Z+j9mpu6Mo8hrpbY+nJbvLLhPC4m5uD5r09i4eBGeLqFd408f12ZR7FxHg2D82gY5jyP+rxmiSAIJnE7g1arxeDBg5GVlYWjR49Wuc38+fOxYMGCSuMbN26ElZWVsSMSoUQDbIiRIuJu2cHIrp5aDPbXQiYRORgRUS1SUFCA5557DtnZ2bCzs3vgtiZTVF555RXs2rULR48ehY+PT5XbVHVExdfXF+np6Q99ofpSq9XYu3cvevXqBblcbtB9m5O6OI9arYBP9sfgi0OxAIAO9Zyw4pmmcLRSGO056+I8ioHzaBicR8Mw53nMycmBi4tLtYqKSZz6mTJlCn777TccPnz4viUFAJRKJZRKZaVxuVxutD9kY+7bnNS1efy/fg0R5uOAWVsv4FhMBp7+8iTWvNAKDT0NW5j/q67No1g4j4bBeTQMc5xHfV6vqBfTCoKAKVOmYPv27di/fz8CAwPFjEOkl/5NPLHt1Q7wc7LC7YxCPPXFMfx2MUnsWEREdYqoRWXy5MlYv349Nm7cCFtbWyQnJyM5ORmFhYVixiKqtgYedvh1Skc8EeKCQrUGUzaex4Kdl7k4HBGRgYhaVFatWoXs7Gx07doVnp6euo8tW7aIGYtILw5WCqwb2xqvdK0HAFj39y08u+Y4ErNYuImIHpfop36q+hg7dqyYsYj0ZiGT4s2+DfDV6FawU1ngfHwWBn56BAejU8WORkRUq/G9fogMqGcjd/w+9Qk08bZHZoEa4749jQ92R0Gt4akgIqJHwaJCZGC+TlbYOqm97h2YVx2MwfDVxxF/t0DsaEREtQ6LCpERqOQyLB7aBF+MagE7lQUibmeh/6dH8EtEotjRiIhqFRYVIiPq38QTf0x7Aq38HZFXXIppmyPw+o8XkFtkfktmExE9ChYVIiPzcbTC5ontMLV7MCQS4OdzCei74ghO8I0NiYgeikWFqAZYyKSY2TsUmye0g4+jJRKzCjFy7Qks+eMqitQaseMREZksFhWiGtQ2yBm7pj2BZ1r5QBCANYdj8eRnfyMyMVvsaEREJolFhaiG2arkWDasGda80BLO1gpEp+Tiyc//xkd/RqO4lEdXiIj+jUWFSCS9G3vgzxmd0b+JBzRaAZ8duIGBnx7F+fhMsaMREZkMFhUiEbnYKPHFqJb4YlQLuNgocD01D0+vOobFv19BQUmp2PGIiETHokJkAvo38cTeGV0wNNwbWgFYe+Qmei0/jANRXIKfiMwbiwqRiXC0VuB/zzbHN2Nbwduh7M6gcd+exuQN55CSUyR2PCIiUbCoEJmY7g3csXdmZ0zsHASZVILfL91B30+P4fAdCUr5nkFEZGZYVIhMkJXCAm/3b4idUzqhua8D8opL8fMtGYasOoGTXCiOiMwIiwqRCWvkZYefX+mA9wY3hJWFgOiUPDy75gSmbT7P00FEZBZYVIhMnEwqwcjWvni3uQYjW/tAIgF+iUhCt48O4rP917myLRHVaSwqRLWEtRx4b3Aj7JzSCeF+Digo0eCjPdfQ/aOD+CUiEYIgiB2RiMjgWFSIapkwb3v8PKkDPhnRHF72KiRlF2Ha5ggM/eIYztzKEDseEZFBsagQ1UJSqQRPNvfG/lldMat3fVgpZIi4nYVhq4/jpe/O4FpKrtgRiYgMgkWFqBZTyWWY0j0EB9/oipFtfCGVAH9dTUHfFYfxxtYLSMoqFDsiEdFjYVEhqgPcbFVY+lRT7JnRBX0be0ArAFvPJqDrRwexYOdlpObyDiEiqp1YVIjqkGA3G6x+oSW2v9oB7YKcUFKqxbq/b6HzsgNY8sdV3M0rFjsiEZFeWFSI6qBwP0dsmtAO619si3A/BxSptVhzOBZPLDuAD3ZHsbAQUa3BokJUR0kkEnQKccG2Vzpg3djWaOJtj4ISDVYdjEGnDw5g4W9XkMpF44jIxLGoENVxEokE3Rq44dcpHbHmhZZo6mOPQrUGXx+9iU7LDmDOjkjczigQOyYRUZUsxA5ARDVDIpGgd2MP9GrkjsPX07Fy33WcicvEDyfisOFkHAY09cLLnYMQ5m0vdlQiIh0WFSIzI5FI0KW+KzqHuOBEbAa+OHgDR66nY+eFJOy8kIROwS6Y2DkIT4S4QCKRiB2XiMwciwqRmZJIJGhfzxnt6znjclI21hyOxW8X7+DojXQcvZGOEDcbjO8UiKHh3lDJZWLHJSIzxWtUiAiNvezxyYhwHJzVFWM7BMBaIcP11DzM3nYJ7Zfuw0d/RiM5mxfeElHNY1EhIh1fJyvMH9wYx2b3wLsDGsLbwRKZBWp8duAGOn6wH6+sP4tjMel8A0QiqjE89UNEldhbyvHSE0EY2yEAf11NwTd/38KpmxnYFZmMXZHJCHazwfNt/TC0hQ/sLeVixyWiOoxFhYjuy0ImRd8wT/QN80R0ci5+OHEL288l4kZqHubvvIKlu6IwoKknRrbxQyt/R158S0QGx6JCRNUS6mGLRUOa4M2+DbDtXCI2nYpHVHIutp1LxLZziQh2s8EzrXwwJNwbbrYqseMSUR3BokJEerFVyTGmQwBGt/fH+dtZ2HwqHjsv3MGN1Dws+SMKH+yORrdQVwxr6YPuDdyhsOClcET06FhUiOiRSCQStPBzRAs/R8wZ2Ai/XkjC1jMJiLidhb+upuKvq6lwtJJjYFMvDAn3Rgs/B54aIiK9sagQ0WOzVckxqq0/RrX1x43UXGw9m4Dt5xKRmluMH07E4YcTcfBzssKQ5l4Y3NwbwW42YkcmolqCRYWIDCrYzRaz+zXEG71DcSzmLnacT8Tuy8mIzyjAp/tv4NP9N9DQ0w4Dm3piUFMv+DlbiR2ZiEwYiwoRGYWFTIrO9V3Rub4rFpWUYu+VFOw4n4gj19Nx9U4Ort7JwYd/RqOpjz36hXmib5gHAl2sxY5NRCaGRYWIjM5KYYEnm3vjyebeyCoowZ+Xk7Hzwh0ci0nHxYRsXEzIxge7o9DAwxZ9wzzQN8wDoe62vKaFiFhUiKhmOVgp8GxrPzzb2g/pecX483Iydkcm41jMXUQl5yIqORcr/roOXydL9Gzojl6N3NEmwAkWMt49RGSOWFSISDQuNkrdRbhZBSXYeyUFuyOTceRGOm5nFGLd37ew7u9bsLeUo0t9V3Rv4IYu9V3haK0QOzoR1RAWFSIyCQ5WCgxv5YvhrXxRUFKKw9fSsfdKCvZHpSCzQI1fLyTh1wtJkEqA5r4O6N7ADZ3ruyLMyx5SKU8REdVVLCpEZHKsFBa6a1U0WgHn4jOxPyoVB6JSEZWci3PxWTgXn4WP9lyDk7UCT4S4oHOIKzqFuMDdjqviEtUlLCpEZNJkUglaBzihdYAT3uzbAElZhTgQnYpD0Wk4FnMXGfkl+CUiCb9EJAEAQtxs0DHYBR2DXdAuyAm2Kr5pIlFtxqJCRLWKl4Ol7roWtUaLc3GZOHw9DYevpSMyKRvXU/NwPTUP3x67BakEaOJtj3ZBzmhXzxnNvW3Fjk9EemJRIaJaSy6Tom2QM9oGOeONPkBWQQmOx9zF0Rvp+PtGOm7dLcCFhGxcSMjGl4djIZNK4GUpQ4QkGm2DXNA6wBHONkqxXwYRPQCLChHVGQ5WCvRr4ol+TTwBAElZhTh58y6Ox9zFidgMxGcU4Ha+BOuOxWHdsTgAQD1Xa7Tyd0JLf0e0DHBEkIs1128hMiEsKkRUZ3k5WGJouA+GhvsAAOLTc7F2xwGoHf1xNi4L11PzEJOWj5i0fGw5cxsA4GglR7ifI5r7OiDczwHNfB1gx+tciETDokJEZsPTXoVWrgL6928EuVyOjPwSnI3LxNm4TJyLy8SFhCxkFqixPyoV+6NSdT9Xz9UazXwc0NTHHk19HdDI0w4quUzEV0JkPlhUiMhsOVkr0KtR2eq3AFBSqsXlpGxE3M7C+fgsRNzOQnxGge6oy7bziQAAC6kEIe62CPOyQ5i3PcK87dDQ0w5WCv4vlcjQ+F8VEdE9Cgspwv0cEe7niHEdy8bu5hXjYkI2LiRk3Xtfoiyk55Xo3lhx69kEAIBEAgQ6W6Ohlx0aeZZ9NPC0hYedite8ED0GFhUiogdwtlGiWwM3dGvgBgAQBAFJ2UW4nJiNyKSce5+zkZJTjNj0fMSm5+P3i3d0P29vKUeohy0aeNiigYcd6rvbIMTdFvaWvO6FqDpYVIiI9CCRSODtYAlvB0v0buyhG0/LLcbVOzm4cu9Iy5WkHMSm5yO7UI1TNzNw6mZGhf242ylR390WwW42ZR+uZZ95uzRRRSwqREQG4GqrhKutKzrXd9WNFak1uJGah+jkXESnlL0z9PWUXNzJLkJKTjFScopx5Hp6hf04WskR5GqDIBfrss+u1qjnag1fJysoLXgBL5kfFhUiIiNRyWX3Lra1rzCeU6TG9ZQ8XE/JvXeLdB5upOYhIbMQmQVq3Z1I/yaVlN1uHehiDX9nKwQ4W8PfuexrPycr3oVEdRaLChFRDbNTycsWmPN3rDBeWKJBTFpe2bUuaXmITctHbHoebqblI79Eg4TMQiRkFuLI9cr7dLdTws/JCr6OVvBxKisvPo6W8HG0hIedChYyaQ29OiLDYlEhIjIRloqqj8AIgoC0vGLE3S3AzfR83ErPR1xGAeLu5iPubgFyi0p1p5JO38qstF+ZVAIPOxV8HMuurfF2tITXvetsvBxU8LS3hLWSvw7INPFvJhGRiZNIJHCzVcHNVoXWAU4VHhMEAVkFasRlFOB2RgHiMwqQkFn2OTGzEIlZhVBrBCRmlX19P7YqC3jZW8LDXgVPexXc7VTwsFfB495ndzsVHK3kvNWaahyLChFRLSaRSOBorYCjtQLNfR0qPa7VCkjNLUZCZgESMguRlF2IxMxCJN0rLneyi5BbVIrcolJEF5Vd9Hs/cllZYXK1VUCbL8UpzVV42FvCzU4JV1slXGzKPjtbK6Gw4KkmMgwWFSKiOkwqlZQdGbFXoVVA1dvkFZciObsQSVlFuJNdiOTsYiTnFCE5uxDJOcVIzSnC3fyS/xyZkeLiqdv3fV57SzlcbBRwsSkrMM73vnayVsDZWlH22UYBJ2sl7C3lkEl5pIaqxqJCRGTmbJQWCHazRbCb7X23KSnVIi2vGCk5RUjKyMfBk+fg6heMjPxSpOYWITW3GOl5xbibV4JSrYDsQjWyC9WISct/6PNLJICDpRxO1go4WingYKWAk7Vc97WjlRwOVnLYWyrgaC2Hg6UC9pZyqORSnooyAywqRET0UAoLqW6huyaeNtDECejfMwRyecUVdrVaAVmFaqTlFuNufjHS80pw916BuZtf/rkEGfll4zlFpRAEILNAjcwCNYCHFxtdJpkU9lZy2Fv+82Gnsij7bCmHnUoOO0sL2KrKvrZVWdz7KPuat3TXDiwqRERkMFKpBE73Tu0A9z9CU06t0SKzoASZ+Wpk5JeUfV1QgqyCf77PLlAjq1CNrIISZBeWFRqNVkCJRou03GKk5RY/UlaFTAqbe+XFRln2Uf61tdICNioL2Cjufa20gJVS9s/XCtm9zxawVspgKZfx6I6RsKgQEZFo5DKp7o6m6hIEAfklGl1xyS5UI6dQjZzC0rKvi8rGcotKy8aLyh7LKSobyysuBQCUaLTIuHd053FJJIClXAYrRVmJsVLIYFn+WV5xrGw7GRQyCWJSJFBHJMHGUgGlvOwxle6zFJZyGZT3vlbIzPNUl0kUlc8//xwffvghkpOT0axZM6xcuRJt2rQROxYREZkgiUSiOwLi4/jw7f9LoxWQX1J2p1NeUSnyiv8pMLlFpcj/1+e8ex/5xaXIL9GUfS4uRcG9rwvUGggCIAhAQYkGBSUaPdPIsCU2spqvG1BZlJUW5X8/y2VQWpR9r5RL//naQqr7UNwbU/zre4VFWQGSW0ihlP0zJpf985itygIOVgr9J9pARC8qW7ZswcyZM7F69Wq0bdsWK1asQJ8+fRAdHQ03Nzex4xERUR0jk0rKrl9RPf47WGu1AgrVZQWlsESD/JJSFJSU6kpL4b3PBSWlKCzR6LYtUmuQV6RGXEIS7JxcUaLR6h4rVmtRpC7btkitgVYoey5BAArvjQPqx85eXQOaeuLz51rU2PP9l+hFZfny5ZgwYQLGjRsHAFi9ejV+//13fPPNN3jrrbdETkdERHR/UqkE1veuadGXWq3GH38koH//lpUuSi4nCALUGgFFpWWlpbzEFKm1KC4t+1yk1qBEU/Z9+ePFpVqUlGpRXHpv/F/fl/xnrERT9ll97/O/x0o0WqhEfjNMUYtKSUkJzp49i9mzZ+vGpFIpevbsiePHj1favri4GMXF/1w0lZOTA6DsD1utNmy7LN+fofdrbjiPhsF5NAzOo2FwHg2juvMoAWApAyxlMkAlA/D4R4L0ZazfsdUhalFJT0+HRqOBu7t7hXF3d3dERUVV2n7p0qVYsGBBpfE9e/bAysrKKBn37t1rlP2aG86jYXAeDYPzaBicR8Mwx3ksKCio9rain/rRx+zZszFz5kzd9zk5OfD19UXv3r1hZ2dn0OdSq9XYu3cvevXqdd9DcvRwnEfD4DwaBufRMDiPhmHO81h+RqQ6RC0qLi4ukMlkSElJqTCekpICDw+PStsrlUoolcpK43K53Gh/yMbctznhPBoG59EwOI+GwXk0DHOcR31er6jvGqVQKNCyZUvs27dPN6bVarFv3z60b99exGRERERkCkQ/9TNz5kyMGTMGrVq1Qps2bbBixQrk5+fr7gIiIiIi8yV6UXn22WeRlpaGuXPnIjk5Gc2bN8fu3bsrXWBLRERE5kf0ogIAU6ZMwZQpU8SOQURERCZG1GtUiIiIiB6ERYWIiIhMFosKERERmSwWFSIiIjJZLCpERERkslhUiIiIyGSxqBAREZHJMol1VB6VIAgA9Htzo+pSq9UoKChATk6O2b0HgyFxHg2D82gYnEfD4DwahjnPY/nv7fLf4w9Sq4tKbm4uAMDX11fkJERERKSv3Nxc2NvbP3AbiVCdOmOitFotkpKSYGtrC4lEYtB95+TkwNfXF7dv34adnZ1B921OOI+GwXk0DM6jYXAeDcOc51EQBOTm5sLLywtS6YOvQqnVR1SkUil8fHyM+hx2dnZm9xfIGDiPhsF5NAzOo2FwHg3DXOfxYUdSyvFiWiIiIjJZLCpERERkslhU7kOpVGLevHlQKpViR6nVOI+GwXk0DM6jYXAeDYPzWD21+mJaIiIiqtt4RIWIiIhMFosKERERmSwWFSIiIjJZLCpERERkslhUqvD5558jICAAKpUKbdu2xalTp8SOVKssXboUrVu3hq2tLdzc3DBkyBBER0eLHavWe//99yGRSDB9+nSxo9Q6iYmJeP755+Hs7AxLS0s0adIEZ86cETtWraLRaDBnzhwEBgbC0tIS9erVw8KFC6v1Xi3m7PDhwxg0aBC8vLwgkUiwY8eOCo8LgoC5c+fC09MTlpaW6NmzJ65fvy5OWBPFovIfW7ZswcyZMzFv3jycO3cOzZo1Q58+fZCamip2tFrj0KFDmDx5Mk6cOIG9e/dCrVajd+/eyM/PFztarXX69Gl8+eWXaNq0qdhRap3MzEx07NgRcrkcu3btwpUrV/Dxxx/D0dFR7Gi1ygcffIBVq1bhs88+w9WrV/HBBx9g2bJlWLlypdjRTFp+fj6aNWuGzz//vMrHly1bhk8//RSrV6/GyZMnYW1tjT59+qCoqKiGk5owgSpo06aNMHnyZN33Go1G8PLyEpYuXSpiqtotNTVVACAcOnRI7Ci1Um5urhASEiLs3btX6NKlizBt2jSxI9Uqb775ptCpUyexY9R6AwYMEMaPH19h7KmnnhJGjRolUqLaB4Cwfft23fdarVbw8PAQPvzwQ91YVlaWoFQqhU2bNomQ0DTxiMq/lJSU4OzZs+jZs6duTCqVomfPnjh+/LiIyWq37OxsAICTk5PISWqnyZMnY8CAARX+XlL1/frrr2jVqhWGDx8ONzc3hIeHY+3atWLHqnU6dOiAffv24dq1awCACxcu4OjRo+jXr5/IyWqvmzdvIjk5ucJ/2/b29mjbti1/5/xLrX5TQkNLT0+HRqOBu7t7hXF3d3dERUWJlKp202q1mD59Ojp27IiwsDCx49Q6mzdvxrlz53D69Gmxo9RasbGxWLVqFWbOnIm3334bp0+fxtSpU6FQKDBmzBix49Uab731FnJyctCgQQPIZDJoNBosXrwYo0aNEjtarZWcnAwAVf7OKX+MWFTIyCZPnozIyEgcPXpU7Ci1zu3btzFt2jTs3bsXKpVK7Di1llarRatWrbBkyRIAQHh4OCIjI7F69WoWFT38+OOP2LBhAzZu3IjGjRsjIiIC06dPh5eXF+eRjIqnfv7FxcUFMpkMKSkpFcZTUlLg4eEhUqraa8qUKfjtt99w4MAB+Pj4iB2n1jl79ixSU1PRokULWFhYwMLCAocOHcKnn34KCwsLaDQasSPWCp6enmjUqFGFsYYNGyI+Pl6kRLXTG2+8gbfeegsjRoxAkyZN8MILL2DGjBlYunSp2NFqrfLfK/yd82AsKv+iUCjQsmVL7Nu3Tzem1Wqxb98+tG/fXsRktYsgCJgyZQq2b9+O/fv3IzAwUOxItVKPHj1w6dIlRERE6D5atWqFUaNGISIiAjKZTOyItULHjh0r3R5/7do1+Pv7i5SodiooKIBUWvFXhkwmg1arFSlR7RcYGAgPD48Kv3NycnJw8uRJ/s75F576+Y+ZM2dizJgxaNWqFdq0aYMVK1YgPz8f48aNEztarTF58mRs3LgRv/zyC2xtbXXnWu3t7WFpaSlyutrD1ta20nU91tbWcHZ25vU+epgxYwY6dOiAJUuW4JlnnsGpU6ewZs0arFmzRuxotcqgQYOwePFi+Pn5oXHjxjh//jyWL1+O8ePHix3NpOXl5eHGjRu672/evImIiAg4OTnBz88P06dPx6JFixASEoLAwEDMmTMHXl5eGDJkiHihTY3Ytx2ZopUrVwp+fn6CQqEQ2rRpI5w4cULsSLUKgCo/1q1bJ3a0Wo+3Jz+anTt3CmFhYYJSqRQaNGggrFmzRuxItU5OTo4wbdo0wc/PT1CpVEJQUJDwzjvvCMXFxWJHM2kHDhyo8v+HY8aMEQSh7BblOXPmCO7u7oJSqRR69OghREdHixvaxEgEgcsKEhERkWniNSpERERkslhUiIiIyGSxqBAREZHJYlEhIiIik8WiQkRERCaLRYWIiIhMFosKERERmSwWFSIiIjJZLCpEZFBjx44VdfnvF154QfdOyQ8zYsQIfPzxx0ZORESPgyvTElG1SSSSBz4+b948zJgxA4IgwMHBoWZC/cuFCxfQvXt3xMXFwcbG5qHbR0ZGonPnzrh58ybs7e1rICER6YtFhYiqrfwNJgFgy5YtmDt3boV3JraxsalWQTCWl156CRYWFli9enW1f6Z169YYO3YsJk+ebMRkRPSoeOqHiKrNw8ND92Fvbw+JRFJhzMbGptKpn65du+K1117D9OnT4ejoCHd3d6xdu1b3ruS2trYIDg7Grl27KjxXZGQk+vXrBxsbG7i7u+OFF15Aenr6fbNpNBr89NNPGDRoUIXxL774AiEhIVCpVHB3d8ewYcMqPD5o0CBs3rz58SeHiIyCRYWIjO67776Di4sLTp06hddeew2vvPIKhg8fjg4dOuDcuXPo3bs3XnjhBRQUFAAAsrKy0L17d4SHh+PMmTPYvXs3UlJS8Mwzz9z3OS5evIjs7Gy0atVKN3bmzBlMnToV7733HqKjo7F792507ty5ws+1adMGp06dQnFxsXFePBE9FhYVIjK6Zs2a4d1330VISAhmz54NlUoFFxcXTJgwASEhIZg7dy7u3r2LixcvAgA+++wzhIeHY8mSJWjQoAHCw8PxzTff4MCBA7h27VqVzxEXFweZTAY3NzfdWHx8PKytrTFw4ED4+/sjPDwcU6dOrfBzXl5eKCkpqXBai4hMB4sKERld06ZNdV/LZDI4OzujSZMmujF3d3cAQGpqKoCyi2IPHDigu+bFxsYGDRo0AADExMRU+RyFhYVQKpUVLvjt1asX/P39ERQUhBdeeAEbNmzQHbUpZ2lpCQCVxonINLCoEJHRyeXyCt9LJJIKY+XlQqvVAgDy8vIwaNAgREREVPi4fv16pVM35VxcXFBQUICSkhLdmK2tLc6dO4dNmzbB09MTc+fORbNmzZCVlaXbJiMjAwDg6upqkNdKRIbFokJEJqdFixa4fPkyAgICEBwcXOHD2tq6yp9p3rw5AODKlSsVxi0sLNCzZ08sW7YMFy9exK1bt7B//37d45GRkfDx8YGLi4vRXg8RPToWFSIyOZMnT0ZGRgZGjhyJ06dPIyYmBn/++SfGjRsHjUZT5c+4urqiRYsWOHr0qG7st99+w6effoqIiAjExcXh+++/h1arRWhoqG6bI0eOoHfv3kZ/TUT0aFhUiMjkeHl54e+//4ZGo0Hv3r3RpEkTTJ8+HQ4ODpBK7/+/rZdeegkbNmzQfe/g4IBt27ahe/fuaNiwIVavXo1NmzahcePGAICioiLs2LEDEyZMMPprIqJHwwXfiKjOKCwsRGhoKLZs2YL27ds/dPtVq1Zh+/bt2LNnTw2kI6JHwSMqRFRnWFpa4vvvv3/gwnD/JpfLsXLlSiOnIqLHwSMqREREZLJ4RIWIiIhMFosKERERmSwWFSIiIjJZLCpERERkslhUiIiIyGSxqBAREZHJYlEhIiIik8WiQkRERCaLRYWIiIhM1v8D7oA56bLeHI8AAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R_discharge = 10000\n",
    "tau_discharge = R_discharge * C\n",
    "time_discharge = np.linspace(0, 5*tau_discharge, 100)\n",
    "V_discharge = V_battery * np.exp(-time_discharge/tau_discharge)\n",
    "\n",
    "plt.plot(time_discharge, V_discharge)\n",
    "plt.xlabel(\"Time (s)\")\n",
    "plt.ylabel(\"Capacitor voltage (V)\")\n",
    "plt.title(\"Discharging capacitor\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14c8389f",
   "metadata": {},
   "source": [
    "### 6. Plot the discharge current magnitude\n",
    "Here we plot **magnitude** only. The discharge current flows opposite to the charging-current direction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "deb0c89a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-03T18:33:27.821431Z",
     "iopub.status.busy": "2026-11-03T18:33:27.821277Z",
     "iopub.status.idle": "2026-11-03T18:33:27.915205Z",
     "shell.execute_reply": "2026-11-03T18:33:27.914309Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "I_discharge = (V_battery / R_discharge) * np.exp(-time_discharge/tau_discharge)\n",
    "\n",
    "plt.plot(time_discharge, I_discharge * 1000)\n",
    "plt.xlabel(\"Time (s)\")\n",
    "plt.ylabel(\"Current magnitude (mA)\")\n",
    "plt.title(\"Discharging current\")\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "59cd53c7",
   "metadata": {},
   "source": [
    "### Try it yourself\n",
    "1. Change `R` from `47000` to `94000`. Run the charging cells again. What happens to the charging speed?\n",
    "2. Restore `R = 47000`. Change `C` from `220e-6` to `110e-6`. What happens?\n",
    "3. Why do both the capacitor voltage and current magnitude decrease during discharge?\n",
    "\n",
    "**Reminder:** The graphs help you understand the physics; show your equations and calculations in the assignment itself."
   ]
  }
 ],
 "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": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
