{
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  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
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    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.7.0"
    },
    "toc": {
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      "title_cell": "Kazalo",
      "title_sidebar": "Kazalo",
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      "toc_position": {},
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    },
    "colab": {
      "name": "Primer_diff_enacbe_analiticno.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "gbv0R0OP2E2F",
        "XBJ_74mu7zB-",
        "iLpLqy3h9OI0"
      ],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/osnove/Dodatno/blob/master/Primer_diff_enacbe_analiticno.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pUMPiVRLaAb0",
        "colab_type": "text"
      },
      "source": [
        "# Primeri uporabe simbolnega računa za analitičen izračun prehodnega pojava\n",
        "\n",
        "Dejan Križaj, 2019\n",
        "\n",
        "**Namen:** Prikazan bo primer uporabe knjižnice Sympy za analitičen izračun diferencialne enačbe prvega reda za nekaj primerov RLC vezij. Pri tem bo v vsakem primeru prikazan nekoliko drugačen način reševanja ali izrisa rešitve.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9rr8qUxl5gs4",
        "colab_type": "text"
      },
      "source": [
        "<div class=\"alert alert-block alert-info\">\n",
        "<b>Namig:</b> Obstajata dve verziji tega dokumenta. Ena je v obliki html datoteke (končnica html), ki je ni mogoče izvajati, druga pa ima končnico ipny (Jupyter Notebook), ki jo lahko izvajamo z Jupyter aplikacijo. To aplikacijo imate lahko naloženo na vašem računalniku in se izvaja v brskalniku, lahko jo ogledujete s spletno aplikacijo nbViewer, s spletnimi aplikacijami Binder ali Google Colab pa jo lahko tudi zaganjate in spreminjate. Več o tem si preberite v \n",
        "<a href=\"http://lbm.fe.uni-lj.si/index.php?option=com_content&view=article&id=59&Itemid=135&lang=si\">tem članku</a>.\n",
        "    \n",
        "Za izvajanje tega zvezka ne potrebujete posebnega znanja programiranja v Pythonu, lahko pa poljubno spreminjate kodo in se sproti učite tudi uporabe programskega jezika.\n",
        "</div>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RgBhQgf9aAb2",
        "colab_type": "text"
      },
      "source": [
        "***\n",
        "## Vklop zaporedne vezave kondenzatorja in upora na enosmerni napetostni vir \n",
        "Rešujemo diferencialno enačbo $R\\frac{\\text{d}i}{\\text{d}t}+\\frac{i}{C}=0$."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qSVSEifSaAb3",
        "colab_type": "text"
      },
      "source": [
        "Najprej vnesemo potrebne knjižnice: "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jkwubJesaAb4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import numpy as np\n",
        "from sympy import *\n",
        "from IPython.display import *\n",
        "import matplotlib.pyplot as plt\n",
        "#matplotlib inline \n",
        "from IPython.display import Math, HTML\n",
        "\n",
        "def load_mathjax_in_cell_output():  # Te vrstice so potrebne, da se izpišejo enačbe. Potrebno le za Colab \n",
        "  display(HTML(\"<script src='https://www.gstatic.com/external_hosted/\"\n",
        "               \"mathjax/latest/MathJax.js?config=default'></script>\"))\n",
        "get_ipython().events.register('pre_run_cell', load_mathjax_in_cell_output)\n",
        "import sympy\n",
        "sympy.init_printing()\n",
        "init_printing(use_latex=True)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "w5YukPc1sL5t",
        "colab_type": "text"
      },
      "source": [
        "Pripravimo spremenljivke, tvorimo enačbo in jo rešimo."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "N9jU9oTYsB0k",
        "colab_type": "code",
        "outputId": "f1ee8684-6339-4e11-c880-90ba3f1543d9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        }
      },
      "source": [
        "var('R C t C1 a Ug') # priprava spremenljivk\n",
        "i = Function(\"i\")(t) # funkcija toka\n",
        "\n",
        "de = Eq(i/C+R*i.diff(t)) # zapis diferencialne enačbe\n",
        "display(de) # izpis enačbe\n",
        "des = dsolve(de,i) # rešitev enačbe\n",
        "display(des) # izpis rešitve\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAAhCAYAAACr3SvgAAAABHNCSVQICAgIfAhkiAAABvxJREFU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\nFClSpEiRIkWKFClSpDie8B9/JAnfyznlhAAAAABJRU5ErkJggg==\n",
            "text/latex": "$$R \\frac{d}{d t} i{\\left (t \\right )} + \\frac{1}{C} i{\\left (t \\right )} = 0$$",
            "text/plain": [
              "  d          i(t)    \n",
              "R⋅──(i(t)) + ──── = 0\n",
              "  dt          C      "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAaCAYAAACzWm4FAAAABHNCSVQICAgIfAhkiAAABZtJREFU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\nJEjQp/EvEs57NPqeB6wAAAAASUVORK5CYII=\n",
            "text/latex": "$$i{\\left (t \\right )} = e^{\\frac{1}{R} \\left(C_{1} - \\frac{t}{C}\\right)}$$",
            "text/plain": [
              "             t\n",
              "        C₁ - ─\n",
              "             C\n",
              "        ──────\n",
              "          R   \n",
              "i(t) = ℯ      "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NTumMNjvaAb8",
        "colab_type": "text"
      },
      "source": [
        "Rešitev diferencialne enačbe je ustrezna, le iz začetnega pogoja je potrebno še določiti konstanto $C_1$. Ta mora izhajati iz pogoja $u_C(t=0^+)=u_C(t=0^-)$. Torej mora biti napetost na kondezatorju ob preklopu enaka nič. Ker mora biti hkrati zadoščeno 2. Kirchoffovemu zakonu, mora biti napetost generatorja ob preklopu enaka napetosti na uporu $u_g(t=0)=U_g=u_R(t=0)=R i(t=0)$ in torej $i(t=0)=U_g/R$.\n",
        "\n",
        "V tem primeru bomo to upoštevali \"ročno\", tako, da bomo sami preuredili rešitev enačbe, saj lahko člen $e^{C_1} $ zapišemo z novo konstanto $a$, torej lahko tvorimo enačbo $i(t)=a e^{\\frac{-t}{RC}}$. V ta namen bomo uporabili funkcijo $Lambda$. \n",
        "\n",
        "Ker je $i(t=0)= a$, je $a=U_g/R$. S tem smo prišli do končne oblike rešitve."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EfV6F-V0aAb8",
        "colab_type": "code",
        "outputId": "71ca0eb1-02cb-44b3-e58b-8a2c63fbf51f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 121
        }
      },
      "source": [
        "des = des.subs(C1,0) # za C1 vstavimo 0 in nato s funkcijo Lambda spremenimo rešitev v bolj praktično obliko\n",
        "display(des)\n",
        "\n",
        "f = Lambda((t,R,C,a),(a* des.rhs)) # ki je a*(desna stran enačbe - rhs=right hand side)\n",
        "#a=Ug/R # a je očitno tok ob času t=0, ki je enak Ug/R\n",
        "display(f(t,R,C,Ug/R))\n",
        "# display(Latex('$i(t) = ' + str(latex(f(t,R,C,Ug/R))) + '$')) # izpišemo rešitev z uporabo Latex sintakse, ne dela v Colabu"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAG0AAAAYCAYAAADwF3MkAAAABHNCSVQICAgIfAhkiAAABH9JREFU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\nHXXU0VH4G7t5GRb1l++VAAAAAElFTkSuQmCC\n",
            "text/latex": "$$i{\\left (t \\right )} = e^{- \\frac{t}{C R}}$$",
            "text/plain": [
              "        -t \n",
              "        ───\n",
              "        C⋅R\n",
              "i(t) = ℯ   "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGgAAAAaCAYAAABb9hlrAAAABHNCSVQICAgIfAhkiAAABSdJREFU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\nRS/C33tdcQq+d1QuAAAAAElFTkSuQmCC\n",
            "text/latex": "$$\\frac{Ug}{R} e^{- \\frac{t}{C R}}$$",
            "text/plain": [
              "    -t \n",
              "    ───\n",
              "    C⋅R\n",
              "Ug⋅ℯ   \n",
              "───────\n",
              "   R   "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lHR_Nt9OaAb_",
        "colab_type": "code",
        "outputId": "36758ac5-12ac-4289-fc9d-eab7c5c55c1a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 287
        }
      },
      "source": [
        "#Pripravimo za iziris\n",
        "\n",
        "x = np.linspace(0,15,100)  # niz vrednosti za x-os - čas\n",
        "R=1e5\n",
        "C=5e-5\n",
        "Ug=2\n",
        "plt.grid(True)\n",
        "plt.xlabel('Čas  /s',fontsize=12)\n",
        "plt.ylabel('Tok  / A',fontsize=16)\n",
        "plt.plot(x,[f(t,R,C,Ug/R) for t in x],color='#008000') # ob izrisu vstavimo vrednosti za R, C in a=Ug/R (1,4,1)\n",
        "plt.ylim(0,2e-5)\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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5dGWe7/w8n2/9nHHLxnmdjjHGWMEyofVv2p+UuikM/nQwW/Zs8TodY0wRZwXLhCQiTLhi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\nAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1U4mjOFD3sfh",
        "colab_type": "text"
      },
      "source": [
        "### Opravi naslednje analize:\n",
        "1. Spreminjaj vrednost kapacitivnosti in opazuj razliko v odzivu. (Ob spremembi vrednosti zaženeš celico s Shift-Enter ali klikom na ikono.\n",
        "2. Spreminjaj vrednost upora in opazuj spremembe. Upornost ne spremeni le naklona odziva pač pa tudi največjo vrednost. Spremeni vrstico kode, ki določa max vrednost ordinate tako, da bo krivulja vedno ustrezno prikazana.\n",
        "\n",
        "<b> Še mali programerski izziv: Spremeni kodo tako, da bo max vrednost abscisne osi vedno enaka 5*R*C (5* časovna konstanta)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oTQU0V1xaAcB",
        "colab_type": "text"
      },
      "source": [
        "***\n",
        "## Vklop tuljave\n",
        "\n",
        "Rešujemo enačbo ${{U}_{g}}={{u}_{R}}(t)+{{u}_{L}}(t)=iR+L\\frac{\\text{d}i}{\\text{d}t}$.\n",
        "V tem primeru bomo preuredili rešitev tako, da bo možno neposredno uporabiti začetni pogoj, ki je $i(t=0)=0$.\n",
        "\n",
        "Najprej zapišemo enačbo v obliki $ L \\frac{\\text{d}i}{\\text{d}t} ={{U}_{g}}-i R$ in nato poiščemo njeno rešitev.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ij9JP_IIaAcC",
        "colab_type": "code",
        "outputId": "1508daf2-46b2-4da8-f28c-7dd7fca1cbbf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        }
      },
      "source": [
        "i = Function(\"i\") # pripravimo funkcijo in spremenljivke ter zapišemo dif enačbo\n",
        "L, R, Ug, t, i0, C1 = symbols('L, R, U_g, t, i0 C1')\n",
        "eq = Eq(L*i(t).diff(t,1),  Ug-R*i(t))\n",
        "display(eq)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMcAAAAhCAYAAABtGL9ZAAAABHNCSVQICAgIfAhkiAAABo9JREFU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\nkz3dQIfD4XA4HA6Hw+FwOBwORwHyH+OXKs2lgJo6AAAAAElFTkSuQmCC\n",
            "text/latex": "$$L \\frac{d}{d t} i{\\left (t \\right )} = - R i{\\left (t \\right )} + U_{g}$$",
            "text/plain": [
              "  d                       \n",
              "L⋅──(i(t)) = -R⋅i(t) + U_g\n",
              "  dt                      "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Dq_VtxnPaAcE",
        "colab_type": "code",
        "outputId": "e83ca834-9449-4778-b9fa-11c4248af070",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 81
        }
      },
      "source": [
        "dsol = dsolve(eq, i(t))  # rešimo diff enačbo\n",
        "display(dsol)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOMAAAAeCAYAAADegqmLAAAABHNCSVQICAgIfAhkiAAACYVJREFU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\nYII=\n",
            "text/latex": "$$i{\\left (t \\right )} = \\frac{1}{R} \\left(U_{g} + e^{\\frac{R}{L} \\left(C_{1} - t\\right)}\\right)$$",
            "text/plain": [
              "              R⋅(C₁ - t)\n",
              "              ──────────\n",
              "                  L     \n",
              "       U_g + ℯ          \n",
              "i(t) = ─────────────────\n",
              "               R        "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Y_0Cj-FdaAcG",
        "colab_type": "text"
      },
      "source": [
        "Sedaj se želimo \"znebiti\" konstante $C_1$ in izraziti enačbo z začetnim pogojem, t.j. $i(t=0^+)=0$.\n",
        "\n",
        "To naredimo tako, da izrazimo enačbo za čas $t=0$ in jo rešimo za $C_1$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T4m32wN0aAcH",
        "colab_type": "code",
        "outputId": "4bdec5d7-4239-4124-fa00-26630c541ec3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 143
        }
      },
      "source": [
        "it0=dsol.subs({'t':0})\n",
        "display(it0)\n",
        "\n",
        "init_solve=solve(it0, C1) # rešimo enačbo za C1\n",
        "\n",
        "display(init_solve)  # prikažemo rešitev"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMYAAAAdCAYAAADxYhOxAAAABHNCSVQICAgIfAhkiAAACJJJREFU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\nAdcTbiAWKFCgQIECBQoUKFCgQIFDDP8Fw/ALuQ6I+kQAAAAASUVORK5CYII=\n",
            "text/latex": "$$i{\\left (0 \\right )} = \\frac{1}{R} \\left(U_{g} + e^{\\frac{C_{1} R}{L}}\\right)$$",
            "text/plain": [
              "              C₁⋅R\n",
              "              ────\n",
              "               L  \n",
              "       U_g + ℯ    \n",
              "i(0) = ───────────\n",
              "            R     "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALoAAAAaCAYAAAAAEkYfAAAABHNCSVQICAgIfAhkiAAACEdJREFU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\nHDlypMA3X5c/K7XEj2cAAAAASUVORK5CYII=\n",
            "text/latex": "$$\\left [ \\frac{L}{R} \\log{\\left (R i{\\left (0 \\right )} - U_{g} \\right )}\\right ]$$",
            "text/plain": [
              "⎡L⋅log(R⋅i(0) - U_g)⎤\n",
              "⎢───────────────────⎥\n",
              "⎣         R         ⎦"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YJnltAQxaAcJ",
        "colab_type": "code",
        "outputId": "986a9660-f94c-4813-d440-a676038b5a45",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        }
      },
      "source": [
        "final = dsol.subs(C1, init_solve[0]) # v rešitev vstavimo C1 in dobimo končno enačbo\n",
        "final"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAUwAAAAeCAYAAABHXycXAAAABHNCSVQICAgIfAhkiAAADKRJREFU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\nQmCC\n",
            "text/latex": "$$i{\\left (t \\right )} = \\frac{1}{R} \\left(U_{g} + e^{\\frac{R}{L} \\left(\\frac{L}{R} \\log{\\left (R i{\\left (0 \\right )} - U_{g} \\right )} - t\\right)}\\right)$$",
            "text/plain": [
              "                ⎛L⋅log(R⋅i(0) - U_g)    ⎞\n",
              "              R⋅⎜─────────────────── - t⎟\n",
              "                ⎝         R             ⎠\n",
              "              ───────────────────────────\n",
              "                           L             \n",
              "       U_g + ℯ                           \n",
              "i(t) = ──────────────────────────────────\n",
              "                       R                 "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "l_aDVobvaAcL",
        "colab_type": "code",
        "outputId": "606269c3-ffcb-4bc7-b595-41c60ebd8caf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        }
      },
      "source": [
        "expand(final)  # drugačen izpis"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAU0AAAAdCAYAAAAuCT6HAAAABHNCSVQICAgIfAhkiAAACUBJREFU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\n",
            "text/latex": "$$i{\\left (t \\right )} = i{\\left (0 \\right )} e^{- \\frac{R t}{L}} + \\frac{U_{g}}{R} - \\frac{U_{g}}{R} e^{- \\frac{R t}{L}}$$",
            "text/plain": [
              "                                -R⋅t \n",
              "             -R⋅t               ─────\n",
              "             ─────                L  \n",
              "               L     U_g   U_g⋅ℯ     \n",
              "i(t) = i(0)⋅ℯ      + ─── - ──────────\n",
              "                      R        R     "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MxFcQslfaAcQ",
        "colab_type": "text"
      },
      "source": [
        "Vstavimo začetni pogoj $i(t=0^+)=i_0=0$ in dobimo končno obliko:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X-lbpvIEaAcR",
        "colab_type": "code",
        "outputId": "1e090349-e88f-4d60-d1d4-a5f08d28eda9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        }
      },
      "source": [
        "zacetni_pogoji = {i(0): 0}\n",
        "i2=final.subs(zacetni_pogoji)\n",
        "simplify(i2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN0AAAAdCAYAAAAuLGmuAAAABHNCSVQICAgIfAhkiAAAB4lJREFU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\nRU5ErkJggg==\n",
            "text/latex": "$$i{\\left (t \\right )} = \\frac{U_{g}}{R} - \\frac{U_{g}}{R} e^{- \\frac{R t}{L}}$$",
            "text/plain": [
              "                  -R⋅t \n",
              "                  ─────\n",
              "                    L  \n",
              "       U_g   U_g⋅ℯ     \n",
              "i(t) = ─── - ──────────\n",
              "        R        R     "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zmKaJT89aAcT",
        "colab_type": "text"
      },
      "source": [
        "Poiščemo še rešitev za napetost z odvajanjem toka (desne strani enačbe i2) in množenjem z induktivnostjo L."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eJ1_SqzkaAcU",
        "colab_type": "code",
        "outputId": "4515672f-6c1f-4555-a5d2-36b9a1225aaa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "source": [
        "u2=symbols('u2')\n",
        "u2=L*i2.rhs.diff(t) # množenje z L in odvodom desne strani enačbe\n",
        "expand(u2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAE4AAAAdCAYAAAAEsFpEAAAABHNCSVQICAgIfAhkiAAAA6hJREFU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\nJvZgv4o94LPiz5E2bdq0aXMA8xeh5OKcokx//gAAAABJRU5ErkJggg==\n",
            "text/latex": "$$U_{g} e^{- \\frac{R t}{L}}$$",
            "text/plain": [
              "     -R⋅t \n",
              "     ─────\n",
              "       L  \n",
              "U_g⋅ℯ     "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tDIR0uLdaAcW",
        "colab_type": "text"
      },
      "source": [
        "### Pripravimo enačbe za izračune\n",
        "\n",
        "Pripravimo podatke in uporabimo funkcijo \"lambdify\" za pretvorbo iz simbolnega zapisa v numeričnega."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NifqUA9SaAcW",
        "colab_type": "code",
        "outputId": "95a7f26d-7f78-458a-a036-33f0f4799937",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 83
        }
      },
      "source": [
        "podatki = {L: 1e-3,C: 1e-5,R: 2, Ug:3} \n",
        "tau=L/R  # časovna konstanta\n",
        "tau2=tau.subs(podatki)  # numeričen izračun časovne konstante z zamenjavo oz. vstavitvijo vrednosti za L in R\n",
        "print('Tau = ',tau2,' s')\n",
        "print(podatki)\n",
        "tok = lambdify(t, i2.args[1].subs(podatki), 'numpy') # tok kot funkcija časa\n",
        "napetost = lambdify(t,u2.subs(podatki), 'numpy')  # napetost kot funkcija časa\n",
        "\n",
        "\n",
        "print('Tok pri 0s: {:g} A'.format(tok(0)))\n",
        "print('Napetost pri 0s: {:g} V'.format(napetost(0)))\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Tau =  0.000500000000000000  s\n",
            "{L: 0.001, 5e-05: 1e-05, R: 2, U_g: 3}\n",
            "Tok pri 0s: 0 A\n",
            "Napetost pri 0s: 3 V\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3OV9yfP1aAcY",
        "colab_type": "text"
      },
      "source": [
        "Sledi priprava enačb za izrise. Naredimo dva niza: cas za izpis gladke krivulje z več točkami in cas2 za izris simbolov v redkih točkah:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B8Sb175LaAcb",
        "colab_type": "code",
        "outputId": "2236fe28-120d-40da-f1c4-8b2d19a97690",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "cas = np.linspace(0, 1e-3, 100)\n",
        "cas2 = np.linspace(0, 1e-3, 5)\n",
        "\n",
        "def slika():\n",
        "    plt.plot(cas, tok(cas), 'C0', label='Tok [A]')\n",
        "    plt.plot(cas, napetost(cas), 'C1', label='Napetost [V]')\n",
        "    plt.plot(cas2, tok(cas2), 'C0o', label='Tok - velik korak')\n",
        "    plt.plot(cas2, napetost(cas2), 'C1o', label='Napetost - velik korak')\n",
        "    plt.xlabel('Čas [s]')\n",
        "    plt.ylabel('Tok [A] / Napetost [V]')\n",
        "    plt.legend(loc=(1.01, 0));\n",
        "    plt.show()\n",
        "slika()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Gtiml3JRSrbXWCbWoW4imRykI6mtsqcco/f0d2PM5Fnu/4KjDtSwqHc5nGZGU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\nweIK5BYaHTMH/HcDP+5P4KH+7dnwZH9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uR9/aoP20mRVdL2aw5Ps7QfveYPn3hEtwzuVB\n+0kze9XMIi7VG2+JzLlH/2Yza4lXTv1J8GdsZvY3ZlZpZv9lZt+Nd36RJDjnb5nZMTP7jZn9h5nd\nFe/8IolTzq+a2QUzO9krVraZ/crMPgj++9V45iZyhbsPmI3w8uu/Be4AbgWOAxN7HbMM2BbsPw7s\nDfYnBsenA+ODOGn9xQR+Ajwe7G8Dnk2BnL8NWLDtToWcg/N+F9gJtAz2fIE/BXYAQ4Kvb0uBnCuB\ngh5xtw+GnIO+OcAM4GSvWD8A1gT7a4DvJzpnbam5DbQ7FvcBVe7+obt/DuwBHu51zMPAa8H+68C3\nzMyC9j3u3u7u1UBVEC9izOCcB4MYBDEfiWNufUlYzgDuvt8DwLtAbpzziyShOZtZGvAi8Odxzqsv\nCc0XeBbY4O5dAO5+zZvzEiDROTvwlWA/C0jGYlbxyBl3PwRcjHC9nrGS9e+XpKCBVljkAP/T4+va\noC3iMe7eCVwCRvZzbl/tI4FPgxh9XSsREpnzFcEjkD8G/vWmM4heonNeDuxz949iNP5oJTrfO4ES\nM3vPzN40swkxyiMaic75KWC/mdUS/r7eFJMsohOPnPszpsf39DlgzBcbtkh0BlphIYnzI+CQu/86\n2QOJJzO7HXgMeCXZY0mgdOAzD78a+u+BV5M8nkRYAXzb3XOBfwJeTvJ4Eiq4A6l3C0hCDLTCog74\neo+vc4O2iMeYWYjwbc9P+jm3r/ZPgBFBjL6ulQiJzJkgxl8Bo4HnY5JB9BKZ873AXUCVmdUAGWZW\nFatEblCiP+Na4I1g/2fA1JvOIHoJy9nMRgPT3P2doH0v8EBs0ohKPHLuz3kzGxvEGgsk45GXpKJk\nT/KIZgNCwIeEJy91T36a1OuYP+PqyU8/CfYncfXkpw8JT6bqMybwz1w9eXNZCuT8FPA2MCxVPude\ncZMxeTPRn/EmYEmw//vAkcGcc9D+MXB3cP5S4KeDIece543j2smbL3L15M0fJDpnbam5JX0AUQ84\n/FcLlYRnRa8L2jYAC4L9oYQLgirCkw/v6HHuuuC800BxfzGD9juCGFVBzPQUyLkzaPtNsK0f7Dn3\num7CC4skfMYjgF8AJ4D/JPzb/GDPeWGQ73HgrZ6xBkHOu4GPgA7Cd6OWBu0jgQPAB8C/AdnJyFlb\n6m16pbeIiIjEzECbYyEiIiJfYiosREREJGZUWIiIiEjMqLAQERGRmFFhISIiIjETuv4hIqnDzOYB\nM4G7gb9w99okD0lEZEBRYSHSg7v/ysxygMMqKkREoqdHISIBM/uame0B/hJ40cz2m9ndNxnzLTM7\nbWYL+jmmxMyqzOxfbuZaIiJfBiosRIBgaeqfAW+5+53uXgisJTYrQi529319dbr7XsKvUhcRGfBU\nWIiEfRPocPdt3Q3uftzdf21mmWZ2wMyOmdkJM3sYwMx+x8x+YWbHzeykmZVc7yJm9l0ze9/MKoK7\nIyIig4rmWIiETQaO9tH3GbDQ3ZvMbBRw2Mz2AfOBenf/DoCZZd3AddYA49293cxGxGLgIiJfJrpj\nIXJ9BvytmVUQXswph/AjkhPAPDP7vpnNdvdLNxCrAig3sz8ivOCbiMigosJCJOwUUNhH32JgNFDo\n7tOB88BQd68EZhAuMP7azNbfwHW+A2wJzjtiZrprKCKDigoLkbCDQLqZPd3dYGZTzWw2kAVccPcO\nM/sm8I2g/3agzd1/DLxIuFjok5kNAb7u7v8OrA7iZsYlGxGRJNFvSyKAu7uZLQR+aGarCc+rqAGe\nA8qBn5vZCeA94L+D06YQ/rPULqADePY6l0kDfhzMxTBgs7t/GvNkRESSSIWFSMDd64E/7KP79yK0\n1QC/jCJ+BzAr+pGJiAwcehQiEl8Xge3Xe0EW8COgMWGjEhGJE3P3ZI9BREREBgndsRAREZGYUWEh\nIiIiMaPCQkRERGJGhYWIiIjEjAoLERERiZn/AwtjyqEHnJooAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uYMeb2ZF53Kh",
        "colab_type": "text"
      },
      "source": [
        "### Opravi naslednje analize:\n",
        "1. Kako vpliva velikost upora in tuljave na odziv? \n",
        "2. Ali oba vplivata na enak način?\n",
        "\n",
        "<b> Še mali programerski izziv za zagnane: Dodaj vrstice kode, s katerimi bi določil časovno konstanto iz analize signala. Npr. tako, da poiščeš čas, ko znaša napetost  $u(t=\\tau) = U_g e^{-1}$. </b> (Namig za en način: 1. tvori niz vrednosti napetosti (kot je narejeno v plotu). 2. izračunaj vrednost napetosti pri $\\tau = RC$. To napetost moraš poiskati v nizu oziroma vrednost, ki je njej najbližje. 3. V ta namen uporabi funkcijo np.where, s katero poiščeš vrednosti večje ali manjše od določene vrednosti. Rezultat je niz vrednosti, ki zadostujejo temu pogoju. 4. Največja vrednost v nizu je tisti indeks, ki ga iščeš. 5.Sedaj le še vstaviš indeks v niz cas in imaš rešitev. Lažje reči kot narediti? Rešitev je na koncu strani.) (Namig za drugi način: Iz odvoda napetosti dobimo $\\frac{du}{dt}=\\frac{d}{dt} (  U_g  e^{-t/ \\tau}) =- U_g/\\tau e^{-t/ \\tau}  $. Če torej izračunam odvod napetosti (numerično) in pogledamo njegovo vrednosti pri t=0, bo ta enaka $-U_g/ \\tau$. Rešitev je na koncu strani)."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UbNcA-FZaAcf",
        "colab_type": "text"
      },
      "source": [
        "***\n",
        "## Vklop kondenzatorja na izmenični vir napetosti"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ung_oQy6aAcf",
        "colab_type": "text"
      },
      "source": [
        "Rešujemo enačbo ${{u}_{g}}=RC\\frac{\\text{d}{{u}_{C}}}{\\text{d}t}+{{u}_{C}}$, \n",
        "kjer je ${{u}_{g}}(t)={{U}_{g}}\\sin {(\\omega t})$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2aDLEawBaAcg",
        "colab_type": "code",
        "outputId": "6e3c2ef7-1c0c-48eb-9f39-b63c5b2c9a58",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 82
        }
      },
      "source": [
        "u = Function('u') # pripravimo funkcijo in spremenljivke ter zapišemo dif enačbo\n",
        "C, R, t, Ug, omega, u0 = symbols('C, R, t, U_g, omega, u0')\n",
        "eq = Eq(R*C*u(t).diff(t),  Ug*sin(omega*t)-u(t))\n",
        "eq"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQQAAAAhCAYAAAA/HtU7AAAABHNCSVQICAgIfAhkiAAACVVJREFU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\nAAAASUVORK5CYII=\n",
            "text/latex": "$$C R \\frac{d}{d t} u{\\left (t \\right )} = U_{g} \\sin{\\left (\\omega t \\right )} - u{\\left (t \\right )}$$",
            "text/plain": [
              "    d                             \n",
              "C⋅R⋅──(u(t)) = U_g⋅sin(ω⋅t) - u(t)\n",
              "    dt                            "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H9hd1LUaaAci",
        "colab_type": "text"
      },
      "source": [
        "Najprej poskušamo identificirati tip diferencialne enačbe. V ta namen uporabimo funkcijo classify_ode."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IsdGaVyZaAcj",
        "colab_type": "code",
        "outputId": "3c4396b9-9a2f-4344-9655-cc23f5a56a60",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 200
        }
      },
      "source": [
        "classify_ode(eq, u(t))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "('1st_linear',\n",
              " 'Bernoulli',\n",
              " 'almost_linear',\n",
              " '1st_power_series',\n",
              " 'lie_group',\n",
              " 'nth_linear_constant_coeff_undetermined_coefficients',\n",
              " 'nth_linear_constant_coeff_variation_of_parameters',\n",
              " '1st_linear_Integral',\n",
              " 'Bernoulli_Integral',\n",
              " 'almost_linear_Integral',\n",
              " 'nth_linear_constant_coeff_variation_of_parameters_Integral')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AiZ7kyzdaAcl",
        "colab_type": "text"
      },
      "source": [
        "Preiskusimo lahko vse zgoraj naštete možne tipe. V našem primeru dobro deluje nth_linear_constant_coeff_undetermined_coefficients"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NRCYKWONaAcm",
        "colab_type": "code",
        "outputId": "e0d194ba-8ab4-4102-9eb1-e6c7d58e1813",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 87
        }
      },
      "source": [
        "dsol = dsolve(eq, u(t),'nth_linear_constant_coeff_undetermined_coefficients')  # rešimo diff enačbo\n",
        "display(dsol)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AAElFTkSuQmCC\n",
            "text/latex": "$$u{\\left (t \\right )} = - \\frac{C R U_{g} \\omega \\cos{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + C_{1} e^{- \\frac{t}{C R}} + \\frac{U_{g} \\sin{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1}$$",
            "text/plain": [
              "                                  -t                \n",
              "                                  ───               \n",
              "         C⋅R⋅U_g⋅ω⋅cos(ω⋅t)       C⋅R   U_g⋅sin(ω⋅t)\n",
              "u(t) = - ────────────────── + C₁⋅ℯ    + ────────────\n",
              "             2  2  2                     2  2  2    \n",
              "            C ⋅R ⋅ω  + 1                C ⋅R ⋅ω  + 1"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GYhgtNP0aAcw",
        "colab_type": "text"
      },
      "source": [
        "Podobno kot v prejšnjem primeru, zamenjamo konstanto $C_1$ za začetni pogoj, $u(t=0)$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q0OtjldNaAcw",
        "colab_type": "code",
        "outputId": "dc1128dc-bbaf-470a-a2ee-c7c372996989",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
        }
      },
      "source": [
        "t0=dsol.args[1].subs({'t':0})\n",
        "eq_init = Eq(u0, t0)  # izrazimo enačbo pri t=0\n",
        "display(eq_init)  # prikažemo i0\n",
        "\n",
        "init_solve=solve(eq_init, C1) # rešimo enačbo za C1\n",
        "\n",
        "display(init_solve)  # prikažemo rešitev\n",
        "final = dsol.subs(C1, init_solve[0]) # v rešitev vstavimo C1 in dobimo končno enačbo\n",
        "final"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMoAAAAlCAYAAAADd3b/AAAABHNCSVQICAgIfAhkiAAABxJJREFU\neJztnHuMXUMcxz9bj7YsqUWjRRVd79Z21yOoWkHQSAi1RYgriKiQKq2URBrPlkTrHUpdbYV6v9qS\nEkVLpFt9UfGKVbbSVos+qD6sP75zcs+ennvPnNtzH7t3Pslkds7M/M7czfnNzG/mNwMOh8NRZtQB\nLwC/ApuAn4BXgON9ZT4E2kzYAnwPXBuQswYYFSL/LmB5sk12OIpLCtgKTAZOAfoAg4FpwLO+cn8A\nY4D9gIOAu4H/gIEmvy9SotND3jELeD3xljscReIkpCQ3Z8mvMfGhSAkG+vIOMM8uN+mLkOLsGSJn\nFXC7ZZsmAM1Al5C8ZmCipRyHIzE+A+ZZlGsC/iLz8fYCXgK2AUeZZ/cB34bUPQgp1NkW7zkcKW7Y\nqAQwFfjYQk7FsHOpG1AB1KIR5VKLsg1ANbAOKUt3YDNwC7DMV6Y5pO5xJg7LC3IrsBj4KEv+WuBE\nCzkVQ9iw60iWehPbfMD1wDPI6B8EvA9Mov00KJuiNAA/I0M/F12AocCrvmcTgBt96T2AjRbtdTgS\n4yo0JdrPouwa4Epfui+yR/qb9P5G1lkhdeejFTWPOuBzNHLchpQOMnbQeb6yrcDVvvSCgKyKx40o\nhecrE5+WJX83Ex+MjPqlvrwWYCFwhUnvauLuARknoBFluknvAqSRkh6LVtmWmLy9TLzBxI1AbzTF\nA00V64A3sv0gh6NQzEQrUin0IfZDhvtsNMUCTYe2Ad0CdccB35m/q5CtshSNKgOQMrQCb/vqNAFP\n+tLjyShbT/Oep5FCLDF1pxt5c5Fy7pTfTy0raoH70Qi5Gu1LrQY+AIaT6aQcZUJXYDT6KDeivZIF\naIPQU4z7ySiEnzPQVOlokz4Y2RerkdG/ELiJzGgDcA9wnS/9LhpZPEabNqwCbgAOM+/+G3gLrbZ1\nZKrQ/tNm9L+bhzqOccCLaIrbBnxaqgY6yoORwIPm70bgH9orUrmTQh9yY571nzP1v6Z9B+HRHbjD\nlMuLMeYFF4bk9TF5bu5a/vREK2OLgYeAT0rbnNikyF9RRpq6y9DqXS6Ctl5WgsZ8g4nDlh89f6Qv\nbYU7SsZGtK8yENkjU0vbnKLRC7gXbaY2Aesjyv9jKzi44dgA/E64Y523obXQVngORgA9YpRfBLyZ\nwHsrhVFocWArMAPtzVQCI5DNlyaz2pg4NWjIei9L/myT3zuBd7WQ8ZC1CekE3unoOKTIb+r1Ldkd\nRhPjTPOSe7LkrwVWBp4NR67im9AqzqkFa108WoiniNNK0koHJNdpVpv8/4i/7DsYLZG3GhmpYAH/\n1MuzTxaECDoEbVT5R5thwMNIWeaaeBZy3iv1mYgfkfLasqJQDXFEMpHtp+F1wPnA80iR/CzKImdf\nE69Dy9xxqEZTtSkmbIdfUTzX7jBjfYiJ/fbJSKTdk0z6RuAc4Hq0epaLQtsoZ8Qo6ygtYe78KaQo\naWCOpRzPN6072izdFqMNM00Ai2n+IjJuDH66op3gNmQggtbktwIXB8o+jp17dgsdx0aJ004XwkNc\nUuRno7SYelEdZS7XrQ2ETL38FTYjH6Fa37Pd0Ym8Y0zaG1H2QVobtFlWYuf81xftntqG7RpeRGzb\n2Ad1Et+gjqUpRt1CyEla1o6EYjHBxE8AR4TkVwHnojM+eXM30sbfzIumIONmFprD/0nmR/c2ZQcH\nZNxJ+KGiSqAXmluDOotW1NGUSk7SsopJivxGlCp0rLoN+XXNQMrzAHJd+cXk5fKMDh1R/HRDxvkK\nZAw1I3+hHmglYY6v7I5OvSqBxcCBZSQnaVmFJEV+iuIxBHmQtKKZ0lrkzvIyOsawd466kYoSly+Q\nB6qf75BzX2fF5hYV0Api2IaXzQ0rNnLyIUlZHpHLqh2QxBVlGNLWa4Aj0Wi0AZ3d7oyksLtFpQb1\nXieHyIi6YcVPLjlxiSsrDYy1KDcEneEfimYhqfhNKwuqUSdYh37HnebvPkm9YDhaafgX7b8EbZbO\ngu0tKl2RA+IVIWVsbljxyCUn7u0puWRlI42dovhJvCcuIo2U32prh8TmFpUqZDCOzZJvc8NKlJy4\nt6dEtSkb6TzqdGRFcSRALepdLokoNwhNoxb5Qn9f/nikFBvQ8N6GRuIRMeRMItxzwuNh2h/+impT\nNtI4RXHEZBj6qPvtoJzZwFNGTj1yB3osRv0uZGwcj+DtKZPJz7v7dvShe2ELsj/9z6L8+JyiVDhx\nblHJRdQNK1EU8vaUGqTAXngNeCTwLOqQU6dWFHcLSzS2t6jkwuaGlSgKeXvKWuAHX1gf8sz6kFNn\nxClKNPORd8KjhN+iUp+1ZoYGNHosCzyfDVxg2Y7lRsZlSCEeAd5BI8wAdP57CcU9qu1fVu2CllMT\nXVZ1dCxsblHJhe0NK1EU6/aUNHbGfCNuWdXhcDgcDofD4XA4is7/t8ReRA03LmEAAAAASUVORK5C\nYII=\n",
            "text/latex": "$$u_{0} = - \\frac{C R U_{g} \\omega}{C^{2} R^{2} \\omega^{2} + 1} + C_{1}$$",
            "text/plain": [
              "        C⋅R⋅U_g⋅ω       \n",
              "u₀ = - ──────────── + C₁\n",
              "        2  2  2         \n",
              "       C ⋅R ⋅ω  + 1     "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV8AAAAhCAYAAAB+6qiEAAAABHNCSVQICAgIfAhkiAAACwJJREFU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\nOxwOh8PhcDgcDofD4XA4HA5HH+P/+cIwUTD32nkAAAAASUVORK5CYII=\n",
            "text/latex": "$$\\left [ \\frac{1}{C^{2} R^{2} \\omega^{2} + 1} \\left(C^{2} R^{2} \\omega^{2} u_{0} + C R U_{g} \\omega + u_{0}\\right)\\right ]$$",
            "text/plain": [
              "⎡ 2  2  2                    ⎤\n",
              "⎢C ⋅R ⋅ω ⋅u₀ + C⋅R⋅U_g⋅ω + u₀⎥\n",
              "⎢────────────────────────────⎥\n",
              "⎢         2  2  2            ⎥\n",
              "⎣        C ⋅R ⋅ω  + 1        ⎦"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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            "text/latex": "$$u{\\left (t \\right )} = - \\frac{C R U_{g} \\omega \\cos{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{U_{g} \\sin{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} \\left(C^{2} R^{2} \\omega^{2} u_{0} + C R U_{g} \\omega + u_{0}\\right)$$",
            "text/plain": [
              "                                                                             -\n",
              "                                                                             ─\n",
              "                                             ⎛ 2  2  2                    ⎞  C\n",
              "         C⋅R⋅U_g⋅ω⋅cos(ω⋅t)   U_g⋅sin(ω⋅t)   ⎝C ⋅R ⋅ω ⋅u₀ + C⋅R⋅U_g⋅ω + u₀⎠⋅ℯ \n",
              "u(t) = - ────────────────── + ──────────── + ─────────────────────────────────\n",
              "             2  2  2           2  2  2                    2  2  2             \n",
              "            C ⋅R ⋅ω  + 1      C ⋅R ⋅ω  + 1               C ⋅R ⋅ω  + 1         \n",
              "\n",
              "t \n",
              "──\n",
              "⋅R\n",
              "  \n",
              "──\n",
              "  \n",
              "  "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "k2NYILoyaAcy",
        "colab_type": "text"
      },
      "source": [
        "Vstavimo začetni pogoj in dobimo končno rešitev:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VEFKFDI1aAcz",
        "colab_type": "code",
        "outputId": "7b232368-136d-4efd-fe57-58daaa13ff8a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 93
        }
      },
      "source": [
        "zacetni_pogoji = {'u0': 0}\n",
        "u2=final.subs(zacetni_pogoji)\n",
        "display((u2))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Rvc/D5/IAAAAASUVORK5CYII=\n",
            "text/latex": "$$u{\\left (t \\right )} = - \\frac{C R U_{g} \\omega \\cos{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{C R U_{g} \\omega e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} + \\frac{U_{g} \\sin{\\left (\\omega t \\right )}}{C^{2} R^{2} \\omega^{2} + 1}$$",
            "text/plain": [
              "                                         -t                \n",
              "                                         ───               \n",
              "                                         C⋅R               \n",
              "         C⋅R⋅U_g⋅ω⋅cos(ω⋅t)   C⋅R⋅U_g⋅ω⋅ℯ      U_g⋅sin(ω⋅t)\n",
              "u(t) = - ────────────────── + ────────────── + ────────────\n",
              "             2  2  2            2  2  2         2  2  2    \n",
              "            C ⋅R ⋅ω  + 1       C ⋅R ⋅ω  + 1    C ⋅R ⋅ω  + 1"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "luSwOuJwaAc1",
        "colab_type": "text"
      },
      "source": [
        "Izračunamo še tok kot $i=C\\frac{\\text{d}{{u}_{C}}}{\\text{d}t}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9wUopLmwaAc1",
        "colab_type": "code",
        "outputId": "df2f13ce-e43b-4f2c-88a0-a76efc23d346",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 93
        }
      },
      "source": [
        "i2=symbols('i2')\n",
        "i2=C*u2.rhs.diff(t) # množenje s C in odvodom desne strani enačbe\n",
        "simplify(i2)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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            "text/latex": "$$\\frac{C U_{g} \\omega e^{- \\frac{t}{C R}}}{C^{2} R^{2} \\omega^{2} + 1} \\left(\\left(C R \\omega \\sin{\\left (\\omega t \\right )} + \\cos{\\left (\\omega t \\right )}\\right) e^{\\frac{t}{C R}} - 1\\right)$$",
            "text/plain": [
              "        ⎛                              t     ⎞  -t \n",
              "        ⎜                             ───    ⎟  ───\n",
              "        ⎜                             C⋅R    ⎟  C⋅R\n",
              "C⋅U_g⋅ω⋅⎝(C⋅R⋅ω⋅sin(ω⋅t) + cos(ω⋅t))⋅ℯ    - 1⎠⋅ℯ   \n",
              "───────────────────────────────────────────────────\n",
              "                     2  2  2                       \n",
              "                    C ⋅R ⋅ω  + 1                   "
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5BEU1yoAaAc3",
        "colab_type": "text"
      },
      "source": [
        "Sedaj lahko ocenimo še pravilnost enačbe. Čeprav je zapis zapleten, lahko ocenimo rešitev pri $CR\\omega >>1$. Najprej izbrišemo 1 in $cos(ut)$, nato še eksponenta, ki se izničita. Ostane nam\n",
        "\n",
        "$\\frac{C U_g \\omega }{C^{2} R^{2} \\omega^{2}} \\left(\\left(C R \\omega \\sin{\\left (\\omega t \\right )}\\right) \\right)$,\n",
        "\n",
        "od koder sledi\n",
        "\n",
        "$\\frac{U_g }{R} \\left(\\left(\\sin{\\left (\\omega t \\right )}\\right) \\right)$,\n",
        "\n",
        "kar je tok, ki ga diktira upornost $R$.\n",
        "\n",
        "Če pa je $CR\\omega << 1$, pa se ohrani cosinusni člen, eksponenta se za velike čase izničita, ostane \n",
        "$\\frac{C U_g \\omega }{C^{2} R^{2} \\omega^{2}+1} \\left(\\left(\\cos{\\left (\\omega t \\right )}\\right) \\right)$ in nato \n",
        "$\\frac{C \\omega U_g}{1} \\left(\\left(\\cos{\\left (\\omega t \\right )}\\right) \\right)$. V tem primeru, npr. nizkih frekvencah, tok skozi vezje diktira \"upornost\" kondenzatorja, ki jo pri izmeničnih signalih imenujemo reaktanca in je enaka $\\frac{1}{\\omega C}$.  \n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QO18r9XMaAc4",
        "colab_type": "code",
        "outputId": "c13557b8-559e-49d1-cabe-6f7b7666bd3e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 83
        }
      },
      "source": [
        "podatki = {C: 1e-6, R: 5, Ug: 2, omega:2000} \n",
        "tau=R*C  # časovna konstanta\n",
        "tau2=tau.subs(podatki)  # numeričen izračun konstante z zamenjavo oz. vstavitvijo vrednosti za L in R\n",
        "print('Tau = ',tau2,' s')\n",
        "print(podatki)\n",
        "napetost = lambdify(t,u2.args[1].subs(podatki), 'numpy')  # napetost kot funkcija časa\n",
        "tok = lambdify(t, i2.subs(podatki), 'numpy') # tok kot funkcija časa\n",
        "\n",
        "print('Tok pri 0s: {:g} A'.format(tok(1)))\n",
        "print('Napetost pri 0s: {:g} V'.format(napetost(1)))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Tau =  5.00000000000000e-6  s\n",
            "{C: 1e-06, R: 5, U_g: 2, omega: 2000}\n",
            "Tok pri 0s: -0.00143249 A\n",
            "Napetost pri 0s: 1.86724 V\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tGRJN9XpaAc5",
        "colab_type": "code",
        "outputId": "9945be17-a3af-4230-ebe9-a6b01300d5af",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "cas = np.linspace(0, 1, 100)\n",
        "\n",
        "def slika():\n",
        "    plt.plot(cas, tok(cas), 'C0', label='Tok [A]')\n",
        "    plt.plot(cas, napetost(cas), 'C1', label='Napetost [V]')\n",
        "    plt.ylabel('Tok [A]  /  Napetost [V]')\n",
        "    plt.legend(loc=(1.01, 0));\n",
        "    plt.show()\n",
        "slika()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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1rj7sVQf4Z4LnUW2JmWzkWZ8QX9sbQ19DEHjsRL1ezlcuhZ5H4NOgpbutjPUp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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lC0O6zDGaAc7",
        "colab_type": "text"
      },
      "source": [
        "Zgornji prikaz ni napačen, problem je le, da sta lahko napetost in tok različnih velikostnih razredov. Zato je bolj primerno izrisati tok in napetost na dveh različnih grafih ali pa na enem grafu ampak z dvema različnima ordinatnima osema. Poleg tega časovni korak ni izbran najbolj ustrezno in ga je potrebno zgostiti\". Iz podatkov izvlečemo \\omega, izračunamo periodo ($\\omega = 2 \\pi f = 2\\pi /T$) in naredimo časovni niz dolg nekaj period. Glej spodaj:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XY6VGTQsaAc8",
        "colab_type": "code",
        "outputId": "5d10e71d-c347-4fd6-c973-e428fe73896c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "om=podatki.get(omega) # iz slovarja (dictionary) podatki izvlečem vrednosti omege\n",
        "T_period=2*np.pi/om  # ena perioda\n",
        "cas = np.linspace(0, 5*T_period, 1000)\n",
        "\n",
        "fig, ax1 = plt.subplots()\n",
        "\n",
        "color = 'tab:red'\n",
        "ax1.set_xlabel('Čas (s)')\n",
        "ax1.set_ylabel('Tok (A)', color=color)\n",
        "ax1.plot(cas, tok(cas), color=color)\n",
        "#ax1.set_ylim(-1e-3,1e-3)\n",
        "ax1.tick_params(axis='y', labelcolor=color)\n",
        "\n",
        "ax2 = ax1.twinx()  # x os za drugi plot naj bo enaka x osi prvega plota\n",
        "\n",
        "color = 'tab:blue'\n",
        "ax2.set_ylabel('Napetost (V)', color=color)  \n",
        "ax2.plot(cas, napetost(cas), color=color)\n",
        "ax2.tick_params(axis='y', labelcolor=color)\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AAHy6R3mxAvc5PjYGqRRuAZmd+/ZzyV4vpBwOtNWSTKtMLpbfCIhfugSAS+C7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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Bt_2JJk_Hw8q",
        "colab_type": "text"
      },
      "source": [
        "### Opravi naslednje analize:\n",
        "1. Kako vpliva velikost upora in kodenzatorja na odziv vezja (tok in napetost)? \n",
        "2. Ali oba vplivata na enak način?\n",
        "3. Kako vpliva frekvenca na odziv vezja?\n",
        "4. Kakšna bi bila oblika napetosti na uporu?\n",
        "5. Zakaj sta tok in napetost na kondenzatorju zamaknjena na četrtino periode.\n",
        "\n",
        "<b> Še mali programerski izziv za zagnane: iz oblike signalov toka in napetosti želimo ugotoviti za koliko sta zamaknjena v času </b> (Namig: 1. tvori niz vrednosti napetosti in toka (kot je narejeno v plotu). 2. uporabi funkcijo np.where, s katero poiščeš vrednosti npr. manjše od 0. Rezultat je niz vrednosti, ki zadostujejo temu pogoju. 3. Vzameš prva indeksa, ki predstavljata mesto, ko je prvič zadoščeno pogoju. 4. Razliko med tema indeksoma vneseš v niz cas in dobiš čas med signaloma. 5. Narediš razmerje med tem časom in časom ene periode in izpišeš."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "W2XKxvNFsd39",
        "colab_type": "text"
      },
      "source": [
        "***\n",
        "## Še nekaj izzivov za nadebudne\n",
        "\n",
        "1. V prvem primeru smo uporabili funkcijo Lambda za tvorjenje analitične enačbe. Na primer, vzemimo funkcijo  $i(t)=A e^{-t/\\tau}sin(\\omega t)$. Funkcijo zapišite, izpišite in izrišite v grafu za poljubne vrednosti $A, \\tau, \\omega$. Rešitev je na koncu zvezka.\n",
        "\n",
        "2. Po vzoru primera vklopa tuljave zapiši diferencialno enačbo za izklop vira (na Ug=0) pri zaporedni vezavi upora in kodenzatorja. Kondenzator je ob izklopu polno naelektren. Reši enačbo in izriši rezultat. Rešitev je na koncu zvezka.\n",
        "\n",
        "3. Zapiši funkcijo, ki izračuna $i(t)={I_0} e^{-t/\\tau}$ in izriši več krivulj na enem grafu za različne vrednosti $\\tau$.Rešitev je na koncu zvezka.\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uim_FKtMaAc-",
        "colab_type": "text"
      },
      "source": [
        "Več:\n",
        "- o uporabi simbolnega računa:\n",
        "    - https://www.southampton.ac.uk/~fangohr/teaching/python/book/html/12-symbolic-computation.html\n",
        "    -"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VHxgoFr_iswx",
        "colab_type": "text"
      },
      "source": [
        "### Rešitve programerskih **izzivov** "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3pOSJbCJGcVs",
        "colab_type": "code",
        "outputId": "26495bea-f004-4737-ec59-2a1ff11286c8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 79
        }
      },
      "source": [
        "#Rešitev programerskega izziva iskanja časovne konstante (prvi način):\n",
        "# To celico skopiraj pod celico z vprašanjem in zaženi\n",
        "# 1 niz vrednosti\n",
        "nap=napetost(cas)   # naredi niz (array)\n",
        "# 2 Max vrednost napetosti\n",
        "Uge_1=np.max(nap) #np.exp(-1)  #Ug*exp(-1)\n",
        "display(Uge_1) # \n",
        "# 3 Indeksi vrednosti, kjer je izpolnjen pogoj\n",
        "xx=np.where(nap >= np.max(nap)*np.exp(-1))  # indeksi, kjer je pogoj izpolnjen\n",
        "# print(xx)\n",
        "# 4 Največja vrednost indeksa\n",
        "x2=((np.max(xx))) \n",
        "# 5 Vnos indeksa v niz cas in izpis\n",
        "print('Tau = % 6.6f s'% cas[x2])"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN8AAAASCAYAAADbjwtGAAAABHNCSVQICAgIfAhkiAAABc1JREFU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\ngDG6SuCH3QAAAABJRU5ErkJggg==\n",
            "text/latex": "$$1.9998954374415385$$",
            "text/plain": [
              "1.9998954374415385"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Tau =  0.013947 s\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Rl7tl_cZhaC7",
        "colab_type": "code",
        "outputId": "437de466-7b8b-4e84-9936-213f6178eebc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 62
        }
      },
      "source": [
        "#Rešitev programerskega izziva iskanja časovne konstante (drugi način):\n",
        "# To celico skopiraj pod celico z vprašanjem in zaženi\n",
        "diferenca=np.diff(nap)  # numeričen izračun defirence (razlika med sosednjimi napetostmi)\n",
        "tau=-cas[1]/(3*diferenca[0])  # cas[1] je prva vrednost v nizu čas = dt; diferenca[0] je diferenca ob času t=0 ; 3 = Ug\n",
        "display(tau)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAASMAAAASCAYAAAAQcbiRAAAABHNCSVQICAgIfAhkiAAABt1JREFU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\nTkSuQmCC\n",
            "text/latex": "$$-0.00011979552202801608$$",
            "text/plain": [
              "-0.00011979552202801608"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hcqgzPEmY30R",
        "colab_type": "code",
        "outputId": "bc2a1f8c-ecbd-486c-9829-c225eff8ef6c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "## mali programerski izziv: Izračun zamika med signaloma\n",
        "# 1\n",
        "nap=napetost(cas) # niz vrednosti napetosti\n",
        "tokk=tok(cas) # niz vrednosti toka\n",
        "\n",
        "\n",
        "# 2\n",
        "index_nap=np.where(nap < 0) # indeksi, kjer je izpolnjen pogoj. Uporabi display(index_nap), da vidiš rezultat\n",
        "# type(index_nap)   # s tem ukazom ugotoviš katerega tipa je niz. Ugotoviš, da je niz tipa tuple ?!\n",
        "index_tokk=np.where(tokk < 0)\n",
        "\n",
        "# 3\n",
        "d_index=index_nap[0][0]-index_tokk[0][0] # Hmm, d_index je t.i. tuple (po slovensko terka), malo drugačen niz .... Glej:  https://realpython.com/python-lists-tuples/\n",
        "\n",
        "# 4\n",
        "Td=cas[d_index]\n",
        "\n",
        "# 5\n",
        "razmerje = Td/T_period \n",
        "s=\"Signala sta zamaknjena za  \"+ str(Td/T_period )+ \" periode\"  # tvorim string za izris s pretvorbo numerične vrednosti v string\n",
        "display(s)\n",
        "print('Signala sta zamaknjena za % 6.2f periode' % razmerje ) # drug način izpisa - na dve decimalki\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "'Signala sta zamaknjena za  0.2502502502502503 periode'"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "Signala sta zamaknjena za   0.25 periode\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-FKel43_Wqu0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nrdM_PLiumBl",
        "colab_type": "text"
      },
      "source": [
        "### Rešitve izzivov za nadebudne"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gbv0R0OP2E2F",
        "colab_type": "text"
      },
      "source": [
        "#### Rešitev prve naloge: Zapis enačbe $i(t)=A e^{-t/\\tau}sin(\\omega t)$ s funkcijo Lambda in izris."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "h16tD-rZuxAR",
        "colab_type": "code",
        "outputId": "6fdf9eeb-6616-4e0c-ad7a-442ff0cfb42e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 317
        }
      },
      "source": [
        "var('A tau omega') # priprava spremenljivk\n",
        "f = Lambda((t,A,tau,omega),A*exp(-t/tau)*sin(omega*t)) \n",
        "display(f(t,A,tau,omega))\n",
        "\n",
        "x = np.linspace(0,15,100)  # niz vrednosti za x-os - čas\n",
        "A=10\n",
        "tau=2\n",
        "omega=2\n",
        "plt.plot(x,[f(t,A, tau, omega) for t in x]) \n",
        "plt.show()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAIAAAAAYCAYAAAAyC/XlAAAABHNCSVQICAgIfAhkiAAABaxJREFU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\n0GcNSpcNgXNRJzER1UBllFFGGWWU8Q8YsrEKLY1a1gAAAABJRU5ErkJggg==\n",
            "text/latex": "$$A e^{- \\frac{t}{\\tau}} \\sin{\\left (\\omega t \\right )}$$",
            "text/plain": [
              "   -t          \n",
              "   ───         \n",
              "    τ          \n",
              "A⋅ℯ   ⋅sin(ω⋅t)"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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mKci3HhzGOfXHRWR2FOTz1NlUxf7+iaxMQdy0fxAzWKuphyIyCwryeVrWVMVk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\ni4j4nIJcRMTn/j/b++oRg1WHkwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "colab_type": "text",
        "id": "XBJ_74mu7zB-"
      },
      "source": [
        "#### Rešitev druge naloge - izklop RC vezja\n",
        "\n",
        "Diferencialna enačba je enaka kot v prvem primeru. Razlika je v začetnem pogoju."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wzfyXyT6zEtG",
        "colab_type": "code",
        "outputId": "5f7aff49-78c7-4582-d3dd-68e91f68281d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 125
        }
      },
      "source": [
        "var('R C t C1 t0 Ug') # priprava spremenljivk\n",
        "i = Function(\"i\")(t) # funkcija toka\n",
        "\n",
        "de = Eq(i/C+R*i.diff(t)) # zapis diferencialne enačbe\n",
        "display(de) # izpis enačbe\n",
        "des = dsolve(de,i) # rešitev enačbe\n",
        "display(des) # izpis rešitve"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAK0AAAAhCAYAAACr3SvgAAAABHNCSVQICAgIfAhkiAAABvxJREFU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\nFClSpEiRIkWKFClSpDie8B9/JAnfyznlhAAAAABJRU5ErkJggg==\n",
            "text/latex": "$$R \\frac{d}{d t} i{\\left (t \\right )} + \\frac{1}{C} i{\\left (t \\right )} = 0$$",
            "text/plain": [
              "  d          i(t)    \n",
              "R⋅──(i(t)) + ──── = 0\n",
              "  dt          C      "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJMAAAAaCAYAAACzWm4FAAAABHNCSVQICAgIfAhkiAAABZtJREFU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\nJEjQp/EvEs57NPqeB6wAAAAASUVORK5CYII=\n",
            "text/latex": "$$i{\\left (t \\right )} = e^{\\frac{1}{R} \\left(C_{1} - \\frac{t}{C}\\right)}$$",
            "text/plain": [
              "             t\n",
              "        C₁ - ─\n",
              "             C\n",
              "        ──────\n",
              "          R   \n",
              "i(t) = ℯ      "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5zNBjx-Y4WwZ",
        "colab_type": "text"
      },
      "source": [
        "Začetni pogoj izhaja iz $u_C(t=t_0^+)=u_C(t=t_0^-)$, ki pa ni enak nič, pač pa napetost na kondenzatorju tik pred izklopom, torej $u_C(t=t_0)=U_g$. Torej bo tok ob preklopu enak $i(t_0)=U_g/R$ ali bolje $i(t_0)=-U_g/R$, saj ima drugo smer (nasprotno)  kot pri polnenju kondenzatorja."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5L3ZB0tF2zcG",
        "colab_type": "code",
        "outputId": "74b05e8a-1678-4083-8220-8ea666b77a13",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 232
        }
      },
      "source": [
        "it0=des.args[1].subs({'t':t0}) # t zamenjamo za t0\n",
        "display(it0)\n",
        "\n",
        "eq_init = Eq(it0, -Ug/R)  # izrazimo enačbo pri t0: i(t0)=Ug/R\n",
        "display(eq_init)\n",
        "\n",
        "init_solve=solve(eq_init, C1) # rešimo enačbo za C1\n",
        "display(init_solve)  # prikažemo rešitev\n",
        "\n",
        "solution = des.subs(C1,init_solve[0]) # v rešitev vstavimo C1 in dobimo končno enačbo\n",
        "display(simplify(solution))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAGQAAAAYCAYAAAAMAljuAAAABHNCSVQICAgIfAhkiAAAA8lJREFU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\n1R2tMAAAAABJRU5ErkJggg==\n",
            "text/latex": "$$e^{\\frac{1}{R} \\left(C_{1} - \\frac{t_{0}}{C}\\right)}$$",
            "text/plain": [
              "      t₀\n",
              " C₁ - ──\n",
              "      C \n",
              " ───────\n",
              "    R   \n",
              "ℯ       "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAMUAAAAcCAYAAADRCXsXAAAABHNCSVQICAgIfAhkiAAABwBJREFU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\nBdtudsnj8Xg8Ho/H4/F4PB5PRedfCuUEhUO64FYAAAAASUVORK5CYII=\n",
            "text/latex": "$$e^{\\frac{1}{R} \\left(C_{1} - \\frac{t_{0}}{C}\\right)} = - \\frac{Ug}{R}$$",
            "text/plain": [
              "      t₀       \n",
              " C₁ - ──       \n",
              "      C        \n",
              " ───────       \n",
              "    R      -Ug \n",
              "ℯ        = ────\n",
              "            R  "
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAALsAAAAbCAYAAAAkjP6EAAAABHNCSVQICAgIfAhkiAAACOJJREFU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\nAABJRU5ErkJggg==\n",
            "text/latex": "$$\\left [ R \\log{\\left (- \\frac{Ug}{R} e^{\\frac{t_{0}}{C R}} \\right )}\\right ]$$",
            "text/plain": [
              "⎡     ⎛      t₀ ⎞⎤\n",
              "⎢     ⎜     ─── ⎟⎥\n",
              "⎢     ⎜     C⋅R ⎟⎥\n",
              "⎢     ⎜-Ug⋅ℯ    ⎟⎥\n",
              "⎢R⋅log⎜─────────⎟⎥\n",
              "⎣     ⎝    R    ⎠⎦"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAN4AAAAcCAYAAAAORwEIAAAABHNCSVQICAgIfAhkiAAACI9JREFU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\ns2aJRCKRSCQSiUQikUgkEolEwud/wg5bb+0K8bAAAAAASUVORK5CYII=\n",
            "text/latex": "$$i{\\left (t \\right )} = - \\frac{Ug}{R} e^{- \\frac{t - t_{0}}{C R}}$$",
            "text/plain": [
              "            -(t - t₀)  \n",
              "            ────────── \n",
              "               C⋅R     \n",
              "       -Ug⋅ℯ           \n",
              "i(t) = ────────────────\n",
              "              R        "
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_eaJ70J94TpE",
        "colab_type": "code",
        "outputId": "4f785124-ddc4-4545-f1a1-c652cfdb8b1a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "zacetne_vrednosti = {t0:1,C:1e-6,Ug:3, R:1e6}\n",
        "print(zacetne_vrednosti)\n",
        "tok = lambdify(t,solution.args[1].subs(zacetne_vrednosti), 'numpy')  # tok kot funkcija časa\n",
        "print('Tok pri 2 s: {:g} A'.format(tok(2))) # testiram"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "stream",
          "text": [
            "{t0: 1, C: 1e-06, Ug: 3, R: 1000000.0}\n",
            "Tok pri 2 s: -1.10364e-06 A\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xXlS8yuD-7IU",
        "colab_type": "code",
        "outputId": "01667188-aad2-465f-85d1-1c31456adf2c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        }
      },
      "source": [
        "cas = np.linspace(0, 5, 100)\n",
        "plt.plot(cas, tok(cas))\n",
        "plt.xlabel('Čas [s]')\n",
        "plt.ylabel('Tok [A] ')\n",
        "plt.show()\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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dvdbddwJzgUlmVgYUu/sCd3dgVtz+yeJOBmZ5zAKgV4iTsI2UHmkGa25p5RdP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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iLpLqy3h9OI0",
        "colab_type": "text"
      },
      "source": [
        "#### Rešitev tretje enačbe - funkcija  $i(t)={I_0} e^{-t/\\tau}$ \n",
        "\n",
        "Zapišem funkcijo in preverim delovanje v grafu z eno krivuljo"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r3O2Cz1OqqGb",
        "colab_type": "code",
        "outputId": "819fd6aa-b075-4380-8a80-8e75472617d0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        }
      },
      "source": [
        "def it(t,a,b):  # funkcija\n",
        "    return a*np.exp(-t/b)\n",
        "\n",
        "cas=np.linspace(0,10,100)\n",
        "tok=it(cas,1,2)\n",
        "plt.plot(cas,tok)  # preverim za eno krivuljo"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f192b682048>]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 55
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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v7XN0B/sJ9v3tdU56clSyD6XQi4HaAa/rgHedaIxzLmhmLUAecHDgIDO7CbgJ\noKys7CQji4hET5LfR5LfR3oMXkttWA8ydc4tcc5VOeeqCgoKhnPVIiJxbyiFvhcoHfC6JLzsuGPM\nLAnIJrRzVEREhslQCn0VUGFmE8wsAFwLLD1mzFLgY+HnVwPPa/5cRGR4DTqHHp4Tvx14htBhi/c7\n5zaZ2d1AtXNuKfBT4H/NrAY4TKj0RURkGA3pOHTn3DJg2THLvjTgeRfwwchGExGRd0JX3hERiRMq\ndBGROKFCFxGJE+bVwShm1gjsPslfz+eYk5YSgL5zYtB3Tgyn8p3HO+eOeyKPZ4V+Ksys2jlX5XWO\n4aTvnBj0nRNDtL6zplxEROKECl1EJE7EaqEv8TqAB/SdE4O+c2KIyneOyTl0ERH5e7G6hS4iIsdQ\noYuIxImYK3QzW2hmW82sxszu8jpPtJlZqZktN7PNZrbJzO7wOtNwMDO/ma01sye9zjIczCzHzB4z\ns9fNbIuZzfc6U7SZ2efC/01vNLNfmdnJ35tuhDKz+82swcw2DliWa2bPmdn28OPoSK0vpgp9wP1N\nLwEqgcVmVultqqgLAnc65yqBecBtCfCdAe4AtngdYhh9D/iDc24qMJM4/+5mVgx8Bqhyzk0ndCXX\neLxK68+Bhccsuwv4k3OuAvhT+HVExFShM+D+ps65HuDN+5vGLedcvXNuTfh5K6H/0Yu9TRVdZlYC\nvB/4iddZhoOZZQPnEboMNc65Hudcs7ephkUSkBa+KU46sM/jPBHnnHuJ0CXFB1oEPBB+/gBwZaTW\nF2uFfrz7m8Z1uQ1kZuXAbGClt0mi7v8BXwD6vQ4yTCYAjcDPwtNMPzGzDK9DRZNzbi/wbWAPUA+0\nOOee9TbVsBnrnKsPP98PjI3UB8daoScsMxsF/Ab4rHPuiNd5osXMLgManHOrvc4yjJKAM4F7nXOz\ngXYi+M/wkSg8b7yI0F9m44AMM/uIt6mGX/jObhE7djzWCn0o9zeNO2aWTKjMH3TOPe51nihbAFxh\nZrsITam918x+6W2kqKsD6pxzb/7L6zFCBR/PLgTecM41Oud6gceBsz3ONFwOmFkRQPixIVIfHGuF\nPpT7m8YVMzNCc6tbnHPf8TpPtDnn/tU5V+KcKyf05/u8cy6ut9ycc/uBWjM7LbzoAmCzh5GGwx5g\nnpmlh/8bv4A43xE8wMB7MH8MeCJSHzykW9CNFCe6v6nHsaJtAXA9sMHMXgsv+7fwbQElfnwaeDC8\nobIT+ITHeaLKObfSzB4D1hA6kmstcXgJADP7FXA+kG9mdcCXgW8Aj5jZDYQuIX5NxNanU/9FROJD\nrE25iIjICajQRUTihApdRJdr1SwAAAAeSURBVCROqNBFROKECl1EJE6o0EVE4oQKXUQkTvx//Cjz\ngISfR/wAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cm02lGtTCBCr",
        "colab_type": "text"
      },
      "source": [
        "Naredim niz vrednosti tau ter zanko, v kateri se izriše več krivulj na grafu za izbrane vrednosti niza tau."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TOcUDexg9jdk",
        "colab_type": "code",
        "outputId": "95bf0d95-9ee8-44d6-a34e-e4a9a5c8a3c0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        }
      },
      "source": [
        "tau=[1,2,3,4] # niz vrednosti tau\n",
        "for i in range(len(tau)):\n",
        "  labela=r'$\\tau = $'+str(tau[i])\n",
        "  plt.plot(cas, it(cas,1,tau[i]),label=labela)\n",
        "plt.xlabel('Čas  /s')\n",
        "plt.ylabel('Tok  /A')\n",
        "plt.legend()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/html": [
              "<script src='https://www.gstatic.com/external_hosted/mathjax/latest/MathJax.js?config=default'></script>"
            ],
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ]
          },
          "metadata": {
            "tags": []
          }
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f192b234978>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 56
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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7y3UNk7ouNFj5AxYtWxAx/SXivy9fUlEUpfoq9kO9YG3/H1LK0WjX9m8BDgER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\ncf8PPVh2W8iYcmQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hgfwlxvR-4By",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}