TI1-4.2_Lleis_de_Kirchhoff.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lleis de Kirchhoff"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import *\n",
    "x, y, z = symbols(\"x y z\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1) \n",
    "Trobar $I_{1}$, $I_{2}$ i $I_{3}$    \n",
    "Dades: $R_{1} = 2 \\ \\Omega$, $R_{2} = 6 \\ \\Omega$, $R_{3} = 4 \\ \\Omega$. $\\mathcal{E}_{1} = 5 \\ V$, $\\mathcal{E}_{2} = 12 \\ V$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](img/Kirchhoff1.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{x: 1/22, y: -13/11, z: -27/22}"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([Eq(x+z-y, 0), Eq(6*y+2*x,-7 ), Eq(-4*z-6*y,12 )],[x,y,z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.045454545454545456, -1.1818181818181819, -1.2272727272727273)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1/22, -13/11, -27/22"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) \n",
    "Trobar $I_{1}$, $I_{2}$ i $I_{3}$    \n",
    "Dades: $R_{1} = 1 \\ \\Omega$, $R_{2} = 4 \\ \\Omega$, $R_{3} = 2 \\ \\Omega$. $\\mathcal{E}_{1} = 12 \\ V$, $\\mathcal{E}_{2} = 5 \\ V$, $\\mathcal{E}_{3} = 7 \\ V$, $r = 1 \\ \\Omega$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](img/Kirchhoff2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{x: 146/31, y: 47/31, z: -99/31}"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([Eq(x+z-y, 0), Eq(5*y+2*x,17 ), Eq(-3*z-5*y,2 )],[x,y,z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4.709677419354839, 1.5161290322580645, -3.193548387096774)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "146/31 , 47/31 , -99/31"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3) \n",
    "Trobar $I_{1}$, $I_{2}$ i $I_{3}$    \n",
    "Dades: $R_{1} = 10 \\ \\Omega$, $R_{2} = 3 \\ \\Omega$, $R_{3} = 6 \\ \\Omega$. $\\mathcal{E}_{1} = 5 \\ V$, $\\mathcal{E}_{2} = 6 \\ V$, $\\mathcal{E}_{3} = 12 \\ V$, $r_{1} = 1 \\ \\Omega$, $r_{2} = 3 \\ \\Omega$, $r_{3} = 2 \\ \\Omega$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](img/Kirchhoff3.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{x: 95/101, y: -11/101, z: -84/101}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([Eq(x+y+z, 0), Eq(-6*y+11*x,11 ), Eq(-8*z+6*y,6 )],[x,y,z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9405940594059405, -0.10891089108910891, -0.8316831683168316)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "95/101,-11/101,-84/101"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4) \n",
    "Trobar $I_{1}$, $I_{2}$ i $I_{3}$    \n",
    "Dades: $R_{1} = 7 \\ \\Omega$, $R_{2} = 12 \\ \\Omega$, $R_{3} = 4 \\ \\Omega$. $\\mathcal{E}_{1} = 5 \\ V$, $\\mathcal{E}_{2} = 3 \\ V$, $\\mathcal{E}_{3} = 12 \\ V$, $\\mathcal{E}_{4} = 12 \\ V$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](img/Kirchhoff4.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{x: 67/40, y: 23/160, z: 291/160}"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([Eq(x+y-z, 0), Eq(12*y-7*x,-10 ), Eq(-4*z-12*y,-9 )],[x,y,z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.675, 0.14375, 1.81875)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "67/40,23/160,291/160"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5) \n",
    "Trobar $I_{1}$, $I_{2}$ i $I_{3}$    \n",
    "Dades: $R_{1} = 8 \\ \\Omega$, $R_{2} = 12 \\ \\Omega$, $R_{3} = 5 \\ \\Omega$, $R_{4} = 2 \\ \\Omega$. $\\mathcal{E}_{1} = 12 \\ V$, $\\mathcal{E}_{2} = 5 \\ V$, $\\mathcal{E}_{3} = 7 \\ V$, $r = 1 \\ \\Omega$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![](img/Kirchhoff5.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{x: 65/209, y: -40/209, z: -105/209}"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solve([Eq(x+z-y, 0), Eq(13*y+8*x,0 ), Eq(-5*z-13*y,5 )],[x,y,z])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.31100478468899523, -0.19138755980861244, -0.5023923444976076)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "65/209, -40/209,-105/209"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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