Aula 5 - Análise de Malhas.ipynb

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   "source": [
    "# Aula 5 - Análise de Malhas\n",
    "\n",
    "Jupyter Notebook desenvolvido por [Gustavo S.S.](https://github.com/GSimas)\n",
    "\n",
    "**A análise de malhas também é\n",
    "conhecida como análise de laço ou\n",
    "método malha corrente.**\n",
    "\n",
    "Lembre-se de que um\n",
    "laço é um caminho fechado que não passa mais de uma vez pelo mesmo nó.\n",
    "Uma malha é um laço que não contém qualquer outro laço dentro de si.\n",
    "\n",
    "O circuito da Figura 3.15a tem dois ramos\n",
    "que se cruzam, porém ele pode ser redesenhado como na Figura 3.15b.\n",
    "o circuito da Figura 3.15a também é planar; entretanto, o circuito da\n",
    "Figura 3.16 é não planar, pois não há nenhuma maneira de redesenhá-lo sem\n",
    "que haja algum cruzamento entre ramos.\n",
    "\n",
    "![](http://i.imgur.com/3Gu3UOb.png)\n",
    "![](http://i.imgur.com/V5yAmq0.png)\n",
    "\n",
    "**Malha é um laço que não contém nenhum outro laço em seu interior.**\n",
    "\n",
    "![](http://i.imgur.com/eihmMJc.png)\n",
    "\n",
    "O sentido da corrente de malha\n",
    "é arbitrário (sentido horário ou\n",
    "anti-horário) e não afeta a validade\n",
    "da solução.\n",
    "\n",
    "Etapas na determinação de correntes de malha:\n",
    "\n",
    "1. Atribua correntes de malha i1, i2, ..., in a n malhas.\n",
    "2. Aplique a LKT a cada uma das n malhas. Use a lei de Ohm para expressar as tensões em termos de correntes de malha.\n",
    "3. Resolva as n equações simultâneas resultantes para obter as correntes de malha.\n",
    "\n",
    "Resolução para a figura 3.17. \n",
    "\n",
    "Malha 1:\n",
    "\n",
    "\\begin{align}\n",
    "{\\Large -V_1 + R_1i_1 + R_3(i_1 - i_2) = 0}\n",
    "\\\\{\\Large (R_1 + R_3)i_1 - R_3i_2 = V_1}\n",
    "\\end{align}\n",
    "\n",
    "Malha 2:\n",
    "\n",
    "\\begin{align}\n",
    "{\\Large R_2i_2 + V_2 + R_3(i_2 - i_1) = 0}\n",
    "\\\\{\\Large -R_3i_1 + (R_2 + R_3)i_2 = -V_2}\n",
    "\\end{align}\n",
    "\n",
    "Reorganizando as equações, temos:\n",
    "\n",
    "\\begin{align}\n",
    "\\begin{bmatrix}\n",
    "R_1 + R_3   & -R_3 \\\\\n",
    "-R_3        & R_2 + R_3\n",
    "\\end{bmatrix}\n",
    "\\begin{bmatrix}\n",
    "i_1 \\\\\n",
    "i_2\n",
    "\\end{bmatrix}\n",
    "=\n",
    "\\begin{bmatrix}\n",
    "V_1 \\\\\n",
    "-V_2\n",
    "\\end{bmatrix}\n",
    "\\end{align}\n",
    "\n",
    "Note que **as correntes de ramo são diferentes das de malha, a menos que a\n",
    "malha esteja isolada**. Para distinguir entre os dois tipos de correntes, usaremos\n",
    "i para indicar correntes de malha e I para indicar correntes de ramo. Os elementos\n",
    "de corrente I1, I2 e I3 são somas algébricas das correntes de malha. Fica\n",
    "evidente da Figura 3.17 que:\n",
    "\n",
    "\\begin{align}\n",
    "{\\Large I_1 = i_1}\n",
    "\\\\{\\Large I_2 = i_2}\n",
    "\\\\{\\Large I_3 = i_1 - i_2}\n",
    "\\end{align}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exemplo 3.5**\n",
    "\n",
    "Para o circuito da Figura 3.18, determine as correntes de ramo I1, I2 e I3 usando a análise\n",
    "de malhas.\n",
    "\n",
    "![](https://i.imgur.com/T4NYpUP.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exemplo 3.5\n",
      "Corrente I1: [[ 1.]] A\n",
      "Corrente I2: [[ 1.]] A\n",
      "Corrente I3: [[ -2.22044605e-16]] A\n"
     ]
    }
   ],
   "source": [
    "print(\"Exemplo 3.5\")\n",
    "import numpy as np\n",
    "\n",
    "V1 = 15\n",
    "V2 = 10\n",
    "\n",
    "#Malha 1:\n",
    "#-V1 + 5i1 + 10(i1 - i2) + V2 = 0\n",
    "    #15i1 - 10i2 = 5\n",
    "    #3i1 - 2i2 = 1\n",
    "    \n",
    "#Malha 2:\n",
    "#-V2 + 10(i2 - i1) + 6i2 + 4i2 = 0\n",
    "    #20i2 - 10i1 = 10\n",
    "    #2i2 - i1 = 1\n",
    "    \n",
    "coef = np.matrix('3 -2;2 -1')\n",
    "res = np.matrix('1;1')\n",
    "I = np.linalg.inv(coef)*res\n",
    "print(\"Corrente I1:\",I[0],\"A\")\n",
    "print(\"Corrente I2:\",I[1],\"A\")\n",
    "print(\"Corrente I3:\",I[0]-I[1],\"A\") #aproximadamente = 0"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problema Prático 3.5**\n",
    "\n",
    "Calcule as correntes de malha i1 e i2 no circuito da Figura 3.19.\n",
    "\n",
    "![](https://i.imgur.com/Lc6Oogw.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problema Prático 3.5\n",
      "Corrente i1: [[ 2.5]] A\n",
      "Corrente i2: [[ 0.]] A\n"
     ]
    }
   ],
   "source": [
    "print(\"Problema Prático 3.5\")\n",
    "V1 = 45\n",
    "V2 = 30\n",
    "\n",
    "#Malha 1:\n",
    "#2i1 + 12(i1 - i2) + 4i1 = V1\n",
    "    #18i1 - 12i2 = 45\n",
    "    #6i1 - 4i2 = 15\n",
    "\n",
    "#Malha 2:\n",
    "#3i2 + 12(i2 - i1) + 9i2 = -V2\n",
    "    #-12i1 + 24i2 = 30\n",
    "    #-2i1 + 4i2 = -5\n",
    "\n",
    "coef = np.matrix(\"6 -4;-2 4\")\n",
    "res = np.matrix(\"15;-5\")\n",
    "I = np.linalg.inv(coef)*res\n",
    "print(\"Corrente i1:\",I[0],\"A\")\n",
    "print(\"Corrente i2:\",I[1],\"A\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exemplo 3.6**\n",
    "\n",
    "Use a análise de malhas para encontrar a corrente Io no circuito da Figura 3.20.\n",
    "\n",
    "![](https://i.imgur.com/0eWp0u2.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exemplo 3.6\n",
      "Corrente i0: [[ 1.5]] A\n"
     ]
    }
   ],
   "source": [
    "print(\"Exemplo 3.6\")\n",
    "V1 = 24\n",
    "CCVS = 4#io\n",
    "\n",
    "#Malha 1:\n",
    "#10(i1 - i2) + 12(i1 - i3) = V1\n",
    "    #22i1 - 10i2 - 12i3 = 24\n",
    "    #11i1 - 5i2 - 6i3 = 12\n",
    "\n",
    "#Malha 2:\n",
    "#24i2 + 4(i2 - i3) + 10(i2 - i1) = 0\n",
    "    #-10i1 + 38i2 - 4i3 = 0\n",
    "    #-5i1 + 19i2 - 2i3 = 0\n",
    "\n",
    "#Malha 3:\n",
    "#12(i3 - i1) + 4(i3 - i2) + 4i0 = 0\n",
    "    #i0 = i1 - i2\n",
    "    #-12i1 - 4i2 + 16i3 + 4(i1 - i2) = 0\n",
    "    #-8i1 - 8i2 + 16i3 = 0\n",
    "    #-i1 - i2 + 2i3 = 0\n",
    "\n",
    "coef = np.matrix(\"11 -5 -6;-5 19 -2;-1 -1 2\")\n",
    "res = np.matrix(\"12;0;0\")\n",
    "I = np.linalg.inv(coef)*res\n",
    "print(\"Corrente i0:\",I[0]-I[1],\"A\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problema Prático 3.6**\n",
    "\n",
    "Usando a análise de malhas, determine Io no circuito da Figura 3.21.\n",
    "\n",
    "![](https://i.imgur.com/81rgSLH.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problema Prático 3.6\n",
      "Corrente i0: [[-4.]] A\n"
     ]
    }
   ],
   "source": [
    "print(\"Problema Prático 3.6\")\n",
    "V1 = 16\n",
    "CCVS = 10#io\n",
    "\n",
    "#Malha 1:\n",
    "#-V1 + 4(i1 - i3) + 2(i1 - i2) = 0\n",
    "    #6i1 - 2i2 - 4i3 = 16\n",
    "    #3i1 - i2 - 2i3 = 8\n",
    "\n",
    "#Malha 2:\n",
    "#2(i2 - i1) + 8(i2 - i3) - CCVS = 0\n",
    "    #-2i1 + 10i2 - 8i3 = 10i0\n",
    "    #i0 = i3\n",
    "    #-i1 + 5i2 - 9i3 = 0\n",
    "\n",
    "#Malha 3:\n",
    "#6i3 + 8(i3 - i2) + 4(i3 - i1) = 0\n",
    "    #-4i1 - 8i2 + 18i3 = 0\n",
    "    #-2i1 - 4i2 + 9i3 = 0\n",
    "\n",
    "coef = np.matrix(\"3 -1 -2;-1 5 -9;-2 -4 9\")\n",
    "res = np.matrix(\"8;0;0\")\n",
    "I = np.linalg.inv(coef)*res\n",
    "print(\"Corrente i0:\",I[2],\"A\")"
   ]
  },
  {
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"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Análise de malhas com fontes de corrente\n",
    "\n",
    "**Caso 1**: Quando existe uma fonte de corrente apenas em uma malha:\n",
    "considere, por exemplo, o circuito da Figura 3.22. Fazemos i2 = –5 A e escrevemos\n",
    "uma equação de malha para a outra malha da maneira usual, isto é:\n",
    "\n",
    "\\begin{align}\n",
    "{\\Large -10 + 4i_1 + 6(i_1 - i_2) = 0}\n",
    "\\\\{\\Large i_1 = -2 A}\n",
    "\\end{align}\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "**Caso 2**: Quando uma fonte de corrente existe entre duas malhas: considere\n",
    "o circuito da Figura 3.23a, por exemplo. Criamos uma supermalha, excluindo\n",
    "a fonte de corrente e quaisquer elementos a ela associados em série,\n",
    "como mostrado na Figura 3.23b. Logo:\n",
    "\n",
    "**Uma supermalha é resultante quando duas malhas possuem uma fonte de\n",
    "corrente (dependente ou independente) em comum.**\n",
    "\n",
    "![](http://i.imgur.com/zLuuvRX.png)\n",
    "\n",
    "uma supermalha deve realizar a LKT como qualquer outra malha. Assim, aplicando\n",
    "a LKT à supermalha da Figura 3.23b, temos:\n",
    "\n",
    "\\begin{align}\n",
    "{\\Large -20 + 6i_1 + 10i_2 + 4i+2 = 0}\n",
    "\\\\{\\Large 6i_1 + 14i_2 = 20}\n",
    "\\\\Assim:\n",
    "\\\\{\\Large i_1 = -3,2 A}\n",
    "\\\\{\\Large i_2 = 2,8 A}\n",
    "\\end{align}"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exemplo 3.7**\n",
    "\n",
    "Para o circuito da Figura 3.24, determine i1 a i4 usando a análise de malhas.\n",
    "\n",
    "![](https://i.imgur.com/2MmMnFa.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Exemplo 3.7\n",
      "Corrente i1: [[-7.5]] A\n",
      "Corrente i4: [[ 2.14285714]] A\n"
     ]
    }
   ],
   "source": [
    "print(\"Exemplo 3.7\")\n",
    "V1 = 10\n",
    "C1 = 5\n",
    "CCCS = 3#io\n",
    "\n",
    "#Supermalha:\n",
    "#2i1 + 4i3 + 8(i3 - i4) + 6i2 = 0\n",
    "    #2i1 + 6i2 + 12i3 - 8i4 = 0\n",
    "    #i4 = -i0\n",
    "    #i1 + 3i2 + 6i3 + 4i0 = 0\n",
    "    #i2 - i3 = 3i0 => i3 = i2 - 3i0\n",
    "    #i2 - i1 = 5 => i1 = i2 - 5\n",
    "    #i2 - 5 + 3i2 + 6(i2 - 3i0) + 4i0 = 0\n",
    "        #10i2 - 14i0 = 5\n",
    "\n",
    "#Malha 4:\n",
    "#V1 + 8(i4 - i3) + 2i4 = 0\n",
    "    #-8i3 + 10i4 = -10\n",
    "    #-4i3 - 5i0 = -5\n",
    "    #-4(i2 - 3i0) - 5i0 = -5\n",
    "        #-4i2 + 7i0 = -5\n",
    "\n",
    "coef = np.matrix(\"10 -14; -4 7\")\n",
    "res = np.matrix(\"5;-5\")\n",
    "I = np.linalg.inv(coef)*res\n",
    "i1 = I[0] - 5\n",
    "i4 = -I[1]\n",
    "print(\"Corrente i1:\",i1,\"A\")\n",
    "print(\"Corrente i4:\",i4,\"A\")"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Problema Prático 3.7**\n",
    "\n",
    "Use a análise de malhas para determinar i1, i2 e i3 na Figura 3.25.\n",
    "\n",
    "![](https://i.imgur.com/WI6KsR9.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Problema Prático 3.7\n",
      "Corrente i1: [[ 4.63157895]] A\n",
      "Corrente i2: [[ 0.63157895]] A\n",
      "Corrente i3: [[ 1.47368421]] A\n"
     ]
    }
   ],
   "source": [
    "print(\"Problema Prático 3.7\")\n",
    "V1 = 8\n",
    "C1 = 4\n",
    "\n",
    "#Supermalha (Malha 1 e Malha 2):\n",
    "#2(i1 - i3) + 4(i2 - i3) + 8i2 = 8\n",
    "    #2i1 + 12i2 - 6i3 = 8\n",
    "    #i1 + 6i2 - 3i3 = 4\n",
    "    #i1 - i2 = 4 => i2 = i1 - 4\n",
    "    #i1 + 6(i1 - 4) - 3i3 = 4\n",
    "        #7i1 - 3i3 = 28\n",
    "\n",
    "\n",
    "#2i3 + 4(i3 - i2) + 2(i3 - i1) = 0\n",
    "    #-2i1 - 4i2 + 8i3 = 0\n",
    "    #-i1 - 2i2 + 4i3 = 0\n",
    "        #-i1 - 2(i1 - 4) + 4i3 = 0\n",
    "        #-3i1 + 4i3 = -8\n",
    "\n",
    "coef = np.matrix(\"7 -3;-3 4\")\n",
    "res = np.matrix(\"28;-8\")\n",
    "I = np.linalg.inv(coef)*res\n",
    "i2 = I[0] - 4\n",
    "print(\"Corrente i1:\",I[0],\"A\")\n",
    "print(\"Corrente i2:\",i2,\"A\")\n",
    "print(\"Corrente i3:\",I[1],\"A\")"
   ]
  }
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