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zokier/impossible_circuit.ipynb

Created February 3, 2014 17:01
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impossible_circuit.ipynb
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"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": " U2/3V\n +-----------+------|-+|------+\n | | |\n | / ^ \\ /\n | _ \\ R1 | I2 | \\ R4\n | / \\ / \\___/ /\n = I1 | | R5 |\n U1 + ^ | VA+-----/\\/\\/\\-----+ VB\n 5V - \\_/ | ___ |\n = / / \\ /\n | \\ R2 | I3 | \\ R4\n | / \\ < /\n | | |\n +-----------+----------------+\n |\n 0 V"
},
{
"cell_type": "code",
"collapsed": false,
"input": "%pylab inline\nfrom sympy import *\ninit_printing(use_latex=True)",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "Populating the interactive namespace from numpy and matplotlib\n"
}
],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": "U1 = Symbol('U_1')\nU2 = Symbol('U_2')\n\nI1 = Symbol('I_1')\nI2 = Symbol('I_2')\nI3 = Symbol('I_3')\n\nR1 = Symbol('R_1')\nR2 = Symbol('R_2')\nR3 = Symbol('R_3')\nR4 = Symbol('R_4')\nR5 = Symbol('R_5')\n\nVA = Symbol('V_A')\nVB = Symbol('V_B')",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": "values = {R1: 100, R2: 100, R3: 400, R4: 300, R5: 200, U1: 5, U2: 3}",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": "# voltage equations (\"mesh analysis\")\neq1 = -U1 + R1*(I1-I2) + R2*(I1-I3)\neq2 = -U2 + R3*(I2) + R5*(I2-I3) + R1*(I2-I1)\neq3 = R2*(I3-I1) + R5*(I3-I2) + R4*I3",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": "currents = solve([eq1, eq2, eq3], [I1, I2, I3])",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": "I2_num = currents[I2].subs(values).evalf() * 1000.0",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": "I1_num = currents[I1].subs(values).evalf() * 1000.0",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 7
},
{
"cell_type": "code",
"collapsed": false,
"input": "I3_num = currents[I3].subs(values).evalf() * 1000.0",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "code",
"collapsed": false,
"input": "I2_num - I3_num # I_R5",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$2.20338983050847$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKIAAAAPBAMAAACVXgkYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\njhdEkvN0PQAAAABJRU5ErkJggg==\n",
"prompt_number": 9,
"text": "2.20338983050847"
}
],
"prompt_number": 9
},
{
"cell_type": "code",
"collapsed": false,
"input": "I1_num - I2_num # I_R1",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$23.8983050847458$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAAPBAMAAAB+abIbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nkJ5612NFiDY7oomjXywp6vq87X8lsAh+4KJE/wAAAABJRU5ErkJggg==\n",
"prompt_number": 10,
"text": "23.8983050847458"
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": "I2_num # I_R3",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$12.3728813559322$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAAPBAMAAAB+abIbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nf5+8OGzdrZHr+8/jLwvQBlljyqqiAAAAAElFTkSuQmCC\n",
"prompt_number": 11,
"text": "12.3728813559322"
}
],
"prompt_number": 11
},
{
"cell_type": "code",
"collapsed": false,
"input": "I1_num - I3_num # I_R2",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$26.1016949152542$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAAPBAMAAAB+abIbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAACx0lEQVQ4Ea2TzUtUURiHn3G8cx3vzHhzV4ua\nNLRo4ZBBHxuHNi67BCVmMEMfQh/kxSI3wsx/4IgUVFiCYIuIBPtalI7SB5GQRNSyaRlFFmaaVrf3\nnHvITctemOF33t85z3nve86B+sadQN+zrPyD48GB/i1GYfefx2qecWVcnVbOZuM4T6q3EmlozaKV\nZPdhUFaeQpGuYtW4ZIm0CfERh91QWQ/YTmclMihWbQbrGuuNEw+CMoewl9FK/FFCFDGPeIn7RDOS\ntXb0eKRK2ONa4fi0chKOifc8Q6xELGOcC9NwAi7jKAWJIYMiPkLsW+qrSqp46RHNk1zUinn1uatQ\n8Ih8zFA3jm2cmBhcgZ6sVrBxIkRJ4xaFGC2pCSqEWJen5ldI3CMZa0F0EdvJkMuQWA4dzZny1oj+\nRIjSlNrFujv9W7VUxFyamp/hutX2mSJXpcYK74UYlxp/G+LnmaxacduLaZVyJ9SwVj5BYsDPTRKf\n01qIm3yql/Q6a7XCMAWYKltlIdpfcMxeUS8i1VKzRKiOoIkDvqaMkluk6uI/iIHHNs8pJwsVGyHy\nkLemRpm8V35yAULlh8RRNaRKWj5CSm2pK8v5f796BeaLfHpcmHutianZdtNhmdriQqNe1OIms5oo\nKBVPUQ1KyeYS6mTSJM06aeF8RbI9B31NhJg569PS3CKJPGjVgSYKSiKZZp2c9VqN8iUps07OWmqE\ne8nu7p5LZVFOPjwZ2avF4xURV6s33d0/zmiUzJHXMy33r6okWs9OlFAPSKrlnfSRD261uq5x2WiQ\n/W7opOGmepgJVyvxh0KUvLsbfU0j7KJzzlqVvOLcojMbqqhvDfPC66qIUyeX8a41aebUK/yGvt5T\naCXZBYPCCYJgBLvhOIxB0/WxCh2zMtCK3qaseLtlgd32vUJvY9E4keajHlNBsIJWcC44G6Jk7n+O\nP5qK+7AMQHjNAAAAAElFTkSuQmCC\n",
"prompt_number": 12,
"text": "26.1016949152542"
}
],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": "I3_num # I_R4",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$10.1694915254237$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKIAAAAPBAMAAACVXgkYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nSUVORK5CYII=\n",
"prompt_number": 13,
"text": "10.1694915254237"
}
],
"prompt_number": 13
},
{
"cell_type": "code",
"collapsed": false,
"input": "I3_num * values[R4] # V_B",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$3050.84745762712$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKIAAAAPBAMAAACVXgkYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nRK5CYII=\n",
"prompt_number": 14,
"text": "3050.84745762712"
}
],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": "((I1_num - I3_num) * values[R2]) # V_A",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$2610.16949152542$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAAPBAMAAAB+abIbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nW4ZUwDmvV6Ho/c/xB38X+ylvRbujAAAAAElFTkSuQmCC\n",
"prompt_number": 15,
"text": "2610.16949152542"
}
],
"prompt_number": 15
},
{
"cell_type": "code",
"collapsed": false,
"input": "# current equations (\"nodal analysis\")\neq4 = ((VA - U1) / R1) + (VA / R2) + ((VA - VB) / R5)\neq5 = ((VB - (U2+U1)) / R3) + (VB / R4) + ((VB - VA) / R5)",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": "voltages = solve([eq4, eq5], [VA, VB])",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 17
},
{
"cell_type": "code",
"collapsed": false,
"input": "VA_num = voltages[VA].subs(values).evalf()",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "code",
"collapsed": false,
"input": "VB_num = voltages[VB].subs(values).evalf()",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": "1000*(VA_num / values[R2]) # I_R2",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$26.1016949152542$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAAPBAMAAAB+abIbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nP5qK+7AMQHjNAAAAAElFTkSuQmCC\n",
"prompt_number": 20,
"text": "26.1016949152542"
}
],
"prompt_number": 20
},
{
"cell_type": "code",
"collapsed": false,
"input": "1000*((values[U1] - VA_num) / values[R1]) # I_R1",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$23.8983050847458$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAAPBAMAAAB+abIbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAIpm7MhCriUTv3c12\nVGZoascqAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAC2klEQVQ4Ea2UzYsTZxzHP5Ps5GUnb+5FPDm+\n1BV6MEKVUpANHhT0sINQilJIEPGirEGLwSoaeuvJFV9QBI0K9lBKg7D0YiUKtQhC5yB4TPQmiqvW\n6FY3Sb/zPLP+BT4wM58839/3O8/bBCbWfAXLG1uI2vd/r4ddJ1bF5DSOhLiT9yp4f40ZZW2swJjP\njr2NRt0Qt4OtTevGrXGq6fh0e6j5pEL3CitKhpggP8QL3WtkR6MO/MmeWIHxMvOj0ahmiKujReuG\nVEB2Njeg2FJgvofTTs2SKhvin5APPIPjeEfvQmGWdNsq8KDMKtnlEvHHwZJ1Q7ZF6m3mItW2tHQZ\nt1Vsk+4b4uem+5HN0A0iJ8ka+VjBeV5GM/4BQ9QkWw9eX4n6aWad+TdI96plcguG1K1Zv4PToUks\n1sgMYiXtaWRkOgqKqBb9iNx6ah36ut0yeGh4kqzGOCQiNc933yixk3p5r0LVJ7MYK09MYlIlhmZe\naM9ij+rrjP3oS4PEaI70K7xFQ7D9Os57mK4nA2eBlSp8bxW3YxL1VkubWNmMPYq5EWUdq0T3pzv/\na3Kbx0NLmtI5myjtmzjR1KSJEt1XqjCkRW4teUhI0g6d161QY/48hYfbB5bUdelbjfF0R7ShVK1r\n1lZ5ZHJybbCk6b3+5Lmv7SqRHMiUDRiLnqm+pWUwFWodu+EBdGyLPvmBUdy6SdSZtJTS2i8sufM+\ny4p9kkMlVXXN6PJqlkYBUz0tynxwWWMMFFDoGyW/f/+hCx2qOk6GtJsJq8i9Fe5my4y/FmdLsLFw\nhumSIc7C76UH8KU+IX4lN0uibRXVarGm1W0ooROzpDi/NNa1Cj26HR3mzByFTm7OvWOJl+QXGQ/d\nc/oe9SJ+Y3fF1CinqMSuSRQ5Ps9KseLp22zx0+qv4SZsm9T/weE1zZgyq4XuifsVnMm9AXz3cF+s\nkJ5612NFiDY7oomjXywp6vq87X8lsAh+4KJE/wAAAABJRU5ErkJggg==\n",
"prompt_number": 21,
"text": "23.8983050847458"
}
],
"prompt_number": 21
},
{
"cell_type": "code",
"collapsed": false,
"input": "1000* (VA_num - VB_num) / values[R5] # I_R5",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$-2.20338983050847$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAALIAAAAPBAMAAACy8IjwAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
"prompt_number": 22,
"text": "-2.20338983050847"
}
],
"prompt_number": 22
},
{
"cell_type": "code",
"collapsed": false,
"input": "1000*(VB_num / values[R4]) # I_R4",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$10.1694915254237$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKIAAAAPBAMAAACVXgkYAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA\nAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAv3aB7AAAAD3RSTlMAzRAiu5mrdu/dZoky\nVEQKohj3AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAC80lEQVQ4Ea2TT4hTVxTGf3kvL8m8l0yCYAW1\nzBNaGRFJoB1o6cJHqQtpq0FnZjNFU/FfpTCxYi1UaKpQ2kI1gsymiK+4UFzNxj8li8nGVRedTVcV\nJgily2q0itNO0u/ey2gXLr1w/3znu+d7551zLpCJ4fVbH2GHAXS+7Mqy1xiKdbyZkzWd1miui+/0\nmJj8QE6fFfc52p96rwvvdD6kODfT6cjo747hVbYYLwc29YKK9z1vGctIwnjqn4U3+0Lnh0/wGiz0\nKAyHTUdvJhrg11lKw+Fw+Bi8HbMxYYuoogsWsIFskmuRS2T5IuEoHOS1aaO44UiNXEyhRebmCWFD\nH4Bvya9QbgcKoWGsX8VkG5SMhwXhQ+3lCpEs/k8JD2AhJm/4hmahTe5fcjo5+juY7Y6eo1qJIOoa\nsxTLDUZXzNnKt7RXE/ID3cgk3iNZe88VM/3niqIZi6Uoj6VUy5+aVqRaZ/TJKihvvLWPgmJchity\n+Voxpk7x2FVbwBGJXj/ZdbTcLsda1mqSmMWEtX2e4j+roLqewmJ0n4yq0JTiAow1neK7bO/p2l/z\nZGN/4GgYlWvx57qIKNXyAsU+wRnW8fsyEVLMNEurMUK2LY+L1m+no20/yHC7q1xZwsRYnf//X7cJ\nB4SnflnhrlHk6umFRRcjBCpbIJvG/pqjmbSwcAaO25OtTJ3Ss8oohaFSSK7vzVtFFdPVOqfkDuBz\nkR8rufccnW+o6DWyEnDBG0X1cfise7ItE6OeRaN0+PDsN00dX8HGqG8FfUp13jDl2r/N0b9Jr9wn\nu4yn/jZDivkWQWUVqDODVniWX2uyFBKu1Yr6VdOPgXJW4Q6coA4XHK13mq/p2shDin9bDaPIJca7\nnlrZgvcZX8yv8dYbupxwPN6UOkW9tWs1/8fOdJsJ9E1Lv9258QlhylKTklOcPj+XsvXUpzAHFkRT\nAjcme/KIdj9Oo6ldCu/o02MwcXMPGb3eNv7ModjRY8PhU/jDXPJ/kMvLH/8BlyTiXtCC3q4AAAAA\nSUVORK5CYII=\n",
"prompt_number": 23,
"text": "10.1694915254237"
}
],
"prompt_number": 23
},
{
"cell_type": "code",
"collapsed": false,
"input": "1000*(((values[U2]+values[U1]) - VB_num) / values[R3]) # I_R3",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$12.3728813559322$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAKEAAAAPBAMAAAB+abIbAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\nf5+8OGzdrZHr+8/jLwvQBlljyqqiAAAAAElFTkSuQmCC\n",
"prompt_number": 24,
"text": "12.3728813559322"
}
],
"prompt_number": 24
},
{
"cell_type": "code",
"collapsed": false,
"input": "VA_num, VB_num",
"language": "python",
"metadata": {},
"outputs": [
{
"latex": "$$\\begin{pmatrix}2.61016949152542, & 3.05084745762712\\end{pmatrix}$$",
"metadata": {},
"output_type": "pyout",
"png": "iVBORw0KGgoAAAANSUhEUgAAAWwAAAAaBAMAAABhvXviAAAAMFBMVEX///8AAAAAAAAAAAAAAAAA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\n",
"prompt_number": 25,
"text": "(2.61016949152542, 3.05084745762712)"
}
],
"prompt_number": 25
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 25
}
],
"metadata": {}
}
]
}
@PyMaster22
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