capacitance.ipdb

capacitance.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython console for SymPy 1.4 (Python 3.7.3-64-bit) (ground types: gmpy)\n",
      "\n",
      "These commands were executed:\n",
      ">>> from __future__ import division\n",
      ">>> from sympy import *\n",
      ">>> x, y, z, t = symbols('x y z t')\n",
      ">>> k, m, n = symbols('k m n', integer=True)\n",
      ">>> f, g, h = symbols('f g h', cls=Function)\n",
      ">>> init_printing()\n",
      "\n",
      "Documentation can be found at https://docs.sympy.org/1.4/\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import *\n",
    "init_session()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "F, L,C, c1, c2, c3, f1, f2, f3 = symbols('F L C c1 c2 c3 f1 f2 f3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle F = \\frac{1}{2 \\pi \\sqrt{C L}}$"
      ],
      "text/plain": [
       "         1     \n",
       "F = ───────────\n",
       "          _____\n",
       "    2⋅π⋅╲╱ C⋅L "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E1= Eq( F, 1/(2*pi*sqrt(L*C)) ) # Formula for Freq for LC tank circuit\n",
    "E1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left( f_{1} = \\frac{1}{2 \\pi \\sqrt{L c_{1}}}, \\  f_{2} = \\frac{1}{2 \\pi \\sqrt{L c_{2}}}, \\  f_{3} = \\frac{1}{2 \\pi \\sqrt{\\frac{L \\left(c_{1} + c_{2}\\right)}{c_{1} c_{2}}}}\\right)$"
      ],
      "text/plain": [
       "⎛          1                  1                       1          ⎞\n",
       "⎜f₁ = ────────────, f₂ = ────────────, f₃ = ─────────────────────⎟\n",
       "⎜           ______             ______               _____________⎟\n",
       "⎜     2⋅π⋅╲╱ L⋅c₁        2⋅π⋅╲╱ L⋅c₂               ╱ L⋅(c₁ + c₂) ⎟\n",
       "⎜                                           2⋅π⋅  ╱  ─────────── ⎟\n",
       "⎝                                               ╲╱      c₁⋅c₂    ⎠"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E2 = E1.subs({ C:c1, F:f1 })\n",
    "E3 = E1.subs({ C:c2, F:f2 })\n",
    "c3=(c1+c2)/(c1*c2)\n",
    "E4 = E1.subs({ C:c3, F:f3 })\n",
    "E2, E3, E4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle \\left[ \\left\\{ L : - \\frac{1}{4 \\pi^{2} f_{3} \\sqrt{f_{1}^{2} + f_{2}^{2}}}, \\  c_{1} : - \\frac{f_{3} \\sqrt{f_{1}^{2} + f_{2}^{2}}}{f_{1}^{2}}, \\  c_{2} : - \\frac{f_{3} \\sqrt{f_{1}^{2} + f_{2}^{2}}}{f_{2}^{2}}\\right\\}, \\  \\left\\{ L : \\frac{1}{4 \\pi^{2} f_{3} \\sqrt{f_{1}^{2} + f_{2}^{2}}}, \\  c_{1} : \\frac{f_{3} \\sqrt{f_{1}^{2} + f_{2}^{2}}}{f_{1}^{2}}, \\  c_{2} : \\frac{f_{3} \\sqrt{f_{1}^{2} + f_{2}^{2}}}{f_{2}^{2}}\\right\\}\\right]$"
      ],
      "text/plain": [
       "⎡⎧                                      ___________              ___________ ⎫\n",
       "⎢⎪                                     ╱   2     2              ╱   2     2  ⎪\n",
       "⎢⎪            -1                 -f₃⋅╲╱  f₁  + f₂         -f₃⋅╲╱  f₁  + f₂   ⎪\n",
       "⎢⎨L: ──────────────────────, c₁: ───────────────────, c₂: ───────────────────⎬\n",
       "⎢⎪              ___________                2                        2        ⎪\n",
       "⎢⎪      2      ╱   2     2               f₁                       f₂         ⎪\n",
       "⎣⎩   4⋅π ⋅f₃⋅╲╱  f₁  + f₂                                                    ⎭\n",
       "\n",
       "  ⎧                                     ___________            ___________⎫⎤\n",
       "  ⎪                                    ╱   2     2            ╱   2     2 ⎪⎥\n",
       "  ⎪             1                 f₃⋅╲╱  f₁  + f₂        f₃⋅╲╱  f₁  + f₂  ⎪⎥\n",
       ", ⎨L: ──────────────────────, c₁: ─────────────────, c₂: ─────────────────⎬⎥\n",
       "  ⎪              ___________               2                      2       ⎪⎥\n",
       "  ⎪      2      ╱   2     2              f₁                     f₂        ⎪⎥\n",
       "  ⎩   4⋅π ⋅f₃⋅╲╱  f₁  + f₂                                                ⎭⎦"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution=solve([ E2, E3, E4 ])\n",
    "solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2.45800103621738 \\cdot 10^{-9}$"
      ],
      "text/plain": [
       "2.45800103621738e-9"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution[1][L].subs({ f1:2500, f2:2030, f3:3200 }).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 1.64883874578444$"
      ],
      "text/plain": [
       "1.64883874578444"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution[1][c1].subs({ f1:2500, f2:2030, f3:3200 }).evalf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 2.50072609409419$"
      ],
      "text/plain": [
       "2.50072609409419"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "solution[1][c2].subs({ f1:2500, f2:2030, f3:3200 }).evalf()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}