{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Estudi d'un circuit RC sèrie" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Un circuit sèrie amb una resistència $R = 10 \\ \\Omega$ i un condensador $C = 162,48 \\ \\mu F$ està connectat a una xarxa monofàsica $U = 200 V$ i $f = 50 Hz$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{matrix}\n", "X_{C} = \\frac{-j}{C \\omega} &\n", "\\omega = 2 \\pi f &\n", "Z = R + X_{C}\n", "\\\\\n", "\\end{matrix}\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Dades" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "R = 10\n", "C = 162.48 * 10**(-6)\n", "U = 220\n", "f = 50\n", "w = 2 * np.pi * f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Càlcul de les impedàncies" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-19.590711852769j" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Xc = 0 -1j/(C*w)\n", "Xc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$X_{C} = 19.59_{-90^{\\circ}} \\ \\Omega$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(10-19.590711852769j)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Z = R + Xc\n", "Z" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "21.995362940816044" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "modZ = np.abs(Z)\n", "modZ" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-62.958143957668284" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "angZ = np.degrees(np.angle(Z))\n", "angZ" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$Z = 22_{-62,96^{\\circ}} \\ \\Omega$" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "\n", "plt.annotate('', xy=(np.real(Z), np.imag(Z)), xytext=(0, 0),\n", " arrowprops=dict(facecolor='blue', shrink=0.05),\n", " )\n", "\n", "plt.annotate('', xy=(np.real(Z), 0), xytext=(0, 0),\n", " arrowprops=dict(facecolor='green', shrink=0.05),\n", " )\n", "\n", "plt.annotate('', xy=(np.real(Z), np.imag(Z)), xytext=(np.real(Z), 0),\n", " arrowprops=dict(facecolor='red', shrink=0.05),\n", " )\n", "\n", "plt.annotate(\"$Z = 22 \\ \\Omega$\", xy=(1.5, -12))\n", "plt.annotate(\"$R = 10 \\ \\Omega$\", xy=(6, -3))\n", "plt.annotate(\"$X_{C} = 19,59 \\ \\Omega$\", xy=(11,-10))\n", "plt.annotate(\"$62,96^{\\circ}$\", xy=(2,-2))\n", "\n", "plt.xlim(0, 25)\n", "plt.ylim(-25, 0)\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Factor de potència" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9920358997298501" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "fdp = np.cos(angZ)\n", "fdp" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$cos(\\varphi) = 0,9920$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Intensitat" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4.547371291596367+8.908624066121842j)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "I = U/Z\n", "I" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10.002108198530951" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "modI = np.abs(I)\n", "modI" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "62.958143957668284" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "angI = np.degrees(np.angle(I))\n", "angI" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$I = 10_{62,96^{\\circ}} \\ A$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "\n", "plt.annotate('', xy=(10*np.real(I), 10*np.imag(I)), xytext=(0, 0),\n", " arrowprops=dict(facecolor='blue', shrink=0.05),\n", " )\n", "\n", "plt.annotate('', xy=(U, 0), xytext=(0, 0),\n", " arrowprops=dict(facecolor='green', shrink=0.05),\n", " )\n", "\n", "plt.annotate(\"$I = 10 \\ A$\", xy=(50, 100))\n", "plt.annotate(\"$U = 220 \\ V$\", xy=(150, 10))\n", "plt.annotate(\"$62,96^{\\circ}$\", xy=(30,20))\n", "\n", "plt.xlim(0, 250)\n", "plt.ylim(0, 250)\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tensions" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(45.47371291596367+89.08624066121843j)" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Ur = R * I\n", "Ur" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "100.02108198530952" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "modUr = np.abs(Ur)\n", "modUr" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "62.958143957668284" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "angUr = np.degrees(np.angle(Ur))\n", "angUr" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$U_{R} = 100_{62,96^{\\circ}} \\ V$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(174.52628708403634-89.08624066121843j)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Uc = Xc * I\n", "Uc" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "195.9484196376383" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "modUc = np.abs(Uc)\n", "modUc" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-27.04185604233172" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "angUc = np.degrees(np.angle(Uc))\n", "angUc" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$U_{C} = 196_{-27,04^{\\circ}} \\ V$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "\n", "plt.annotate('', xy=(np.real(Ur), np.imag(Ur)), xytext=(0, 0),\n", " arrowprops=dict(facecolor='blue', shrink=0.05),\n", " )\n", "\n", "plt.annotate('', xy=(U, 0), xytext=(0, 0),\n", " arrowprops=dict(facecolor='green', shrink=0.05),\n", " )\n", "\n", "plt.annotate('', xy=(U, 0), xytext=(np.real(Ur), np.imag(Ur)),\n", " arrowprops=dict(facecolor='red', shrink=0.05),\n", " )\n", "\n", "\n", "plt.annotate(\"$U_{R} = 45,47 \\ V$\", xy=(0, 100))\n", "plt.annotate(\"$U_{C} = 174,5 \\ V$\", xy=(125, 75))\n", "plt.annotate(\"$U = 220 \\ V$\", xy=(100, 10))\n", "plt.annotate(\"$62,96^{\\circ}$\", xy=(30,20))\n", "\n", "plt.xlim(0, 250)\n", "plt.ylim(0, 250)\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Potències" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1000.4216841512007-1959.8972945468051j)" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "S = U * np.conj(I)\n", "S" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2200.463803676809" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "modS = np.abs(S)\n", "modS" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-62.958143957668284" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "angS = np.degrees(np.angle(S))\n", "angS" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$S = 2200_{-62,96^{\\circ}} \\ VA$" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000.4216841512007" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "P = np.real(S)\n", "P" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$P = 1000 \\ W$" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-1959.8972945468051" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Q = np.imag(S)\n", "Q" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$Q = -1960 \\ var$" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "\n", "plt.annotate('', xy=(np.real(S), np.imag(S)), xytext=(0, 0),\n", " arrowprops=dict(facecolor='blue', shrink=0.05),\n", " )\n", "\n", "plt.annotate('', xy=(np.real(S), 0), xytext=(0, 0),\n", " arrowprops=dict(facecolor='green', shrink=0.05),\n", " )\n", "\n", "plt.annotate('', xy=(np.real(S), np.imag(S)), xytext=(np.real(S), 0),\n", " arrowprops=dict(facecolor='red', shrink=0.05),\n", " )\n", "\n", "plt.annotate(\"$S = 2200 \\ VA$\", xy=(50, -1200))\n", "plt.annotate(\"$P = 1000 \\ W$\", xy=(500, -300))\n", "plt.annotate(\"$Q = -1960 \\ var$\", xy=(1100,-1000))\n", "plt.annotate(\"$62,96^{\\circ}$\", xy=(125,-175))\n", "\n", "plt.xlim(0, 2500)\n", "plt.ylim(-2500, 0)\n", "plt.axis('off')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "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": 4 }