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{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Chapter 27: A.c. bridges</h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 1, page no. 485</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#determine the values of Rx and Cx at balance.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"R2 = 2500;# in ohms\n",
"C2 = 0.2E-6;# IN fARADS\n",
"R3 = 1;\n",
"R4 = 1;\n",
"w = 2000*math.pi;\n",
"#calculation:\n",
"Rx = R4*(1 + w*w*C2*C2*R2*R2)/(R2*R3*w*w*C2*C2)\n",
"Cx = R3*C2/(R4*(1 + w*w*C2*C2*R2*R2))\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Resistance Rx = R4(1 + w*w*C2*C2*R2*R2)/(R2*R3*w*w*C2*C2) and Capacitance Cx = R3*C2/(R4*(1 + w*w*C2*C2*R2*R2))\"\n",
"print \"\\n (b)at balance Rx = \",round(Rx/1000,2),\"KOhm and Cx = \", round(Cx*1E9,2),\"nF\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Resistance Rx = R4(1 + w*w*C2*C2*R2*R2)/(R2*R3*w*w*C2*C2) and Capacitance Cx = R3*C2/(R4*(1 + w*w*C2*C2*R2*R2))\n",
"\n",
" (b)at balance Rx = 2.75 KOhm and Cx = 18.4 nF"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 2, page no. 487</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine, when the bridge is balanced, (a) the value of resistance R1, and (b) the frequency of the bridge.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"R2 = 30000;# in ohms\n",
"R3 = 30000;# in ohms\n",
"R4 = 1000;# in ohms\n",
"C2 = 1e-9;# IN fARADS\n",
"C3 = 1e-9;# IN fARADS\n",
"\n",
"#calculation:\n",
" #the bridge is balanced\n",
"R1 = R4/((R3/R2) + (C2/C3))\n",
" #frequency, f\n",
"f = 1/(2*math.pi*((C2*C3*R2*R3)**0.5))\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Resistance R1 = \",R1,\" ohm\\n\"\n",
"print \"\\n (b)frequency, f is \",round(f,2),\"Hz\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Resistance R1 = 500.0 ohm\n",
"\n",
"\n",
" (b)frequency, f is 5305.16 Hz"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 3, page no. 487</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#determine, when the bridge is balanced, \n",
"#(a) the value of resistance Rx, (b) the value of capacitance Cx,\n",
"#(c) the phase angle of the unknown arm, (d) the power factor of the unknown arm and (e) its loss angle.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"R3 = 600;# in ohms\n",
"R4 = 200;# in ohms\n",
"C2 = 0.2e-6;# IN fARADS\n",
"C3 = 4000e-12;# IN fARADS\n",
"f = 1500;#in Hz\n",
"\n",
"#calculation:\n",
" #the bridge is balanced\n",
" #Resistance, Rx\n",
"Rx = R4*C3/C2\n",
" #Capacitance, Cx\n",
"Cx = C2*R3/R4\n",
" #Phase angle\n",
"phi = math.atan(1/(2*math.pi*f*Cx*Rx))\n",
"phid = phi*180/math.pi# in degrees\n",
" #Power factor of capacitor\n",
"Pc = math.cos(phi)\n",
" #Loss angle,\n",
"de = 90 - phid\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Resistance Rx = \",round(Rx,2),\" ohm\\n\"\n",
"print \"\\n (b)capacitance, Cx is \",round(Cx*1E9,2),\"pFarad\\n\"\n",
"print \"\\n (c)phasor diagram = \",round(phid,2),\"deg lead \"\n",
"print \"\\n (d)power factor is \",round(Pc,2),\" \\n\"\n",
"print \"\\n (e)Loss angle = \",round(de,2),\"deg\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Resistance Rx = 4.0 ohm\n",
"\n",
"\n",
" (b)capacitance, Cx is 600.0 pFarad\n",
"\n",
"\n",
" (c)phasor diagram = 88.7 deg lead \n",
"\n",
" (d)power factor is 0.02 \n",
"\n",
"\n",
" (e)Loss angle = 1.3 deg\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}
|
