From 9d260e6fae7328d816a514130b691fbd0e9ef81d Mon Sep 17 00:00:00 2001 From: hardythe1 Date: Fri, 3 Jul 2015 12:23:43 +0530 Subject: add/remove books --- .../Chapter2.ipynb | 2381 ++++++++++++++++++++ 1 file changed, 2381 insertions(+) create mode 100755 Electrical_Measurements_Measuring_Instruments_by_K._Shinghal/Chapter2.ipynb (limited to 'Electrical_Measurements_Measuring_Instruments_by_K._Shinghal/Chapter2.ipynb') diff --git a/Electrical_Measurements_Measuring_Instruments_by_K._Shinghal/Chapter2.ipynb b/Electrical_Measurements_Measuring_Instruments_by_K._Shinghal/Chapter2.ipynb new file mode 100755 index 00000000..27e9fedf --- /dev/null +++ b/Electrical_Measurements_Measuring_Instruments_by_K._Shinghal/Chapter2.ipynb @@ -0,0 +1,2381 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 2 - Analog measurement of electrical quantities" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 1 - pg 130" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "for Ist method\n", + "wattmeter reading is (W)= 804.0\n", + "percentage error is high (%) = 0.5\n", + "for 2nd method\n", + "wattmeter reading (W)= 802.5\n", + "percentage error is high (%) = 0.3125\n" + ] + } + ], + "source": [ + "#pg 130\n", + "#Example 2.1:#wattmeter reading and error\n", + "#calculate the wattmeter reading\n", + "import math,cmath\n", + "#given\n", + "print \"for Ist method\"\n", + "v=50;#volts\n", + "i=20;#amperes\n", + "pf=0.8;#power factor\n", + "pl=v*i*pf;#true power\n", + "vc=(50*pf)+1j*v*math.sqrt(1-pf**2);#complex form \n", + "ic=i+1j*0;#\n", + "r1=0.01;#ohms\n", + "#calculations and results\n", + "vpl=vc+(i*r1);#voltage across pressure coil\n", + "wrlc1=(vpl.real)*(ic.real);#\n", + "er=(wrlc1-pl)/(pl);#\n", + "print \"wattmeter reading is (W)=\",wrlc1\n", + "print \"percentage error is high (%) = \",er*100\n", + "print \"for 2nd method\"\n", + "r2=1000;#ohms\n", + "ic1=ic+(vc/r2);#\n", + "wrlc2=(vc.real)*(ic1.real)+(vc.imag)*(ic1.imag);#\n", + "er1=(wrlc2-pl)/(pl);#\n", + "print \"wattmeter reading (W)=\",wrlc2\n", + "print \"percentage error is high (%) = \",er1*100\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 2 - pg 131" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "self inductance (mH) = 2.0\n" + ] + } + ], + "source": [ + "#pg 131\n", + "#Example 2.2:#self inductance\n", + "#calculate the self inductance\n", + "#given\n", + "c=20.;#pF\n", + "rs=10000.;#ohms\n", + "#calculations\n", + "l=(c*10**-12)*rs**2;#henry\n", + "#results\n", + "print \"self inductance (mH) = \",l*10**3\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 3 - pg 131" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "percentage error is (%) = 0.39\n" + ] + } + ], + "source": [ + "#pg 131\n", + "#Example 2.3:#percentage error\n", + "#calculate the percentage error\n", + "#given\n", + "import math\n", + "v=100;#volts\n", + "i=10;#amperes\n", + "pf=0.45;#power factor\n", + "f=50;#Hz\n", + "l=25;#mH\n", + "r=4000;#ohms\n", + "#calculations\n", + "tp=v*i*pf;#true power in watts\n", + "b=math.atan((2*math.pi*f*l*10**-3)/r);#phase angle in radians\n", + "e=v*i*math.tan(b)*math.sqrt(1-pf**2);#\n", + "per=(e*100)/(tp);#\n", + "#results\n", + "print \"percentage error is (%) = \",round(per,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 4 - pg 131" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "true power in (kW) = 851.3\n", + "answer is wrong in the textbook\n" + ] + } + ], + "source": [ + "#pg 131\n", + "#Example 2.4:#true power\n", + "#calculate the true power\n", + "#given\n", + "import math\n", + "from math import cos\n", + "ph=45.;#degree\n", + "th=90.;#radians\n", + "dela=-45.;#radians\n", + "f=50.;#Hz\n", + "l=15.;#mH\n", + "r=300.;#ohms\n", + "#calculations\n", + "b=math.atan((2*math.pi*f*l*10**-3)/r);#in radians\n", + "k=((cos(ph/57.3))/(cos(b)*cos(42/57.3)));#\n", + "nr=20;#nomianl ratio\n", + "e=-0.3;#\n", + "er=(e*nr)/100;#\n", + "ar1=nr-er;#actual ratio\n", + "nr1=100;#nomianl ratio\n", + "e1=0.9;#\n", + "er1=(e1*nr1)/100;#\n", + "ar2=nr1-er1;#actual ratio\n", + "p=450;#watts\n", + "tp=ar1*ar2*k*p;#\n", + "#results\n", + "print \"true power in (kW) = \",round(tp*10**-3,1)\n", + "print 'answer is wrong in the textbook'\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 5 - pg 132" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torque in Nm when angle is 45 degree (Nm) = 6.68e-06\n", + "torque in Nm when angle is 90 degree (Nm) = 9.45e-06\n" + ] + } + ], + "source": [ + "#pg 132\n", + "#Example 2.5:#torque\n", + "#calculate the torque required\n", + "#given\n", + "import math\n", + "from math import sin\n", + "d=2.5;#diameter in cm\n", + "n=500;#turns\n", + "b=1.1;#mWb/m**2\n", + "v=100;#volts\n", + "pf=0.7;#power factor\n", + "rp=2000;#ohms\n", + "#calculations\n", + "x=((math.pi*(d*10**-2)**2*n*b*10**-3*v*pf)/(4*rp));#\n", + "ang1=45;#degree\n", + "ang2=90;#degree\n", + "td1=x*sin(ang1/57.3);#\n", + "td2=x*sin(ang2/57.3);#\n", + "#results\n", + "print \"torque in Nm when angle is 45 degree (Nm) = \",round(td1,8)\n", + "print \"torque in Nm when angle is 90 degree (Nm) = \",round(td2,8)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 6 - pg 133" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "unknown resistance is (ohm)= 2784.0\n", + "answer is wrong in the textbook\n" + ] + } + ], + "source": [ + "#pg 133\n", + "#Example 2.6:#resistance\n", + "#calculate the resistance\n", + "#given\n", + "import math\n", + "la=4.78;#henry\n", + "ra=298.;#ohms\n", + "lb=3.;#henry\n", + "rb=190.;#ohms\n", + "v=200.;#volts\n", + "#calculations\n", + "r=((la*100*lb*100*math.pi**2)-(ra*rb))/(rb+ra);#ohm\n", + "#results\n", + "print \"unknown resistance is (ohm)=\",round(r,0)\n", + "print 'answer is wrong in the textbook'\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 7 - pg 133" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "addition resistance (ohm) = 2750.0\n" + ] + } + ], + "source": [ + "#pg 133\n", + "#Example 2.7:#resistance\n", + "#calculate the addition in resistance\n", + "#given\n", + "i=20.;#amperes\n", + "v=100.;#volts\n", + "pf=1;#power factor\n", + "rp=5500.;#ohms\n", + "th=150.;#angle\n", + "wd=20;#watts per degree\n", + "#calculations\n", + "p=v*i*pf;#watts\n", + "kd=((rp*th)/p);#constant\n", + "rp1=wd*kd;#in ohms\n", + "adr=rp1-rp;#\n", + "#results\n", + "print \"addition resistance (ohm) = \",adr\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 8 - pg 134" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "resistance in (ohm) = 120.0\n", + "load impedance in (ohm) = 75.0\n", + "impedance of combination in (ohm) = 53.57\n", + "power absorbed by the load in (W) = 546.6\n", + "power factor of the load = 0.4555\n", + "total power supply is (W) = 1296.6\n", + "total power factor = 0.772\n" + ] + } + ], + "source": [ + "#pg 134\n", + "#Example 2.8:#resistance,impedance,power,power factor ,voltage and power factor\n", + "#calculate the total power factor,supply, impedance and resistance\n", + "#given\n", + "v=300.;#volts\n", + "i2=2.5;#amperes\n", + "#calculations and results\n", + "r=v/i2;#ohms\n", + "print \"resistance in (ohm) =\",r\n", + "i3=4;#amperes\n", + "zl=v/i3;#ohms\n", + "print \"load impedance in (ohm) = \",zl\n", + "v=300;#volts\n", + "i2=2.5;#amperes\n", + "r=v/i2;#ohms\n", + "i1=5.6;#amperes\n", + "z=v/i1;#ohms\n", + "print \"impedance of combination in (ohm) = \",round(z,2)\n", + "i3=4;#amperes\n", + "pl=((i1**2-i2**2-i3**2)*r)/2;#in watts\n", + "print \"power absorbed by the load in (W) = \",pl\n", + "pl=((i1**2-i2**2-i3**2)*r)/2;#in watts\n", + "pfl=((i1**2-i2**2-i3**2)/(2*i2*i3));#power factor\n", + "print \"power factor of the load = \",pfl\n", + "pr=i2**2*r;#in watts\n", + "tps=pl+pr;#in watts\n", + "print \"total power supply is (W) = \",tps\n", + "tps=pl+pr;#in watts\n", + "tpf=tps/(v*i1);#power factor\n", + "print \"total power factor = \",round(tpf,3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 9 - pg 135" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "average power to be read by wattmeter is (W) = 127.32\n" + ] + } + ], + "source": [ + "#pg 135\n", + "#Example 2.9:#wattmeter reading\n", + "#calculate the average power\n", + "import math,scipy\n", + "from scipy import integrate\n", + "v=24.;#volts\n", + "r1=6.;#ohms\n", + "vm=100;#volts\n", + "t0=0.;#\n", + "t1=(1./100);#\n", + "f=50.;#Hz\n", + "#calculations\n", + "i=v/r1;#in amperes\n", + "z=2*math.pi*f;#\n", + "def fun(t):\n", + "\ty=math.sin(z*t)\n", + "\treturn y\n", + "x=scipy.integrate.quad(fun,t0,(t1/2.));#\n", + "p=vm*(1/t1)*i*x[0];#\n", + "#results\n", + "print \"average power to be read by wattmeter is (W) = \",round(p,2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 10 - pg 136" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "load impedance in (ohm) = 20.0\n", + "impedance of combination in (ohm) = 35.0\n", + "power absorbed by the load is,(W) = 202.0\n", + "power absorbed by the non inductive resistor is,(W) = 300.0\n", + "power factor of load is 0.63\n", + "power factor of the whole circuit is 0.9\n" + ] + } + ], + "source": [ + "#pg 136\n", + "#Example 2.10:#load impedance and combination impedance\n", + "#calculate the power factor and power, load\n", + "#given\n", + "v3=80.;#volts\n", + "i=4.;#amperes\n", + "v1=140;#volts\n", + "#calculations and results\n", + "zl=v3/i;#ohms\n", + "z=v1/i;#ohms\n", + "print \"load impedance in (ohm) = \",zl\n", + "print \"impedance of combination in (ohm) = \",z\n", + "v2=75.;#volts (it is given 72 in the textbook)\n", + "r=v2/i;#\n", + "pl=((v1**2-v2**2-v3**2)/(2*r));#watts\n", + "pr=i**2*r;#watts\n", + "print \"power absorbed by the load is,(W) = \",pl\n", + "print \"power absorbed by the non inductive resistor is,(W) = \",pr\n", + "pfl=((v1**2-v2**2-v3**2)/(2*v2*v3));#power factor of the load\n", + "tp=pr+pl;#total power in watts\n", + "pfc=tp/(v1*i);#power factor\n", + "print \"power factor of load is\",round(pfl,2)\n", + "print \"power factor of the whole circuit is\",round(pfc,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 11 - pg 136" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "wattmeter (W1) reading in (kW) = 85.0\n", + "wattmeter (W2) reading in (kW) = 215.0\n" + ] + } + ], + "source": [ + "#pg 136\n", + "#Example 2.11:#wattmeters readings\n", + "#calculate the wattmeters readings\n", + "import math\n", + "from math import sqrt\n", + "#given\n", + "pf=0.8;#\n", + "#calculations\n", + "td=(sqrt(1-pf**2))/pf;#\n", + "sr=300;#kW\n", + "df=(sr/sqrt(3))*td;#\n", + "w2=(sr+df)/2;#\n", + "w1=sr-w2;#\n", + "#results\n", + "print \"wattmeter (W1) reading in (kW) = \",round(w1)\n", + "print \"wattmeter (W2) reading in (kW) = \",round(w2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 12 - pg 137" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "power factor of the system = 0.189\n", + "capacitance (micro-F) = 322.0\n" + ] + } + ], + "source": [ + "#pg 137\n", + "#Example 2.12:#power factor and capacitance\n", + "#calculate the capacitance and power factor\n", + "import math\n", + "from math import atan,sqrt,cos\n", + "#given\n", + "w1=-2000.;#watts\n", + "w2=4000.;#watts\n", + "v=400.;#volts\n", + "pfn=0.5;#power factor\n", + "f=50.;#Hz\n", + "#calculations\n", + "ph=math.atan((sqrt(3.)*(w2-w1))/(w2+w1)) *57.3;#in degree\n", + "pf=cos(ph/57.3);#\n", + "w=w1+w2;#total power\n", + "vp=(v/sqrt(3));#phase voltage\n", + "pp=w/3.;#power per phase\n", + "pi=(pp)/(vp*pf);#phase current\n", + "pim=vp/pi;#phase impedance\n", + "rip=pim*pf;#resistance each phase\n", + "rep=(sqrt(pim**2-rip**2));#reactance of each phase\n", + "pimb=rip/pfn;#impedance per phase\n", + "repn=(sqrt(pimb**2-rip**2));#reactance per phase\n", + "cp=rep-repn;#capacitive reactance\n", + "c=((1/(2*math.pi*f*cp)));#\n", + "#results\n", + "print \"power factor of the system = \",round(pf,3)\n", + "print \"capacitance (micro-F) = \",round(c*10**6)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 13 - pg 138" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "power factor = 0.866\n", + "line current is (A)= 83.3\n" + ] + } + ], + "source": [ + "#pg 138\n", + "#Example 2.13:#power factor and line current\n", + "#calculate the line current and power factor\n", + "#given\n", + "import math\n", + "x=1;#\n", + "w=50;#kW\n", + "v=400.;#volts\n", + "#calculations\n", + "w2=2*x;#\n", + "w1=x;#\n", + "ph=math.atan((math.sqrt(3)*(w2-w1))/(w2+w1))*57.3;#in degree\n", + "pf=math.cos(ph/57.3);#power factor\n", + "il=((w/(math.sqrt(3)*v*pf)))*10**3;#in amperes\n", + "#results\n", + "print \"power factor = \",round(pf,3)\n", + "print \"line current is (A)=\",round(il,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 14 - pg 138" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "when both readings are positive\n", + "power is (W) = 6900.0\n", + "power factor (leading) = 0.866\n", + "when second readig is negative\n", + "power is (W) = 2300.0\n", + "power factor (leading) = 0.189\n" + ] + } + ], + "source": [ + "#pg 138\n", + "#Example 2.14:#total power and power factor\n", + "#calculate the total power and power factor\n", + "#given\n", + "import math\n", + "print \"when both readings are positive\"\n", + "w2=2300.;#watts\n", + "w1=4600.;#watts\n", + "#calculations and results\n", + "p1=w2+w1;#\n", + "ph=57.3*math.atan((math.sqrt(3)*(w2-w1))/(w2+w1));#in degree\n", + "pf=math.cos(ph/57.3);#power factor\n", + "print \"power is (W) = \",p1\n", + "print \"power factor (leading) = \",round(pf,3)\n", + "print \"when second readig is negative\"\n", + "w21=-2300.;#watts\n", + "w1=4600.;#watts\n", + "p2=w21+w1;#\n", + "ph2=57.3*math.atan((math.sqrt(3)*(w21-w1))/(w21+w1));#in degree\n", + "pf1=math.cos(ph2/57.3);#power factor\n", + "print \"power is (W) = \",p2\n", + "print \"power factor (leading) = \",round(pf1,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 15 - pg 139" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "load current in amperes = 5.0\n" + ] + } + ], + "source": [ + "#pg 139\n", + "#Example 2.15:#load current\n", + "#calculate the load current\n", + "#given\n", + "import math\n", + "from math import atan,cos,sqrt\n", + "rw=3550.;#reading of wattmeter\n", + "rp=806.;#watts\n", + "#calculations\n", + "ph=atan((sqrt(3)*rp)/rw);#in degree\n", + "pf=cos(ph/57.3);#power factor\n", + "v=440;#volts\n", + "i=((rw)/(sqrt(3)*v*pf));#amperes\n", + "#results\n", + "print \"load current in amperes = \",round(i)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 16 - pg 139" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "error (slow) in percentage = 9.1\n" + ] + } + ], + "source": [ + "#pg 139\n", + "#Example 2.16:#error\n", + "#calculate the error percentage\n", + "#given\n", + "import math\n", + "from math import sin\n", + "d=87./57.3;#radians\n", + "pf=0.5;#\n", + "#calculations\n", + "n=(1./4)*sin(d-60/57.3);#\n", + "nc=(1./4)*pf*sin(d);#\n", + "e=((n-nc)/nc)*100;#error\n", + "#results\n", + "print \"error (slow) in percentage = \",round(-e,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 17 - pg 140" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "error (%) = 1.82\n" + ] + } + ], + "source": [ + "#pg 140\n", + "#Example 2.17:#error\n", + "#calculate the error\n", + "#given\n", + "import math,scipy\n", + "from scipy import integrate \n", + "i=5;#amperes\n", + "t0=0;#\n", + "t1=30./60;#\n", + "e=0.56;#kWh\n", + "v1=220;#volts\n", + "#calculations\n", + "def function(t):\n", + "\ty=5\n", + "\treturn y\n", + "x=scipy.integrate.quad(function,t0,t1);#\n", + "v=(e*10**3)/x[0];#volts\n", + "ae=v1*i*t1*10**-3;#actual energy\n", + "e=((e-ae)/ae)*100;#error\n", + "#results\n", + "print \"error (%) = \",round(e,2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18 - pg 140" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "time duration (seconds) = 367.0\n", + "limits of accuracy (%) = 0.73\n" + ] + } + ], + "source": [ + "#pg 140\n", + "#Example 2.18:#time and error\n", + "#calculate the time duration and limits of accuracy\n", + "#given\n", + "nd=500.;#dvisions\n", + "cr=0.1;#dvisions can read\n", + "ie=0.05;#inherent error\n", + "tea=0.1;#total error allowable\n", + "cr1=0.01;#seconds\n", + "cr2=0.1;#seconds\n", + "nd1=500/10.;#\n", + "#calculations\n", + "re=(cr/nd)*100;#reading error\n", + "te=re+ie;#total error\n", + "per=tea-te;#permissible error\n", + "ersw=cr1*100;#error in reading stop watch\n", + "erss=cr2*100;#error in stopping and starting\n", + "ter=ersw+erss;#total error\n", + "t=per/ter;#seconds\n", + "er1=(cr/nd1)*100;#new reading error\n", + "ie1=((ie*nd)/nd1);#new inherent error\n", + "ter1=er1+ie1;#\n", + "la=ter1+per;#\n", + "#results\n", + "print \"time duration (seconds) = \",round(1./t)\n", + "print \"limits of accuracy (%) = \",la\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 19 - pg 141" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "error (slow) is (%) 1.66\n" + ] + } + ], + "source": [ + "#pg 141\n", + "#Example 2.19:#error\n", + "#calculate the error\n", + "#given\n", + "import math\n", + "n=40.;#revolutions\n", + "rc=0.12;#registration constant\n", + "e2=22000;#volts\n", + "e1=110;#volts\n", + "i2=500;#amperes\n", + "i1=5;#amperes\n", + "i=5.25;#amperes\n", + "lv=110;#volts\n", + "pf=1;#\n", + "t=61;#seconds\n", + "#calculations\n", + "err=n/rc;#energy recorded in kWh is\n", + "ae=((math.sqrt(3)*e2*lv*i*i2*pf*t)/(e1*i1*3600))*10**-3;#kWh\n", + "e=((err-ae)/ae)*100;#\n", + "#results\n", + "print \"error (slow) is (%)\",round(-e,2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 20 - pg 142" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "error (fast) in recording (%) = 0.2\n", + "limit of error in the meter is 0.07 % or 0.33 % \n" + ] + } + ], + "source": [ + "#pg 142\n", + "#Example 2.20:#error and limit of error\n", + "#calculate the error and limit of error\n", + "#given\n", + "mc=1200.;#meter constant in rev/kWh\n", + "n=40.;#revolutions\n", + "tp=99.8;#seconds\n", + "v=240;#volts\n", + "i=5;#amperes\n", + "#calculations\n", + "err=n/mc;#energy recorded in kWh\n", + "ae=((v*i*tp*10**-3)/3600);#actual energy in kWh\n", + "e=((err-ae)/ae)*100;#error\n", + "n=500;#divisions\n", + "rn=0.1;#dvision reading accuracy\n", + "per=((rn/n)*100);#possible error\n", + "ie=0.05;#inherent error\n", + "per1=(((rn/10)/tp)*100);#possible error\n", + "her=((ie/tp)*100);#human error\n", + "tpr=per+per1+her+ie;#total possible error\n", + "li1=e-tpr;#\n", + "li2=e+tpr;#\n", + "#results\n", + "print \"error (fast) in recording (%) = \",round(e,2)\n", + "print \"limit of error in the meter is \",round(li1,2),\"% or \",round(li2,2),\"% \"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 21 - pg 143" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "total monthly bill in Rs 19295.0\n", + "power factor is 0.78\n", + "load factor is 0.96\n", + "average cost per unit (kWh) in paisa is 15.4\n", + "total monthly bill and load factor is calculated wrong in the book due to rounding off error\n" + ] + } + ], + "source": [ + "#pg 143\n", + "#Example 2.21:#consumer monthly bill ,power factor and average cost per unit\n", + "#calculate the consumer monthly bill ,power factor and average cost per unit\n", + "#given\n", + "import math\n", + "from math import sqrt\n", + "kwh=125000.;#\n", + "kvarh=100000.;#\n", + "kw=180;#\n", + "kvar=125;#\n", + "d=30.;#days\n", + "t=24.;#hours a day\n", + "#calculations\n", + "kvah=sqrt(kwh**2+kvarh**2);#kVAh\n", + "mkva=sqrt(kw**2+kvar**2);#kVA\n", + "pkva=15;#rupees\n", + "pkvah=0.1;#reupees\n", + "tmb=pkva*mkva+pkvah*kvah;#in Rs\n", + "pf=kwh/kvah;#power factor\n", + "lf=((kwh/(d*t))/kw);#load factor\n", + "avcp=tmb/kwh;#in paisa\n", + "#results\n", + "print \"total monthly bill in Rs\",round(tmb)\n", + "print \"power factor is\",round(pf,2)\n", + "print \"load factor is\",round(lf,2)\n", + "print \"average cost per unit (kWh) in paisa is\",round(avcp*100,1)\n", + "print 'total monthly bill and load factor is calculated wrong in the book due to rounding off error'\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 22 - pg 143" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "number of revolution per kWh is,(revolutions/kWh)= 3273.0\n", + "full load speed r.p.s = 1.0\n", + "error (fast) in percentage = 0.84\n", + "numberof revolutions is calcultaed wrong in the textbook due to rounding off error\n" + ] + } + ], + "source": [ + "#pg 143\n", + "#Example 2.22:#full load speed and error\n", + "#calculate the full load speed and error\n", + "#given\n", + "v=220.;#volts\n", + "n=30.;#revolutions\n", + "i=5.;#in amperes\n", + "t=59.5;#seconds\n", + "#calculations\n", + "wrv=((v*i*10**-3)/(3600.));#kWh\n", + "mc=((3600.*10**3)/(v*i));#rev/kWh\n", + "ec=((v*i*10**-3)/(3600.));#kWh\n", + "sfl=mc*ec;#rps\n", + "hler=n*ec;#kWh\n", + "hlf=(((i/2.)*v*10**-3*t)/(3600.));#kWh\n", + "e=(hler-hlf)/hlf;#\n", + "#results\n", + "print \"number of revolution per kWh is,(revolutions/kWh)=\",round(mc)\n", + "print \"full load speed r.p.s = \",sfl\n", + "print \"error (fast) in percentage = \",round(e*100,2)\n", + "print 'numberof revolutions is calcultaed wrong in the textbook due to rounding off error'\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 23 - pg 144" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "shunt resistance when current is 10mA (ohm) = 52.63\n", + "shunt resistance when current is 75mA (ohm) = 6.71\n", + "shunt resistance when current is 100mA (ohm) = 2.004\n" + ] + } + ], + "source": [ + "#pg 144\n", + "#Example 2.23:#shunt resistance \n", + "#calculate the shunt resistance \n", + "#given\n", + "ra=1000.;#armature resistance in ohms\n", + "i=10.;#mA\n", + "ia=500.;#micro amperes\n", + "i1=75;#mA\n", + "i3=100;#mA\n", + "#calculations\n", + "rsh1=((ra)/((i/(ia*10**-3))-1));#in ohms\n", + "rsh2=((ra)/((i1/(ia*10**-3))-1));#in ohms\n", + "ia3=0.4*ia;#micro amperes\n", + "rsh3=((ra)/((i3/(ia3*10**-3))-1));#in ohms\n", + "#results\n", + "print \"shunt resistance when current is 10mA (ohm) = \",round(rsh1,2)\n", + "print \"shunt resistance when current is 75mA (ohm) = \",round(rsh2,2)\n", + "print \"shunt resistance when current is 100mA (ohm) = \",round(rsh3,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 24 - pg 144" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "shunt resistance in milli ohm is 0.60012\n", + "power consumption in shunt is,(W)= 9.37\n", + "series resistance in kilo ohm is 24.997\n", + "power consumption in the series resistance is,(W)= 15.623\n" + ] + } + ], + "source": [ + "#pg 144\n", + "#Example 2.24:#shunt resistance and series resistance\n", + "#calculate the shunt resistance and series resistance\n", + "#given\n", + "i=125.;#amperes\n", + "ia=25.;#armature current in mA\n", + "ra=3;#ohms\n", + "#calculations\n", + "ish=i-(ia*10**-3);#amperes\n", + "rsh=((ia*ra)/ish);#milli ohms\n", + "pcs=ish**2*rsh*10**-3;#watts\n", + "rv=625;#volts\n", + "rs=((rv-(ra*ia*10**-3))/(ia*10**-3))*10**-3;#killo ohms\n", + "pc=(ia*10**-3)**2*rs*10**3;#watts\n", + "#results\n", + "print \"shunt resistance in milli ohm is\",round(rsh,5)\n", + "print \"power consumption in shunt is,(W)=\",round(pcs,2)\n", + "print \"series resistance in kilo ohm is\",rs\n", + "print \"power consumption in the series resistance is,(W)=\",round(pc,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 25 - pg 145" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "when micro meter resistance is 25 ohm\n", + "multiplying power for the shunt for a 1250 ohm is 4.02\n", + "multiplying power for the shunt for a 2500 ohm is 2.01\n", + "when micro meter resistance is 2500 ohm\n", + "multiplying power for the shunt for a 1250 ohm is 6.0\n", + "multiplying power for the shunt for a 2500 ohm is 3.0\n" + ] + } + ], + "source": [ + "#pg 145\n", + "#Example 2.25:#mulitplying power\n", + "#calculate the mulitplying power in all cases\n", + "print \"when micro meter resistance is 25 ohm\"\n", + "#given\n", + "ra=25.;#ohms\n", + "rsh=5000.;#ohms\n", + "r1=1250.;#ohms\n", + "r2=2500;#ohms\n", + "#calculations and results\n", + "n=((ra+rsh)/r1);#\n", + "n2=((ra+rsh)/r2);#\n", + "print \"multiplying power for the shunt for a 1250 ohm is\",n\n", + "print \"multiplying power for the shunt for a 2500 ohm is\",n2\n", + "print \"when micro meter resistance is 2500 ohm\"\n", + "ra1=2500.;#ohms\n", + "rsh=5000.;#ohms\n", + "r1=1250.;#ohms\n", + "n1=((ra1+rsh)/r1);#\n", + "r2=2500.;#ohms\n", + "n3=((ra1+rsh)/r2);#\n", + "print \"multiplying power for the shunt for a 1250 ohm is\",n1\n", + "print \"multiplying power for the shunt for a 2500 ohm is\",n3\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 26 - pg 145" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "voltage is,(V)= 487.0\n", + "resistance is ,(k-ohm)= 27.0\n", + "resistance is calculated wrong in the textbook due to rounding off error\n" + ] + } + ], + "source": [ + "#pg 145\n", + "#Example 2.26:#resistance\n", + "#calculate the resistance\n", + "r1=185.;#ohm\n", + "r2=205.;#ohm\n", + "r3=215.;#ohm\n", + "R31=195.;#OHM\n", + "r4=200.;#ohm\n", + "r5=1100.;#ohm\n", + "v1=85.;#V\n", + "#calculations\n", + "R=r1+r2+r3+r4+R31;#ohm\n", + "R1=(R-r4)+((r5*r4)/(r5+r4));#\n", + "V=(v1*R1)/round(R1-(R-r4));#V\n", + "I=round(V)/R;#A\n", + "vd4=I*r4;#V\n", + "x=0.5;#% allowable\n", + "vd41=(vd4)-(vd4*x)/100;#\n", + "rv=((vd41*(R-r4)*r4))/((V*r4)-((R*vd41)));#\n", + "#results\n", + "print \"voltage is,(V)=\",round(V)\n", + "print \"resistance is ,(k-ohm)=\",round(rv*10**-3)\n", + "print 'resistance is calculated wrong in the textbook due to rounding off error'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 27 - pg 146" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(a). The sensitivity of an instrument,S1 = 0.0099\n", + "(b). The resistance,R(ohm) = 200.0\n", + "The relative sensitivity,S = 0.012\n" + ] + } + ], + "source": [ + "#pg 146\n", + "#Example 2.27: Sensitivity\n", + "#calculate the sensitivity and resistance, relative sensitivity\n", + "#given data :\n", + "I1=0.1;# in mA\n", + "R1=50.;# in ohm\n", + "I2=10.;# in mA\n", + "I3=10.1;# in mA\n", + "I5=10;# in mA\n", + "V=2;# in Volt\n", + "#calculations\n", + "I4=I2-I1;\n", + "Rsh=I1*R1/(I3-I1);\n", + "Im1=Rsh*I4/(R1+Rsh);\n", + "S1=(I1-Im1)/(I3-I4);\n", + "R=V/(I5*10**-3);\n", + "# formula : Im=((I3-Im)*(R-V))/R1;\n", + "Im2=(0.8*I3)-8;\n", + "Im3=(0.8*I4)-8\n", + "S2=(Im2-Im3)/(I3-I4);\n", + "S=S1/S2;\n", + "#results\n", + "print \"(a). The sensitivity of an instrument,S1 = \",round(S1,4)\n", + "print \"(b). The resistance,R(ohm) = \",R\n", + "print \"The relative sensitivity,S = \",round(S,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 28 - pg 147" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Shunt resistance,Rs(ohm) = 0.01\n", + "Inductance,Ls(micro-H) = 10.0\n", + "Current,Ia1(A) = 4.81\n", + "Error,(%)(low) = 3.8\n" + ] + } + ], + "source": [ + "#pg 147\n", + "#Example 2.28: Error\n", + "#calculate the Error, shunt resistance and inductance\n", + "#given data :\n", + "import math\n", + "from math import sqrt\n", + "La=90*10**-6;# in micro-H\n", + "Ra=0.09;# in ohm\n", + "I=50;# in A\n", + "Ia=5;# in A\n", + "f=50;# in Hz\n", + "#calculations\n", + "LsbyRs=La/Ra;\n", + "w=2*math.pi*f;\n", + "Rs=Ra/9;\n", + "Ls=LsbyRs*Rs*10**6;\n", + "Ls1=0;# shunt is non-inductive \n", + "Ia1=(Rs*I)/sqrt((Ra+Rs)**2+(w**2*La**2));\n", + "Error=((Ia-Ia1)/Ia)*100;\n", + "#results\n", + "print \"Shunt resistance,Rs(ohm) = \",Rs\n", + "print \"Inductance,Ls(micro-H) = \",Ls\n", + "print \"Current,Ia1(A) = \",round(Ia1,2)\n", + "print \"Error,(%)(low) = \",round(Error,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 29 - pg 148" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "area is (cm^2)= 188.0\n", + "error is (%)= 8.11\n" + ] + } + ], + "source": [ + "#pg 148\n", + "#Example 2.29 :area and percentage error\n", + "#calculate the area and error\n", + "#given data \n", + "import math\n", + "from math import sqrt\n", + "v1=18.;#kV\n", + "c1=60.;#pF\n", + "v2=2.;#\n", + "d=2.5;#cm\n", + "#calculations\n", + "q=v2*10**3*c1*10**-12;#\n", + "cs=q/(v1*10**3);#F\n", + "eo=8.854*10**-12;#\n", + "a=((cs*d*10**-2)/(eo));#\n", + "c2=50;#pf\n", + "x=c1-c2;#\n", + "stf=((v2*10**3)**2*x*10**-12);#\n", + "v=sqrt(stf/(x*10**-12*2))/1000;#kV\n", + "c3=c2+(x/2);#pf\n", + "x1=c3/(cs*10**12);#\n", + "V1=(x1+1)*v#\n", + "V=10*sqrt(2);#V\n", + "er=((V-V1)/V1)*100;#\n", + "#results\n", + "print \"area is (cm^2)=\",round(a*10**4)\n", + "print \"error is (%)=\",round(er,2)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 30 - pg 150" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The percentage error in case 1 (%) = -15.25\n", + "The percentage error in case 2 (%) = -0.688\n", + "The answers are a bit different due to rounding off error in textbook\n" + ] + } + ], + "source": [ + "#pg 150\n", + "#Example 2.30: % Error\n", + "#calculate the percentage error \n", + "#given data :\n", + "Ra=2.;# in ohm\n", + "Rsh=0.0004;# constant\n", + "alfa=0.004;\n", + "t1=288.;# in K\n", + "t2=333.;# in K\n", + "I=100.;# in A\n", + "Rs=50.;# in ohm\n", + "#calculations\n", + "theta=t2-t1;\n", + "Ra1=Ra+(alfa*Ra*theta);\n", + "N1=1+(Ra/Rsh);\n", + "Ia=I/N1;\n", + "N2=1+(Ra1/Rsh);\n", + "Ia1=I/N2;\n", + "epsilon1=(Ia1-Ia)*100/Ia;\n", + "N3=1+((Ra+Rs)/Rsh);\n", + "Ia2=I*10**3/N3;\n", + "N4=1+((Ra1+Rs)/Rsh);\n", + "Ia3=I*10**3/N4;\n", + "epsilon2=(Ia3-Ia2)*100/Ia2;\n", + "#results\n", + "print \"The percentage error in case 1 (%) = \",round(epsilon1,2)\n", + "print \"The percentage error in case 2 (%) = \",round(epsilon2,3)\n", + "print 'The answers are a bit different due to rounding off error in textbook'\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 31 - pg 151" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "electromotive force is (mV)= 24.632\n", + "resistance is (ohm)= 105.263\n" + ] + } + ], + "source": [ + "#pg 151\n", + "#Example 2.31: Resistance and electromotive force\n", + "#calculate the electromotive force and resistance\n", + "#given data :\n", + "import numpy\n", + "from numpy import linalg\n", + "i1=20.;# in mA\n", + "i2=400.;# in mA\n", + "v1=19.5;# in mV\n", + "v2=23.4;# in mV\n", + "y=100;#mV\n", + "#calculations\n", + "i3=i1/i2;\n", + "K1=i1/i3;\n", + "x1=v1/K1;#\n", + "k2=y/i3;#\n", + "x2=v2/k2;#\n", + "A=numpy.matrix([[1, -x1],[1, -x2]]);\n", + "B=numpy.matrix([[v1],[v2]]);#\n", + "X=numpy.dot(numpy.linalg.inv(A),B);#\n", + "#results\n", + "print \"electromotive force is (mV)=\",round(X[0,0],3)\n", + "print \"resistance is (ohm)=\",round(X[1,0],3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 32 - pg 151" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Error (%) = 1.4\n" + ] + } + ], + "source": [ + "#pg 151\n", + "#Example 2.32: error\n", + "#calculate the error\n", + "#given data :\n", + "import math\n", + "V=20*10**3;# in V\n", + "v1=2*10**3;# in V\n", + "R=10*10**3;# in ohm\n", + "f=50.;# in Hz\n", + "#calculations\n", + "r=R*v1/V;\n", + "w=2*math.pi*f;\n", + "C=0.60*10**-6;# in F\n", + "v=V/((R/r)*math.sqrt(1+((w**2*C**2*r**2*(R-r)**2)/R**2)));\n", + "Error=((v1-v)/v1)*100;\n", + "#results\n", + "print \"Error (%) = \",round(Error,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 33 - pg 152" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(i). Flux in the core (mWb) = 0.591\n", + "(ii). The actual ratio K = 161.04\n", + "(iii). The phase angle (degree) = 0.215\n" + ] + } + ], + "source": [ + "#pg 152\n", + "#Example 2.33: Flux, actual ratio and phase angle\n", + "#calculate the Flux, actual ratio and phase angle\n", + "#given data :\n", + "import math\n", + "from math import sin,cos\n", + "I=5.;# in A\n", + "r1=4.;# in ohm\n", + "r2=0.2;# in ohm\n", + "Ts=160;# in turns\n", + "F=50;# in Hz\n", + "I0=6;# in A\n", + "theta1=30/57.3;# in radians\n", + "#calculations\n", + "Es=I*(r1+r2);\n", + "fi=Es*10**3/(4.44*Ts*F);\n", + "Ie=I0*cos(theta1);# in A\n", + "Im=I0*sin(theta1);# in A\n", + "dela=0;\n", + "K=Ts+(((Ie*cos(dela))+(Im*sin(dela)))/I);\n", + "theta=(180/math.pi)*(((Im*cos(dela))-(Ie*sin(dela)))/(Ts*I));\n", + "#results\n", + "print \"(i). Flux in the core (mWb) = \",round(fi,3)\n", + "print \"(ii). The actual ratio K = \",round(K,2)\n", + "print \"(iii). The phase angle (degree) = \",round(theta,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 34 - pg 152" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(a). The ratio error (%) = -0.0436\n", + "(b). phase angle is 0.0 degree 3.438 minutes \n" + ] + } + ], + "source": [ + "#pg 152\n", + "#Example 2.34: The ratio errror and phase angle error\n", + "#calculate the ratio error and phase angle\n", + "#given data :\n", + "import math\n", + "from math import sin,cos,sqrt\n", + "I=5.;# in A\n", + "n=1000./5;# normal ratio\n", + "sin_alfa=0.4;\n", + "Im=1;# in A\n", + "dela=0;\n", + "#calculations\n", + "cos_alfa=sqrt(1-sin_alfa**2);\n", + "I0=Im/cos_alfa;\n", + "Ie=I0*sin_alfa;\n", + "K=n+(((Ie*cos(dela))+(Im*sin(dela)))/I);\n", + "er=(n-K)*100/K;\n", + "eph=(180/math.pi)*(((Im*cos(dela))-(Ie*sin(dela)))/(n*I));\n", + "x=round(eph);#\n", + "y=eph-x;#\n", + "#results\n", + "print \"(a). The ratio error (%) = \",round(er,4)\n", + "print \"(b). phase angle is \",x,\" degree \",round(y*60,3),\" minutes \"\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 35 - pg 153" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The ratio error,(%) = -0.744\n", + "The phase angle,(degree) = -0.252\n", + "The answers are a bit different due to rounding off error in textbook\n" + ] + } + ], + "source": [ + "#pg 153\n", + "#Example 2.35: The ratio errror and phase angle error\n", + "#calculate the ratio error and phase angle\n", + "#given data :\n", + "import math\n", + "from math import sin,cos,asin\n", + "I=5.;# in A\n", + "n=198.;# in turns\n", + "L=12.5;#in VA\n", + "f=50.;# assume in Hz\n", + "Ie=10.;# in A\n", + "Im=15.;# in A\n", + "l=1.*10**-3;# in H\n", + "#calculations\n", + "Kn=1000./I;\n", + "Zs=L/I**2;\n", + "Re=2*math.pi*f*l;# in ohm\n", + "dela=asin(Re/Zs)*180/math.pi;\n", + "K=n+(((Ie*cos(dela))+(Im*sin(dela)))/I);\n", + "Rerror=(Kn-K)*100./K;\n", + "eph=(180/math.pi)*(((Im*cos(dela))-(Ie*sin(dela)))/(n*I));\n", + "#results\n", + "print \"The ratio error,(%) = \",round(Rerror,3)\n", + "print \"The phase angle,(degree) = \",round(eph,3)\n", + "print 'The answers are a bit different due to rounding off error in textbook'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 36 - pg 154" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "phase angle is -4.7 minutes\n", + "load is (VA)= 12.5\n" + ] + } + ], + "source": [ + "#pg 154\n", + "#Example 2.36: phase angle error load in VA\n", + "#calculate the phase angle error load\n", + "#given data \n", + "import math\n", + "from math import sqrt\n", + "v1=1000.;#V\n", + "v2=100.;#V\n", + "xp=65.4;#ohm\n", + "rp=97.5;#ohm\n", + "pf=0.4;#\n", + "im=0.02;#A\n", + "Xp=110;#ohm\n", + "#calculations\n", + "r=v1/v2;#\n", + "sd=pf;#\n", + "csd=sqrt(1-pf**2);#\n", + "ie=im*(pf/csd);#A\n", + "th=((ie*xp)-(im*rp))/(r*v2);#rad\n", + "thd=th*(180/math.pi);#\n", + "iss=(r*((im*rp)-(ie*xp)))/(Xp);\n", + "va=iss*v2;#VA\n", + "#results\n", + "print \"phase angle is \",round(thd*60,1),\"minutes\"\n", + "print \"load is (VA)=\",round(va,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 37 - pg 155" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "flux is (m-Wb)= 0.18\n", + "ratio error is (%)= -3.61\n" + ] + } + ], + "source": [ + "#pg 155\n", + "#Example 2.37: flux and current ratio error\n", + "#calculate the flux and ratio error\n", + "#given\n", + "n1=1000.;#A\n", + "n2=5.;#A\n", + "r=1.6;#ohm\n", + "wt=1.5;#watt\n", + "f=50;#Hz\n", + "cd1=1;#\n", + "sd=0;#\n", + "#calculations\n", + "kn=n1/n2;#\n", + "ts=kn;#\n", + "es=n2*r;#v\n", + "ph=es/(4.44*f*kn);#m Wb\n", + "ep=es/kn;#\n", + "ie=wt/ep;#A\n", + "K=((kn+(ie/n2)));#\n", + "re=((kn-K)/K)*100;#\n", + "#results\n", + "print \"flux is (m-Wb)=\",round(ph*10**3,2)\n", + "print \"ratio error is (%)=\",round(re,2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 38 - pg 155" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "RCF for case (a) = 1.0165\n", + "phase error for case (a) (%)= -1.623\n", + "phase angle error for case (a) 10.3 minutes\n", + "RCF for case (b) = 1.0075\n", + "phase error for case (b) (%)= -0.744\n", + "phase angle error for case (b)is 51.6 minutes\n", + "RCF for case (c) = 0.9925\n", + "phase error for case (c) (%)= 0.756\n", + "phase angle error for case (c) is 51.6 minutes\n", + "RCF for case (d) = 1.00825\n", + "phase error for case (d) (%)= -0.82\n", + "phase angle error for case (d) is 5.157 minutes\n", + "RCF for case (e) = 1.00375\n", + "phase error for case (e) (%)= -0.374\n", + "phase angle error for case (e) is 25.8 minutes\n", + "RCF for case (f) = 0.99625\n", + "phase error for case (f) (%)= 0.376\n", + "phase angle error for case (f) is 25.8 minutes\n" + ] + } + ], + "source": [ + "#pg 155\n", + "#Example 2.38: RCF ,ratio error and phase angle error\n", + "#calculate the ratio error, phase angle error and RCF in all cases\n", + "import math\n", + "from math import sqrt\n", + "#given\n", + "vp=2000.;#V\n", + "n=20.;#\n", + "va1=50.;#\n", + "pfl1=0.6;#lagging\n", + "va2=25.;#V\n", + "ie=0;#\n", + "im=0;#\n", + "cd1=0.6;#\n", + "rs1=0.75;#ohm\n", + "rp1=300.;#ohm\n", + "xs1=1.5;#ohm\n", + "xp1=600.;#ohm\n", + "#calculations and results\n", + "vs=vp/n;#\n", + "iss=va1/vs;#A\n", + "iss2=va2/vs;#A\n", + "sd1=sqrt(1-cd1**2);#\n", + "Rp1=n**2*rs1+rp1;#ohm\n", + "Xp1=n**2*xs1+xp1;#ohm\n", + "vps1=n+((iss/n)*(Rp1*cd1+Xp1*sd1))/vs;#\n", + "RCF1=vps1/n;#\n", + "er1=((n-vps1)/vps1)*100;#%\n", + "per1=((iss*(Xp1*cd1-Rp1*sd1))/(n**2*vs))*(180/math.pi);#degree\n", + "per1a=round(per1);#\n", + "x1=per1-per1a;#\n", + "print \"RCF for case (a) = \",RCF1\n", + "print \"phase error for case (a) (%)=\",round(er1,3)\n", + "print \"phase angle error for case (a) \",round(x1*60,1),\" minutes\"\n", + "cd11=1;#\n", + "sd11=sqrt(1-cd11**2);#\n", + "vps2=n+((iss/n)*(Rp1*cd11+Xp1*sd11))/vs;#\n", + "RCF2=vps2/n;#\n", + "er2=((n-vps2)/vps2)*100;#%\n", + "per2=((iss*(Xp1*cd11-Rp1*sd11))/(n**2*vs))*(180/math.pi);#degree\n", + "per1a1=round(per2);#\n", + "x2=per1-per1a1;#\n", + "print \"RCF for case (b) =\",RCF2\n", + "print \"phase error for case (b) (%)=\",round(er2,3)\n", + "print \"phase angle error for case (b)is \",round(per2*60,1),\" minutes\"\n", + "cd12=0.6;#\n", + "sd12=-0.8;#\n", + "vps3=n+((iss/n)*(Rp1*cd12+Xp1*sd12))/vs;#\n", + "RCF3=vps3/n;#\n", + "er3=((n-vps3)/vps3)*100;#%\n", + "per3=((iss*(Xp1*cd12-Rp1*sd12))/(n**2*vs))*(180/math.pi);#degree\n", + "per1a1=round(per2);#\n", + "x2=per1-per1a1;#\n", + "print \"RCF for case (c) =\",RCF3\n", + "print \"phase error for case (c) (%)=\",round(er3,3)\n", + "print \"phase angle error for case (c) is \",round(per3*60,1),\" minutes\"\n", + "cd13=0.6;#\n", + "sd13=0.8;#\n", + "vps4=n+((iss2/n)*(Rp1*cd13+Xp1*sd13))/vs;#\n", + "RCF4=vps4/n;#\n", + "er4=((n-vps4)/vps4)*100;#%\n", + "per4=((iss2*(Xp1*cd13-Rp1*sd13))/(n**2*vs))*(180/math.pi);#degree\n", + "per1a1=round(per2);#\n", + "x2=per1-per1a1;#\n", + "print \"RCF for case (d) =\",RCF4\n", + "print \"phase error for case (d) (%)=\",round(er4,2)\n", + "print \"phase angle error for case (d) is \",round(per4*60,3),\" minutes\"\n", + "cd14=1;#\n", + "sd14=0;#\n", + "vps5=n+((iss2/n)*(Rp1*cd14+Xp1*sd14))/vs;#\n", + "RCF5=vps5/n;#\n", + "er5=((n-vps5)/vps5)*100;#%\n", + "per5=((iss2*(Xp1*cd14-Rp1*sd14))/(n**2*vs))*(180/math.pi);#degree\n", + "per1a1=round(per2);#\n", + "x2=per1-per1a1;#\n", + "print \"RCF for case (e) =\",RCF5\n", + "print \"phase error for case (e) (%)=\",round(er5,3)\n", + "print \"phase angle error for case (e) is \",round(per5*60,1),\" minutes\"\n", + "cd15=0.6;#\n", + "sd16=-0.8;#\n", + "vps6=n+((iss2/n)*(Rp1*cd15+Xp1*sd16))/vs;#\n", + "RCF6=vps6/n;#\n", + "er6=((n-vps6)/vps6)*100;#%\n", + "per6=((iss2*(Xp1*cd15-Rp1*sd16))/(n**2*vs))*(180/math.pi);#degree\n", + "per1a1=round(per2);#\n", + "x2=per1-per1a1;#\n", + "print \"RCF for case (f) =\",RCF6\n", + "print \"phase error for case (f) (%)=\",round(er6,3)\n", + "print \"phase angle error for case (f) is \",round(per6*60,1),\" minutes\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 39 - pg 158" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ratio error (%)= -1.26\n", + "RCF = 1.01275\n", + "phase angle error (degree)= 0.73\n" + ] + } + ], + "source": [ + "#pg 158\n", + "#Example 2.39: ,ratio error and phase angle error\n", + "#calculate the ratio error,RCF and phase angle error\n", + "#given\n", + "import math\n", + "from math import cos, sin\n", + "vp=1000.;#V\n", + "iss=5.;#A\n", + "VA=25.;#\n", + "wt=0.25;#W\n", + "im=15.;#A\n", + "xs=1.;#ohm\n", + "rs=5.;#ohm\n", + "#calculations\n", + "n=vp/iss;#\n", + "vs=VA/iss;#\n", + "vp=iss/n;#V\n", + "ie=wt/vp;#A\n", + "dl=math.atan(xs/rs)*57.3;#\n", + "dlr=dl*(math.pi/180);#\n", + "K=n+((ie*cos(dl/57.3)+im*sin(dl/57.3))/iss);#\n", + "re=((n-K)/K)*100;#per\n", + "RCF=K/n;#\n", + "eph=(180/math.pi)*(((im*cos(dl/57.3))-(ie*sin(dl/57.3)))/(n*iss));\n", + "#results\n", + "print \"ratio error (%)=\",round(re,2)\n", + "print \"RCF =\",round(RCF,5)\n", + "print \"phase angle error (degree)=\",round(eph,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 40 - pg 159" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "true value of voltage is,(V)= 2030.0\n", + "true value of current is,(A)= 80.4\n", + "true value of power is ,(kW)= 149.4\n" + ] + } + ], + "source": [ + "#pg 159\n", + "#Example 2.40: true value of voltage ,current and power\n", + "#calculate the true value of voltage ,current and power\n", + "#given\n", + "import math\n", + "from math import acos,cos\n", + "vs=102.;#V\n", + "iss=4.;#A\n", + "ws=375.;#W\n", + "rcf=0.995;#\n", + "rcf1=1.005;#\n", + "a1=2000.;#\n", + "a2=100.;#\n", + "#calculations\n", + "ph=acos(ws/(iss*vs))*57.3;#degree\n", + "ph1=round(ph);#\n", + "x=ph-ph1;#\n", + "y=x*60;#\n", + "angd=y+22+10;#\n", + "ang=angd/60.;#\n", + "ta=ph1+ang;#\n", + "nr=a1/a2;#\n", + "avr=rcf*nr;#\n", + "pv=avr*vs;#\n", + "acr=rcf1*(a2/nr);#\n", + "pc=acr*iss*iss;#A\n", + "psd=pv*pc*cos(ta/57.3)*10**-3;#\n", + "#results\n", + "print \"true value of voltage is,(V)=\",round(pv)\n", + "print \"true value of current is,(A)=\",pc\n", + "print \"true value of power is ,(kW)=\",round(psd,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 41 - pg 160" + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "primary current is,(A)= 498.415\n", + "phase error is (radian)= 0.0058\n" + ] + } + ], + "source": [ + "#pg 160\n", + "#Example 2.41:primary current ,phase error \n", + "#calculate the primary current ,phase error \n", + "#given\n", + "import math,cmath\n", + "from math import cos,sin\n", + "zs=0.433+1j*0.25;#ohm\n", + "zs1=0.15+1j*0.0;#ohm\n", + "nt=2.;#turns\n", + "l1=8.;#\n", + "l2=4.;#\n", + "tnt=198;#turns\n", + "iss=5;#A\n", + "#calculations\n", + "zs2=zs+zs1;#ohm\n", + "zsa=math.sqrt((zs2.real)**2+(zs2.imag)**2);#\n", + "zsng=math.atan(zs2.imag/zs2.real);#\n", + "ie=l2/nt;#\n", + "im=l1/nt;#\n", + "K=((tnt/2.)+((ie*cos(zsng))+(im*sin(zsng)))/iss);#\n", + "ip=K*iss;#A\n", + "th=((im*cos(zsng))-(ie*sin(zsng)))/((tnt/2)*iss);#\n", + "#results\n", + "print \"primary current is,(A)=\",round(ip,3)\n", + "print \"phase error is (radian)=\",round(th,4)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 42 - pg 160" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ratio error (%)= -1.26\n", + "RCF = 1.01275\n", + "phase angle error (degree)= 0.73\n" + ] + } + ], + "source": [ + "#pg 158\n", + "#Example 2.39: ,ratio error and phase angle error\n", + "#calculate the ratio error,RCF and phase angle error\n", + "#given\n", + "import math\n", + "from math import cos, sin\n", + "vp=1000.;#V\n", + "iss=5.;#A\n", + "VA=25.;#\n", + "wt=0.25;#W\n", + "im=15.;#A\n", + "xs=1.;#ohm\n", + "rs=5.;#ohm\n", + "#calculations\n", + "n=vp/iss;#\n", + "vs=VA/iss;#\n", + "vp=iss/n;#V\n", + "ie=wt/vp;#A\n", + "dl=math.atan(xs/rs)*57.3;#\n", + "dlr=dl*(math.pi/180);#\n", + "K=n+((ie*cos(dl/57.3)+im*sin(dl/57.3))/iss);#\n", + "re=((n-K)/K)*100;#per\n", + "RCF=K/n;#\n", + "eph=(180/math.pi)*(((im*cos(dl/57.3))-(ie*sin(dl/57.3)))/(n*iss));\n", + "#results\n", + "print \"ratio error (%)=\",round(re,2)\n", + "print \"RCF =\",round(RCF,5)\n", + "print \"phase angle error (degree)=\",round(eph,3)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 43 - pg 161" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "current is (mA)= 1.1474\n", + "The answer is a bit different due to rounding off error in textbook\n" + ] + } + ], + "source": [ + "#pg 161\n", + "#Example 2.43 :percentage change in current\n", + "#calculate the current\n", + "#given data\n", + "import math,cmath\n", + "r=0.5;#kilo ohm\n", + "r1=1.;#kilo ohm\n", + "f=50.;#Hz\n", + "V=1.;#V\n", + "#calculations\n", + "z1=((1j*r1*r)/(r1+1j*r));#kilo-ohm\n", + "z1m=abs(z1);#kilo-ohm\n", + "z2=((1j*r1*r)/(r+1j*r1));#kilo-ohm\n", + "z2m=abs(z2);#kilo-ohm\n", + "tz=z1m+z2m;#kilo-ohm\n", + "i=V/tz;#A\n", + "v1=i*z1m*10**-3;#V\n", + "v2=i*10**-3*z2m;#V\n", + "df=f-((f*5)/100);#Hz\n", + "rc1=((r*df)/f);#k-ohm\n", + "rc2=((r1*df)/f);#k-ohm\n", + "z1n=((1j*rc1)/(r1+1j*rc1));#\n", + "z1nm=abs(z1n);#k-ohm\n", + "z2n=((1j*rc2*r)/(r+1j*rc2));#\n", + "z2nm=abs(z2n);#k-ohm\n", + "znw=z1nm+z2nm;#k-ohm\n", + "inn=V/znw;#\n", + "#results\n", + "print \"current is (mA)=\",round(inn,4)\n", + "print 'The answer is a bit different due to rounding off error in textbook'" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 44 - pg 162" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "inductance is (H)= 9.73\n", + "frequency is (Hz)= 41.7\n" + ] + } + ], + "source": [ + "#pg 162\n", + "#Example 2.44 :Inductance\n", + "#calculate the inductance and frequency\n", + "#given data\n", + "import math,cmath\n", + "c=1.;#micro-F\n", + "f1=60.;#Hz\n", + "f=50.;#Hz\n", + "#calculations\n", + "l1=((c*10**6)/(f1**2*(2*math.pi)**2));#\n", + "r1=100;#ohm\n", + "z1=r1+1j*((2*math.pi*f*l1)-(1/(2*math.pi*f*c*10**-6)));#ohm\n", + "c2=1.5;#micro-F\n", + "l2=((-z1.imag)+(1/(2*math.pi*c2)))/100;#H\n", + "f2=(1/(2*math.pi))*math.sqrt(1/(l2*c2*10**-6));#Hz\n", + "#results\n", + "print \"inductance is (H)=\",round(l2,2)\n", + "print \"frequency is (Hz)=\",round(f2,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 45 - pg 163" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "true value of voltage is,(V)= 2030.0\n", + "true value of current is,(A)= 80.4\n", + "true value of power is ,(kW)= 149.4\n" + ] + } + ], + "source": [ + "#pg 159\n", + "#Example 2.40: true value of voltage ,current and power\n", + "#calculate the true value of voltage ,current and power\n", + "#given\n", + "import math\n", + "from math import acos,cos\n", + "vs=102.;#V\n", + "iss=4.;#A\n", + "ws=375.;#W\n", + "rcf=0.995;#\n", + "rcf1=1.005;#\n", + "a1=2000.;#\n", + "a2=100.;#\n", + "#calculations\n", + "ph=acos(ws/(iss*vs))*57.3;#degree\n", + "ph1=round(ph);#\n", + "x=ph-ph1;#\n", + "y=x*60;#\n", + "angd=y+22+10;#\n", + "ang=angd/60.;#\n", + "ta=ph1+ang;#\n", + "nr=a1/a2;#\n", + "avr=rcf*nr;#\n", + "pv=avr*vs;#\n", + "acr=rcf1*(a2/nr);#\n", + "pc=acr*iss*iss;#A\n", + "psd=pv*pc*cos(ta/57.3)*10**-3;#\n", + "#results\n", + "print \"true value of voltage is,(V)=\",round(pv)\n", + "print \"true value of current is,(A)=\",pc\n", + "print \"true value of power is ,(kW)=\",round(psd,1)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 46 - pg 163" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Series resistance,Rs(ohm) = 8000.0\n", + "answer is wrong in the textbook due to rounding off error\n" + ] + } + ], + "source": [ + "#pg 160\n", + "#Example 2.42: Resistance\n", + "#calculate the Series resistance\n", + "import math\n", + "#given data :\n", + "f=50.;#/ in Hz\n", + "r=2000.;# in ohm\n", + "L=0.5;# in H\n", + "V=100.;# in V\n", + "#calculations\n", + "Zm=math.sqrt(r**2+(2*math.pi*f*L));\n", + "im=V/Zm;\n", + "Rs=(500.-(im*Zm))/im;\n", + "#results\n", + "print \"Series resistance,Rs(ohm) = \",round(Rs)\n", + "print 'answer is wrong in the textbook due to rounding off error'\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.9" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} -- cgit