{
 "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"
   ]
  }
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