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+{

+ "cells": [

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "# Chapter 5 - Magnetic measurement"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 1 - pg 304"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 1,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Capacity of the capacitor (micro-F) =  2.12\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 304\n",

+    "#Example 5.1: Capacity of the capacitor\n",

+    "#calculate the Capacity of the capacitor\n",

+    "#given data :\n",

+    "import math\n",

+    "Ig=0.0001;# in A\n",

+    "T0=3.;# in sec\n",

+    "theta0=200.;\n",

+    "theta=45.;\n",

+    "V=100.;# in V\n",

+    "#calculations\n",

+    "Q=(Ig*T0*theta0)/(theta*2*math.pi);\n",

+    "C=(Q/V)*10**6;\n",

+    "#results\n",

+    "print \"Capacity of the capacitor (micro-F) = \",round(C,2)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 2 - pg 304"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 2,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Coulomb sensitivity (mm/micro-C) =  8.89\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 304\n",

+    "#Example 5.2: Coulomb sensitivity\n",

+    "#calculate te Coulomb sensitivity\n",

+    "#given data :\n",

+    "C=1.5*10**-6;# in F\n",

+    "V=15;# in V\n",

+    "d1=20;# in cm\n",

+    "#calculations\n",

+    "Q=C*V;\n",

+    "Sb=(d1/Q)*10**-5;\n",

+    "#resutls\n",

+    "print \"Coulomb sensitivity (mm/micro-C) = \",round(Sb,2)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 3 - pg 305"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 4,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Logarithmic increment =  0.2231\n",

+      "undamped frequency is (Hz)= 0.1253\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 305\n",

+    "#Example 5.3: Logarithmic increment\n",

+    "#calculate the Logarithmic increment and frequency\n",

+    "#given data :\n",

+    "import math\n",

+    "theta1=12.5;\n",

+    "theta2=10.;\n",

+    "#calculations\n",

+    "lamda=math.log(theta1/theta2);\n",

+    "x=lamda**2;#\n",

+    "y=x/(math.pi**2-x);#\n",

+    "y1=math.sqrt(y);#\n",

+    "f=0.125;#Hz\n",

+    "fo=f/(math.sqrt(1-y1**2));#Hz\n",

+    "#results\n",

+    "print \"Logarithmic increment = \",round(lamda,4)\n",

+    "print \"undamped frequency is (Hz)=\",round(fo,4)"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 4 - pg 305"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 6,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Flux density B(Wb/m^2) =  55.56\n",

+      "permeability mu(H/m) =  60.0\n",

+      "flux density is calculed wrong in the textbook\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 305\n",

+    "#Example 5.4: Flux density\n",

+    "#calculate the flux density\n",

+    "#given data :\n",

+    "I1=5.;# in A\n",

+    "I2=10.;# in A\n",

+    "N1=100.;# number of turns\n",

+    "N2=200.;#number of turns\n",

+    "l=30*10**-2;# in m\n",

+    "R=200.;# in ohm\n",

+    "theta1=45.;# in degree\n",

+    "theta2=30.;# in degree\n",

+    "As=0.3*10**-4;# in m**2\n",

+    "M=100*10**-3;# in H\n",

+    "#calculations\n",

+    "k=(2*M*I1)/(R*theta1);\n",

+    "H=(N1*I2)/l;\n",

+    "fi=(R*k*theta2)/(2*N2);\n",

+    "B=fi/As;\n",

+    "mu=H/B;\n",

+    "#results\n",

+    "print \"Flux density B(Wb/m^2) = \",round(B,2)\n",

+    "print \"permeability mu(H/m) = \",mu\n",

+    "print 'flux density is calculed wrong in the textbook'\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 5 - pg 309"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 8,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Flux density,B(Wb/m^2) =  1.25\n",

+      "Relative permeability =  521.0\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 309\n",

+    "#Example 5.5: Flux density and relative permeability\n",

+    "#calculate the Flux density and relative permeability\n",

+    "#given data :\n",

+    "import math\n",

+    "A=5*10**-4;# in m**2\n",

+    "d=25*10**-2;# in m\n",

+    "N1=150;# turns\n",

+    "N2=300;# turns\n",

+    "k=2*10**-6;# coulomb per division\n",

+    "R=2500;# in ohm\n",

+    "I=10;# in A\n",

+    "theta=75;# in division\n",

+    "#calculations\n",

+    "l=math.pi*d;\n",

+    "mu_0=4*math.pi*10**-7;\n",

+    "B=(k*theta*R)/(2*N2*A);\n",

+    "H=(N1*I)/l;\n",

+    "mu_r=(B/(mu_0*H));\n",

+    "#results\n",

+    "print \"Flux density,B(Wb/m^2) = \",B\n",

+    "print \"Relative permeability = \",round(mu_r)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 6 - pg 308"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 9,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "In case of total flux is (Wb)= 0.027\n",

+      "In case of useful flux is (Wb)= 0.0228\n",

+      "leakage coefficient is = 1.185\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 308\n",

+    "#Example 5.6 #flux per pole and leakage cofficient\n",

+    "#calculate the flux per pole and leakage cofficient\n",

+    "#given data:\n",

+    "k=0.15;#micro-C\n",

+    "th=120.;#divisions\n",

+    "th1=135.;#divisions\n",

+    "r=4500.;#ohm\n",

+    "n=3.;#turns\n",

+    "#calculations\n",

+    "ft=(k*10**-6*th*r)/n;#Wb\n",

+    "n1=4;#\n",

+    "ft1=(k*10**-6*th1*r)/n1;#Wb\n",

+    "lk=ft/ft1;#\n",

+    "#results\n",

+    "print \"In case of total flux is (Wb)=\",ft\n",

+    "print \"In case of useful flux is (Wb)=\",round(ft1,4)\n",

+    "print \"leakage coefficient is =\",round(lk,3)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 7 - pg 308"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 10,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "relative permeability = 30.7\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 308\n",

+    "#Example 5.7 #relative permeability\n",

+    "#calculate the relative permeability\n",

+    "#given data\n",

+    "import math\n",

+    "n1=320.;#turns\n",

+    "n2=250.;#turns\n",

+    "i=10.;#A\n",

+    "l=32.;#cm\n",

+    "fl=2.5*10**-4;#Wb\n",

+    "sd=100;#\n",

+    "sd1=270;#/\n",

+    "#calculations\n",

+    "N=(n1*i)/(l*10**-2);#AT/m\n",

+    "k=(fl*i)/sd;#\n",

+    "mo=4*math.pi*10**-7;#\n",

+    "A=0.35;#cm**2\n",

+    "ur=((k*sd1)/(2*mo*N*A*10**-4*n2));#\n",

+    "#results\n",

+    "print \"relative permeability =\",round(ur,1)"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 8 - pg 309"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 11,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "The shunt resistance S(ohm) =  0.0127\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 309\n",

+    "#Example 5.7 # Shunt resistance\n",

+    "#calculate the shunt resistance\n",

+    "#given data :\n",

+    "N=800.;# turns\n",

+    "I=10.;# in A\n",

+    "reluctance=150000;# in AT per Wb\n",

+    "K=.15*10**-3;# in Wb turns/ division\n",

+    "rs=0.025;# in ohm\n",

+    "Ns=1;\n",

+    "theta=120;#divisions\n",

+    "#calculations\n",

+    "fi=(N*I)/reluctance;\n",

+    "S=(K*rs*theta)/((fi*Ns)-(K*theta));\n",

+    "#results\n",

+    "print \"The shunt resistance S(ohm) = \",round(S,4)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 9 - pg 310"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 12,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "The magnetic potential difference between two points,(AT) =  697.0\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 310\n",

+    "#Example 5.9 # Magnetic pole difference\n",

+    "#calculate the Magnetic pole difference\n",

+    "#given data :\n",

+    "N=150.;# turns\n",

+    "I=1.2;# in A\n",

+    "theta=300.;# divisions\n",

+    "t=155.;#change in mmf in division\n",

+    "#calculations\n",

+    "mmf=N*I;\n",

+    "r=2*mmf;# du to reversal\n",

+    "K=360/t;\n",

+    "M=(K*theta);\n",

+    "#results\n",

+    "print \"The magnetic potential difference between two points,(AT) = \",round(M)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 10 - pg 310"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 13,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "relative permeability = 521.0\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 310\n",

+    "#Example 5.10 #relative permeability\n",

+    "#calculate the relative permeability\n",

+    "#given data\n",

+    "import math\n",

+    "n1=600.;#turns\n",

+    "i=3.;#A\n",

+    "d=30.;#cm\n",

+    "ass=6.;#cm^2;#\n",

+    "t1=500.;#turns\n",

+    "r=250.;#ohms\n",

+    "k=3000.;#micro-C\n",

+    "#calculations\n",

+    "H=(n1*i)/(math.pi*d*10**-2);#\n",

+    "mo=4*math.pi*10**-7;#\n",

+    "x=mo*H;#\n",

+    "y=ass*10**-4*x;#\n",

+    "z=t1*y;#\n",

+    "z1=2*z;#\n",

+    "it=z1/r;#\n",

+    "ur=(k*10**-6)/it;#\n",

+    "#results\n",

+    "print \"relative permeability =\",round(ur)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 11 - pg 311"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 14,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Fluxmeter deflection (degree) =  76.4\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 311\n",

+    "#Example 5.11 # Fluxmeter deflection\n",

+    "#calculate the Fluxmeter deflection\n",

+    "#given data :\n",

+    "import math\n",

+    "l=5*10**-2;# in m\n",

+    "N=40;# turns\n",

+    "B=5*10**-3;# in Wb/m**2\n",

+    "b=1.5*10**-2;# in m\n",

+    "cs=2*10**-4;# in  m**2\n",

+    "B1=0.05;# in Wb/m**2\n",

+    "#calculations\n",

+    "fi=B1*cs;\n",

+    "del_fi=2*fi;\n",

+    "theta=(del_fi*10)/(N*B*l*b);\n",

+    "#results\n",

+    "print \"Fluxmeter deflection (degree) = \",round((theta*(180/math.pi)),1)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 12 - pg 311"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 16,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Hysteresis current component of the loss (W)= 266.7\n",

+      "Eddy current component of the loss (W)= 158.3\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 311\n",

+    "#Example 5.12 #hysteresis and eddy current components\n",

+    "#calculate the hysteresis and eddy current components\n",

+    "#given data\n",

+    "import numpy\n",

+    "w1=132.;#W\n",

+    "f1=20.;#Hz\n",

+    "w2=425.;#W\n",

+    "f2=50.;#Hz\n",

+    "#calculations\n",

+    "x=w1/f1;#\n",

+    "y=w2/f2;#\n",

+    "A=numpy.matrix([[1, f1],[1, f2]]);#\n",

+    "B=numpy.matrix([[x],[y]]);#\n",

+    "X=numpy.dot(numpy.linalg.inv(A),B);#\n",

+    "Wh=X[0,0]*f2;#W\n",

+    "We=X[1,0]*f2**2;#W\n",

+    "#results\n",

+    "print \"Hysteresis current component of the loss (W)=\",round(Wh,1)\n",

+    "print \"Eddy current component of the loss (W)=\",round(We,1)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 13 - pg 312"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 17,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "hysteresis loss is (W)= 22.0\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 312\n",

+    "#Example 5.13 #hysteresis loss\n",

+    "#calculate the hysteresis loss\n",

+    "#given data\n",

+    "Hx=125.;#AT/m\n",

+    "ah=200.;#cm**2\n",

+    "ba=0.15;#Wb/m**2\n",

+    "lo=50;#loos\n",

+    "kg=8.5*10**3;#kg/m**3\n",

+    "#calculations\n",

+    "le=ah*Hx*ba;#J/m**3\n",

+    "po=lo*le;#W/m**3\n",

+    "lkg=po/kg;#watt\n",

+    "#results\n",

+    "print \"hysteresis loss is (W)=\",round(lkg)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 14 - pg 312"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 18,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "The flux density B(Wb/m^2) =  0.121\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 312\n",

+    "#Example 5.14 # flux density\n",

+    "#calculate the flux density\n",

+    "#given data :\n",

+    "R=200+50.;# in ohm\n",

+    "k=100*10**-6;# in coulomb\n",

+    "theta=80.;# divisions\n",

+    "A=55*10**-4;# in m**2\n",

+    "N=1500;# turns\n",

+    "#calculations\n",

+    "B=(R*k*theta)/(2*A*N);\n",

+    "#results\n",

+    "print \"The flux density B(Wb/m^2) = \",round(B,3)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 15 - pg 313"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 19,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "loss is (W)= 0.617\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 313\n",

+    "#Example 5.15 #loss\n",

+    "#calculate the loss\n",

+    "#given data\n",

+    "f=50.;#Hz\n",

+    "k=2.3*10**-2;#\n",

+    "x=1.7;#\n",

+    "wi=0.6;#W\n",

+    "bm=0.5;#Wb/m**2\n",

+    "f1=20;#Hz\n",

+    "bm1=1;#\n",

+    "#calculations\n",

+    "kd=((wi-(k*bm**x*f))/(bm**2*f**2));#\n",

+    "wi1=((k*bm1**x*f1)+(kd*bm1**2*f1**2));#\n",

+    "#results\n",

+    "print \"loss is (W)=\",round(wi1,3)"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 16 - pg 313"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 21,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "magnetic flux is (Wb/m^2)= 0.714\n",

+      "flux density is (AT/m^2)= 400.0\n",

+      "relative permeability is = 1421.03\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 313\n",

+    "#Example 5.16 #MAGNETIC FORCE ,FLUX DENSITY AND RELATIVE PERMEABILITY\n",

+    "#calculate the MAGNETIC FORCE ,FLUX DENSITY AND RELATIVE PERMEABILITY\n",

+    "#given data\n",

+    "import math\n",

+    "k=1;#micro-C\n",

+    "th=100.;#turns\n",

+    "r=5000.;#ohm\n",

+    "n2=350.;#turns\n",

+    "ass=10.;#cm**2\n",

+    "n1=100.;#turns\n",

+    "i=4.;#A\n",

+    "l=100.;#cm\n",

+    "#calculations\n",

+    "b=((k*th*r*10**-6)/(2*n2*ass*10**-4));#Wb/m**2\n",

+    "H=(n1*i)/(l*10**-2);#AT/m**2\n",

+    "mo=4*math.pi*10**-7;#\n",

+    "ur=b/(mo*H);#\n",

+    "#results\n",

+    "print \"magnetic flux is (Wb/m^2)=\",round(b,3)\n",

+    "print \"flux density is (AT/m^2)=\",H\n",

+    "print \"relative permeability is =\",round(ur,2)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 17 - pg 314"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 20,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "Constant is (Wb-turn/scale-div)= 1.005e-07\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 314\n",

+    "#Example 5.17 # fluxmeter\n",

+    "#calculate the Constant of fluxmeter\n",

+    "#given data :\n",

+    "import math\n",

+    "N1=800.;# turns\n",

+    "I=5;# in A\n",

+    "l=1;# in m\n",

+    "A=5*10**-4;# in m**2\n",

+    "N=500;# turns\n",

+    "theta=25.;# divisions\n",

+    "#calculations\n",

+    "H=(N1*I)/l;\n",

+    "B=(4*math.pi*10**-7*H);\n",

+    "fi=B*A*10**8;\n",

+    "K=((2*N*fi*10**-8)/(theta));\n",

+    "#results\n",

+    "print \"Constant is (Wb-turn/scale-div)=\",round(K*10**-3,10)\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

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