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+{

+ "cells": [

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "# Chapter 1 - Philosophy of Measurement"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 1 - pg 33"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 3,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "arithmetic mean is (V)= 100.0\n",

+      "average deviation is (V)= 0.084\n",

+      "standard deviation is (V)= 0.1192\n",

+      "probable error is (V)= 0.0804\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.1:#ARITHEMATIC MEAN,AVERAGE DEVIATION ,STANDARD DEVIATION AND PROBABLE ERROR\n",

+    "#calculate the ARITHEMATIC MEAN,AVERAGE DEVIATION ,STANDARD DEVIATION AND PROBABLE ERROR\n",

+    "#given\n",

+    "import math, numpy\n",

+    "T=numpy.array([99.7,99.8,99.9,100,100.1,100.2,100.3]);#VOLTS\n",

+    "f=numpy.array([2,8,20,40,21,6,3]);#frequency of occurence\n",

+    "q=numpy.array([T[0]*f[0],T[1]*f[1],T[2]*f[2],T[3]*f[3],T[4]*f[4],T[5]*f[5],T[6]*f[6]]);#\n",

+    "#calculations\n",

+    "AM=(q[0]+q[1]+q[2]+q[3]+q[4]+q[5]+q[6])/100;#arithematic mean in mm\n",

+    "qb=numpy.zeros(7)\n",

+    "for i in range(0,7):\n",

+    "    qb[i]= T[i]-AM\n",

+    "\n",

+    "Q= numpy.array([qb[0],qb[1],qb[2],qb[3],qb[4],qb[5],qb[6]]);#\n",

+    "AV=(-qb[0]*f[0]-qb[1]*f[1]-qb[2]*f[2]-qb[3]*f[3]+qb[4]*f[4]+qb[5]*f[5]+qb[6]*f[6])/100;#\n",

+    "SD=math.sqrt(((qb[0]**2*f[0])+(qb[1]**2*f[1])+(qb[2]**2*f[2])+(qb[3]**2*f[3])+(qb[4]**2*f[4])+(qb[5]**2*f[5])+(qb[6]**2*f[6]))/100);#standard deviation\n",

+    "r1= 0.6745*SD;#PROBABLE ERROR OF ONE READING\n",

+    "#results\n",

+    "print\"arithmetic mean is (V)=\",AM\n",

+    "print\"average deviation is (V)=\",AV\n",

+    "print\"standard deviation is (V)=\",round(SD,4)\n",

+    "print\"probable error is (V)=\",round(r1,4)"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 2 - pg 34"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 4,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "when current reading is 5mA\n",

+      "apparent resistance in kilo ohms is 20.0\n",

+      "percentage gross error is 13.33\n",

+      "when current reading is 50mA\n",

+      "apparent resistance in kilo ohms is 2.0\n",

+      "percentage gross error is 1.33\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.2:#APPRABET RESISTANCE AND PERCENTAGE GROSS ERROR\n",

+    "#calculate the APPARENT RESISTANCE AND PERCENTAGE GROSS ERROR\n",

+    "#given\n",

+    "print\"when current reading is 5mA\"\n",

+    "vr=100.;#voltmeter reading\n",

+    "ir=5.;#mA\n",

+    "#calculations and results\n",

+    "rt=vr/(ir);#in kilo ohms\n",

+    "print\"apparent resistance in kilo ohms is\",rt\n",

+    "vm=150.;#range of voltmeter\n",

+    "s=1.;#kilo ohms per volts sensivity\n",

+    "rv=s*vm;#kilo ohms\n",

+    "rx=((rt*rv)/(rv-rt));#kilo ohms\n",

+    "ge=((rx-rt)/rx)*100;#percentage gross error\n",

+    "print\"percentage gross error is\",round(ge,2)\n",

+    "print\"when current reading is 50mA\"\n",

+    "vr=100.;#voltmeter reading\n",

+    "ir1=50.;#mA\n",

+    "rt1=vr/(ir1);#in kilo ohms\n",

+    "print\"apparent resistance in kilo ohms is\",rt1\n",

+    "vm=150.;#range of voltmeter\n",

+    "s=1;#kilo ohms per volts sensivity\n",

+    "rv=s*vm;#kilo ohms\n",

+    "rx1=((rt1*rv)/(rv-rt1));#kilo ohms\n",

+    "ge1=((rx1-rt1)/rx1)*100;#percentage gross error\n",

+    "print\"percentage gross error is\",round(ge1,2)\n",

+    "\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 3 - pg 35"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 5,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "limiting error at 150 V is (%)= 5.0\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.3:#limiting error\n",

+    "#calculate the limiting error\n",

+    "#given\n",

+    "fs=1.5;#full scale in percentage\n",

+    "vr=500.;#voltmeter reading\n",

+    "#calculations\n",

+    "ea=(fs/100)*vr;#volts\n",

+    "le=150;#limiting error voltage\n",

+    "lep=((ea/le)*100);#limiting error\n",

+    "#results\n",

+    "print \"limiting error at 150 V is (%)=\",lep\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 4 - pg 35"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 7,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "arithmetic mean is, (V)= 100.0\n",

+      "average deviation is, (V)= 0.2\n",

+      "standard deviation is, (V)= 0.228\n",

+      "Variance is ,(V)= 0.052\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.4:#ARITHMETIC MEAN,AVERAGE DEVIATION ,STANDARD DEVIATION AND PROBABLE ERROR\n",

+    "#calculate the ARITHMETIC MEAN,AVERAGE DEVIATION ,STANDARD DEVIATION AND PROBABLE ERROR\n",

+    "#given\n",

+    "import math,numpy\n",

+    "T=numpy.array([99.7,99.8,100,100.2,100.3]);#VOLTS\n",

+    "q=numpy.array([T[0],T[1],T[2],T[3],T[4]]);#\n",

+    "#calculations\n",

+    "AM=(q[0]+q[1]+q[2]+q[3]+q[4])/5;#arithematic mean in mm\n",

+    "qb=numpy.zeros(6)\n",

+    "for i in range(0,5):\n",

+    "    qb[i]= T[i]-AM;\n",

+    "\n",

+    "Q= numpy.array([qb[0],qb[1],qb[2],qb[3],qb[4]]);#\n",

+    "AV=(-qb[0]-qb[1]-qb[2]+qb[3]+qb[4])/5;#\n",

+    "SD=math.sqrt(((qb[0]**2)+(qb[1]**2)+(qb[2]**2)+(qb[3]**2)+(qb[4]**2))/5);#standard deviation\n",

+    "V=SD**2;#\n",

+    "#results\n",

+    "print\"arithmetic mean is, (V)=\",AM\n",

+    "print\"average deviation is, (V)=\",AV\n",

+    "print\"standard deviation is, (V)=\",round(SD,3)\n",

+    "print\"Variance is ,(V)=\",V"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 5 - pg 36"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 8,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "power is,(W)= 1344.8\n",

+      "error in power is,(W)= 40.606\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.5:#error\n",

+    "#calculate the error in power\n",

+    "#given\n",

+    "i=8.2;#in amperes\n",

+    "r=20.;#ohms\n",

+    "nd=100.;#divisions\n",

+    "ra=10.;#range in amperes\n",

+    "d=0.5;#divisions\n",

+    "amcr=1.;#ammemeter constant error\n",

+    "crr=-0.2;#construction error\n",

+    "#calculations\n",

+    "p=i**2*r;#watts\n",

+    "rd1=ra/nd;#reading of one division\n",

+    "per=((d*rd1)/i)*100;#possible ameter rwading error\n",

+    "ter=amcr+per;#total ammeter error\n",

+    "ep=(((2*ter)+crr)/nd)*p;#\n",

+    "#results\n",

+    "print \"power is,(W)=\",p\n",

+    "print \"error in power is,(W)=\",round(ep,3)\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 6 - pg 37"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 9,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "arithmetic mean is (V)= 100.0\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.6:#ARITHMETIC MEAN\n",

+    "#calculate the arithmetic mean\n",

+    "#given\n",

+    "import numpy\n",

+    "T=numpy.array([99.7,99.8,99.9,100,100.1,100.2,100.3]);#VOLTS\n",

+    "f=numpy.array([2,8,20,40,21,6,3]);#frequency of occurence\n",

+    "#calculations\n",

+    "qb=numpy.zeros(8)\n",

+    "for i in range (0,7):\n",

+    "    qb[i]=T[i]-T[5];\n",

+    "\n",

+    "prdtc=(qb[0]*f[0])+(qb[1]*f[1])+(qb[2]*f[2])+(qb[3]*f[3])+(qb[4]*f[4])+(qb[5]*f[5])+(qb[6]*f[6])\n",

+    "am=T[5]+(prdtc/100);#arithemetic mean\n",

+    "#results\n",

+    "print \"arithmetic mean is (V)=\",am\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 7 - pg 37"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 11,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "limiting error for power is, (%)= 3.3\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.7:#limiting error\n",

+    "#calculate the limiting error for power\n",

+    "#given\n",

+    "fse=1.;#full scale deflection\n",

+    "vr=150.;#range in volts\n",

+    "v1=100.;#volts\n",

+    "ve=100.;#range in mA\n",

+    "#calculations\n",

+    "ev=(fse/100)*vr;#voltas\n",

+    "le100=((ev)/v1)*100;#in percentage\n",

+    "ee=(fse/100)*ve;#mA\n",

+    "e1=55;#mA\n",

+    "le50=((ee/e1)*100);#in percentage\n",

+    "ler=le100+le50;#\n",

+    "#results\n",

+    "print \"limiting error for power is, (%)=\",round(ler,1)"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 8 - pg 37"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 12,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "volume is,(m^3)= 0.216\n",

+      "percentage error in volume is,(%)= 3.0\n",

+      "error in volume is,(m^3)= 0.00648\n"

+     ]

+    }

+   ],

+   "source": [

+    "#pg 37\n",

+    "#Example 1.8:# error\n",

+    "#calculate the volume, percentage error\n",

+    "#given\n",

+    "fse=1.;#full scale deflection\n",

+    "e=0.60;#meters\n",

+    "#calculations\n",

+    "v=(e)**3;#volume in m^3\n",

+    "ev=3*fse;#error in volume\n",

+    "evv=(ev/100)*v;#\n",

+    "#results\n",

+    "print \"volume is,(m^3)=\",v\n",

+    "print \"percentage error in volume is,(%)=\",ev\n",

+    "print \"error in volume is,(m^3)=\",evv\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 9 - pg 38"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 14,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "current in the circuit is,(A)= 2.375\n",

+      "error in current is,(A)= 0.0356\n",

+      "percentage error in current is,(%)= 1.5\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.9:#error\n",

+    "#calculate the error in circuit\n",

+    "#given\n",

+    "v=95.;#volts\n",

+    "r=40.;#ohms\n",

+    "evv=0.95;#error in voltage\n",

+    "err=-0.2;#error in resistance\n",

+    "#calculations\n",

+    "i=v/r;#amperes\n",

+    "err1=(err/r)*100;#percentage error \n",

+    "evv1=(evv/v)*100;#percentage error\n",

+    "x=evv1-err1;#\n",

+    "ei=(x/100)*i;#\n",

+    "#results\n",

+    "print \"current in the circuit is,(A)=\",i\n",

+    "print \"error in current is,(A)=\",round(ei,4)\n",

+    "print \"percentage error in current is,(%)=\",x"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 10 - pg 38"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 15,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "parralel resistance case\n",

+      "magnitude of resistance in ohms is =  17.391\n",

+      "limiting error in ohms is =  4.348\n",

+      "percentage error (%) =  25.0\n",

+      "series resistance case\n",

+      "magnitude of resistance in ohms is =  170.0\n",

+      "percentage error (%) =  5.0\n",

+      "limiting error in ohms is =  8.5\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.10:#MAGNITUDE AND LIMITING ERROR\n",

+    "#calculate the magnitude of resistance and limiting error\n",

+    "#given\n",

+    "print \"parralel resistance case\"\n",

+    "r1=40.;#ohms\n",

+    "er1=5.;#percentage error\n",

+    "r2=80.;#ohms\n",

+    "er2=5.;#percentage error\n",

+    "r3=50.;#ohms\n",

+    "er3=5.;#percentage error\n",

+    "#calculations\n",

+    "rp=((r1*r2*r3)/(r1*r2+r2*r3+r3*r1));#ohms\n",

+    "Y=(r1*r2+r2*r3+r3*r1);#ohms\n",

+    "ex=er1+er2+er3;#percentage error\n",

+    "ey1=er1+er2;#\n",

+    "ey2=er2+er3;#\n",

+    "ey3=er3+er1;#\n",

+    "y=(((r1*r2*ey1)/Y)+((r2*r3*ey2)/Y)+((r3*r1*ey3)/Y));#error\n",

+    "mer=(y+ex)*rp;#\n",

+    "#results\n",

+    "print \"magnitude of resistance in ohms is = \",round(rp,3)\n",

+    "print \"limiting error in ohms is = \",round(mer/100,3)\n",

+    "print \"percentage error (%) = \",(y+ex)\n",

+    "print \"series resistance case\"\n",

+    "rs=r1+r2+r3;#ohms\n",

+    "er=(((r1/rs)*er1)+((r2/rs)*er2)+((r3/rs)*er3));#\n",

+    "mer1=(er/100)*rs;#ohms\n",

+    "print \"magnitude of resistance in ohms is = \",rs\n",

+    "print \"percentage error (%) = \",er\n",

+    "print \"limiting error in ohms is = \",mer1\n"

+   ]

+  },

+  {

+   "cell_type": "markdown",

+   "metadata": {},

+   "source": [

+    "## Example 11 - pg 39"

+   ]

+  },

+  {

+   "cell_type": "code",

+   "execution_count": 17,

+   "metadata": {

+    "collapsed": false

+   },

+   "outputs": [

+    {

+     "name": "stdout",

+     "output_type": "stream",

+     "text": [

+      "magnitude in ohm =  151.0\n",

+      "percentage error when error in both (PS) and (Q) is positive (%) =  0.5\n",

+      "error in ohms when error in both (PS) and (Q) is positive (ohms) =  0.755\n",

+      "percentage error when error in (PS) is positive and (Q) is negative (%) =  1.5\n",

+      "error in ohms when error in (PS) is positive and (Q) is negative (ohms) =  2.265\n"

+     ]

+    }

+   ],

+   "source": [

+    "#Example 1.11:#MAGNITUDE AND LIMITING ERROR\n",

+    "#calculate the magintude of resistance in ohm and error\n",

+    "#given\n",

+    "r1=50;#ohms\n",

+    "er1=0.5;#percentage error\n",

+    "r2=100;#ohms\n",

+    "er2=0.5;#percentage error\n",

+    "r3=75.5;#ohms\n",

+    "er3=0.5;#percentage error\n",

+    "#calculations\n",

+    "x=((r2/r1)*r3);#ohms\n",

+    "eps=er1+er2;#\t\n",

+    "erpsq=eps-er3;#when error in both (PS) and (Q) is positive\n",

+    "erpsq1=eps+er3;#when error in (PS) is positive and (Q) is negetive\n",

+    "oer1=(erpsq/100)*x;#ohms\n",

+    "oer2=(erpsq1/100)*x;#ohms\n",

+    "#results\n",

+    "print \"magnitude in ohm = \",x\n",

+    "print \"percentage error when error in both (PS) and (Q) is positive (%) = \",erpsq\n",

+    "print \"error in ohms when error in both (PS) and (Q) is positive (ohms) = \",oer1\n",

+    "print \"percentage error when error in (PS) is positive and (Q) is negative (%) = \",erpsq1\n",

+    "print \"error in ohms when error in (PS) is positive and (Q) is negative (ohms) = \",oer2\n"

+   ]

+  }

+ ],

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