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+{
+ "metadata": {
+  "name": "Chapter_8"
+ }, 
+ "nbformat": 2, 
+ "worksheets": [
+  {
+   "cells": [
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h1>Chapter 8:Fundamentals of measuring instruments <h1>"
+     ]
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.1, Page Number: 507<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''Flux density calculation'''", 
+      "", 
+      "#variable declaration", 
+      "fi=10.0*10**-6        # fi-flux", 
+      "inch=2.54*10**-2      # length", 
+      "A=inch**2             # area", 
+      "", 
+      "#calculation", 
+      "B =fi/A", 
+      "", 
+      "#Result", 
+      "print('Flux Density B= %.1f mT'%(B*1000))"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "Flux Density B= 15.5 mT"
+       ]
+      }
+     ], 
+     "prompt_number": 1
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.2, Page Number: 508<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''Power Dissipation and accuracy of result'''", 
+      "", 
+      "#variable Declaration", 
+      "i=10*10**-3                  # current in A", 
+      "R=1000.0                     # resistance in ohm", 
+      "P=(i**2)*R                   # Power", 
+      "err_R=10.0                   # Error in Resistance measurement", 
+      "err_I=(2.0/100)*25*100/10    # Error in current measurement", 
+      "", 
+      "#calculation", 
+      "err_I2=2*err_I", 
+      "err_p=err_I2+err_R", 
+      "", 
+      "#Result", 
+      "print('%% error in I^2 = \u00b1 %d%%\\n%% error in Power = \u00b1 %d%%'%(err_I2,err_p))"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "% error in I^2 = \u00b1 10%", 
+        "% error in Power = \u00b1 20%"
+       ]
+      }
+     ], 
+     "prompt_number": 2
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.3, Page Number: 508<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''max and min levels of input supply current'''", 
+      "", 
+      "#variable Declaration", 
+      "i1=37.0                        # current in branch 1 ", 
+      "i2=42.0                        # current in branch 2", 
+      "i3=13.0                        # current in branch 3", 
+      "i4=6.7                         # current in branch 4", 
+      "", 
+      "#Calculation", 
+      "Imax=(i1+i2)+(i1+i2)*(3.0/100)+(i3+i4)+(i3+i4)*(1.0/100)", 
+      "Imin=(i1+i2)-(i1+i2)*(3.0/100)+(i3+i4)-(i3+i4)*(1.0/100)", 
+      "", 
+      "#result", 
+      "print('Maximum level of total supply current = %.3f mA'%Imax)", 
+      "print('\\nMinimum level of total supply current = %.3f mA'%Imin)"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "Maximum level of total supply current = 101.267 mA", 
+        "", 
+        "Minimum level of total supply current = 96.133 mA"
+       ]
+      }
+     ], 
+     "prompt_number": 3
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.4, Page Number:508<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''Time constant for thermometer'''", 
+      "", 
+      "import math", 
+      "", 
+      "#(a)", 
+      "", 
+      "#variable declaration", 
+      "T=200.0                   # intermediate temperature ", 
+      "T0=300.0                  # final temperature ", 
+      "Ti=70.0                   # initial temperature ", 
+      "t=3.0                     # time in seconds ", 
+      "", 
+      "#calculation", 
+      "x=(T-T0)/(Ti-T0)", 
+      "tow=-t/math.log(x)", 
+      "", 
+      "#result", 
+      "print('(a)\\nTime constant  tow=%.1f s'%tow)", 
+      "", 
+      "", 
+      "#(b)", 
+      "", 
+      "#variable declaration", 
+      "t1=5.0                    # time in seconds ", 
+      "#calculation", 
+      "T5=T0+((Ti-T0)*math.e**(-t1/tow))", 
+      "", 
+      "#result", 
+      "print('\\n(b)\\nTemperature after 5 seconds T5 = %.2f\u00b0C'%T5)"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "(a)", 
+        "Time constant  tow=3.6 s", 
+        "", 
+        "(b)", 
+        "Temperature after 5 seconds T5 = 242.61\u00b0C"
+       ]
+      }
+     ], 
+     "prompt_number": 4
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.5, Page Number:<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''Error calculation of second order instrument'''", 
+      "", 
+      "import math", 
+      "", 
+      "#variable declaration", 
+      "w=9.0              # excitation frequency", 
+      "wn=6.0             # natural frequency", 
+      "dr=0.6             # damping ratio", 
+      "", 
+      "#calculations", 
+      "", 
+      "x=w/wn", 
+      "Ar=1/math.sqrt(((1-(x)**2)**2)+(2*dr*x)**2)", 
+      "err=(1-Ar)*100", 
+      "", 
+      "#Result", 
+      "print('A=%.3f'%Ar)", 
+      "print('\\nError = %.2f%%'%err)"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "A=0.456", 
+        "", 
+        "Error = 54.37%"
+       ]
+      }
+     ], 
+     "prompt_number": 5
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.6, PAge Number: 510<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''Output of first order instrument for unit step input'''", 
+      "", 
+      "#variable Declaration", 
+      "t=2.0                  # output  to be calculated after t seconds", 
+      "", 
+      "#calculation", 
+      "y=1-math.e**(-(t-1.5)/0.5)", 
+      "", 
+      "#result", 
+      "print('y(t)at t=2 will be y(t)=%.3f'%y)"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "y(t)at t=2 will be y(t)=0.632"
+       ]
+      }
+     ], 
+     "prompt_number": 6
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.7, Page Number: 510<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''Statistic of Temperature readings'''", 
+      "", 
+      "import math", 
+      "", 
+      "#variable declaration", 
+      "", 
+      "#Temperature Readings", 
+      "x1=98.5                     # Reading 1", 
+      "x2=99.0                     # Reading 2", 
+      "x3=99.5                     # Reading 3 ", 
+      "x4=100.0                    # Reading 4", 
+      "x5=100.5                    # Reading 5", 
+      "x6=101.0                    # Reading 6", 
+      "x7=101.5                    # Reading 7", 
+      "# Frequency", 
+      "f1=4.0                      # Reading 1", 
+      "f2=13.0                     # Reading 2", 
+      "f3=19.0                     # Reading 3", 
+      "f4=35.0                     # Reading 4", 
+      "f5=17.0                     # Reading 5", 
+      "f6=10.0                     # Reading 6", 
+      "f7=2.0                      # Reading 7", 
+      "", 
+      "#(i) Arithmatic Mean", 
+      "", 
+      "#calculation", 
+      "x_bar=((x1*f1)+(x2*f2)+(x3*f3)+(x4*f4)+(x5*f5)+(x6*f6)+(x7*f7))/(f1+f2+f3+f4+f5+f6+f7)", 
+      "", 
+      "#result", 
+      "print('(i)\\n\\tArithmatic Mean = %.2f\u00b0C'%x_bar)", 
+      "", 
+      "#(ii) Average Deviation", 
+      "", 
+      "#calculation", 
+      "D=(abs(x1-x_bar)*f1)+(abs(x2-x_bar)*f2)+(abs(x3-x_bar)*f3)+(abs(x4-x_bar)*f4)", 
+      "D=D+(abs(x5-x_bar)*f5)+(abs(x6-x_bar)*f6)+(abs(x7-x_bar)*f7)", 
+      "D=D/(f1+f2+f3+f4+f5+f6+f7)", 
+      "", 
+      "#result", 
+      "print('\\n(ii)\\n\\tAverage Deviation =%.4f\u00b0C'%D)", 
+      "", 
+      "#Standard deviation", 
+      "", 
+      "#Calculation", 
+      "sigma=((x1-x_bar)**2*f1)+((x2-x_bar)**2*f2)+((x3-x_bar)**2*f3)+((x4-x_bar)**2*f4)", 
+      "sigma=sigma+((x5-x_bar)**2*f5)+((x6-x_bar)**2*f6)+((x7-x_bar)**2*f7)", 
+      "sigma=math.sqrt(sigma)", 
+      "sigma=sigma/math.sqrt(f1+f2+f3+f4+f5+f6+f7)", 
+      "", 
+      "#result", 
+      "print('\\n(iii)\\n\\tStandard deviation = %.3f\u00b0C'%sigma)", 
+      "", 
+      "#variance", 
+      "", 
+      "#result", 
+      "print('\\n(iv)\\n\\tVariance = %.4f\u00b0C'%(sigma**2))", 
+      "", 
+      "#Probable Error", 
+      "", 
+      "#result", 
+      "print('\\n(v)\\n\\tProbable Error= %.4f\u00b0C'%(0.6745*sigma))"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "(i)", 
+        "\tArithmatic Mean = 99.93\u00b0C", 
+        "", 
+        "(ii)", 
+        "\tAverage Deviation =0.5196\u00b0C", 
+        "", 
+        "(iii)", 
+        "\tStandard deviation = 0.671\u00b0C", 
+        "", 
+        "(iv)", 
+        "\tVariance = 0.4501\u00b0C", 
+        "", 
+        "(v)", 
+        "\tProbable Error= 0.4525\u00b0C"
+       ]
+      }
+     ], 
+     "prompt_number": 7
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.8, Page Number: 511<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''Calculation of damping coefficient and natural frequency for 2nd order instrument'''", 
+      "", 
+      "import math", 
+      "", 
+      "#variable Declaration", 
+      "wn=math.sqrt(3.0)             # natural frequency of osscilation", 
+      "", 
+      "#Calculation", 
+      "x=3.2/(2*wn)", 
+      "", 
+      "#Result", 
+      "print('Damping coefficient = %.3f\\nNatural frequency of Oscillation = %.3f'%(x,wn))"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "Damping coefficient = 0.924", 
+        "Natural frequency of Oscillation = 1.732"
+       ]
+      }
+     ], 
+     "prompt_number": 8
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.9, Page Number: 512<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''calculation of Amplitude inaccuracy and phase shift from transfer function'''", 
+      "", 
+      "import math", 
+      "#variable declaration", 
+      "w=100.0                   # natural frequency of osscilation", 
+      "", 
+      "#calculation", 
+      "fi=-math.atan(0.1*w)-math.atan(0.5*w)", 
+      "A=1/(math.sqrt(1+(0.1*w)**2)*(math.sqrt(1+(0.5*w)**2)))", 
+      "A=1*1000.0/math.ceil(1000*A)", 
+      "err=(1-1.0/A)*100", 
+      "", 
+      "#Result", 
+      "print('A=K/%d\\n%% error = %.1f%%\\nfi = %.2f\u00b0'%(A,err,fi*180/math.pi))"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "A=K/500", 
+        "% error = 99.8%", 
+        "fi = -173.14\u00b0"
+       ]
+      }
+     ], 
+     "prompt_number": 9
+    }, 
+    {
+     "cell_type": "markdown", 
+     "source": [
+      "<h3>Example 8.10, Page Number: 512<h3>"
+     ]
+    }, 
+    {
+     "cell_type": "code", 
+     "collapsed": false, 
+     "input": [
+      "'''temperature and altitude calculation from first order thermometer placed in balloon'''", 
+      "", 
+      "#calculations", 
+      "R=0.15*10/50            # Temperature gradient", 
+      "K=1.0                   # constant", 
+      "tow=15.0                # time constant ", 
+      "", 
+      "#Calculations", 
+      "deg=K*R*tow", 
+      "", 
+      "#(i)", 
+      "a=15-deg", 
+      "", 
+      "#(ii)", 
+      "alt_red=deg*50.0/0.15", 
+      "h=5000-alt_red", 
+      "", 
+      "#result", 
+      "print('(i)The actual temperature when instrument reads 15\u00b0C is %.2f\u00b0C'%a)", 
+      "print('\\n The true temperature at 5000 metres = %.2f '%a)", 
+      "print('\\n(ii)\\nThe true altitude at which 15\u00b0C occurs is %d metres'%h)"
+     ], 
+     "language": "python", 
+     "outputs": [
+      {
+       "output_type": "stream", 
+       "stream": "stdout", 
+       "text": [
+        "(i)The actual temperature when instrument reads 15\u00b0C is 14.55\u00b0C", 
+        "", 
+        " The true temperature at 5000 metres = 14.55 ", 
+        "", 
+        "(ii)", 
+        "The true altitude at which 15\u00b0C occurs is 4850 metres"
+       ]
+      }
+     ], 
+     "prompt_number": 10
+    }
+   ]
+  }
+ ]
+}
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