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