{ "metadata": { "name": "", "signature": "sha256:dcab5285f135b4dffae4292e0eb7017128ede4af1f4e78fe0491e5a728481399" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 5 : Primary Sensing Elements and Transducers" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.1 Page No : 179" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "D = 15.*10**-3;\n", "P = 300.*10**3;\n", "sm = 300.*10**6;\n", "\n", "# Calculations and Results\n", "t = (3*D**2*P/(16*sm))**0.5;\n", "print \" thickness(m) = \", t\n", "P = 150*10**3;\n", "v = 0.28;\n", "E = 200*10**9;\n", "dm = 3*(1-v**2)*D**4*P/(256*E*t**3);\n", "print \" deflection at center for Pressure of 150 kN/m2(m) = \", dm\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " thickness(m) = 0.000205395959064\n", " deflection at center for Pressure of 150 kN/m2(m) = 4.73232289684e-05\n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.2 Page No : 181" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "T = 100.;\n", "G = 80.*10**9;\n", "d = 2.*15*10**-3;\n", "\n", "# Calculations\n", "th = 16*T/(math.pi*G*d**3)\n", "\n", "# Results\n", "print \" angle of twist(rad) = \", th\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " angle of twist(rad) = 0.000235785100877\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.3 Page No : 183" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "E = 110*10**9;\n", "t = 0.073*10**-3;\n", "b = 0.51*10**-3;\n", "l = 370*10**-3;\n", "\n", "# Calculations\n", "th = math.pi/2;\n", "T = (E*b*t**3)*th/(12*l);\n", "\n", "# Results\n", "print \" Controlling torque(Nm) = \", T\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ " Controlling torque(Nm) = 7.72090748389e-06\n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.4 Page No : 185" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "Rnormal = 10000./2;\n", "Rpl = 10000./50;\n", "Rc1 = Rnormal-3850;\n", "\n", "# Calculations and Results\n", "Dnormal = Rc1/Rpl;\n", "print \"Displacement(mm) = \", Dnormal\n", "Rc2 = Rnormal-7560;\n", "Dnormal = Rc2/Rpl;\n", "print \"Displacement(mm) = \", Dnormal\n", "print \"since one lacement is positive and other is negative so two lacements are in the opposite direction\"\n", "Re = 10*1./200;\n", "print \"Resolution (mm) = \", Re\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Displacement(mm) = 5.75\n", "Displacement(mm) = -12.8\n", "since one lacement is positive and other is negative so two lacements are in the opposite direction\n", "Resolution (mm) = 0.05\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.5 Page No : 187" ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "import math \n", "from matplotlib.pyplot import plot\n", "\n", "# Variables\n", "# plot the graph of error versus K\n", "K = [0, 0.25, 0.5, 0.75, 1];\n", "V = [0, -0.174, -0.454, -0.524, 0];\n", "\n", "# Results\n", "plot(K,V)\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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LX8Ji61bo0gXefNOWMQeBFzdbLyQl/oCqroZrroF334Xnn4f99/c6IpH83HorVFbC9Ole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\n", "text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.6 Page No : 189" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "RAB = 125.;\n", "Rtotal = 5000.;\n", "R2 = 75/125.*Rtotal;\n", "R4 = 2500.;\n", "ei = 5.;\n", "\n", "# Calculations\n", "eo = ((R2/Rtotal)-(R4/Rtotal))*ei;\n", "\n", "# Results\n", "print \"output voltage (V) = \", eo\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "output voltage (V) = 0.5\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.7 Page No : 191" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "Rm = 10000.;\n", "Rp = Rm/15.;\n", "R = 600.;\n", "P = 5.;\n", "\n", "# Calculations and Results\n", "ei = (P*R)**0.5;\n", "print \"Maximum excitation voltage (V) = \", ei\n", "S = ei/360;\n", "print \"Sensitivity (V/degree) = \", S\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Maximum excitation voltage (V) = 54.7722557505\n", "Sensitivity (V/degree) = 0.152145154863\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.8 Page No : 193" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "Rwga = 1./400;\n", "\n", "# Calculations\n", "Re = Rwga/5;\n", "\n", "# Results\n", "print \"Resolution (mm) = \", Re\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Resolution (mm) = 0.0005\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.9 Page No : 195" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "mo = 0.8;\n", "sr = 250;\n", "sm = sr/mo;\n", "\n", "# Calculations and Results\n", "R = sm*1;\n", "print \"resolution of 1mm movement\", R\n", "Rq = 300/1000;\n", "print \"resolution required = \", Rq\n", "print \"since the resolution of potentiometer is higher than the resolution required so it is suitable for the application\",\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resolution of 1mm movement 312.5\n", "resolution required = 0\n", "since the resolution of potentiometer is higher than the resolution required so it is suitable for the application\n" ] } ], "prompt_number": 12 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.10 Page No : 197" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculations and Results\n", "Pd = (10.**2)/150;\n", "print \"Power dissipation (W) = \", Pd\n", "th_pot = 80.+Pd*30*10**-3;\n", "PDa = 1-(10*10**-3)*(th_pot-35);\n", "print \"Power dissipation allowed(W) = \", PDa\n", "print \"Since power dissipation is higher than the dissipation allowed so potentiometer is not suitable\"\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Power dissipation (W) = 0.666666666667\n", "Power dissipation allowed(W) = 0.5498\n", "Since power dissipation is higher than the dissipation allowed so potentiometer is not suitable\n" ] } ], "prompt_number": 13 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.11 Page No : 199" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Gf = 4.2;\n", "\n", "# Calculations\n", "v = (Gf-1)/2;\n", "\n", "# Results\n", "print \"Possion s ratio = \", v\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Possion s ratio = 1.6\n" ] } ], "prompt_number": 14 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.12 Page No : 201" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "strain = -5.*10**-6;\n", "Gf = -12.1;\n", "R = 120.;\n", "\n", "# Calculations and Results\n", "dR_nickel = Gf*R*strain;\n", "print \"change in resistance of nickel(ohm) = \", dR_nickel\n", "Gf = 2;\n", "R = 120;\n", "dR_nicrome = Gf*R*strain;\n", "print \"change in resistance of nicrome(ohm) = \", dR_nicrome\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "change in resistance of nickel(ohm) = 0.00726\n", "change in resistance of nicrome(ohm) = -0.0012\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.13 Page No : 203" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "s = 100.*10**6;\n", "E = 200.*10**9;\n", "\n", "# Calculations\n", "strain = s/E;\n", "Gf = 2;\n", "r_perunit = Gf*strain*100;\n", "\n", "# Results\n", "print \"Percentage change in resistance = \", r_perunit\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Percentage change in resistance = 0.1\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.14 Page No : 205" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "b = 0.02;\n", "d = 0.003;\n", "I = (b*d**3)/12;\n", "E = 200*10**9;\n", "x = 12.7*10**-3;\n", "l = 0.25;\n", "F = 3*E*I*x/l**3;\n", "x = 0.15;\n", "M = F*x;\n", "t = 0.003;\n", "\n", "# Calculations\n", "s = (M*t)/(I*2);\n", "strain = s/E;\n", "dR = 0.152;\n", "R = 120;\n", "Gf = (dR/R)/strain;\n", "\n", "# Results\n", "print \"Gauge factor = \", Gf\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Gauge factor = 2.30873918538\n" ] } ], "prompt_number": 17 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.15 Page No : 207" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "dR = 0.013;\n", "R = 240;\n", "l = 0.1;\n", "Gf = 2.2;\n", "\n", "# Calculations and Results\n", "dl = (dR/R)*l/Gf;\n", "print \"change in length(m) = \", dl\n", "strain = dl/l;\n", "E = 207*10**9;\n", "s = E*strain;\n", "A = 4*10**-4;\n", "F = s*A;\n", "print \"Force(N)\", F\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "change in length(m) = 2.46212121212e-06\n", "Force(N) 2038.63636364\n" ] } ], "prompt_number": 18 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.16 Page No : 209" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "th1 = 30.;\n", "th2 = 60.;\n", "th0 = th1+th2/2;\n", "Rth1 = 4.8;\n", "Rth2 = 6.2;\n", "Rth0 = 5.5;\n", "\n", "# Calculations\n", "ath0 = (1/Rth0)*(Rth2-Rth1)/(th2-th1);\n", "\n", "# Results\n", "print \"alpha at o degree(/degree C) = \", ath0\n", "print \"5.5[1+0.0085(th-45)]\",\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "alpha at o degree(/degree C) = 0.00848484848485\n", "5.5[1+0.0085(th-45)]\n" ] } ], "prompt_number": 19 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.17 Page No : 211" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "th1 = 100.;\n", "th2 = 130.;\n", "\n", "# Calculations\n", "th0 = th1+th2/2;\n", "Rth1 = 573.40;\n", "Rth2 = 605.52;\n", "Rth0 = 589.48;\n", "ath0 = (1/Rth0)*(Rth2-Rth1)/(th2-th1);\n", "\n", "# Results\n", "print \"alpha at o degree(/degree C) = \", ath0\n", "print \"Linear approximation is: Rth = 589.48[1+0.00182(th-115)]\",\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "alpha at o degree(/degree C) = 0.00181629006356\n", "Linear approximation is: Rth = 589.48[1+0.00182(th-115)]\n" ] } ], "prompt_number": 20 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.18 Page No : 213" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Rth0 = 100.;\n", "ath0 = 0.00392;\n", "dth = 65.-25;\n", "\n", "# Calculations and Results\n", "R65 = Rth0*(1+ath0*dth);\n", "print \"resistance at 65 degree C(ohm) = \", R65\n", "\n", "th = (((150./100)-1)/ath0)+25;\n", "print \"Temperature (degree C)\", th\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance at 65 degree C(ohm) = 115.68\n", "Temperature (degree C) 152.551020408\n" ] } ], "prompt_number": 22 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.19 Page No : 215" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Rth0 = 10;\n", "ath0 = 0.00393;\n", "dth = 150-20;\n", "\n", "# Calculations\n", "R150 = Rth0*(1+ath0*dth);\n", "\n", "# Results\n", "print \"resistance at 150 degree C(ohm) = \", R150\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance at 150 degree C(ohm) = 15.109\n" ] } ], "prompt_number": 23 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.20 Page No : 217" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "th = 30.;\n", "th0 = 50.;\n", "tc = 120.;\n", "\n", "# Calculations\n", "t = -120*(math.log(1-(th/th0)));\n", "\n", "# Results\n", "print \"time(s) = \", t\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "time(s) = 109.954887825\n" ] } ], "prompt_number": 24 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.21 Page No : 219" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "R25 = 100;\n", "ath = -0.05;\n", "dth = 35-25;\n", "\n", "# Calculations\n", "R35 = R25*(1+ath*dth);\n", "\n", "# Results\n", "print \"resistance at 35 degree C(ohm) = \", R35\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance at 35 degree C(ohm) = 50.0\n" ] } ], "prompt_number": 25 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.22 Page No : 221" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# Variables\n", "Ro = 3980.;\n", "Ta = 273.;\n", "\n", "# Calculations and Results\n", "print \"3980 = a*3980*math.exp(b/273)\",\n", "Rt50 = 794;\n", "Ta50 = 273+50;\n", "print \"794 = a*3980*math.exp(b/323)\",\n", "print \"on solving\",\n", "print \" b = 2843\", \"a = 30*10**-6\"\n", "Ta40 = 273+40;\n", "Rt40 = (30*10**-6)*3980*math.exp(2843./313);\n", "print \"resistance at 40 degree C (ohm)\", Rt40\n", "Rt100 = (30*10**-6)*3980*math.exp(2843./373);\n", "print \"resistance at 100 degree C (ohm)\", Rt100\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "3980 = a*3980*math.exp(b/273) 794 = a*3980*math.exp(b/323) on solving b = 2843 a = 30*10**-6\n", "resistance at 40 degree C (ohm) 1051.3086649\n", "resistance at 100 degree C (ohm) 243.887690913\n" ] } ], "prompt_number": 26 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.23 Page No : 223" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Calculations\n", "th = ((1-1800./2000)/0.05)+70;\n", "dth = th-70;\n", "\n", "# Results\n", "print \"change in temperature (degree C)\", dth\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "change in temperature (degree C) 2.0\n" ] } ], "prompt_number": 27 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.24 Page No : 225" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "C = 500.*10**-12;\n", "R20 = 10000.*(1-0.05*(20-25));\n", "\n", "# Calculations and Results\n", "f20 = 1/(2*math.pi*R20*C);\n", "print \"Frequency of oscillation at 20 degree C (Hz)\", f20\n", "R25 = 10000*(1-0.05*(25-25));\n", "f25 = 1./(2*math.pi*R25*C);\n", "print \"Frequency of oscillation at 25 degree C (Hz)\", f25\n", "R30 = 10000*(1-0.05*(30-25));\n", "f30 = 1./(2*math.pi*R30*C);\n", "print \"Frequency of oscillation at 30 degree C (Hz)\", f30\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Frequency of oscillation at 20 degree C (Hz) 25464.7908947\n", "Frequency of oscillation at 25 degree C (Hz) 31830.9886184\n", "Frequency of oscillation at 30 degree C (Hz) 42441.3181578\n" ] } ], "prompt_number": 28 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.25 Page No : 227" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Calculations and Results\n", "Se_thermocouple = 500-(-72);\n", "print \"Sensitivity of thermocouple (micro V/degree C) = \", Se_thermocouple\n", "Vo = Se_thermocouple*100*10**-6;\n", "print \"maximum output voltage(V) = \", Vo\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Sensitivity of thermocouple (micro V/degree C) = 572\n", "maximum output voltage(V) = 0.0572\n" ] } ], "prompt_number": 29 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.26 Page No : 229" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# calculations and results\n", "ET = 27.07+0.8;\n", "print 'Required e.m.f.(mV)',ET\n", "print \"temperature corresponding to 27.87 mV is 620 degree C\",\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Required e.m.f.(mV) 27.87\n", "temperature corresponding to 27.87 mV is 620 degree C\n" ] } ], "prompt_number": 30 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.27 Page No : 231" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "Rm = 50;\n", "Re = 12;\n", "\n", "# Calculations and Results\n", "E = 33.3*10**-3;\n", "i = 0.1*10**-3;\n", "Rs = (E/i)-Rm-Re;\n", "print \"series resistance (ohm) = \", Rs\n", "Re = 13;\n", "i1 = E/(Rs+Re+Rm);\n", "AE = ((i1-i)/i)*800;\n", "print \"approximate error due to rise in resistance of 1 ohm in Re (degree C) = \", AE\n", "R_change = 50*0.00426*10;\n", "i1 = E/(Rs+Re+Rm+R_change);\n", "AE = ((i1-i)/i)*800;\n", "print \"approximate error due to rise in Temp. of 10 (degree C) = \", AE\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "series resistance (ohm) = 271.0\n", "approximate error due to rise in resistance of 1 ohm in Re (degree C) = -2.39520958084\n", "approximate error due to rise in Temp. of 10 (degree C) = -7.44949870586\n" ] } ], "prompt_number": 31 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.28 Page No : 233" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "E_20 = 0.112*10**-3;# emf at 20degree C\n", "E_900 = 8.446*10**-3;\n", "E_1200 = 11.946*10**-3;\n", "\n", "# Calculations and Results\n", "E1 = E_900-E_20;\n", "E2 = E_1200-E_20;\n", "print \"E1 = 1.08*R1/(R1+2.5+R2) (i)\",\n", "print \"E2 = 1.08*(R1+2.5)/(R1+2.5+R2) (ii)\",\n", "print \"on solving (i) and (ii)\",\n", "R1 = 5.95;\n", "R2 = 762.6;\n", "print \"value of resistance R1 (ohm) = \", R1\n", "print \"value of resistance R2 (ohm) = \", R2\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "E1 = 1.08*R1/(R1+2.5+R2) (i) E2 = 1.08*(R1+2.5)/(R1+2.5+R2) (ii) on solving (i) and (ii) value of resistance R1 (ohm) = 5.95\n", "value of resistance R2 (ohm) = 762.6\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.29 Page No : 235" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Calculations\n", "linearity_percentage = (0.003/1.5)*100;\n", "\n", "# Results\n", "print \"percentage linearity = \", linearity_percentage\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "percentage linearity = 0.2\n" ] } ], "prompt_number": 33 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.30 Page No : 237" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "print \"lacement = 0.5\"\n", "Vo = 2.*10**-3;\n", "Se_LVDT = Vo\n", "print \"lacement \"\n", "print \"senstivity of the LVDT (V/mm)\", Se_LVDT\n", "\n", "# Calculations and Results\n", "Af = 250.;\n", "Se_instrument = Se_LVDT*Af;\n", "print \"senstivity of instrument (V/mm)\", Se_instrument\n", "sd = 5./100;\n", "Vo_min = 50./5;\n", "Re_instrument = 1*1/1000;\n", "print \"resolution of instrument in mm\", Re_instrument\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "lacement = 0.5\n", "lacement \n", "senstivity of the LVDT (V/mm) 0.002\n", "senstivity of instrument (V/mm) 0.5\n", "resolution of instrument in mm 0\n" ] } ], "prompt_number": 34 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.31 Page No : 239" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "b = 0.02;\n", "t = 0.004;\n", "I = (1./12)*b*t**3;\n", "F = 25.;\n", "l = 0.25;\n", "E = 200.*10**9;\n", "\n", "# Calculations and Results\n", "x = (F*l**3)/(3*E*I);\n", "print \"deflection (m)\", x\n", "DpF = x/F;\n", "Se = DpF*0.5*1000;\n", "Re = (10./1000)*(2./10);\n", "F_min = Re/Se;\n", "F_max = 10/Se;\n", "print \"minimum force (N)\", F_min\n", "print \"maximum force (N)\", F_max\n", "print \"\", Se\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "deflection (m) 0.006103515625\n", "minimum force (N) 0.016384\n", "maximum force (N) 81.92\n", " 0.1220703125\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.32 Page No : 241" ] }, { "cell_type": "code", "collapsed": false, "input": [ "print \"permittivity of the air e0 = 8.85*10**-12\"\n", "# Variables\n", "e0 = 8.85*10**-12;\n", "w = 25*10**-3;\n", "\n", "# Calculations\n", "d = 0.25*10**-3;\n", "Se = -4*e0*w/d;\n", "\n", "# Results\n", "print \"sensitivity of the transducer (F/m) = \", Se\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "permittivity of the air e0 = 8.85*10**-12\n", "sensitivity of the transducer (F/m) = -3.54e-09\n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.33 Page No : 243" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "C1 = 370*10**-12;\n", "d1 = 3.5*10**-3;\n", "\n", "# Calculations\n", "d2 = 2.9*10**-3;\n", "C2 = C1*d1/d2;\n", "\n", "# Results\n", "print \"the value of the capacitance afte the application of pressure (F) = \", C2\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "the value of the capacitance afte the application of pressure (F) = 4.46551724138e-10\n" ] } ], "prompt_number": 38 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.34 Page No : 245" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "fo1 = 100.*10**3;\n", "d1 = 4.;\n", "d2 = 3.7;\n", "\n", "# Calculations\n", "fo2 = ((d2/d1)**0.5)*fo1;\n", "dfo = fo1-fo2;\n", "\n", "# Results\n", "print \"change in frequency of the oscillator (Hz)\", dfo\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "change in frequency of the oscillator (Hz) 3823.07969164\n" ] } ], "prompt_number": 39 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.35 Page No : 247" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "L_air = (3.1-3)/2;\n", "D_stress = 100/L_air;\n", "e0 = 8.85*10**-12;\n", "l = 20.*10**-3;\n", "D2 = 3.1;\n", "D1 = 3;\n", "\n", "# Calculations and Results\n", "C = (2*math.pi)*e0*l/(math.log(D2/D1));\n", "print \"capacitance(F) = \", C\n", "l = (20*10**-3)-(2*10**-3);\n", "C_new = (2*math.pi)*e0*l/(math.log(D2/D1));\n", "C_change = C-C_new;\n", "print \"change in capacitance(F) = \", C_change\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "capacitance(F) = 3.39167370734e-11\n", "change in capacitance(F) = 3.39167370734e-12\n" ] } ], "prompt_number": 40 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.36 Page No : 249" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "M = 0.95;\n", "w = 2.*math.pi*20;\n", "\n", "# Calculations and Results\n", "tc = (1/w)*((M**2)/(1-M**2))**0.5;\n", "print \"time constant (s)\", tc\n", "ph = ((math.pi/2)-(math.atan(w*tc)))*(180/math.pi);\n", "print \"phase shift(deg)\", ph\n", "C = (8.85*10**-12*300*10**-6)/(0.125*10**-3);\n", "R = tc/C;\n", "print \"series resistance (ohm)\", R\n", "M = 1./(1+(1./(2*math.pi*5*tc)**2))**0.5;\n", "print \"amplitude ratio = \", M\n", "Eb = 100;\n", "x = 0.125*10**-3;\n", "Vs = Eb/x;\n", "print \"voltage sensitivity (V/m)\", Vs\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "time constant (s) 0.0242109278459\n", "phase shift(deg) 18.1948723388\n", "series resistance (ohm) 1139874192.37\n", "amplitude ratio = 0.605390338483\n", "voltage sensitivity (V/m) 800000.0\n" ] } ], "prompt_number": 41 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.37 Page No : 251" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "e0 = 8.85*10**-12;\n", "A = 500*10**-6;\n", "d = 0.2*10**-3;\n", "C = e0*A/d;\n", "d1 = 0.18*10**-3;\n", "C_new = e0*A/d1;\n", "\n", "# Calculations and Results\n", "C_change = C_new-C;\n", "Ratio = (C_change/C)/(0.02/0.2);\n", "print \"ratio of per unit change of capacitance to per unit change of diaplacement\", Ratio\n", "d1 = 0.19*10**-3;\n", "e1 = 1;\n", "d2 = 0.01*10**-3;\n", "e2 = 8;\n", "C = (e0*A)/((d1/e1)+(d2/e2));\n", "d1_new = 0.17*10**-3;\n", "C_new = (e0*A)/((d1_new/e1)+(d2/e2));\n", "C_change = C_new-C;\n", "Ratio = (C_change/C)/(0.02/0.2);\n", "print \"ratio of per unit change of capacitance to per unit change of diaplacement\", Ratio\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "ratio of per unit change of capacitance to per unit change of diaplacement 1.11111111111\n", "ratio of per unit change of capacitance to per unit change of diaplacement 1.16788321168\n" ] } ], "prompt_number": 42 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.40 Page No : 253" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "g = 0.055;\n", "t = 2*10**-3;\n", "P = 1.5*10**6;\n", "\n", "# Calculations and Results\n", "Eo = g*t*P;\n", "print \"output voltage(V) = \", Eo\n", "e = 40.6*10**-12;\n", "d = e*g;\n", "print \"charge sensitivity (C/N) = \", d\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "output voltage(V) = 165.0\n", "charge sensitivity (C/N) = 2.233e-12\n" ] } ], "prompt_number": 43 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.41 Page No : 255" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "g = 0.055;\n", "t = 1.5*10**-3;\n", "Eo = 100;\n", "\n", "# Calculations\n", "P = Eo/(g*t);\n", "A = 25.*10**-6;\n", "F = P*A;\n", "\n", "# Results\n", "print \"Force(N) = \", F\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Force(N) = 30.303030303\n" ] } ], "prompt_number": 44 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.42 Page No : 257" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "A = 25.*10**-6;\n", "F = 5.;\n", "P = F/A;\n", "d = 150*10**-12;\n", "e = 12.5*10**-9;\n", "g = d/(e);\n", "t = 1.25*10**-3;\n", "\n", "# Calculations\n", "Eo = (g*t*P);\n", "strain = P/(12*10**6);\n", "Q = d*F;\n", "C = Q/Eo;\n", "\n", "# Results\n", "print \"strain = \", strain\n", "print \"charge(C) = \", Q\n", "print \"capacitance(F) = \", C\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "strain = 0.0166666666667\n", "charge(C) = 7.5e-10\n", "capacitance(F) = 2.5e-10\n" ] } ], "prompt_number": 45 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.43 Page No : 259" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "d = 2.*10**-12;\n", "t = 1.*10**-3;\n", "Fmax = 0.01;\n", "e0 = 8.85*10**-12;\n", "er = 5.;\n", "\n", "# Calculations and Results\n", "A = 100*10**-6;\n", "Eo_peak_to_peak = 2*d*t*Fmax/(e0*er*A);\n", "print \"peak voltage swing under open conditions\", Eo_peak_to_peak\n", "Rl = 100*10**6;\n", "Cl = 20*10**-12;\n", "d1 = 1*10**-3;\n", "Cp = e0*er*A/d1;\n", "C = Cp+Cl;\n", "w = 1000;\n", "m = (w*Cp*Rl/(1+(w*C*Rl)**2)**0.5);\n", "El_peak_to_peak = (2*d*t*Fmax/(e0*er*A))*m;\n", "\n", "print \"peak voltage swing under loaded conditions\", El_peak_to_peak\n", "E = 90*10**9;\n", "dt = 2*Fmax*t/(A*E);\n", "print \"maximum change in crystal thickness (m)\", dt\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "peak voltage swing under open conditions 0.0090395480226\n", "peak voltage swing under loaded conditions 0.00151556405344\n", "maximum change in crystal thickness (m) 2.22222222222e-12\n" ] } ], "prompt_number": 47 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.44 Page No : 261" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "M = 0.95;\n", "tc = 1.5*10**-3;\n", "\n", "# Calculations and Results\n", "w = (1/tc)*((M**2)/(1-M**2))**0.5;\n", "print \"minimum frequency (rad/s)\", w\n", "ph = ((math.pi/2)-(math.atan(w*tc)))*(180/math.pi);\n", "print \"phase shift(deg)\", ph\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "minimum frequency (rad/s) 2028.2899482\n", "phase shift(deg) 18.1948723388\n" ] } ], "prompt_number": 49 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.45 Page No : 263" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "Kq = 40.*10**-3;\n", "Cp = 1000.*10**-12;\n", "\n", "# Calculations and Results\n", "K = Kq/Cp;\n", "print \"sensitivity of the transducer(V/m)\", K\n", "Cc = 300*10**-12;\n", "Ca = 50*10**-12;\n", "C = Cp+Cc+Ca;\n", "Hf = Kq/C;\n", "print \"high frequency sensitivity (V/m)\", Hf\n", "R = 1*10**6;\n", "tc = R*C;\n", "M = 0.95;\n", "w = (1/tc)*((M**2)/(1-M**2))**0.5;\n", "f = w/(2*math.pi);\n", "print \"minimum frequency (s)\", w\n", "print \"now f = 10Hz\",\n", "f = 10;\n", "w = 2*math.pi*f;\n", "tc = (1/w)*((M**2)/(1-M**2))**0.5;\n", "C_new = tc/R;\n", "Ce = C_new-C;\n", "print \"external shunt capacitance(F)\", Ce\n", "Hf_new = Kq/C_new;\n", "print \"new value of high frequency sensitivity (V/m)\", Hf_new\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "sensitivity of the transducer(V/m) 40000000.0\n", "high frequency sensitivity (V/m) 29629629.6296\n", "minimum frequency (s) 2253.655498\n", "now f = 10Hz external shunt capacitance(F) 4.70718556919e-08\n", "new value of high frequency sensitivity (V/m) 826073.256145\n" ] } ], "prompt_number": 50 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.46 Page No : 265" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "#\n", "\n", "# Variables\n", "R = 10.**6;\n", "C = 2500.*10**-12;\n", "tc = R*C;\n", "t = 2.*10**-3;\n", "d = 100.*10**-12;\n", "\n", "# Calculations and Results\n", "F = 0.1;\n", "el = 10.**3*(d*F*(math.exp(-t/tc))/C);\n", "print \"voltage just before t = 2ms (mV)\", el\n", "el_after = 10.**3*(d*F*(math.exp(-t/tc)-1)/C);\n", "print \"voltage just after t = 2ms (mV)\", el_after\n", "print \"when t = 10ms\",\n", "t = 10.*10**-3;\n", "T = 2.*10\n", "e_10 = 10.**3*(d*F*(math.exp((-T/tc)-1))*(math.exp(-(t-T))/tc)/C)\n", "print \"output voltage 10 ms after the application of impulse(mV) \", e_10\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "voltage just before t = 2ms (mV) 1.79731585647\n", "voltage just after t = 2ms (mV) -2.20268414353\n", "when t = 10ms output voltage 10 ms after the application of impulse(mV) 0.0\n" ] } ], "prompt_number": 55 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.47 Page No : 267" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "# to prove time constant should be approximately 20T to keep undershoot within 5%\n", "# Variables\n", "print \"Let T = 1\",\n", "T = 1.;\n", "el = 0.95;\n", "\n", "# Calculations\n", "tc = -T/math.log(el);\n", "\n", "# Results\n", "print \"time constant\", tc\n", "print \"as T = 1 so time constant should be approximately equal to 20T\",\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Let T = 1 time constant 19.4957257462\n", "as T = 1 so time constant should be approximately equal to 20T\n" ] } ], "prompt_number": 56 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.48 Page No : 269" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Variables\n", "Kh = -1*10**-6;\n", "I = 3;\n", "B = 0.5;\n", "\n", "# Calculations\n", "t = 2.*10**-3;\n", "Eh = Kh*I*B/t;\n", "\n", "# Results\n", "print \"output voltage (V)\", Eh\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "output voltage (V) -0.00075\n" ] } ], "prompt_number": 57 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.49 Page No : 271" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Calculations\n", "Th_wavelength = 1.24*10**-6/1.8\n", "\n", "# Results\n", "print \"Threshold wavelength (m)\", Th_wavelength\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Threshold wavelength (m) 6.88888888889e-07\n" ] } ], "prompt_number": 58 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.50 Page No : 273" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "# Variables\n", "E_imparted = (1.24*10**-6)/(0.2537*10**-6);\n", "B_energy = E_imparted-4.30;\n", "em_ratio = 0.176*10**12;\n", "\n", "# Calculations\n", "v = (2*B_energy*em_ratio)**0.5;\n", "\n", "# Results\n", "print \"maximum velocity of emitted photo electrons (m/s)\", v\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "maximum velocity of emitted photo electrons (m/s) 454815.603242\n" ] } ], "prompt_number": 59 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.51 Page No : 275" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "\n", "# Variables\n", "Ri = 30;\n", "Rf = 100;\n", "t = 10.;\n", "tc = 72.;\n", "\n", "# Calculations\n", "Rt = Ri+(Rf-Ri)*(1-math.exp(-t/tc));\n", "\n", "# Results\n", "print \"resistance of the cell (K ohm)\", Rt\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "resistance of the cell (K ohm) 39.0772691917\n" ] } ], "prompt_number": 60 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.52 Page No : 277" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Calculations and Results\n", "I_power = 250*0.2*10**-6;\n", "print \"incident power (W)\", I_power\n", "\n", "Rl = 10.*10**3;\n", "C = 2.*10**-12;\n", "fc = 1./(2*math.pi*Rl*C);\n", "print \"cut off frequency (Hz)\", fc\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "incident power (W) 5e-05\n", "cut off frequency (Hz) 7957747.15459\n" ] } ], "prompt_number": 61 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.53 Page No : 279" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "I = 2.2*10**-3;\n", "Eo = 0.33;\n", "Rl = 100.;\n", "\n", "# Calculations and Results\n", "Ri = (Eo/I)-100;\n", "print \"internal resistance of cell (ohm)\", Ri\n", "Vo = 0.33*(math.log(25)/math.log(10));\n", "print \"open circuit voltage for a radiant incidence of 25 W/m2 (V) = \", Vo\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "internal resistance of cell (ohm) 50.0\n", "open circuit voltage for a radiant incidence of 25 W/m2 (V) = 0.461320202862\n" ] } ], "prompt_number": 62 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 5.54 Page No : 281" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# Variables\n", "A = 1935*10**-6;\n", "r = 0.914;\n", "S_angle = A/r**2;\n", "I = 180.;\n", "\n", "# Calculations\n", "L_flux = I*S_angle;\n", "\n", "# Results\n", "print \"lumnious flux = \", L_flux\n", "print \"Corresponding to lumnious flux o.417 lm and a load resistance of 800 ohm the current is 120 micro Ampere\",\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "lumnious flux = 0.416928019765\n", "Corresponding to lumnious flux o.417 lm and a load resistance of 800 ohm the current is 120 micro Ampere\n" ] } ], "prompt_number": 63 } ], "metadata": {} } ] }