{ "metadata": { "name": "", "signature": "sha256:e254c8288fbd2f2cd14434e82e95f71176cc32f312efb578ff8980e82a33844f" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 5:Bridge Measurements" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.1:Pg-101" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# To find deflection caused by the given unbalance\n", "# Modern Electronic Instrumentation And Measurement Techniques\n", "# By Albert D. Helfrick, William D. Cooper\n", "# First Edition Second Impression, 2009\n", "# Dorling Kindersly Pvt. Ltd. India\n", "# Example 5-1 in Page 101\n", "\n", "\n", "# Given data\n", "# Resistances of the 4 arms in ohm\n", "R_1 = 1000.0\n", "R_2 = 100.0\n", "R_3 = 200.0\n", "R_4 = 2005.0\n", "\n", "E = 5 # battery EMF in volt\n", "S_I = 10*(10**-3)/(10**-6) #Current sensitivity in m/A\n", "R_g = 100.0 #Internal resistance of galvanometer in ohm\n", "\n", "#Calculations\n", "\n", "#Calculations are made wrt fig 5-3 in page 103\n", "#Bridge balance occurs if arm BC has a resistance of 2000 ohm. The diagram shows arm BC has as a resistance of 2005 ohm\n", "\n", "#To calculate the current in the galvanometer, the ckt is thevenised wrt terminals B and D.\n", "#The potenttial from B to D, with the galvanometer removed is the Thevenin voltage\n", "\n", "# E_TH = E_AD - E_AB \n", "\n", "E_TH = E * ((R_2/(R_2+R_3)) - (R_1/ (R_1+R_4)))\n", "R_TH = ((R_2 * R_3/(R_2+R_3)) + (R_1 * R_4/ (R_1+R_4)))\n", "\n", "#When the galvanometer is now connected to the output terminals, The current through the galvanometer is\n", "\n", "I_g = E_TH /(R_TH +R_g)\n", "d = I_g * S_I\n", "print \"The deflection of the galvanometer = \",round(d*1000,2),\" mm\"\n", "\n", "#Result\n", "# The deflection of the galvanometer = 33.26 mm \n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The deflection of the galvanometer = 33.26 mm\n" ] } ], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.2:pg-102" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# To check the capability of detecting unbalance\n", "# Modern Electronic Instrumentation And Measurement Techniques\n", "# By Albert D. Helfrick, William D. Cooper\n", "# First Edition Second Impression, 2009\n", "# Dorling Kindersly Pvt. Ltd. India\n", "# Example 5-2 in Page 102\n", "\n", "\n", "\n", "\n", "# Given data\n", "# Resistances of the 4 arms in ohm\n", "R_1 = 1000.0\n", "R_2 = 100.0\n", "R_3 = 200.0\n", "R_4 = 2005\n", "\n", "E = 5 # battery EMF in volt\n", "S_I = 1*(10**-3)/(10**-6) #Current sensitivity in m/A\n", "R_g = 500 #Internal resistance of galvanometer in ohm\n", "\n", "\n", "\n", "\n", "#Calculations\n", "\n", "#Calculations are made wrt fig 5-3 in page 103\n", "#Bridge balance occurs if arm BC has a resistance of 2000 ohm. The diagram shows arm BC has as a resistance of 2005 ohm\n", "\n", "#To calculate the current in the galvanometer, the ckt is thevenised wrt terminals B and D.\n", "#The potenttial from B to D, with the galvanometer removed is the Thevenin voltage\n", "\n", "# E_TH = E_AD - E_AB \n", "\n", "E_TH = E * ((R_2/(R_2+R_3)) - (R_1/ (R_1+R_4)))\n", "R_TH = ((R_2 * R_3/(R_2+R_3)) + (R_1 * R_4/ (R_1+R_4)))\n", "\n", "#When the galvanometer is now connected to the output terminals, The current through the galvanometer is\n", "\n", "I_g = E_TH /(R_TH +R_g)\n", "d = I_g * S_I\n", "print \"The deflection of the galvanometer = \",round(d*1000,2),\" mm\"\n", "print 'Given that galvanometer is capable of detecting a deflection of 1mm'\n", "print 'Hence looking at the result,it can be seen that this galvanometer produces a deflection that can be easily observed'\n", "\n", "#Result\n", "# The deflection of the galvanometer = 2.247 mm \n", "# Given that galvanometer is capable of detecting a deflection of 1mm \n", " \n", "# Hence looking at the result,it can be seen that this galvanometer produces a deflection that can be easily observed \n", " \n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The deflection of the galvanometer = 2.25 mm\n", "Given that galvanometer is capable of detecting a deflection of 1mm\n", "Hence looking at the result,it can be seen that this galvanometer produces a deflection that can be easily observed\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.3:Pg-111" ] }, { "cell_type": "code", "collapsed": false, "input": [ "\n", "\n", "# To find the unknown impedence\n", "# Modern Electronic Instrumentation And Measurement Techniques\n", "# By Albert D. Helfrick, William D. Cooper\n", "# First Edition Second Impression, 2009\n", "# Dorling Kindersly Pvt. Ltd. India\n", "# Example 5-3 in Page 111\n", "\n", "\n", "\n", "\n", "# Given data\n", "# The given polar forms in textbook is represented in rect form\n", "Z_1 = 17.36482 +1j *98.48078\n", "Z_2 = 250\n", "Z_3 = 346.4102 +1j *200\n", "\n", "#Calculations\n", "#The first condition for bridge balance is Z_1*Z_4 = Z_2*Z_3\n", "mod_Z_4 = (abs(Z_2)*abs(Z_3))/abs(Z_1)\n", "\n", "#The second condition for bridge balance requires that sum of the phase angles of opposite arms be equal\n", "theta_Z_4 = math.atan(Z_2.imag)+math.atan(Z_3.imag)-math.atan(Z_1.imag)*180/math.pi\n", "\n", "print \"The impedence of the unknown arm =\",round(mod_Z_4),\" ohm /_ \",round(theta_Z_4),\" deg\\n\"\n", "print \"Here the magnitude of impedence is 1000 and phase angle is 50 in degrees\\n\"\n", "print \"The above value indicates that we are dealing with a capacitive element, possibly consisting of a series combination of a resistor and capacitance\"\n", "#Result\n", "# The impedence of the unknown arm = 1000 ohm /_ -50 deg\n", "# Here the magnitude of impedence is 1000 and phase angle is 50 in degrees\n", "# The above value indicates that we are dealing with a capacitive element, possibly consisting of a series combination of a resistor and capacitance \n", " \n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The impedence of the unknown arm = 1000.0 ohm /_ -88.0 deg\n", "\n", "Here the magnitude of impedence is 1000 and phase angle is 50 in degrees\n", "\n", "The above value indicates that we are dealing with a capacitive element, possibly consisting of a series combination of a resistor and capacitance\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.4:pg-112" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# To find the unknown impedence\n", "# Modern Electronic Instrumentation And Measurement Techniques\n", "# By Albert D. Helfrick, William D. Cooper\n", "# First Edition Second Impression, 2009\n", "# Dorling Kindersly Pvt. Ltd. India\n", "# Example 5-4 in Page 112\n", "\n", "\n", "\n", "\n", "# Given data\n", "# The notations are wrt to the figure 5-10 in page 109\n", "\n", "#Arm AB\n", "R_1 = 450\n", "#Arm BC\n", "R_2 = 300\n", "C = 0.265 *(10**-6)\n", "#Arm DA\n", "R_3 = 200\n", "L = 15.9*(10**-3)\n", "f = 1000\n", "\n", "#Calculations\n", "w = 2*math.pi*f\n", "Z_1 = 450\n", "Z_2 = R_2 - 1j *floor(1/(w*C))\n", "Z_3 = R_3 + 1j*ceil(w*L)\n", "\n", "Z_4 = Z_1*Z_3/Z_2\n", "print \"The impedence of the unknown arm = \",round(imag(Z_4)),\" ohm\\n\"\n", "print \"The result indicates that Z_4 is a pure inductance with an inductive reactance of 150 ohm at a frequency of 1 khz.\\n\"\n", "\n", "L_ans = imag(Z_4)/w\n", "print \"The inductance present in the arm CD = \",round(L_ans*1000,1),\"m H\"\n", "\n", "#Result\n", "# The impedence of the unknown arm = 150i ohm\n", "# The result indicates that Z_4 is a pure inductance with an inductive reactance of 150 ohm at a frequency of 1 khz.\n", "# The inductance present in the arm CD = 23.9m H \n", "\n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The impedence of the unknown arm = 150.0 ohm\n", "\n", "The result indicates that Z_4 is a pure inductance with an inductive reactance of 150 ohm at a frequency of 1 khz.\n", "\n", "The inductance present in the arm CD = 23.9 m H\n" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Ex5.5:pg-119" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# To balance the unbalanced bridge\n", "# Modern Electronic Instrumentation And Measurement Techniques\n", "# By Albert D. Helfrick, William D. Cooper\n", "# First Edition Second Impression, 2009\n", "# Dorling Kindersly Pvt. Ltd. India\n", "# Example 5-5 in Page 119\n", "\n", "\n", "\n", "\n", "# Given data\n", "Z_1 = -1000j\n", "Z_2 = 500\n", "Z_3 = 1000\n", "Z_4 = 100+500j\n", "\n", "# The balance is not possible with this condition as theta_1+theta_4 will be slightly negative than theta_2+theta3\n", "# Balance can be achieved by 2 methods:\n", "print \"First option is to modify Z_1 so that its phase angle is decreased to less than 90deg by placing a resistor in parallel with the capacitor.\"\n", "# The resistance R_1 can be determined by the standard approach\n", "\n", "#Calculations\n", "Y_1 = Z_4/(Z_2*Z_3)\n", "#Also,\n", "# Y_1 = (1/R) + %i/1000\n", "# equating both the equations and solving for R_1\n", "\n", "R_1 = 1/(Y_1-(1j/1000 ))\n", "print \"The value of the resistor R_1 in parallel with capacitor = \",R_1.real,\" ohm\\n\",\n", "\n", "# It should be noted that the addition of R_1 upsets the first balance condition as the magnitude of Z_1 is changed\n", "# Hence the variable R_3 should be adjusted to compensate this effect\n", "\n", "print 'The second option is to modify the phase angle of arm 2 or arm 3 by adding series capacitor'\n", "Z_3_1 = Z_1 *Z_4/Z_2\n", "# substituting for the component values and solving for X_C yeilds\n", "\n", "X_C = abs(1000- Z_3_1)/-1j\n", "print \"The value of the reactance of the capacitor used, X_C = \",X_C.imag,\" ohm\"\n", "\n", "\n", "#In this case the magnitude of the Z_3 is increased so that the first balance condition is changed\n", "#A small adjustment of R_3 is necessary to restore balance\n", "\n", "#Result\n", "# First option is to modify Z_1 so that its phase angle is decreased to less than 90deg by placing a resistor in parallel with the capacitor. \n", "# The value of the resistor R_1 in parallel with capacitor = 5000 ohm\n", " \n", "# The second option is to modify the phase angle of arm 2 or arm 3 by adding series capacitor \n", "# The value of the reactance of the capacitor used, X_C = 200 ohm \n", "\n", "\n", "\n", "\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "First option is to modify Z_1 so that its phase angle is decreased to less than 90deg by placing a resistor in parallel with the capacitor.\n", "The value of the resistor R_1 in parallel with capacitor = 5000.0 ohm\n", "The second option is to modify the phase angle of arm 2 or arm 3 by adding series capacitor\n", "The value of the reactance of the capacitor used, X_C = 200.0 ohm\n" ] } ], "prompt_number": 5 } ], "metadata": {} } ] }