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"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": {}
}
]
}