{ "metadata": { "name": "", "signature": "sha256:bba21646340635cd25e22fb5f80c8550eb87632b564d8cf0b5f47b826da1d6e4" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter 2 : Forces in a Electromagnetic System" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.1 Page No : 5" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "# GIVEN DATA\n", "A = 0.0001; # The Cross-sectional area of core in metre-square \n", "Mo = 4*math.pi*(10)**(-7); # Permeability of air in Henre/metre\n", "Mr = 1000; # Relative permeability of core\n", "N1 = 10;N2=20;N3=10; # Number of turns\n", "I1 = 1.0;I2=0.5;I3=1.5; # Currents in Amphere\n", "d = 2.5; # Dimension of inner window in centimetre\n", "w = 1.0; # Each limb wide in centimeter\n", "\n", "\n", "# CALCULATIONS\n", "F = (N1*I1)+(N2*I2)-(N3*I3); # MMF in Amphere-turns (minus because third coil produces the flux in opposite direction to that of other to coils)\n", "L = ((d*4)+(I2*2*4))*10**-2; # Length of the Magnetic path in metre (4-is sides of the windows)(2-Going and returning of current I2)\n", "R = L/(Mr*Mo*A); # Relucmath.tance of the Magnetic path in MKS unit of Relucmath.tance\n", "phi = (F*10**3)/R; # Flux in milli-Weber\n", "B = phi/A; # Flux Density in Weber/metre Square\n", "H = F/L; # Magnetic Field Intensity in Amphere-turns/Metre\n", "\n", "\n", "# DISPLAY RESULTS\n", "\n", "print (\"EXAMPLE : 2.1 : SOLUTION :-\") ;\n", "print \" a) Flux in the core, phi = %.6f mWb \"%(phi);\n", "print \" b) Flux Density in the core, B = %.2f Wb/metre square \"%(B);\n", "print \" c) Magnetic Field Intensity in the core, H = %.2f At/m \"%(H);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "EXAMPLE : 2.1 : SOLUTION :-\n", " a) Flux in the core, phi = 0.004488 mWb \n", " b) Flux Density in the core, B = 44.88 Wb/metre square \n", " c) Magnetic Field Intensity in the core, H = 35.71 At/m \n" ] } ], "prompt_number": 1 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.2 Page No : 9" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "# GIVEN DATA\n", "\n", "N = 100; # Number of turns\n", "La = 0.3; # Mean arc length of material \"a\" is a Nickel-iron alloy in Metre\n", "Lb = 0.2; # Mean arc length of material \"b\" is a Steel in Metre\n", "Lc = 0.1; # Mean arc length of material \"c\" is a Cast Steel in Metre\n", "a = 0.001; # Area of the all Materials \"a,b,c\" in Metre-Square\n", "phi = 6*10**-4; # Magnetic Flux in Weber\n", "mue_0 = 4*math.pi*10** -7; # Permeability of the air in Henry/Meter\n", "\n", "\n", "# CALCULATIONS\n", "\n", "B = phi/a; # Flux Density in Telsa (Here Flux Density same for all the Materials \"a,b,c\" because Area of Cross Section is Same)\n", "Ha = 10; # Fileld Intensity in Amphere-Turn/Meter Correspounding to Flux density (B) of material \"a\" obtained from the Smath.degrees(math.atanard B-H curve\n", "Hb = 77; # Fileld Intensity in Amphere-Turn/Meter Correspounding to Flux density (B) of material \"b\" obtained from the Smath.degrees(math.atanard B-H curve\n", "Hc = 270; # Fileld Intensity in Amphere-Turn/Meter Correspounding to Flux density (B) of material \"c\" obtained from the Smath.degrees(math.atanard B-H curve\n", "F = (Ha*La)+(Hb*Lb)+(Hc*Lc); # The Total MMF Required in Amphere-Turns\n", "I = F/N; # Current flowing through the Coil in Amphere\n", "mue_r_a = B/(Ha*mue_0); # Relatative permeability of the Material \"a\"\n", "mue_r_b = B/(Hb*mue_0); # Relatative permeability of the Material \"a\"\n", "mue_r_c = B/(Hc*mue_0); # Relatative permeability of the Material \"a\"\n", "Ra = (Ha*La)/phi; # Relucatnce of the Material \"a\" in MKS unit\n", "Rb = (Hb*Lb)/phi; # Relucatnce of the Material \"b\" in MKS unit\n", "Rc = (Hc*Lc)/phi; # Relucatnce of the Material \"c\" in MKS unit\n", "L = (N*phi)/I; # Inducmath.tance of the Coil in Henry\n", "\n", "\n", "# DISPLAY RESULTS\n", "print (\"EXAMPLE : 2.2 : SOLUTION :-\") ;\n", "print \" a) The Total MMF , F = %.1f At \"%(F);\n", "print \" b) Current flowing through the Coil , I = %.3f A \"%(I);\n", "print \" c.1) Relatative permeability of the Material a, mue_r_a = %.f \"%(mue_r_a);\n", "print \" c.2) Relatative permeability of the Material b, mue_r_b = %.f \"%(mue_r_b);\n", "print \" c.3) Relatative permeability of the Material c, mue_r_c = %.f \"%(mue_r_c);\n", "print \" c.4) Relucatnce of the Material a, Ra= %.f MKS unit \"%(Ra);\n", "print \" c.5) Relucatnce of the Material b, Rb= %.1f MKS unit \"%(Rb);\n", "print \" c.6) Relucatnce of the Material c, Rc= %.f MKS unit \"%(Rc);\n", "print \" d) Inductance of the Coil , L = %.4f H \"%(L);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "EXAMPLE : 2.2 : SOLUTION :-\n", " a) The Total MMF , F = 45.4 At \n", " b) Current flowing through the Coil , I = 0.454 A \n", " c.1) Relatative permeability of the Material a, mue_r_a = 47746 \n", " c.2) Relatative permeability of the Material b, mue_r_b = 6201 \n", " c.3) Relatative permeability of the Material c, mue_r_c = 1768 \n", " c.4) Relucatnce of the Material a, Ra= 5000 MKS unit \n", " c.5) Relucatnce of the Material b, Rb= 25666.7 MKS unit \n", " c.6) Relucatnce of the Material c, Rc= 45000 MKS unit \n", " d) Inductance of the Coil , L = 0.1322 H \n" ] } ], "prompt_number": 3 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.3 Page No : 11" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# GIVEN DATA\n", "F = 35; # Total MMF in Amphere-Turns\n", "Lc = 0.1; # Inducmath.tance of The Material \"c\" in Henry \n", "a = 0.001; # Area of the all Materials \"a,b,c\" in Metre-Square\n", "\n", "\n", "# CALCULATIONS\n", "Hc = F/Lc; # Field Intensity in Amphere-Turns/Meter (Given that entire MMf apperas on Material \"c\" Because of the highest relucmath.tance about 45000 MKS unit From Example 2.2)\n", "Bc = 0.65; # Flux density of material \"c\" in in Telsa obtained from the Smath.degrees(math.atanard B-H curve\n", "phi = Bc*a; # Flux in the core in Weber\n", "Ba = Bc; # Flux density of material \"a\" in in Telsa Same because Area of Cross Section is Same\n", "Bb = Bc; # Flux density of material \"b\" in in Telsabecause Area of Cross Section is Same\n", "\n", "\n", "# DISPLAY RESULTS\n", "print (\"EXAMPLE : 2.3 : SOLUTION :-\") ;\n", "print \" a) Flux in the core , phi = %.5f Wb \"%(phi);\n", "print \" b) Flux density of material a,b, c , Ba = Bb = Bc %.2f T \"%(Ba);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "EXAMPLE : 2.3 : SOLUTION :-\n", " a) Flux in the core , phi = 0.00065 Wb \n", " b) Flux density of material a,b, c , Ba = Bb = Bc 0.65 T \n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.4 Page No : 12" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "# GIVEN DATA\n", "# Refer figure 2.7:- Page no. 41\n", "a = 0.0001; # Cross Sectional Area of the Core in Meter-Square\n", "Li = 0.158; # Total length of the Path abcdef in Meter (4.0*4.0 - 0.2 = 15.8cm = 0.158m)\n", "Lg = 0.002; # Length of the air gap in Meter\n", "mue_0 = 4*math.pi*10**-7; # Permeability of the air in Henry/Meter\n", "mue_r = 10000; # Permeability of the core\n", "N = 10; # Number of Turns\n", "I = 1.0; # Current in the Coil in Amphere\n", "v = 50; # hall effect sensor generates volatge produces in milli volt per 1 Telsa\n", "Li_new = 0.16; # Length of the Flux path in Absence of the Air gap in Meter\n", "\n", "\n", "# CALCUALTIONS\n", "F = N*I; # MMF of the Coil in Amphere-turn\n", "Ri = Li/(mue_0*mue_r*a); # Relucatnce of the Iron Coil in MKS unit\n", "Rg = Lg/(mue_0*a); # Relucatnce of air gap in MKS unit\n", "R = Ri+Rg; # Total Relucmath.tance in MKS unit\n", "phi = F/R; # Flux in the Core in Weber\n", "B = phi/a; # FLux density in the core(Presence of the Air gap) in Weber/Meter-Square\n", "HEV = B*50; # Output of the Hall effect Sensor device in Milli-Volt\n", "R_new = Li_new/(mue_0*mue_r*a) # Relucamath.tance of the Magnetic Circuit in Absence of the Air gap\n", "phi_new = F/R_new; # New Flux in the Core in Weber\n", "B_new = phi_new/a; # New FLux density in the core in Weber/Meter-Square\n", "Ratio = B_new/B; # Ratio of the Flux Density in Absence of the Air gap and in the presence of the Air gap \n", "\n", "\n", "# DISPLAY RESULTS\n", "print (\"EXAMPLE : 2.4 : SOLUTION :-\") ;\n", "print \" a) Flux density in the corePresence of the Air gap) , B = %.8f Wb/Meter-Square \"%(B);\n", "print \" b) Output of the Hall effect Sensor device , HEV = %.7f mV \"%(HEV);\n", "print \" c) Ratio of the Flux Density in Absence of the Air gap and in the presence of the Air gap , Ratio = %.2f \"%(Ratio);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "EXAMPLE : 2.4 : SOLUTION :-\n", " a) Flux density in the corePresence of the Air gap) , B = 0.00623394 Wb/Meter-Square \n", " b) Output of the Hall effect Sensor device , HEV = 0.3116969 mV \n", " c) Ratio of the Flux Density in Absence of the Air gap and in the presence of the Air gap , Ratio = 125.99 \n" ] } ], "prompt_number": 5 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Example 2.5 Page No : 13" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math \n", "\n", "\n", "# GIVEN DATA\n", "# Refer figure 2.3(a):- Page no. 36\n", "B = 1.0; # Flux Density in the Core in Weber/Meter-Square\n", "Liron = 0.55; # Mean length of the flux path of Iron in Meter\n", "Lair = 0.002; # Mean length of the flux path of Air Gap in Meter\n", "I = 20; # Coil Current in Amphere\n", "H = 200; # Field Intensity in Amphere-Turns/Meter\n", "mue_r = 20000; # Relative permeability of Ferrite core\n", "mue_0 = 4*math.pi*10**-7; # Permeability of the air in Henry/Meter\n", "a = 0.0025; # Area of the Cross sectional of the core oin Metre-Square\n", "\n", "\n", "# CALCULATIONS \n", "phi = B*a; # Toatl Flux in the core in Weber\n", "Rair = Lair/(mue_0*a); # Relucatnce in the Air gap\n", "Fair = Rair*phi; # MMf in the Air gap in Amphere-Turns\n", "Firon = H*Liron; # MMf in the Iron core in Amphere-Turns\n", "F = Firon+Fair; # Total MMF in Amphere-Turns\n", "N = F/I; # Number of turns in the Coil\n", "F_new = B/(mue_0*mue_r); # Field Intensity in Amphere-Turns/Meter\n", "F_new_total = (Fair+F_new); # Total MMF in Amphere-Turns\n", "N_new = F_new_total/I; # Number of turns in the Coil\n", "\n", "\n", "# DISPLAY RESULTS\n", "print (\"EXAMPLE : 2.5 : SOLUTION :-\") ;\n", "print \" a) Number of turns in the Coil in air gap made of Silicon Steel having an field intensity \\\n", "\\n200At/m corresounds to 1.0 T Flux Density , N = %.2f appoximately 85 \"%(N);\n", "print \" b) Number of turns in the Coil for a ferrite core of having Relative premeability of 20000 and\\\n", "\\n magnetic Field Density corresponnds to 1.0 T , N_new = %.2f appoximately 82 \"%(N_new);\n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "EXAMPLE : 2.5 : SOLUTION :-\n", " a) Number of turns in the Coil in air gap made of Silicon Steel having an field intensity \n", "200At/m corresounds to 1.0 T Flux Density , N = 85.08 appoximately 85 \n", " b) Number of turns in the Coil for a ferrite core of having Relative premeability of 20000 and\n", " magnetic Field Density corresponnds to 1.0 T , N_new = 81.57 appoximately 82 \n" ] } ], "prompt_number": 6 } ], "metadata": {} } ] }