{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6: MAGNETIC CIRCUITS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.1,Page number: 167\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the magnetic field strength and total flux passing through a coil.\"\"\"\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration:\n",
"N=200 #Number of turns in the coil \n",
"l=0.60 #Length(Circumference) of the wooden ring(in metres)\n",
"A=500e-06 #Cross-sectional area of the ring(in square-metres)\n",
"I=4 #Current through the coil(in Amperes)\n",
"\n",
"\n",
"#Calculations:\n",
"H=(N*I)/l\n",
"rel_per=1\n",
"per=(4*pi)*(1e-07)\n",
"B=per*rel_per*H\n",
"flux=B*A\n",
"\n",
"\n",
"#Result:\n",
"print \"(a)The magnetic field strength is %.2f A/m.\" %(H)\n",
"print \"(b)The flux density is %.2f micro T.\" %(B*1000000)\n",
"print \"(c)The total flux is %.5f micro Wb.\" %(flux*1000000)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The magnetic field strength is 1333.33 A/m.\n",
"(b)The flux density is 1675.52 micro T.\n",
"(c)The total flux is 0.83776 micro Wb.\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2,Page number: 168\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the magnetomotive force(mmf) required to produce flux.\"\"\"\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration:\n",
"flux=0.015 #Flux across the air-gap(in Webers)\n",
"l=2.5e-03 #Length of the air-fap(in metres)\n",
"A=200e-04 #Effective area of the air-gap(in square-metres)\n",
"\n",
"\n",
"#Calculations:\n",
"B=flux/A\n",
"abs_per=(4*pi)*(1e-07)\n",
"H=B/abs_per\n",
"mmf=H*l\n",
"\n",
"\n",
"#Result:\n",
"print \"The magneto motive force(mmf) required is %.2f At.\" %(mmf)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magneto motive force(mmf) required is 1492.08 At.\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3,Page number: 168\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the reluctance of a mild-steel ring.\"\"\"\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration:\n",
"N=200 #Number of turns in the coil\n",
"abs_per=(4*pi)*(1e-07) #Absolute permeability of free space \n",
"rel_per=380 #Relative permeability of mild-steel\n",
"l=400e-03 #Length(Circumference) of the mild-steel ring(in metres)\n",
"A=500e-06 #Cross-sectional area of the mild-steel ring(in square-metres)\n",
"flux=800e-06 #Flux in the ring(in Webers) \n",
"\n",
"\n",
"#Calculations:\n",
"Rel=l/(abs_per*rel_per*A)\n",
"mmf=flux*Rel\n",
"I=mmf/N\n",
"\n",
"\n",
"#Result:\n",
"print \"(a)The reluctance of the ring is %6e A/Wb.\" %(Rel)\n",
"print \"(b)The magnetising current is %.2f A.\" %(I)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The reluctance of the ring is 1.675315e+06 A/Wb.\n",
"(b)The magnetising current is 6.70 A.\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4,Page number: 171\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the current in the coil to produce a flux density of 0.9 T in the air gap.\"\"\"\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration:\n",
"B=0.90 #Flux Density in the air gap(in Tesla) \n",
"N=4000 #Number of turns in the core\n",
"l_core=220e-03 #Length of the core(in metres)\n",
"A_core=50e-06 #Cross-sectional area of the core(in square-metres)\n",
"H_core=820 #Magnetic field intensity of the core(in Ampere per metre) \n",
"l_gap=1e-03 #Length of the air-gap(in metres)\n",
"A_gap=50e-06 #Cross-sectional area of the air gap(in square-metres)\n",
"\n",
"\n",
"#Calculations:\n",
"mmf_core=H_core*l_core\n",
"abs_per=(4*pi*(1e-07))\n",
"H_gap=B/abs_per\n",
"mmf_air_gap=H_gap*l_gap\n",
"Total_mmf=mmf_core+mmf_air_gap\n",
"I=Total_mmf/N\n",
"\n",
"\n",
"#Result:\n",
"print \"The magnetisation current is %.5f A.\" %(I)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetisation current is 0.22415 A.\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5,Page number: 173"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the magnetising current required to produce a flux across the air gap.\"\"\"\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration:\n",
"w=40e-03 #Width of the core(in metres)\n",
"d=50e-03 #Depth of the core(in metres)\n",
"lg=2.0e-03 #Length of the air gap(in metres)\n",
"Ag=2500e-06 #Area of the air gap(in square metres)\n",
"N=800 #Number of turns in the coil\n",
"flux=2.50e-03 #Flux across the air gap(in Webers)\n",
"lf=1.2 #Leakage Factor\n",
"abs_per=(4*pi)*(1e-07) #Absolute permeability of free space(Henry per metre) \n",
"lc=600e-03 #Length of the core(in metres)\n",
"\n",
"\n",
"#Calculations:\n",
"Ac=w*d\n",
"Bg=flux/Ag\n",
"Hg=Bg/abs_per\n",
"mmf_g=Hg*lg\n",
"eff_Ac=0.92*Ac\n",
"flux_c=flux*lf\n",
"Bc=flux_c/eff_Ac\n",
"Hc=4000.0\n",
"mmf_c=Hc*lc\n",
"mmf=mmf_c+mmf_g\n",
"I=mmf/N\n",
"\n",
"\n",
"#Result:\n",
"print \"The magnetising current required to produce a flux of 0.0025 Wb across the air gap is %.2f A.\" %(I)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The magnetising current required to produce a flux of 0.0025 Wb across the air gap is 4.99 A.\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.6,Page number: 174"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the current in the coil.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"lA=0.3 #Length of silicon steel material(in metres)\n",
"lB=0.2 #Length of low-carbon mild steel material(in metres)\n",
"lC=0.1 #Length of cast iron material(in metres)\n",
"N=100 #Number of turns in the exciting coil\n",
"A=0.001 #Cross-sectional area(in square-metres)\n",
"flux=600e-06 #Flux in the coil(in Webers)\n",
"abs_per=(4*pi)*(1e-07)#Absolute permeability of free space(in Henry per metre)\n",
"\n",
"\n",
"#Calculations:\n",
"B=flux/A\n",
"B_A=B\n",
"B_C=B\n",
"B_C=B\n",
"\"\"\"From magnetisation characteristics of ferromagnetic materials,\"\"\"\n",
"H_A=20.0\n",
"H_B=700.0\n",
"H_C=2500.0\n",
"\"\"\"According to Kirchoff's magnetomotive force law(KML),the total mmf required, tot_mmf= mmf_A+mmf_B+mmf_C.\"\"\"\n",
"tot_mmf=(H_A*lA)+(H_B*lB)+(H_C*lC)\n",
"I=tot_mmf/N\n",
"rel_A=B/(abs_per*H_A)\n",
"rel_B=B/(abs_per*H_B)\n",
"rel_C=B/(abs_per*H_C)\n",
"R_A=(H_A*lA)/flux\n",
"R_B=(H_B*lB)/flux\n",
"R_C=(H_C*lC)/flux\n",
"\n",
"\n",
"#Result:\n",
"print \"(a)The mmf for setting up a flux of 600 micro Weber is %.2f At.\" %(tot_mmf)\n",
"print \"(b)The current in the coil is %.2f A.\" %(I)\n",
"print \"(c)The relative permeability of:\\n Material A: %.2f\\n Material B: %.2f\\n Material C: %.2f.\\n\" %(rel_A,rel_B,rel_C)\n",
"print \" The reluctances are :\\n R_A=%.2f At/Wb \\n R_B=%.2f At/Wb \\n R_C=%.2f At/Wb.\" %(R_A,R_B,R_C)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)The mmf for setting up a flux of 600 micro Weber is 396.00 At.\n",
"(b)The current in the coil is 3.96 A.\n",
"(c)The relative permeability of:\n",
" Material A: 23873.24\n",
" Material B: 682.09\n",
" Material C: 190.99.\n",
"\n",
" The reluctances are :\n",
" R_A=10000.00 At/Wb \n",
" R_B=233333.33 At/Wb \n",
" R_C=416666.67 At/Wb.\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7,Page number: 175"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the current in the exciting coil.\"\"\"\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration:\n",
"N=300 #Number of the turns in the exciting coil\n",
"flux=600e-06 #Flux in the air gap(in Webers)\n",
"lg=1e-03 #Length of the air gap(in metres)\n",
"lc=40e-02 #Mean length of the core(in metres)\n",
"A=4e-04 #Cross sectional area of the core(in square metres)\n",
"abs_per=(4*pi)*1e-07 #Absolute permeability of free space(in Henry per metre)\n",
"\n",
"\n",
"#Calculations:\n",
"B=flux/A\n",
"Hg=B/abs_per\n",
"mmf_g=Hg*lg\n",
"mmf_c=3000*lc\n",
"mmf=mmf_g+mmf_c\n",
"I=mmf/N\n",
"\n",
"\n",
"#Result:\n",
"print \"The current in the exciting coil to set up a flux of 600 micro Weber in the air gap is %.2f A.\" %(I)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The current in the exciting coil to set up a flux of 600 micro Weber in the air gap is 7.98 A.\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.8,Page number: 175 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the current in the exciting coil.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"l1=10e-02 #Length of first side of the magnetic circuit(in metres)\n",
"l2=18e-02 #Length of second side of the magnetic circuit(in metres)\n",
"l3=18e-02 #Length of third side of the magnetic circuit(in metres)\n",
"A1=6.25e-04 #Cross sectional area of l1 path(in square-metre) \n",
"A2=3.00e-04 #Cross sectional area of l2 path(in square-metre)\n",
"A3=3.00e-04 #Cross sectional area of l3 path(in square-metre)\n",
"lg=2e-03 #Length of air gap(in metres)\n",
"rel_per=800.0 #Relative permeability of core material\n",
"N=600 #Number of turns\n",
"flux=100e-06 #Flux in the air gap(in Webers)\n",
"abs_per=(4*pi)*1e-07 #Absolute permeability of free space(in Farad per metre)\n",
"\n",
"\n",
"#Calculations:\n",
"Bg=flux/A1\n",
"Hg=Bg/abs_per\n",
"mmf_g=Hg*lg\n",
"B1=Bg\n",
"H1=B1/(rel_per*abs_per)\n",
"mmf_1=H1*l1\n",
"flux2=flux/2.0\n",
"B2=flux2/A2\n",
"H2=B2/(rel_per*abs_per)\n",
"mmf_2=H2*l2\n",
"tot_mmf=mmf_g+mmf_1+mmf_2\n",
"I=tot_mmf/N\n",
"\n",
"\n",
"#Result:\n",
"print \"The current in the 600 turn exciting coil is %.3f A.\" %(I) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The current in the 600 turn exciting coil is 0.501 A.\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.9,Page number: 176 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the value of exciting current.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"A_B=0.01 #Area of cross section of limb B(in square metre)\n",
"A_C=0.02 #Area of cross section of limb C(in square metre)\n",
"l_B=1e-03 #Length of air gap in limb B(in metres)\n",
"l_C=2e-03 #Length of air gap in limb C(in metres)\n",
"flux_B=1.5e-03 #Flux in limb B(in Webers)\n",
"N=500 #Number of turns in the coil\n",
"abs_per=(4*pi)*(1e-07)#Absolute permeability of free space(in Henry per metre) \n",
"\n",
"\n",
"#Calculations:\n",
"\"\"\"The mmf across parallel paths must be same. \n",
" (R_B*flux_B)=(R_C*flux_C);\"\"\"\n",
"flux_C=flux_B*(l_B/l_C)*(A_C/A_B)\n",
"flux=flux_B+flux_C\n",
"R_B=l_B/(abs_per*A_B)\n",
"R_C=l_C/(abs_per*A_C)\n",
"R_net=1.0/((1.0/R_B)+(1.0/R_C))\n",
"I=(flux*R_net)/N\n",
"\n",
"\n",
"#Result:\n",
"print \"The flux in limb A is %e Wb.\" %(flux)\n",
"print \"The current in the exciting coil is %e A.\" %(I) "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The flux in limb A is 3.000000e-03 Wb.\n",
"The current in the exciting coil is 2.387324e-01 A.\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.10,Page number: 177 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the ampere turns required to produce a flux.\"\"\"\n",
"\n",
"from math import pi\n",
"\n",
"#Variable Declaration:\n",
"abs_per=(4*pi)*(1e-07) #Absolute permeability of free space(in Henry per metre)\n",
"D=21e-02 #Mean diameter of the ring(in metres)\n",
"A=10e-04 #Cross sectional area(in square metre)\n",
"flux=0.8e-03 #Flux to be produced(in Webers)\n",
"lg=0.4e-03 #Length of the air gap(in metres) \n",
"rel_i=166.0 #Relative permeability of iron\n",
"rel_s=800.0 #Relative permeability of steel\n",
"\n",
"\n",
"#Calculations:\n",
"B=flux/A\n",
"li=(pi*D)/2.0\n",
"ls=(pi*D)/2.0\n",
"mmf_g=(B/abs_per)*lg\n",
"mmf_i=(B/(abs_per*rel_i))*li\n",
"mmf_s=(B/(abs_per*rel_s))*ls\n",
"mmf=mmf_g+mmf_i+mmf_s\n",
"\n",
"\n",
"#Result:\n",
"print \"The total ampere turns required is %.2f At.\" %(mmf)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The total ampere turns required is 1782.21 At.\n"
]
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.11,Page number: 177 "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Question:\n",
"\"\"\"Finding the ampere turns of the coil wound on the central limb.\"\"\"\n",
"\n",
"#Variable Declaration:\n",
"flux=1e-03 #Flux in the central limb(in Webers)\n",
"Ac=8e-04 #Area of the central limb(in square metres)\n",
"As=5e-04 #Area of each side limb(in square metres)\n",
"l=0.15 #Length of the central limb(in metres)\n",
"lg=0.001 #Length of the air gap(in metres)\n",
"abs_per=(4*pi)*1e-07 #Absolute permeability of free space(in Henry per metre)\n",
"l1=0.34 #Length of the part ABCD(in metres)\n",
"\n",
"\n",
"#Calculations:\n",
"B=flux/Ac\n",
"\"\"\"Corresponding to this value of B, H is 500 At/m from the table.\"\"\"\n",
"mmf_DG=500*l\n",
"Hg=1.25/abs_per\n",
"mmf_g=Hg*lg\n",
"B1=(flux/2.0)/As\n",
"\"\"\"Corresponding to this value of B, H is 200 At/m from the table.\"\"\"\n",
"mmf_1=200*l1\n",
"mmf_tot=mmf_DG+mmf_g+mmf_1\n",
"\n",
"\n",
"#Result:\n",
"print \"The required ampere turns of the coil wound on the central limb is %.2f At.\" %(mmf_tot)\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required ampere turns of the coil wound on the central limb is 1137.72 At.\n"
]
}
],
"prompt_number": 3
}
],
"metadata": {}
}
]
}