{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"CHAPTER 1: ELECTROMECHANICAL FUNDAMENTALS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.1, Page number 5"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"t = 50.0*10**-3 #Time(second)\n",
"phi = 8.0*10**6 #Uniform magnetic field(maxwells)\n",
"\n",
"#Calculation\n",
"E_av = (phi/t)*10**-8 #Average voltage generated in the conductor(V) \n",
"\n",
"#Result\n",
"print('Average voltage generated in the conductor , E_av = %.1f V' %E_av)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Average voltage generated in the conductor , E_av = 1.6 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.2, Page number 6"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"l = 18.0 #Length of the conductor(inches)\n",
"B = 50000.0 #Uniform magnetic field(lines/sq.inches)\n",
"d = 720.0 #Distance travelled by conductor(inches)\n",
"t = 1.0 #Time taken for the conductor to move(second)\n",
"\n",
"#Calculation\n",
"#Case(a)\n",
"v = d/t #Velocity with which the conductor moves(inches/second)\n",
"e = B*l*v*10**-8 #Instantaneous induced EMF(V)\n",
"#Case(b)\n",
"A = d*l #Area swept by the conductor while moving(sq.inches)\n",
"phi = B*A #Uniform magnetic field(lines) \n",
"E = (phi/t)*10**-8 #Average induced EMF(V)\n",
"\n",
"#Result\n",
"print('Case(a): Instantaneous induced EMF , e = %.2f V' %e)\n",
"print('Case(b): Average induced EMF , E = %.2f V' %E)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Instantaneous induced EMF , e = 6.48 V\n",
"Case(b): Average induced EMF , E = 6.48 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.3, Page number 8"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"l = 18.0 #Length of the conductor(inches)\n",
"B = 50000.0 #Uniform magnetic field(lines/sq.inches)\n",
"d = 720.0 #Distance travelled by conductor(inches)\n",
"t = 1.0 #Time taken for the conductor to move(second)\n",
"theta = 75.0 #Angle between the motion of the conductor and field(degree)\n",
"\n",
"#Calculation\n",
"v = d/t #Velocity with which the conductor moves(inches/second)\n",
"E = B*l*v*math.sin(theta*math.pi/180)*10**-8 #Instantaneous induced voltage(V)\n",
"\n",
"#Result\n",
"print('Average induced voltage , E = %.2f V' %E)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Average induced voltage , E = 6.26 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.4, Page number 9"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"v = 1.5 #Velocity of moving conductor(m/s)\n",
"l = 0.4 #Length of the conductor(m)\n",
"B = 1 #Uniform field(tesla)\n",
"theta_a = 90.0 #Angle between the motion of the conductor and field(Degree)\n",
"theta_b = 35.0 #Angle between the motion of the conductor and field(Degree)\n",
"theta_c = 120.0 #Angle between the motion of the conductor and field(Degree)\n",
"\n",
"#Calculation\n",
"E_a = B*l*v*math.sin(theta_a*math.pi/180) #Voltage induced in the conductor(V)\n",
"E_b = B*l*v*math.sin(theta_b*math.pi/180) #Voltage induced in the conductor(V)\n",
"E_c = B*l*v*math.sin(theta_c*math.pi/180) #Voltage induced in the conductor(V)\n",
"\n",
"#Result\n",
"print('Case(a): Voltage induced in the conductor , E = %.1f V' %E_a)\n",
"print('Case(b): Voltage induced in the conductor , E = %.3f V' %E_b)\n",
"print('Case(c): Voltage induced in the conductor , E = %.2f V' %E_c)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Voltage induced in the conductor , E = 0.6 V\n",
"Case(b): Voltage induced in the conductor , E = 0.344 V\n",
"Case(c): Voltage induced in the conductor , E = 0.52 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.5, Page number 19"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"no_of_conductors = 40.0 #Number of conductors\n",
"A = 2.0 #Number of parallel paths\n",
"path = A\n",
"flux_per_pole = 6.48*10**8 #Flux per pole(lines) \n",
"N = 30.0 #Speed of the prime mover(rpm)\n",
"R_per_path = 0.01 #Resistance per path\n",
"I = 10.0 #Current carrying capacity of each conductor(A)\n",
"P = 2.0 #Number of poles\n",
"\n",
"#Calculation\n",
"phi_T = P*flux_per_pole #Total flux linked in one revolution(lines)\n",
"t = (1/N)*(60) #Time for one revolution(s/rev)\n",
"#Case(a)\n",
"e_av_per_conductor = (phi_T/t)*10**-8 #Average voltage generated(V/conductor)\n",
"E_per_path = (e_av_per_conductor)*(no_of_conductors/path) #Average voltage generated(V/path)\n",
"#Case(b)\n",
"E_g = E_per_path #Generated armature voltage(V)\n",
"#Case(c)\n",
"I_a = (I/path)*(2*path) #Armature current delivered to an external load(A)\n",
"#Case(d)\n",
"R_a = (R_per_path)/path*(no_of_conductors/P) #Armature resistance(ohm)\n",
"#Case(e)\n",
"V_t = E_g-(I_a*R_a) #Terminal voltage of the generator(V)\n",
"#Case(f)\n",
"P = V_t*I_a #Generator power rating(W)\n",
"\n",
"#Result\n",
"print('Case(a): Average voltage generated per path , E/path = %.1f V/path' %E_per_path)\n",
"print('Case(b): Generated armature voltage , E_g = %.1f V' %E_g)\n",
"print('Case(c): Armature current delivered to an external load , I_a = %.f A' %I_a)\n",
"print('Case(d): Armature resistance , R_a = %.1f \u03a9' %R_a)\n",
"print('Case(e): Terminal voltage of the generator , V_t = %.1f V' %V_t)\n",
"print('Case(f): Generator power rating , P = %.f W' %P)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Average voltage generated per path , E/path = 129.6 V/path\n",
"Case(b): Generated armature voltage , E_g = 129.6 V\n",
"Case(c): Armature current delivered to an external load , I_a = 20 A\n",
"Case(d): Armature resistance , R_a = 0.1 \u03a9\n",
"Case(e): Terminal voltage of the generator , V_t = 127.6 V\n",
"Case(f): Generator power rating , P = 2552 W\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.6, Page number 20"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"no_of_conductors = 40.0 #Number of conductors\n",
"path = 4.0 #Number of parallel paths\n",
"flux_per_pole = 6.48*10**8 #Flux per pole(lines) \n",
"N = 30.0 #Speed of the prime mover(rpm)\n",
"R_per_path = 0.01 #Resistance per path\n",
"I = 10.0 #Current carrying capacity of each conductor(A)\n",
"P = 4.0 #Number of poles\n",
"\n",
"#Calculation\n",
"phi_T = 2*flux_per_pole #Total flux linked in one revolution(lines). From Example 1.5\n",
"t = (1/N)*(60) #Time for one revolution(s/rev)\n",
"#Case(a)\n",
"e_av_per_conductor = (phi_T/t)*10**-8 #Average voltage generated(V/conductor)\n",
"E_per_path = (e_av_per_conductor)*(no_of_conductors/path) #Average voltage generated(V/path)\n",
"#Case(b)\n",
"E_g = E_per_path #Generated armature voltage(V)\n",
"#Case(c)\n",
"I_a = (I/path)*(4*path) #Armature current delivered to an external load(A)\n",
"#Case(d)\n",
"R_a = (R_per_path)/path*(no_of_conductors/P) #Armature resistance(ohm)\n",
"#Case(e)\n",
"V_t = E_g-(I_a*R_a) #Terminal voltage of the generator(V)\n",
"#Case(f)\n",
"P = V_t*I_a #Generator power rating(W)\n",
"\n",
"#Result\n",
"print('Case(a): Average voltage generated per path , E/path = %.1f V/path' %E_per_path)\n",
"print('Case(b): Generated armature voltage , E_g = %.1f V' %E_g)\n",
"print('Case(c): Armature current delivered to an external load , I_a = %.f A' %I_a)\n",
"print('Case(d): Armature resistance , R_a = %.3f \u03a9' %R_a)\n",
"print('Case(e): Terminal voltage of the generator , V_t = %.1f V' %V_t)\n",
"print('Case(f): Generator power rating , P = %.f W' %P)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Average voltage generated per path , E/path = 64.8 V/path\n",
"Case(b): Generated armature voltage , E_g = 64.8 V\n",
"Case(c): Armature current delivered to an external load , I_a = 40 A\n",
"Case(d): Armature resistance , R_a = 0.025 \u03a9\n",
"Case(e): Terminal voltage of the generator , V_t = 63.8 V\n",
"Case(f): Generator power rating , P = 2552 W\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.7, Page number 23"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"N = 1.0 #Number of turns\n",
"phi = 6.48*10**8 #Magnetic flux(lines)\n",
"rpm = 30.0 #Number of revolution\n",
"s = rpm/60 #Number of revolution of the coil per second(rev/s)\n",
"\n",
"#Calculation\n",
"E_av_per_coil = 4*phi*N*s*10**-8 #Average voltage per coil(V/coil)\n",
"E_av_per_coil_side = E_av_per_coil*(1.0/2) #Average voltage per conductor(V/conductor)\n",
"\n",
"#Result\n",
"print('Case(a): Average voltage per coil , E_av/coil = %.2f V/coil' %E_av_per_coil)\n",
"print('Case(b): Average voltage per conductor , E_av/coil side = %.2f V/conductor' %E_av_per_coil_side)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Average voltage per coil , E_av/coil = 12.96 V/coil\n",
"Case(b): Average voltage per conductor , E_av/coil side = 6.48 V/conductor\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.8, Page number 23"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"N = 1.0 #Number of turns\n",
"phi_lines = 6.48*10**8 #Magnetic flux(lines/pole)\n",
"rpm = 30.0 #Number of revolution per second\n",
"s = rpm/60 #Number of revolution of the coil per second(rev/s)\n",
"\n",
"#Calculation\n",
"phi = phi_lines*10**-8 #Magnetic flux(Wb)\n",
"omega = rpm*2*math.pi*(1.0/60) #Angular velocity(rad/s)\n",
"E_av_per_coil = 0.63662*omega*phi*N #Average voltage per coil(V/coil)\n",
"\n",
"#Result\n",
"print('Average voltage per coil , E_av/coil = %.2f V/coil' %E_av_per_coil)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Average voltage per coil , E_av/coil = 12.96 V/coil\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.9, Page number 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"P = 2.0 #Number of poles\n",
"Z = 40.0 #Number of conductors\n",
"a = 2.0 #Parallel paths\n",
"phi = 6.48*10**8 #Magnetic flux(lines/pole)\n",
"S = 30.0 #Speed of the prime mover\n",
"\n",
"#Calculation\n",
"E_g = (phi*Z*S*P)/(60*a)*10**-8 #Average voltage between the brushes(V)\n",
"\n",
"#Result\n",
"print('Average voltage between the brushes , E_g = %.1f V' %E_g)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Average voltage between the brushes , E_g = 129.6 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.10, Page number 24"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"no_of_coils = 40.0 #Number of coils\n",
"N = 20.0 #Number of turns in each coil\n",
"omega = 200.0 #Angular velocity of armature(rad/s)\n",
"phi = 5.0*10**-3 #Flux(Wb/pole)\n",
"a = 4.0 #Number of parallel paths\n",
"P = 4.0 #Number of poles\n",
"\n",
"#Calculation\n",
"Z = no_of_coils*2.0*N #Number of conductors\n",
"E_g = (phi*Z*omega*P)/(2*math.pi*a) #Voltage generated by the armature between brushes(V)\n",
"\n",
"#Result\n",
"print('Case(a): Number of conductors , Z = %.f conductors' %Z)\n",
"print('Case(b): Voltage between brushes generated by the armature , E_g = %.1f V' %E_g)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Number of conductors , Z = 1600 conductors\n",
"Case(b): Voltage between brushes generated by the armature , E_g = 254.6 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.11, Page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"l = 0.5 #Length of the conductor(m)\n",
"A = 0.1*0.2 #Area of the pole face(sq.meter)\n",
"phi = 0.5*10**-3 #Magnetic flux(Wb)\n",
"I = 10.0 #Current in the conductor(A)\n",
"\n",
"#Calculation\n",
"B = phi/A #Flux density(Wb/m^2)\n",
"F = B*I*l*1000 #Magnitude of force(mN)\n",
"\n",
"#Result\n",
"print('Case(a): Magnitude of the force , F = %.f mN' %F)\n",
"print('Case(b): The direction of the force on the conductor is %.f mN in an upward direction' %F)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Magnitude of the force , F = 125 mN\n",
"Case(b): The direction of the force on the conductor is 125 mN in an upward direction\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.12, Page number 26"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#Variable declaration\n",
"l = 0.5 #Length of the conductor(m)\n",
"A = 0.1*0.2 #Area of the pole face(sq.meter)\n",
"phi = 0.5*10**-3 #Magnetic flux(Wb)\n",
"I = 10.0 #Current in the conductor(A)\n",
"theta = 75.0 #Angle between the conductor and the flux density(degree)\n",
"\n",
"#Calculation\n",
"B = phi/A #Flux density(Wb/m^2)\n",
"F = B*I*l*math.sin(theta*math.pi/180)*1000 #Magnitude of force(mN)\n",
"\n",
"#Result\n",
"print('Magnitude of the force , F = %.2f mN in an vertically upward direction' %F)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Magnitude of the force , F = 120.74 mN in an vertically upward direction\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.13, Page number 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"R_a = 0.25 #Armature resistance(ohm)\n",
"V_a = 125.0 #DC bus voltage(V)\n",
"I_a = 60.0 #Armature current(A)\n",
"\n",
"#Calculation\n",
"E_c = V_a-(I_a*R_a) #Counter EMF generated in the armature conductors of motor(V)\n",
"\n",
"#Result\n",
"print('Counter EMF generated in the armature conductors of motor , E_c = %.f V' %E_c)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Counter EMF generated in the armature conductors of motor , E_c = 110 V\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1.14, Page number 29"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Variable declaration\n",
"V_a = 110.0 #Voltage across armature(V)\n",
"I_a = 60.0 #Armature current(A)\n",
"R_a = 0.25 #Armature resistance(ohm)\n",
"P = 6.0 #Number of poles\n",
"a = 12.0 #Number of paths\n",
"Z = 720.0 #No. of armature conductors\n",
"S = 1800.0 #Speed(rpm)\n",
"\n",
"#Calculation\n",
"E_g = V_a+(I_a*R_a) #Generated EMF in the armature(V)\n",
"phi_lines = E_g*60*a/(Z*S*P*10**-8) #Flux per pole in lines(lines/pole)\n",
"phi_mWb = phi_lines*10**-8*1000 #Flux per pole milliwebers(mWb)\n",
"\n",
"#Result\n",
"print('Case(a): Generated EMF in the armature , E_g = %.f V' %E_g)\n",
"print('Case(b): Flux per pole in lines , \u03a6 = %.2e lines/pole' %phi_lines)\n",
"print('Case(c): Flux per pole milliwebers , \u03a6 = %.1f mWb' %phi_mWb)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Case(a): Generated EMF in the armature , E_g = 125 V\n",
"Case(b): Flux per pole in lines , \u03a6 = 1.16e+06 lines/pole\n",
"Case(c): Flux per pole milliwebers , \u03a6 = 11.6 mWb\n"
]
}
],
"prompt_number": 1
}
],
"metadata": {}
}
]
}