{
"metadata": {
"name": "",
"signature": "sha256:18b2ae9034d59ad1d2a71a370085420c43adb19c1da344e7757efdb47969ddb0"
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"nbformat": 3,
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"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h1>Chapter 21: D.c. machines</h1>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 1, page no. 354</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Z = 600;# no. of conductors\n",
"c = 2;# for a wave winding\n",
"p = 4;# no. of pairs\n",
"n = 625/60;# in rev/sec\n",
"Phi = 20E-3;# in Wb\n",
"\n",
"#calculation:\n",
" #Generated e.m.f., E = 2*p*Phi*n*Z/c\n",
"E = 2*p*Phi*n*Z/c\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n the generated e.m.f is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" the generated e.m.f is 500.0 V "
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 2, page no. 354</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Z = 50*16;# no. of conductors\n",
"p = 1;# let no. of pairs\n",
"c = 2*p;# for a lap winding\n",
"Phi = 30E-3;# in Wb\n",
"E = 240;# in Volts\n",
"\n",
"#calculation:\n",
" #Generated e.m.f., E = 2*p*Phi*n*Z/c\n",
" #Rearranging gives, speed\n",
"n = E*c/(2*p*Phi*Z)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n the speed at which the machine must be driven is \",round(n,2),\" rev/sec \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" the speed at which the machine must be driven is 10.0 rev/sec "
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 3, page no. 354</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Z = 1200;# no. of conductors\n",
"p = 1;# let, no. of pairs\n",
"c = 2*p;# for a lap winding\n",
"Phi = 30E-3;# in Wb\n",
"n = 500/60;# in rev/sec\n",
"\n",
"#calculation:\n",
" #Generated e.m.f., E = 2*p*Phi*n*Z/c\n",
"E = 2*p*Phi*n*Z/c\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Generated e.m.f. is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Generated e.m.f. is 300.0 V "
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 4, page no. 355</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Z = 1200;# no. of conductors\n",
"p = 4;# let, no. of pairs\n",
"c = 2;# for a wave winding\n",
"Phi = 30E-3;# in Wb\n",
"n = 500/60;# in rev/sec\n",
"\n",
"#calculation:\n",
" #Generated e.m.f., E = 2*p*Phi*n*Z/c\n",
"E = 2*p*Phi*n*Z/c\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Generated e.m.f. is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Generated e.m.f. is 1200.0 V "
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 5, page no. 355</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"E1 = 150; # in Volts\n",
"x = 0.2;\n",
"\n",
"#calculation:\n",
"E2 = E1*(1- x)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Generated e.m.f. is \",round(E2,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Generated e.m.f. is 120.0 V "
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 6, page no. 356</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"n1 = 30;# in rev/sec\n",
"E1 = 200;# in Volts\n",
"n2 = 20;# in rev/sec\n",
"E2 = 250;# in Volts\n",
"\n",
"#calculation:\n",
" #generated e.m.f., E proportional to phi*w and since w = 2*pi*n, then\n",
" # E proportional to phi*n\n",
" # E1/E2 = Phi1*n1/(Phi2*n2)\n",
" # let Phi2/Phi1 = Phi\n",
"Phi = E2*n1/(E1*n2)\n",
"Phi_inc = (Phi - 1)*100#/in percent\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n percentage increase in the flux per pole is \",round(Phi_inc,2),\" percent \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" percentage increase in the flux per pole is 87.5 percent "
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 7, page no. 357</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ra = 0.30;# in ohms\n",
"Ia = 30;# in Amperes\n",
"E = 200;# in Volts\n",
"\n",
"#calculation:\n",
" #terminal voltage,\n",
" #V = E - Ia*Ra\n",
"V = E - Ia*Ra\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n terminal voltage of a generator is \",round(V,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" terminal voltage of a generator is 191.0 V "
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 8, page no. 357</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"RL = 60;# in ohms\n",
"Ia = 8;# in Amperes\n",
"Ra = 1;# in ohms\n",
"\n",
"#calculation:\n",
" #terminal voltage,\n",
" #V = Ia*RL\n",
"V = Ia*RL\n",
" #Generated e.m.f., E\n",
"E = V + Ia*Ra\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)terminal voltage is \",round(V,2),\" V \"\n",
"print \"\\n (b)generated e.m.f. is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)terminal voltage is 480.0 V \n",
"\n",
" (b)generated e.m.f. is 488.0 V "
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 9, page no. 357</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"E1 = 150;# in Volts\n",
"n1 = 20;# in rev/sec\n",
"Phi1 = 0.10;# in Wb\n",
"n2 = 25;# in rev/sec\n",
"Phi2 = 0.10;# in Wb\n",
"n3 = 20;# in rev/sec\n",
"Phi3 = 0.08;# in Wb\n",
"n4 = 24;# in rev/sec\n",
"Phi4 = 0.07;# in Wb\n",
"\n",
"#calculation:\n",
" #generated e.m.f., E proportional to phi*w and since w = 2*pi*n, then\n",
" # E proportional to phi*n\n",
" # E1/E2 = Phi1*n1/(Phi2*n2)\n",
"E2 = E1*Phi2*n2/(Phi1*n1)\n",
"E3 = E1*Phi3*n3/(Phi1*n1)\n",
"E4 = E1*Phi4*n4/(Phi1*n1)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)the generated e.m.f is \",round(E2,2),\" V \"\n",
"print \"\\n (b)generated e.m.f. is \",round(E3,2),\" V \"\n",
"print \"\\n (c)generated e.m.f. is \",round(E4,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)the generated e.m.f is 187.5 V \n",
"\n",
" (b)generated e.m.f. is 120.0 V \n",
"\n",
" (c)generated e.m.f. is 126.0 V "
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 10, page no. 359</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ps = 20000;# in Watts\n",
"Vs = 200;# in Volts\n",
"Rs = 0.1;# in ohms\n",
"Rf = 50;# in ohms\n",
"Ra = 0.04;# in ohms\n",
"\n",
"#calculation:\n",
" #Load current, I\n",
"Is = Ps/Vs\n",
" #Volt drop in the cables to the load\n",
"Vd = Is*Rs\n",
" #Hence terminal voltage,\n",
"V = Vs + Vd\n",
" #Field current, If\n",
"If = V/Rf\n",
" #Armature current\n",
"Ia = If + Is\n",
" #Generated e.m.f. E\n",
"E = V + Ia*Ra\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)terminal voltage is \",round(V,2),\" V \"\n",
"print \"\\n (b)generated e.m.f. is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)terminal voltage is 210.0 V \n",
"\n",
" (b)generated e.m.f. is 214.17 V "
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 11, page no. 361</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Is = 80;# in amperes\n",
"Vs = 200;# in Volts\n",
"Rf = 40;# in ohms\n",
"Rse = 0.02;# in ohms\n",
"Ra = 0.04;# in ohms\n",
"\n",
"#calculation:\n",
" #Volt drop in series winding\n",
"Vse = Is*Rse\n",
" #P.d. across the field winding = p.d. across armature\n",
"V1 = Vs + Vse\n",
" #Field current, If\n",
"If = V1/Rf\n",
" #Armature current\n",
"Ia = If + Is\n",
" #Generated e.m.f. E\n",
"E = V1 + Ia*Ra\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n generated e.m.f. is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" generated e.m.f. is 205.0 V "
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 12, page no. 363</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ps = 10000;# in Watt\n",
"Pl = 600;# in Watt\n",
"Ra = 0.75;# in ohms\n",
"Rf = 125;# in ohms\n",
"V = 250;# in Volts\n",
"\n",
"#calculation:\n",
" #Output power Ps = V*I\n",
" #from which, load current I\n",
"I = Ps/V\n",
" #Field current, If\n",
"If = V/Rf\n",
" #Armature current\n",
"Ia = If + I\n",
" #Efficiency,\n",
"eff = Ps*100/((V*I) + (Ia*Ia*Ra) + (If*V) + (Pl))# in Percent\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Efficiency is \",round(eff,2),\" percent \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Efficiency is 80.5 percent "
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 13, page no. 364</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ra = 0.2;# in ohms\n",
"V = 240;# in Volts\n",
"Ia = 50;# in Amperes\n",
"\n",
"#calculation:\n",
" #For a motor, V = E + Ia*Ra\n",
"E = V - Ia*Ra\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n back e.m.f. is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" back e.m.f. is 230.0 V "
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 14, page no. 365</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ra = 0.25;# in ohms\n",
"V = 300;# in Volts\n",
"Ig = 100;# in Amperes\n",
"Im = 80;# in Amperes\n",
"\n",
"#calculation:\n",
" #As a generator, generated e.m.f.,\n",
" # E = V + Ia*Ra\n",
"Eg = V + Ig*Ra\n",
" #For a motor, generated e.m.f. (or back e.m.f.),\n",
" # E = V - Ia*Ra\n",
"E = V - Im*Ra\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)As a generator, generated e.m.f. is \",round(Eg,2),\" V \"\n",
"print \"\\n (b)back e.m.f. is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)As a generator, generated e.m.f. is 325.0 V \n",
"\n",
" (b)back e.m.f. is 280.0 V "
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 15, page no. 366</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"p = 4;\n",
"c = 2;# for a wave winding\n",
"Phi = 25E-3;# Wb\n",
"Z = 900;\n",
"Ia = 30;# in Amperes\n",
"\n",
"#calculation:\n",
" #torque T = p*Phi*Z*Ia/(pi*c)\n",
"T = p*Phi*Z*Ia/(1*math.pi*c)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n the torque exerted is \",round(T,2),\" Nm \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" the torque exerted is 429.72 Nm "
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 16, page no. 366</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"V = 350;# in Volts\n",
"Ra = 0.5;# in ohms\n",
"n = 15;# in rev/sec\n",
"Ia = 60;# in Amperes\n",
"\n",
"#calculation:\n",
" #Back e.m.f. E = V - Ia*Ra\n",
"E = V - Ia*Ra\n",
" #torque T = E*Ia/(2*n*pi)\n",
"T = E*Ia/(2*n*math.pi)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n the torque exerted is \",round(T,2),\" Nm \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" the torque exerted is 203.72 Nm "
]
}
],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 17, page no. 366</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"p = 1;# let\n",
"c = 2*p;# for a lap winding\n",
"Phi = 20E-3;# Wb\n",
"Z = 500;\n",
"V = 250;# in Volts\n",
"Ra = 1;# in ohms\n",
"Ia = 40;# in Amperes\n",
"\n",
"#calculation:\n",
" #Back e.m.f. E = V - Ia*Ra\n",
"E = V - Ia*Ra\n",
" #E.m.f. E = 2*p*Phi*n*Z/c\n",
" # rearrange,\n",
"n = E*c/(2*p*Phi*Z)\n",
" #torque T = E*Ia/(2*n*pi)\n",
"T = E*Ia/(2*n*math.pi)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)speed n is \",round(n,2),\" rev/sec \"\n",
"print \"\\n (b)the torque exerted is \",round(T,2),\" Nm \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)speed n is 21.0 rev/sec \n",
"\n",
" (b)the torque exerted is 63.66 Nm "
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 18, page no. 367</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"T1 = 25;# in Nm\n",
"T2 = 35;# in Nm\n",
"Ia1 = 16;# in Amperes\n",
"V = 100;# in Volts\n",
"x = 0.15;\n",
"\n",
" #calculation:\n",
" #the shaft torque T of a generator is proportional to (phi*Ia),\n",
" #where Phi is the flux and Ia is the armature current. Thus, T = k*Phi*Ia, where k is a constant.\n",
" #The torque at flux phi1 and armature current Ia1 is T1 = k*Phi1*Ia1.\n",
" #similarly T2 = k*Phi2*Ia2\n",
"\n",
"Ia2 = T2*Ia1/(0.85*T1)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n armature current at the new value of torque is \",round(Ia2,2),\" A \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" armature current at the new value of torque is 26.35 A "
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 19, page no. 367</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"T = 12;# in Nm\n",
"I = 15;# in Amperes\n",
"V = 100;# in Volts\n",
"n = 1500/60;# in rev/sec\n",
"\n",
"#calculation:\n",
" #the efficiency of a generator = (output power/input power)*100 %\n",
" #The output power is the electrical output, i.e. VI watts. \n",
" #The input power to a generator is the mechanical power in the shaft driving the generator, \n",
" #i.e. T*w or T(2*pi*n) watts, where T is the torque in Nm and n is speed of rotation in rev/s. Hence, for a generator \n",
" #efficiency = V*I*100/(T*2*pi*n) %\n",
"eff = V*I*100/(T*2*math.pi*n)# in Percent\n",
" #The input power = output power + losses\n",
" # hence, T*2*math.pi*n = V*I + losses\n",
"Pl = T*2*math.pi*n - V*I\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a) efficiency is \",round(eff,2),\" % \"\n",
"print \"\\n (b) power loss is \",round(Pl,2),\" W \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a) efficiency is 79.58 % \n",
"\n",
" (b) power loss is 384.96 W "
]
}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 20, page no. 368</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Rf = 150;# in Ohms\n",
"Ra = 0.4;# in Ohms\n",
"I = 30;# in Amperes\n",
"V = 240;# in Volts\n",
"\n",
"#calculation:\n",
" #Field current If\n",
"If = V/Rf\n",
" #Supply current I = Ia + If\n",
" #Hence armature current, Ia\n",
"Ia = I - If\n",
" #Back e.m.f. E = V -\u0004 Ia*Ra\n",
"E = V - (Ia*Ra)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a) current in the armature is \",round(Ia,2),\" A \"\n",
"print \"\\n (b) Back e.m.f. E is \",round(E,2),\" V \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a) current in the armature is 28.4 A \n",
"\n",
" (b) Back e.m.f. E is 228.64 V "
]
}
],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 21, page no. 370</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ia1 = 30;# in Amperes\n",
"Ia2 = 45;# in Amperes\n",
"Ra = 0.4;# in ohm\n",
"n1 = 1350/60;# in Rev/sec\n",
"V = 200;# in Volts\n",
"\n",
"#calculation:\n",
" #The relationship E proportional to (Phi*n) applies to both generators and motors. For a motor,\n",
" #E = V - (Ia*Ra)\n",
"E1 = V - (Ia1*Ra)\n",
"E2 = V - (Ia2*Ra)\n",
" #The relationship, E1/E2 = Phi1*n1/Phi2*n2, applies to both generators and motors.\n",
" #Since the flux is constant, Phi1 = Phi2\n",
"n2 = E2*n1/(E1)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n the speed of the motor is \",round(n2,2),\" rev/sec \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" the speed of the motor is 21.78 rev/sec "
]
}
],
"prompt_number": 22
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 22, page no. 370</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ia1 = 30;# in Amperes\n",
"Ra = 0.4;# in ohm\n",
"n = 800/60;# in Rev/sec\n",
"V = 220;# in Volts\n",
"x= 0.1;\n",
"\n",
"#calculation:\n",
" #For a d.c. shunt-wound motor, E = V - (Ia*Ra),Hence initial generated e.m.f.,\n",
"E1 = V - (Ia1*Ra)\n",
" #The generated e.m.f. is also such that E proportional to (Phi*n) \n",
" #so at the instant the flux is reduced, the speed has not had time to change, and\n",
"E = E1*(1-x)\n",
" #Hence, the voltage drop due to the armature resistance is\n",
"Vd = V - E\n",
" #The instantaneous value of the current is\n",
"Ia = Vd/Ra\n",
" #T proportional to (Phi*Ia), since the torque is constant,\n",
" #Phi1*Ia1 = Phi2*Ia2, The flux 8 is reduced by 10%, hence\n",
"Ia2 = Ia1/0.9\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)instantaneous value of the current \",round(Ia,2),\" A \"\n",
"print \"\\n (b)steady state value of armature current, \",round(Ia2,2),\" A \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)instantaneous value of the current 82.0 A \n",
"\n",
" (b)steady state value of armature current, 33.33 A "
]
}
],
"prompt_number": 23
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 23, page no. 372</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ia1 = 15;# in Amperes\n",
"Ia2 = 30;# in Amperes\n",
"Rf = 0.3;# in ohms\n",
"Ra = 0.2;# in ohm\n",
"n1 = 24;# in Rev/sec\n",
"V = 240;# in Volts\n",
"x= 2;\n",
"\n",
"#calculation:\n",
" #generated e.m.f., E, at initial load, is given by\n",
"E1 = V - Ia1*(Ra + Rf)\n",
" #When the current is increased to 30 A, the generated e.m.f. is given by:\n",
"E2 = V - Ia2*(Ra + Rf)\n",
" #E proportional to (Phi*n)\n",
" #E1/E2 = Phi1*n1/Phi2*n2\n",
"n2 = E2*n1/(2*E1) \n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)generated e.m.f., E is \",round(E1,2),\" V \"\n",
"print \"\\n (b)speed of motor, n2, \",round(n2,2),\" rev/sec \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)generated e.m.f., E is 232.5 V \n",
"\n",
" (b)speed of motor, n2, 11.61 rev/sec "
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 24, page no. 374</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"I = 80;# in Amperes\n",
"C = 1500;# in Watt\n",
"Rf = 40;# in ohms\n",
"Ra = 0.2;# in ohm\n",
"n = 1000/60;# in Rev/sec\n",
"V = 320;# in Volts\n",
"\n",
"#calculation:\n",
" #Field current, If\n",
"If = V/Rf\n",
" #Armature current Ia\n",
"Ia = I - If\n",
" #Efficiency\n",
"eff = ((V*I - (Ia*Ia*Ra) - (If*V) - C)/(V*I))*100 # in percent\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n efficiency is\",round(eff,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" efficiency is 80.09 %"
]
}
],
"prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 25, page no. 374</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"I = 40;# in Amperes\n",
"Rf = 0.05;# in ohms\n",
"Ra = 0.15;# in ohm\n",
"V = 250;# in Volts\n",
"\n",
"#calculation:\n",
" #However for a series motor, If = 0 and the Ia*Ia*Ra loss needs to be I*I*(\u0011Ra + Rf)\n",
" #For maximum efficiency I*I*\u0011(Ra + Rf) = C\n",
" #Efficiency\n",
"eff = ((V*I - (2*I*I*(Ra + Rf)))/(V*I))*100 # in percent\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n efficiency is\",round(eff,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" efficiency is 93.6"
]
}
],
"prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 26, page no. 375</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"T = 15;# in Nm\n",
"n = 1200/60;# in rev/sec\n",
"eff = 0.8;\n",
"V = 200;# in Volts\n",
"\n",
"#calculation:\n",
"I = T*2*math.pi*n/(V*eff)\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n current supplied, I is \",round(I,2),\"A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" current supplied, I is 11.78 A"
]
}
],
"prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 27, page no. 376</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 2;# in ohm\n",
"n = 30;# in rev/sec\n",
"I = 10;# in A\n",
"C = 300;# in Watt\n",
"V = 400;# in Volts\n",
"\n",
"#calculation:\n",
" #Efficiency\n",
"eff = ((V*I - (I*I*R) - C)/(V*I))*100 # in percent\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n efficiency is\",round(eff,2),\"%\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" efficiency is 87.5 %"
]
}
],
"prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 28, page no. 378</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ia1 = 120;# in A\n",
"Ia2 = 60;# in A\n",
"Ra = 0.2;# in ohm\n",
"n1 = 10;# in rev/sec\n",
"R = 0.5;# in ohm\n",
"x = 0.8;\n",
"V = 500;# in Volts\n",
"\n",
"#calculation:\n",
" #back e.m.f. at Ia1\n",
"E1 = V - Ia1*Ra\n",
" #at Ia2\n",
"E2 = V - Ia2*(Ra + R)\n",
" #E1/E2 = Phi1*n1/Phi2*n2\n",
"n2 = n1*E2/E1\n",
" #Back e.m.f. when Ia2\n",
"E3 = V - Ia2*Ra\n",
"n3 = n1*E3/(x*E1)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)speed n2 is \",round(n2,2),\" rev/sec\"\n",
"print \"\\n (b)speed n3 is \",round(n3,2),\" rev/sec\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)speed n2 is 9.62 rev/sec\n",
"\n",
" (b)speed n3 is 12.82 rev/sec"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 29, page no. 379</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ia1 = 90;# in Amperes\n",
"Ra = 0.1;# in ohm\n",
"Rse = 0.05;# in ohm\n",
"Rd = 0.2;# in Ohm\n",
"n1 = 15;# in rev/sec\n",
"V = 300;# in Volts\n",
"\n",
"#calculation:\n",
" #e.m.f. E1\n",
"E1 = V - Ia1*(Ra + Rse)\n",
" #With the Rd diverter in parallel with Rse\n",
" #equivalent resistance, Re\n",
"Re = Rd*Rse/(Rd+Rse)\n",
" #Torque, T proprtional to Ia*Phi and for full load torque, Ia1*Phi1 = Ia2*Phi2\n",
" #Since flux is proportional to field current Phi1 proportional to Ta1 and Phi2 Proportional to I1\n",
"I1 = (Ia1*Ia1*0.8)**0.5\n",
" #By current division, current I1\n",
"Ia2 = I1/(Rd/(Rd + Rse))\n",
" #Hence e.m.f. E2\n",
"E2 = V - Ia2*(Ra + Re)\n",
" #E1/E2 = Phi1*n1/Phi2*n2\n",
"n2 = E2*Ia1*n1/(I1*E1)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n speed n2 is \",round(n2,2),\" rev/sec\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" speed n2 is 16.74 rev/sec"
]
}
],
"prompt_number": 29
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Example 30, page no. 380</h3>"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Ia1 = 25;# in Amperes\n",
"Ra = 0.4;# in ohm\n",
"Rse = 0.2;# in ohm\n",
"n1 = 800/60;# in rev/sec\n",
"n2 = 600/60;# in rev/sec\n",
"V = 400;# in Volts\n",
"\n",
"#calculation:\n",
" #e.m.f. E1\n",
"E1 = V - Ia1*(Ra + Rse)\n",
" #At n2, since the current is unchanged, the flux is unchanged.\n",
" #E1/E2 = n1/n2\n",
"E2 = E1*n2/n1\n",
" #and E2 = V - Ia1(\u0011Ra + Rse + R)\n",
"R = (V - E2)/Ia1 - Ra - Rse\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Resistance is \",round(R,2),\" ohm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Resistance is 3.85 ohm"
]
}
],
"prompt_number": 30
}
],
"metadata": {}
}
]
}