{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Chapter 15: Single-phase series a.c. circuits
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 1, page no. 214
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#(a) Calculate the reactance of a coil \n",
"#(b) Determine the inductance of the coil.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"L = 0.32;# in Henry\n",
"f1 = 50;# in Hz\n",
"f2 = 5000;# in Hz\n",
"Z = 124;# in ohms\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f1*L\n",
"L = Z/(2*math.pi*f2)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Inductive reactance, XL = \",round(XL,2),\" ohms \\n\"\n",
"print \"\\n (b)Inductance L = \",round((L/1E-3),2),\" mH \\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Inductive reactance, XL = 100.53 ohms \n",
"\n",
"\n",
" (b)Inductance L = 3.95 mH "
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 2, page no. 214
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate its inductive reactance and the resulting current if connected to\n",
"#(a) a 240 V, 50 Hz supply, and (b) a 100 V, 1 kHz supply.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"L = 0.040;# in Henry\n",
"V1 = 240;# in volts\n",
"V2 = 100;# in volts\n",
"f1 = 50;# in Hz\n",
"f2 = 1000;# in Hz\n",
"\n",
"#calculation:\n",
"XL1 = 2*math.pi*f1*L\n",
"I1 = V1/XL1\n",
"XL2 = 2*math.pi*f2*L\n",
"I2 = V2/XL2\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Inductive reactance, XL = \",round( XL1,2),\" ohms and current I = \",round( I1,2),\" A\\n\"\n",
"print \"\\n (b)Inductive reactance, XL = \",round( XL2,2),\" ohms and current I = \",round( I2,2),\" A\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Inductive reactance, XL = 12.57 ohms and current I = 19.1 A\n",
"\n",
"\n",
" (b)Inductive reactance, XL = 251.33 ohms and current I = 0.4 A"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 3, page no. 215
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the capacitive reactance of a capacitor of 10 \u03bcF when connected to a circuit of frequency (a) 50 Hz (b) 20 kHz\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"C = 10E-6;# in Farads\n",
"f1 = 50;# in Hz\n",
"f2 = 20000;# in Hz\n",
"\n",
"#calculation:\n",
"Xc1 = 1/(2*math.pi*f1*C)\n",
"Xc2 = 1/(2*math.pi*f2*C)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Capacitive reactance, Xc = \",round( Xc1,2),\" ohms \"\n",
"print \"\\n (b)Capacitive reactance, Xc = \",round( Xc2,2),\" ohms \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Capacitive reactance, Xc = 318.31 ohms \n",
"\n",
" (b)Capacitive reactance, Xc = 0.8 ohms "
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 4, page no. 215
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the value of its capacitance.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Z = 40;# in ohms\n",
"f = 50;# in Hz\n",
"\n",
"#calculation:\n",
"C = 1/(2*math.pi*f*Z)\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Capacitance,C = \",round((C/1E-6),2),\" uF \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Capacitance,C = 79.58 uF "
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 5, page no. 215
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the current taken by a 23 \u03bcF capacitor when connected to a 240 V, 50 Hz supply.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"C = 23E-6;# in Farads\n",
"f = 50;# in Hz\n",
"V = 240;# in volts\n",
"\n",
"#calculation:\n",
"Xc = 1/(2*math.pi*f*C)\n",
"I = V/Xc\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n current I = \",round(I,2),\" A \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" current I = 1.73 A "
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 6, page no. 216
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Find the supply voltage and the phase angle between current and voltage\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Vr = 12;# in volts\n",
"Vl = 5;# in volts\n",
"\n",
"#calculation:\n",
"V = (Vr**2 + Vl**2)**0.5\n",
"phi = math.atan(Vl/Vr)\n",
"phid = phi*180/math.pi\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n supply voltage V = \",V,\" V, phase angle between current and voltage is \", round(phid,2),\"deg lagging\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" supply voltage V = 13.0 V, phase angle between current and voltage is 22.62 deg lagging"
]
}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 7, page no. 216
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate (a) the reactance, (b) the impedance, and (c) the current taken from a 240 V, 50 Hz supply. \n",
"#Determine also the phase angle between the supply voltage and current\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"V = 240;# in volts\n",
"R = 4;# in ohms\n",
"L = 0.00955;# in Henry\n",
"f = 50;# in Hz\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f*L\n",
"Z = (R**2 + XL**2)**0.5\n",
"I = V/Z\n",
"phid = math.atan(XL/R)*180/math.pi\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Inductive reactance, XL = \",round(XL,2),\" ohms\"\n",
"print \"\\n (b)Impedance, Z = \",round(Z,2),\" ohms\"\n",
"print \"\\n (c)Current, I = \",round(I,2),\" A\"\n",
"print \"\\n (d)phase angle between the supply voltage and current is \",round(phid,2),\"deg lagging\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Inductive reactance, XL = 3.0 ohms\n",
"\n",
" (b)Impedance, Z = 5.0 ohms\n",
"\n",
" (c)Current, I = 48.0 A\n",
"\n",
" (d)phase angle between the supply voltage and current is 36.87 deg lagging\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 8, page no. 217
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the resistance, impedance, inductive reactance and inductance of the coil.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"Vdc = 12;# in volts\n",
"Vac = 240;# in volts\n",
"Iac = 20;# in Amperes\n",
"Idc = 2;# in Amperes\n",
"f = 50;# in Hz\n",
"\n",
"#calculation:\n",
"R = Vdc/Idc\n",
"Z = Vac/Iac\n",
"XL = (Z**2 - R**2)**0.5\n",
"L = XL/(2*math.pi*f)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Resistance, R = \",R,\" ohms\"\n",
"print \"\\n (b)Impedance, Z = \",Z,\" ohms\"\n",
"print \"\\n (c)Inductive reactance, XL = \",round(XL,2),\" ohms\"\n",
"print \"\\n (d)Inductance, L = \",round(L,2),\" H\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Resistance, R = 6.0 ohms\n",
"\n",
" (b)Impedance, Z = 12.0 ohms\n",
"\n",
" (c)Inductive reactance, XL = 10.39 ohms\n",
"\n",
" (d)Inductance, L = 0.03 H"
]
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 9, page no. 217
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate (a) the inductive reactance of the coil, \n",
"#(b) the impedance of the circuit, \n",
"#(c) the current in the circuit, \n",
"#(d) the p.d. across each component, and \n",
"#(e) the circuit phase angle.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 200;# in ohms\n",
"L = 0.3183;# in henry\n",
"V = 240;# in volts\n",
"f = 50;# in Hz\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f*L\n",
"Z = (R**2 + XL**2)**0.5\n",
"I = V/Z\n",
"VL = I*XL\n",
"VR = I*R\n",
"phid = math.atan(XL/R)*180/math.pi\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Inductive reactance, XL = \",round(XL,2),\" ohms\"\n",
"print \"\\n (b)Impedance, Z = \",round(Z,2),\" ohms\"\n",
"print \"\\n (c)current, I = \",round(I,2),\" A\"\n",
"print \"\\n (d)p.d. across Inductor, VL = \",round(VL,2),\" V and p.d. across resistance, VR = \",round(VR,2),\" V\"\n",
"print \"\\n (e)circuit phase angle is \",round(phid,2),\" deg lagging\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Inductive reactance, XL = 100.0 ohms\n",
"\n",
" (b)Impedance, Z = 223.61 ohms\n",
"\n",
" (c)current, I = 1.07 A\n",
"\n",
" (d)p.d. across Inductor, VL = 107.33 V and p.d. across resistance, VR = 214.66 V\n",
"\n",
" (e)circuit phase angle is 26.56 deg lagging\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 10, page no. 218
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate (a) the circuit impedance, \n",
"#(b) the current flowing, \n",
"#(c) the p.d. across the resistance, \n",
"#(d) the p.d. across the inductance and \n",
"#(e) the phase angle between voltage and current.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 100;# in ohms\n",
"L = 0.2;# in henry\n",
"Vmax = 200;# in volts\n",
"w = 500;# in rad/sec\n",
"\n",
"#calculation:\n",
"Vrms = 0.707*Vmax\n",
"f = w/(2*math.pi)\n",
"XL = 2*math.pi*f*L\n",
"Z = (R**2 + XL**2)**0.5\n",
"I = Vrms/Z\n",
"VL = I*XL\n",
"VR = I*R\n",
"phid = math.atan(XL/R)*180/math.pi\n",
"\n",
"\\\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Impedance, Z = \",round(Z,2),\" ohms\"\n",
"print \"\\n (b)current, I = \",round(I,2),\" A\"\n",
"print \"\\n (c)p.d. across resistance, VR = \",round(VR,2),\" V\"\n",
"print \"\\n (d)p.d. across Inductor, VL = \",round(VL,2),\" V\"\n",
"print \"\\n (e)circuit phase angle is \",phid,\"deg\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Impedance, Z = 141.42 ohms\n",
"\n",
" (b)current, I = 1.0 A\n",
"\n",
" (c)p.d. across resistance, VR = 99.98 V\n",
"\n",
" (d)p.d. across Inductor, VL = 99.98 V\n",
"\n",
" (e)circuit phase angle is 45.0 deg"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 11, page no. 218
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#determine the value of the supply voltage and the voltage across the 1.273 mH inductance.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 30;# in ohms\n",
"L = 1.2273E-3;# in henry\n",
"f = 5000;# in Hz\n",
"VR = 6;# in volts\n",
"\n",
"#calculation:\n",
"I =VR/R\n",
"XL = 2*math.pi*f*L\n",
"Z = (R**2 + XL**2)**0.5\n",
"V = I*Z\n",
"VL = I*XL\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)supply voltage = \",round(V,2),\" Volts\"\n",
"print \"\\n (b)p.d. across Inductor, VL = \",round(VL,2),\" V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)supply voltage = 9.77 Volts\n",
"\n",
" (b)p.d. across Inductor, VL = 7.71 V"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 12, page no. 219
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine (a) the impedance of the circuit, \n",
"#(b) the current in the circuit, \n",
"#(c) the circuit phase angle, \n",
"#(d) the p.d. across the 60 ohm resistor\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 60;# in ohms\n",
"Rc = 20;# in ohms\n",
"L = 159.2E-3;# in henry\n",
"f = 50;# in Hz\n",
"V = 240;# in volts\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f*L\n",
"Rt = R + Rc\n",
"Z = (Rt**2 + XL**2)**0.5\n",
"I = V/Z\n",
"phid = math.atan(XL/Rt)*180/math.pi\n",
"VR = I*R\n",
"Zc = (Rc**2 + XL**2)**0.5\n",
"Vc = I*Zc\n",
"VL = I*XL\n",
"VRc = I*Rc\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Impedance, Z = \",round(Z,2),\" ohms\"\n",
"print \"\\n (b)current, I = \",round(I,3),\" A\"\n",
"print \"\\n (c)circuit phase angle is \",round(phid,0),\"deg lagging\"\n",
"print \"\\n (d)p.d. across resistance, VR = \",round( VR,1),\" V\"\n",
"print \"\\n (e)p.d. across coil, Vc = \",round(Vc,1),\" V\"\n",
"print \"\\n (f1)p.d. across Inductor, VL = \",round(VL,2),\" V\"\n",
"print \"\\n (f2)p.d. across coil resistance, VRc = \",round(VRc,2),\" V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Impedance, Z = 94.35 ohms\n",
"\n",
" (b)current, I = 2.544 A\n",
"\n",
" (c)circuit phase angle is 32.0 deg lagging\n",
"\n",
" (d)p.d. across resistance, VR = 152.6 V\n",
"\n",
" (e)p.d. across coil, Vc = 137.0 V\n",
"\n",
" (f1)p.d. across Inductor, VL = 127.23 V\n",
"\n",
" (f2)p.d. across coil resistance, VRc = 50.88 V"
]
}
],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 13, page no. 220
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate (a) the impedance, and (b) the current taken from a 240 V, 50 Hz supply. \n",
"#Find also the phase angle between the supply voltage and the current.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 25;# in ohms\n",
"C = 45E-6;# in Farads\n",
"f = 50;# in Hz\n",
"V = 240;# in volts\n",
"\n",
"#calculation:\n",
"Xc = 1/(2*math.pi*f*C)\n",
"Z = (R**2 + Xc**2)**0.5\n",
"I = V/Z\n",
"phid = math.atan(Xc/R)*180/math.pi\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Impedance, Z = \",round(Z,2),\" ohms\"\n",
"print \"\\n (b)current, I = \",round(I,2),\" A\"\n",
"print \"\\n (c)phase angle between the supply voltage and current is \",round(phid,2),\"deg leading\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Impedance, Z = 75.02 ohms\n",
"\n",
" (b)current, I = 3.2 A\n",
"\n",
" (c)phase angle between the supply voltage and current is 70.54 deg leading"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 14, page no. 221
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate: (a) the value of capacitance, C, \n",
"#(b) the supply voltage, \n",
"#(c) the phase angle between the supply voltage and current, \n",
"#(d) the p.d. across the resistor, and\n",
"#(e) the p.d. across the capacitor\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 40;# in ohms\n",
"f = 60;# in Hz\n",
"I = 3;#in amperes\n",
"Z = 50;# in ohms\n",
"\n",
"#calculation:\n",
"Xc = (Z**2 - R**2)**0.5\n",
"C = 1/(2*math.pi*f*Xc)\n",
"V = I*Z\n",
"phid = math.atan(Xc/R)*180/math.pi\n",
"VR = I*R\n",
"Vc = I*Xc\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)capacitance, C = \",round((C/1E-6),2),\" uF\"\n",
"print \"\\n (b)Voltage, V = \",V,\" Volts\"\n",
"print \"\\n (c)phase angle between the supply voltage and current is \",round(phid,2),\"deg leading\"\n",
"print \"\\n (d)p.d. across resistance, VR = \", VR,\" V\"\n",
"print \"\\n (e)p.d. across Capacitor, Vc = \",Vc,\" V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)capacitance, C = 88.42 uF\n",
"\n",
" (b)Voltage, V = 150 Volts\n",
"\n",
" (c)phase angle between the supply voltage and current is 36.87 deg leading\n",
"\n",
" (d)p.d. across resistance, VR = 120 V\n",
"\n",
" (e)p.d. across Capacitor, Vc = 90.0 V"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 15, page no. 222
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate (a) the current flowing, \n",
"#(b) the phase difference between the supply voltage and current, \n",
"#(c) the voltage across the coil and \n",
"#(d) the voltage across the capacitor\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 5;# in ohms\n",
"C = 100E-6;# in Farads\n",
"L = 0.12;# in Henry\n",
"f = 50;# in Hz\n",
"V = 300;# in volts\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f*L\n",
"Xc = 1/(2*math.pi*f*C)\n",
"X = XL - Xc\n",
" #Since XL is greater than Xc, the circuit is inductive.\n",
"Z = (R**2 + (XL-Xc)**2)**0.5\n",
"I = V/Z\n",
"phid = math.atan((XL-Xc)/R)*180/math.pi\n",
"Zcl = (R**2 + XL**2)**0.5\n",
"Vcl = I*Zcl\n",
"phidc = math.atan(XL/R)*180/math.pi\n",
"Vc = I*Xc\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Current,I = \",round(I,2),\" A\"\n",
"print \"\\n (b)phase angle between the supply voltage and current is \",round(phid,2),\"deg\"\n",
"print \"\\n (c)Voltage across the coil, Vcoil = \",round(Vcl,0),\" Volts\"\n",
"print \"\\n (d)p.d. across Capacitor, Vc = \",round(Vc,0),\" V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Current,I = 38.91 A\n",
"\n",
" (b)phase angle between the supply voltage and current is 49.57 deg\n",
"\n",
" (c)Voltage across the coil, Vcoil = 1480.0 Volts\n",
"\n",
" (d)p.d. across Capacitor, Vc = 1239.0 V"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 16, page no. 224
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate (a) the circuit current, \n",
"#(b) the circuit phase angle and \n",
"#(c) the voltage drop across each impedance.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R1 = 8;# in ohms\n",
"C = 0.25E-6;# in Farads\n",
"L = 130E-6;# in Henry\n",
"Rc = 5;# in ohms\n",
"R2 = 10;# in ohms\n",
"f = 20000;# in Hz\n",
"V = 40;# in volts\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f*L\n",
"Xc = 1/(2*math.pi*f*C)\n",
"X = Xc - XL\n",
"R = R1 + R2 + Rc\n",
" #Since Xc is greater than XL, the circuit is capacitive.\n",
"Z = (R**2 + (Xc-XL)**2)**0.5\n",
"I = V/Z\n",
"phid = math.atan((Xc-XL)/R)*180/math.pi\n",
"V1 = I*R1\n",
"V2 = I*((Rc**2 + XL**2)**0.5)\n",
"V3 = I*((R2**2 + Xc**2)**0.5)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Current,I = \",round(I,2),\" A\"\n",
"print \"\\n (b)circuit phase angle is \",round(phid,2),\"deg leading\"\n",
"print \"\\n (c1)Voltage across the Resistance of 8 ohms = \",round(V1,2),\" Volts\"\n",
"print \"\\n (c2)Voltage across the coil, Vcoil = \",round(V2,2),\" Volts\"\n",
"print \"\\n (c3)p.d. across Capacitor resistance circuit = \",round(V3,2),\" Volts\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Current,I = 1.44 A\n",
"\n",
" (b)circuit phase angle is 33.97 deg leading\n",
"\n",
" (c1)Voltage across the Resistance of 8 ohms = 11.54 Volts\n",
"\n",
" (c2)Voltage across the coil, Vcoil = 24.64 Volts\n",
"\n",
" (c3)p.d. across Capacitor resistance circuit = 48.12 Volts"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 17, page no. 224
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the p.d.\u2019s V1 and V2 for the circuit\n",
"#determine the supply voltage V and the circuit phase angle.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R1 = 4;# in ohms\n",
"C = 1.273E-6;# in Farads\n",
"L = 0.286E-3;# in Henry\n",
"R2 = 8;# in ohms\n",
"f = 5000;# in Hz\n",
"I = 5;# in amperes\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f*L\n",
"phid1 = math.atan(XL/R1)*180/math.pi\n",
"V1 = I*((R1**2 + XL**2)**0.5)\n",
"Xc = 1/(2*math.pi*f*C)\n",
"V2 = I*((R2**2 + Xc**2)**0.5)\n",
"phid2 = math.atan(Xc/R2)*180/math.pi\n",
"Z = ((R1+R2)**2 + (Xc-XL)**2)**0.5\n",
"V = I*Z\n",
"phid = math.atan((Xc-XL)/(R1+R2))*180/math.pi\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Voltage supply, V = \",round(V,2),\" V\"\n",
"print \"\\n (b)circuit phase angle is \",round(phid,2),\"deg leading\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Voltage supply, V = 100.08 V\n",
"\n",
" (b)circuit phase angle is 53.16 deg leading"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 18, page no. 226
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#At what frequency does resonance occur?\n",
"#Find the current flowing at the resonant frequency.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 10;# in ohms\n",
"C = 60E-6;# in Farads\n",
"L = 125E-3;# in Henry\n",
"V = 120;# in Volts\n",
"\n",
"#calculation:\n",
"fr = 1/(2*math.pi*(L*C)**0.5)\n",
" #At resonance, XL = Xc and impedance Z = R\n",
"I = V/R\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Resonance frequency,Fr = \",round(fr,2),\" Hz\"\n",
"print \"\\n (b)Current, I = \",round(I,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Resonance frequency,Fr = 58.12 Hz\n",
"\n",
" (b)Current, I = 12.0"
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 19, page no. 226
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#find (a) the circuit resistance, and (b) the circuit capacitance.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"L = 0.05E-3;# in Henry\n",
"fr = 200000;# in Hz\n",
"V = 0.002;# in Volts\n",
"I = 0.1E-3;# in amperes\n",
"#calculation:\n",
"# L-C-R\n",
"#At resonance, XL = Xc and impedance Z = R\n",
"R = V/I\n",
"C = 1/(L*(2*math.pi*fr)**2)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Resistance, R = \",round(R,2),\" ohms\"\n",
"print \"\\n (b)Capacitance, C = \",round((C/1E-9),2),\"nF\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Resistance, R = 20.0 ohms\n",
"\n",
" (b)Capacitance, C = 12.67 nF"
]
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 20, page no. 227
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine (a) the resonant frequency, and \n",
"#(b) the current at resonance. \n",
"#How many times greater than the supply voltage is the voltage across the reactances at resonance?\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"L = 80E-3;# in Henry\n",
"C = 0.25E-6;# in Farads\n",
"R = 12.5;# in ohms\n",
"V = 100;# in Volts\n",
"\n",
"#calculation:\n",
"fr = 1/(2*math.pi*((L*C)**0.5))\n",
" #At resonance, XL = Xc and impedance Z = R\n",
"I = V/R\n",
"VL = I*(2*math.pi*fr*L)\n",
"Vc = I/(2*math.pi*fr*C)\n",
"Vm = VL/V\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)the resonant frequency = \",round(fr,2),\" Hz\"\n",
"print \"\\n (b)Current, I = \",round(I,2),\"\"\n",
"print \"\\n (b)Voltage magnification at resonance = \",round(Vm,2),\" V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)the resonant frequency = 1125.4 Hz\n",
"\n",
" (b)Current, I = 8.0 \n",
"\n",
" (b)Voltage magnification at resonance = 45.25 V"
]
}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 21, page no. 228
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the Qfactor of the circuit at resonance\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"L = 60E-3;# in Henry\n",
"C = 30E-6;# in Farads\n",
"R = 2;# in ohms\n",
"\n",
"#calculation:\n",
"Q = ((L/C)**0.5)/R\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n At resonance, Q-factor = \",round(Q,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" At resonance, Q-factor = 22.36"
]
}
],
"prompt_number": 21
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 22, page no. 228
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine (a) the resonant frequency, \n",
"#(b) the current at resonance,\n",
"#(c) the voltages across the coil and the capacitor at resonance, and\n",
"#(d) the Q-factor of the circuit.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"L = 100E-3;# in Henry\n",
"C = 2E-6;# in Farads\n",
"R = 10;# in ohms\n",
"V = 50;# in Volts\n",
"\n",
"#calculation:\n",
"fr = 1/(2*math.pi*((L*C)**0.5))\n",
" #At resonance, XL = Xc and impedance Z = R\n",
"I = V/R\n",
"VL = I*(2*math.pi*fr*L)\n",
"Vc = I/(2*math.pi*fr*C)\n",
"Q = VL/V\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)the resonant frequency = \",round(fr,2),\" Hz\"\n",
"print \"\\n (b)Current, I = \",round(I,2),\"\"\n",
"print \"\\n (c)Voltage across coil at resonance is \",round(VL,2),\"V \"\n",
"print \"and Voltage across capacitance at resonance is \",round( Vc,2),\"V\"\n",
"print \"\\n (d)At resonance, Q-factor = \",round(Q,2)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)the resonant frequency = 355.88 Hz\n",
"\n",
" (b)Current, I = 5.0 \n",
"\n",
" (c)Voltage across coil at resonance is 1118.03 V and Voltage across capacitance at resonance is 1118.03 V\n",
"\n",
" (d)At resonance, Q-factor = 22.36"
]
}
],
"prompt_number": 22
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 23, page no. 230
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the bandwidth of the filter.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"L = 20E-3;# in Henry\n",
"R = 10;# in ohms\n",
"fr = 5000;# in Hz\n",
"\n",
"#calculation:\n",
"Qr = (2*math.pi*fr)*L/R\n",
"bw = fr/Qr\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Bandwidth, (f2-f1) = \",round(bw,2),\" Hz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Bandwidth, (f2-f1) = 79.58 Hz"
]
}
],
"prompt_number": 23
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 24, page no. 231
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Find the power dissipated in the resistor.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 5000;# in ohms\n",
"Imax = 0.250;# in Amperes\n",
"\n",
"#calculation:\n",
"Irms = 0.707*Imax\n",
"P = Irms*Irms*R\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Power, P = \",round(P,2),\" Watts\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Power, P = 156.2 Watts"
]
}
],
"prompt_number": 24
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 25, page no. 231
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the power dissipated.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"R = 60;# in ohms\n",
"L = 75E-3;# in Henry\n",
"V = 110;# in Volts\n",
"f = 60;# in Hz\n",
"\n",
"#calculation:\n",
"XL = 2*math.pi*f*L\n",
"Z = (R**2 + XL**2)**0.5\n",
"I = V/Z\n",
"P = I*I*R\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Power, P = \",round(P,2),\" Watts\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Power, P = 165.02 Watts"
]
}
],
"prompt_number": 25
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 26, page no. 232
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Find the value of the inductance.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"VI = 300;# in VA\n",
"V = 150;# in Volts\n",
"f = 50;# in Hz\n",
"\n",
"#calculation:\n",
"I = VI/V\n",
"XL = V/I\n",
"L = XL/(2*math.pi*f)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n Inductance = \",round(L,2),\" H\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" Inductance = 0.24 H"
]
}
],
"prompt_number": 26
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 27, page no. 232
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the rated power output and the corresponding reactive power.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"VI = 200000;# in VA\n",
"pf = 0.8;# power factor\n",
"\n",
"#calculation:\n",
"P = VI*pf\n",
"Q = VI*math.sin(math.acos(pf))\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n rated power output is \",round(P/1000,2),\"KW and the corresponding reactive power is \",round(Q/1000,2),\"kvar\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" rated power output is 160.0 KW and the corresponding reactive power is 120.0 kvar"
]
}
],
"prompt_number": 27
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 28, page no. 233
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate (a) the resistance, \n",
"#(b) the impedance, \n",
"#(c) the reactance, \n",
"#(d) the power factor, and \n",
"#(e) the phase angle between voltage and current.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"V = 120;# in Volts\n",
"f = 50;# in Hz\n",
"P = 400;# in Watt\n",
"I = 8;# in Amperes\n",
"\n",
"#calculation:\n",
"R = P/(I*I)\n",
"Z = V/I\n",
"XL = (Z**2 - R**2)**0.5\n",
"pf = P/(V*I)\n",
"phi = math.acos(pf)*180/math.pi\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)resistance = \",round(R,2),\" ohm \"\n",
"print \"\\n (b)Impedance Z = \",round(Z,2),\" Ohm \"\n",
"print \"\\n (c)reactance = \",round(XL,2),\" ohm \"\n",
"print \"\\n (d)Power factor = \",round(pf,2),\"\"\n",
"print \"\\n (e)phase angle = \",round(phi,2),\"deg lagging\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)resistance = 6.25 ohm \n",
"\n",
" (b)Impedance Z = 15.0 Ohm \n",
"\n",
" (c)reactance = 13.64 ohm \n",
"\n",
" (d)Power factor = 0.42 \n",
"\n",
" (e)phase angle = 65.38 deg lagging"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 29, page no. 233
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Find (a) the current flowing, (b) the phase angle,\n",
"#(c) the resistance, (d) the impedance, and (e) the capacitance.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"V = 100;# in Volts\n",
"f = 60;# in Hz\n",
"P = 100;# in Watt\n",
"pf = 0.5;# power factor\n",
"\n",
"#calculation:\n",
"I = P/(pf*V)\n",
"phi = math.acos(pf)*180/math.pi\n",
"R = P/(I*I)\n",
"Z = V/I\n",
"Xc = (Z**2 - R**2)**0.5\n",
"C = 1/(2*math.pi*f*Xc)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Current I = \",round(I,2),\" A \"\n",
"print \"\\n (b)phase angle = \",round(phi,2),\"deg leading\"\n",
"print \"\\n (c)resistance = \",round(R,2),\" ohm \"\n",
"print \"\\n (d)Impedance Z = \",round(Z,2),\" Ohm \"\n",
"print \"\\n (e)capacitance = \",round((C/1E-6),2),\"uF \""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Current I = 2.0 A \n",
"\n",
" (b)phase angle = 60.0 deg leading\n",
"\n",
" (c)resistance = 25.0 ohm \n",
"\n",
" (d)Impedance Z = 50.0 Ohm \n",
"\n",
" (e)capacitance = 61.26 uF "
]
}
],
"prompt_number": 6
}
],
"metadata": {}
}
]
}