{
"metadata": {
"name": ""
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Chapter 24: Application of complex numbers to series a.c. circuits
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 1, page no. 433
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the values of the resistance and the series-connected inductance or capacitance for each of the following impedances:\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"z1 = 12 + 5j;\n",
"z2 = -40j;\n",
"r3 = 30;\n",
"theta3 = 60;# in degrees\n",
"r4 = 2.20E6; \n",
"theta4 = -30;# in degrees\n",
"f = 50;# in Hz\n",
"\n",
"#calculation:\n",
" #for an R-L series circuit, impedance\n",
" # Z = R + iXL\n",
"Ra = z1.real\n",
"XLa = z1.imag\n",
"La = XLa/(2*math.pi*f)\n",
" #for a purely capacitive circuit, impedance Z = -iXc\n",
"Xcb = abs(z2.imag)\n",
"Cb = 1/(2*math.pi*f*Xcb)\n",
"z3 = r3*cmath.cos(theta3*math.pi/180) + (r3*cmath.sin(theta3*math.pi/180))*1j\n",
"Rc = z3.real\n",
"XLc = z3.imag\n",
"Lc = XLc/(2*math.pi*f)\n",
"z4 = r4*cmath.cos(theta4*math.pi/180) + (r4*cmath.sin(theta4*math.pi/180))*1j\n",
"Rd = z4.real\n",
"Xcd = abs(z4.imag)\n",
"Cd = 1/(2*math.pi*f*Xcd)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)an impedance (12 + i5)ohm represents a resistance of \",round( Ra,2),\" ohm \"\n",
"print \"in series with an inductance of \",round(La*1000,2),\"mH\"\n",
"print \"\\n (b)an impedance -40i ohm represents a pure capacitor of capacitance \",round(Cb*1E6,2),\"uF\"\n",
"print \"\\n (c)an impedance 30/_60deg ohm represents a resistance of \",round(Rc,2),\" ohm \"\n",
"print \"in series with an inductance of \",round(Lc*1000,2),\"mH\"\n",
"print \"\\n (d)an impedance 2.20 x 10^6 /_-30deg ohm represents a resistance of \",round(Rd/1000,2),\"kohm \"\n",
"print \" in series with a capacitor of capacitance \",round(Cd*1E9,2),\"nF\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)an impedance (12 + i5)ohm represents a resistance of 12.0 ohm \n",
"in series with an inductance of 15.92 mH\n",
"\n",
" (b)an impedance -40i ohm represents a pure capacitor of capacitance 79.58 uF\n",
"\n",
" (c)an impedance 30/_60deg ohm represents a resistance of 15.0 ohm \n",
"in series with an inductance of 82.7 mH\n",
"\n",
" (d)an impedance 2.20 x 10^6 /_-30deg ohm represents a resistance of 1905.26 kohm \n",
" in series with a capacitor of capacitance 2.89 nF\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 2, page no. 434
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine, in polar and rectangular forms, the current flowing in an inductor of negligible resistance and inductance\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"L = 0.1592 ;# in Henry\n",
"V = 250;# in Volts\n",
"f = 50;# in Hz\n",
"R = 0;# in ohms\n",
"\n",
"#calculation:\n",
" #for an R\u00e2\u20ac\u201cL series circuit, impedance\n",
" # Z = R + iXL\n",
"XL = 2*math.pi*f*L\n",
"Z = R + 1j*XL\n",
"I = V/Z\n",
"x = I.real\n",
"y = I.imag\n",
"r = (x**2 + y**2)**0.5\n",
"if ((x==0)&(y<0)):\n",
" theta = -90\n",
"elif ((x==0)&(y>0)):\n",
" theta = +90\n",
"else:\n",
" theta = cmath.phase(complex(x,y))*180/math.pi\n",
"\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n current is (\",round(r,2),\"/_\",theta,\"deg) A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" current is ( 5.0 /_ -90 deg) A"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 3, page no. 435
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the value of the supply p.d.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"C = 3E-6 ;# in farad\n",
"f = 1000;# in Hz\n",
"ri = 2.83;\n",
"thetai = 90;# in degrees\n",
"\n",
"#calculation:\n",
" #Capacitive reactance Xc\n",
"Xc = 1/(2*math.pi*f*C)\n",
" # circuit impedance Z\n",
"Z = -1*1j*Xc\n",
"I = ri*math.cos(thetai*math.pi/180) + 1j*ri*math.sin(thetai*math.pi/180)\n",
"V = I*Z\n",
"x = V.real\n",
"y = V.imag\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n supply p.d. is \",round(abs(V),0),\"V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" supply p.d. is 150.0 V"
]
}
],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 4, page no. 435
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine (a) the resistance, (b) the capacitance, \n",
"#(c) the modulus of the impedance, and (d) the current flowing and its phase angle,\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"V = 240;# in Volts\n",
"f = 50;# in Hz\n",
"Z = 30 - 50j;\n",
"\n",
"#calculation:\n",
" #Since impedance Z = 30 - i50,\n",
" #resistance\n",
"R = Z.real\n",
" #capacitive reactance\n",
"Xc = abs(Z.imag)\n",
" #capacitance\n",
"C = 1/(2*math.pi*f*Xc)\n",
" #modulus of impedance\n",
"modZ = (R**2 + Xc**2)**0.5\n",
"I = V/Z\n",
"x = I.real\n",
"y = I.imag\n",
"r = (x**2 + y**2)**0.5\n",
"theta = cmath.phase(complex(x,y))*180/math.pi\n",
"\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)resistance is \",round( R,2),\" ohm\"\n",
"print \"\\n (b)capacitance is \",round(C*1E6,2),\"uFarad\"\n",
"print \"\\n (c)modulus of impedance is \",round(modZ,2),\" ohm\"\n",
"print \"\\n (d)current flowing and its phase angle is (\",round( r,2),\"/_\",round( theta,2),\"deg) A\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)resistance is 30.0 ohm\n",
"\n",
" (b)capacitance is 63.66 uFarad\n",
"\n",
" (c)modulus of impedance is 58.31 ohm\n",
"\n",
" (d)current flowing and its phase angle is ( 4.12 /_ 59.04 deg) A"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 5, page no. 436
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine (a) the impedance of the circuit,\n",
"#(b) the current and circuit phase angle, \n",
"#(c) the p.d. across the 32 ohm resistor, and (d) the p.d. across the coil\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"V = 200;# in Volts\n",
"f = 50;# in Hz\n",
"R = 32;# in ohms\n",
"L = 0.15;# in Henry\n",
"\n",
"#calculation:\n",
" #Inductive reactance XL\n",
"XL = 2*math.pi*f*L\n",
" #impedance, Z\n",
"Z = R + 1j*XL\n",
" #Current I\n",
"I = V/Z\n",
"xi = I.real\n",
"yi = I.imag\n",
"ri = (xi**2 + yi**2)**0.5\n",
"if ((xi==0)&(yi<0)):\n",
" thetai = -90\n",
"elif ((xi==0)&(yi>0)):\n",
" thetai = +90\n",
"else:\n",
" thetai = cmath.phase(complex(xi,yi))*180/math.pi\n",
"\n",
" #P.d. across the resistor\n",
"VR = I*R\n",
"xr = VR.real\n",
"yr = VR.imag\n",
"rr = (xr**2 + yr**2)**0.5\n",
"thetar = cmath.phase(complex(xr,yr))*180/math.pi\n",
" #P.d. across the coil, VL\n",
"VL = I*1j*XL\n",
"xl = VL.real\n",
"yl = VL.imag\n",
"rl = (xl**2 + yl**2)**0.5\n",
"thetal = cmath.phase(complex(xl,yl))*180/math.pi\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)impedance is \",round(Z.real,2),\" + \",round( Z.imag,2),\")i ohm\"\n",
"print \"\\n (b)current flowing and its phase angle is lagging the voltage = (\",round( ri,2),\"/_\",round( thetai,2),\"deg) A\"\n",
"print \"\\n (c)P.d. across the resistor is (\",round(rr,2),\"/_\",round(thetar,2),\"deg) V\"\n",
"print \"\\n (d)P.d. across the coil, VL is (\",round(rl,2),\"/_\",round(thetal,2),\"deg) V\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)impedance is 32.0 + 47.12 )i ohm\n",
"\n",
" (b)current flowing and its phase angle is lagging the voltage = ( 3.51 /_ -55.82 deg) A\n",
"\n",
" (c)P.d. across the resistor is ( 112.36 /_ -55.82 deg) V\n",
"\n",
" (d)P.d. across the coil, VL is ( 165.46 /_ 34.18 deg) V"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 6, page no. 436
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the value of impedance\n",
"#determine the value of the components forming the series circuit.\n",
"from __future__ import division\n",
"import math\n",
"#initializing the variables:\n",
"V = 120 + 200j;# in Volts\n",
"f = 5E6;# in Hz\n",
"I = 7 + 16j;# in amperes\n",
"\n",
"#calculation:\n",
" #impedance, Z\n",
"Z = V/I\n",
"R = Z.real\n",
"X = Z.imag \n",
"if ((R>0)&(X<0)):\n",
" C = -1/(2*math.pi*f*X)\n",
"#Results\n",
" print \"\\n\\n Result \\n\\n\"\n",
" print \"\\n The series circuit thus consists of a resistor of resistance \",round(R,2),\" ohm \"\n",
" print \"and a capacitor of capacitive reactance\", round(X*-1,3),\"ohm and capacitance is\",round(C*1E9,2),\" nFarad\\n\"\n",
"elif ((R>0)&(X>0)):\n",
" L = 2*math.pi*f*X\n",
"#Results\n",
" print \"\\n\\n Result \\n\\n\"\n",
" print \"\\n The series circuit thus consists of a resistor of resistance \",round(R,2),\" ohm \"\n",
" print \" and a inductor of insuctance \",round(L*100,2),\" mHenry\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" The series circuit thus consists of a resistor of resistance 13.25 ohm \n",
"and a capacitor of capacitive reactance 1.705 ohm and capacitance is 18.67 nFarad\n",
"\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 7, page no. 437
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#determine the value of impedance Z2.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"rv = 70;# in volts\n",
"thetav = 30;# in degrees\n",
"ri = 3.5;# in amperes\n",
"thetai = -20;# in degrees\n",
" #z1 consist of two resistance\n",
"R1 = 4.36;# in ohms\n",
"R2 = -2.1j;# in ohms\n",
"\n",
" #calculation:\n",
"V = rv*math.cos(thetav*math.pi/180) + 1j*rv*math.sin(thetav*math.pi/180)\n",
"I = ri*math.cos(thetai*math.pi/180) + 1j*ri*math.sin(thetai*math.pi/180)\n",
" #impedance, Z\n",
"Z = V/I\n",
" #Total impedance Z = z1 + z2\n",
"Z1 = R1 + R2\n",
"Z2 = Z - Z1\n",
"x = Z2.real\n",
"y = Z2.imag \n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n impedance Z2 is \",round(x,2),\" + (\",round(y,2),\")i ohm\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" impedance Z2 is 8.5 + ( 17.42 )i ohm"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 8, page no. 437
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#determine (a) the supply voltage, (b) the voltage across the 90 \u000e resistance, \n",
"#(c) the voltage across the inductance, and (d) the circuit phase angle.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"R = 90;# in ohms\n",
"XL = 150;# in ohms\n",
"ri = 1.35;# in amperes\n",
"thetai = 0;# in degrees\n",
"\n",
"#calculation:\n",
"I = ri*math.cos(thetai*math.pi/180) + 1j*ri*math.sin(thetai*math.pi/180)\n",
" #Circuit impedance Z\n",
"Z = R + 1j*XL\n",
" #Supply voltage, V\n",
"V = I*Z\n",
" #Voltage across 90 ohm\u000e resistor\n",
"VR = V.real\n",
"#Voltage across inductance, VL\n",
"VL = V.imag\n",
"xv = V.real\n",
"yv = V.imag\n",
"rv = (xv**2 + yv**2)**0.5\n",
"thetav = cmath.phase(complex(xv,yv))*180/math.pi\n",
"phi = thetav - thetai\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)Supply voltage, V is \",xv,\" + (\",yv,\")i V\\n\"\n",
"print \"\\n (b)Voltage across 90 ohm resistor, VR is \",VR,\" V\\n\"\n",
"print \"\\n (c)Voltage across inductance, VL is \",VL,\" V\\n\"\n",
"print \"\\n (d)Circuit phase angle is \",round(phi,2),\"deg lagging\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)Supply voltage, V is 121.5 + ( 202.5 )i V\n",
"\n",
"\n",
" (b)Voltage across 90 ohm resistor, VR is 121.5 V\n",
"\n",
"\n",
" (c)Voltage across inductance, VL is 202.5 V\n",
"\n",
"\n",
" (d)Circuit phase angle is 59.04 deg lagging"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 9, page no. 438
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine (a) the rms value of voltage (in polar form),\n",
"#(b) the circuit impedance, (c) the rms current flowing, and\n",
"#(d) the circuit phase angle.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"R = 25;# in ohms\n",
"L = 0.02;# in henry\n",
"Vm = 282.8;# in volts\n",
"w = 628.4;# in rad/sec\n",
"phiv = math.pi/3;# phase angle\n",
"\n",
"#calculation:\n",
" #rms voltage\n",
"Vrms = 0.707*Vm*math.cos(phiv) + 0.707*Vm*math.sin(phiv)*1j\n",
" #frequency\n",
"f = w/(2*math.pi)\n",
" #Inductive reactance XL\n",
"XL = 2*math.pi*f*L\n",
" #Circuit impedance Z\n",
"Z = R + XL*1j\n",
" #Rms current\n",
"Irms = Vrms/Z\n",
"phii = cmath.phase(complex(Irms.real, Irms.imag))*180/math.pi\n",
"phi = phiv*180/math.pi - phii\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)the rms value of voltage is \",round(Vrms.real,2),\" + (\",round( Vrms.imag,2),\")i V\\n\"\n",
"print \"\\n (b)the circuit impedance is \",round(R,2),\" + (\",round( XL,2),\")i ohm\\n\"\n",
"print \"\\n (c)the rms current flowing is \",round(Irms.real,2),\" + (\",round( Irms.imag,2),\")i A\\n\"\n",
"print \"\\n (d)Circuit phase angle is \",round(phi,2),\"deg lagging\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)the rms value of voltage is 99.97 + ( 173.15 )i V\n",
"\n",
"\n",
" (b)the circuit impedance is 25.0 + ( 12.57 )i ohm\n",
"\n",
"\n",
" (c)the rms current flowing is 5.97 + ( 3.92 )i A\n",
"\n",
"\n",
" (d)Circuit phase angle is 26.69 deg lagging\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 10, page no. 438
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine the current flowing in the circuit\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"R = 12;# in ohms\n",
"L = 0.10;# in henry\n",
"C = 120E-6;# in Farads\n",
"f = 50;# in Hz\n",
"V = 240;# in volts\n",
"\n",
"#calculation:\n",
" #Inductive reactance, XL\n",
"XL = 2*math.pi*f*L\n",
" #Capacitive reactance, Xc\n",
"Xc = 1/(2*math.pi*f*C)\n",
" #Circuit impedance Z\n",
"Z = R + 1j*(XL - Xc)\n",
"I = V/Z\n",
"phii = cmath.phase(complex(I.real, I.imag))*180/math.pi\n",
"phiv = 0# in degrees\n",
"phi = phiv - phii\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n the current flowing is \",round(abs(I),1),\"/_\",round(cmath.phase(complex(I.real,I.imag))*180/math.pi,1),\"deg A\\n\"\n",
"print \"and Circuit phase angle is \",round(phi,1),\"deg lagging\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" the current flowing is 18.5 /_ -22.2 deg A\n",
"\n",
"and Circuit phase angle is 22.2 deg lagging\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 11, page no. 439
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#determine the values of R and L, Determine also the voltage across the coil and the voltage across the capacitor.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"C = 50E-6;# in Farads\n",
"f = 50;# in Hz\n",
"V = 225;# in volts\n",
"ri = 1.5;# in Amperes\n",
"thetai = -30;# in degrees\n",
"\n",
"#calculation:\n",
"I = ri*math.cos(thetai*math.pi/180) + 1j*ri*math.sin(thetai*math.pi/180)\n",
" #Capacitive reactance, Xc\n",
"Xc = 1/(2*math.pi*f*C)\n",
" #Circuit impedance Z\n",
"Z = V/I\n",
"R = Z.real\n",
"XL = Z.imag + Xc\n",
" #inductance L\n",
"L = XL/(2*math.pi*f)\n",
" #Voltage across coil\n",
"Zcoil = R + 1j*XL\n",
"Vcoil = I*Zcoil\n",
" #Voltage across capacitor,\n",
"Vc = I*(-1j*Xc)\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n (a)resistance is \",round(R,2),\" ohm and inductance is \",round( L,3),\" H\\n\"\n",
"print \"\\n (b)voltage across the coil is \",round(Vcoil.real,2),\" + (\",round( Vcoil.imag,2),\")i V\\n\"\n",
"print \"\\n (c)voltage across the capacitor is \",round(Vc.real,2),\" + (\",round( Vc.imag,2),\")i V\\n\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" (a)resistance is 129.9 ohm and inductance is 0.441 H\n",
"\n",
"\n",
" (b)voltage across the coil is 272.75 + ( 82.7 )i V\n",
"\n",
"\n",
" (c)voltage across the capacitor is -47.75 + ( -82.7 )i V"
]
}
],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Example 12, page no. 440
"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Determine also the value of the supply voltage V and the circuit phase angle.\n",
"from __future__ import division\n",
"import math\n",
"import cmath\n",
"#initializing the variables:\n",
"C = 2.653E-6;# in Farads\n",
"R1 = 8;# in ohms\n",
"R2 = 5;# in ohms\n",
"L = 0.477E-3;# in Henry\n",
"f = 4000;# in Hz\n",
"ri = 6;# in Amperes\n",
"thetai = 0;# in degrees\n",
"\n",
"#calculation:\n",
"I = ri*math.cos(thetai*math.pi/180) + 1j*ri*math.sin(thetai*math.pi/180)\n",
" #Capacitive reactance, Xc\n",
"Xc = 1/(2*math.pi*f*C)\n",
" #impedance Z1\n",
"Z1 = R1 - 1j*Xc\n",
" #inductive reactance XL\n",
"XL = 2*math.pi*f*L\n",
" #impedance Z2,\n",
"Z2 = R2 + 1j*XL\n",
" #voltage V1\n",
"V1 = I*Z1\n",
" #voltage V2\n",
"V2 = I*Z2\n",
" #Supply voltage, V\n",
"V = V1 + V2\n",
"phiv = cmath.phase(complex(V.real, V.imag))*180/math.pi\n",
"phi = phiv - thetai\n",
"\n",
"\n",
"#Results\n",
"print \"\\n\\n Result \\n\\n\"\n",
"print \"\\n supply voltage is \",round(V.real,2),\" + (\",round( V.imag,2),\")i V\\n\"\n",
"print \"and Circuit phase angle is \",round(phi,2),\"deg leading\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
" Result \n",
"\n",
"\n",
"\n",
" supply voltage is 78.0 + ( -18.06 )i V\n",
"\n",
"and Circuit phase angle is -13.03 deg leading"
]
}
],
"prompt_number": 2
}
],
"metadata": {}
}
]
}