Chapter 15: Single-phase series a.c. circuits

Example 1, page no. 214

In [1]:
from __future__ import division
import math
#initializing  the  variables:
L  =  0.32;#  in  Henry
f1  =  50;#  in  Hz
f2  =  5000;#  in  Hz
Z  =  124;#  in  ohms

#calculation:
XL  =  2*math.pi*f1*L
L  =  Z/(2*math.pi*f2)


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Inductive  reactance,  XL  =  ",round(XL,2),"  ohms  \n"
print  "\n  (b)Inductance  L  =  ",round((L/1E-3),2),"  mH  \n"


  Result  



  (a)Inductive  reactance,  XL  =   100.53   ohms  


  (b)Inductance  L  =   3.95   mH

Example 2, page no. 214

In [2]:
from __future__ import division
import math
#initializing  the  variables:
L  =  0.040;#  in  Henry
V1  =  240;#  in  volts
V2  =  100;#  in  volts
f1  =  50;#  in  Hz
f2  =  1000;#  in  Hz

#calculation:
XL1  =  2*math.pi*f1*L
I1  =  V1/XL1
XL2  =  2*math.pi*f2*L
I2  =  V2/XL2

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Inductive  reactance,  XL  =  ",round(  XL1,2),"  ohms  and  current  I  =  ",round(  I1,2),"  A\n"
print  "\n  (b)Inductive  reactance,  XL  =  ",round(  XL2,2),"  ohms  and  current  I  =  ",round(  I2,2),"  A\n"


  Result  



  (a)Inductive  reactance,  XL  =   12.57   ohms  and  current  I  =   19.1   A


  (b)Inductive  reactance,  XL  =   251.33   ohms  and  current  I  =   0.4   A

Example 3, page no. 215

In [3]:
from __future__ import division
import math
#initializing  the  variables:
C  =  10E-6;#  in  Farads
f1  =  50;#  in  Hz
f2  =  20000;#  in  Hz

#calculation:
Xc1  =  1/(2*math.pi*f1*C)
Xc2  =  1/(2*math.pi*f2*C)


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Capacitive  reactance,  Xc  =  ",round(  Xc1,2),"  ohms  "
print  "\n  (b)Capacitive  reactance,  Xc  =  ",round(  Xc2,2),"  ohms  "


  Result  



  (a)Capacitive  reactance,  Xc  =   318.31   ohms  

  (b)Capacitive  reactance,  Xc  =   0.8   ohms

Example 4, page no. 215

In [4]:
from __future__ import division
import math
#initializing  the  variables:
Z  =  40;#  in  ohms
f  =  50;#  in  Hz

#calculation:
C  =  1/(2*math.pi*f*Z)

#Results
print  "\n\n  Result  \n\n"
print  "\n  Capacitance,C  =  ",round((C/1E-6),2)," uF  "


  Result  



  Capacitance,C  =   79.58  uF

Example 5, page no. 215

In [5]:
from __future__ import division
import math
#initializing  the  variables:
C  =  23E-6;#  in  Farads
f  =  50;#  in  Hz
V  =  240;#  in  volts

#calculation:
Xc  =  1/(2*math.pi*f*C)
I  =  V/Xc


#Results
print  "\n\n  Result  \n\n"
print  "\n  current  I  =  ",round(I,2),"  A  "


  Result  



  current  I  =   1.73   A

Example 6, page no. 216

In [7]:
from __future__ import division
import math
#initializing  the  variables:
Vr  =  12;#  in  volts
Vl  =  5;#  in  volts

#calculation:
V  =  (Vr**2  +  Vl**2)**0.5
phi  =  math.atan(Vl/Vr)
phid  =  phi*180/math.pi


#Results
print  "\n\n  Result  \n\n"
print  "\n  supply  voltage  V  =  ",V,"  V,  phase  angle  between  current  and  voltage  is  ",  round(phid,2),"deg lagging"


  Result  



  supply  voltage  V  =   13.0   V,  phase  angle  between  current  and  voltage  is   22.62 deg lagging

Example 7, page no. 216

In [8]:
from __future__ import division
import math
#initializing  the  variables:
V  =  240;#  in  volts
R  =  4;#  in  ohms
L  =  0.00955;#  in  Henry
f  =  50;#  in  Hz

#calculation:
XL  =  2*math.pi*f*L
Z  =  (R**2  +  XL**2)**0.5
I  =  V/Z
phid  = math.atan(XL/R)*180/math.pi

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Inductive  reactance,  XL  =  ",round(XL,2),"  ohms"
print  "\n  (b)Impedance,  Z  =  ",round(Z,2),"  ohms"
print  "\n  (c)Current,  I  =  ",round(I,2),"  A"
print  "\n  (d)phase  angle  between  the  supply  voltage  and  current  is  ",round(phid,2),"deg lagging\n"


  Result  



  (a)Inductive  reactance,  XL  =   3.0   ohms

  (b)Impedance,  Z  =   5.0   ohms

  (c)Current,  I  =   48.0   A

  (d)phase  angle  between  the  supply  voltage  and  current  is   36.87 deg lagging

Example 8, page no. 217

In [8]:
from __future__ import division
import math
#initializing  the  variables:
Vdc  =  12;#  in  volts
Vac  =  240;#  in  volts
Iac  =  20;#  in  Amperes
Idc  =  2;#  in  Amperes
f  =  50;#  in  Hz

#calculation:
R  =  Vdc/Idc
Z  =  Vac/Iac
XL  =  (Z**2  -  R**2)**0.5
L  =  XL/(2*math.pi*f)


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Resistance,  R  =  ",R,"  ohms"
print  "\n  (b)Impedance,  Z  =  ",Z,"  ohms"
print  "\n  (c)Inductive  reactance,  XL  =  ",round(XL,2),"  ohms"
print  "\n  (d)Inductance,  L  =  ",round(L,2),"  H"


  Result  



  (a)Resistance,  R  =   6.0   ohms

  (b)Impedance,  Z  =   12.0   ohms

  (c)Inductive  reactance,  XL  =   10.39   ohms

  (d)Inductance,  L  =   0.03   H

Example 9, page no. 217

In [9]:
from __future__ import division
import math
#initializing  the  variables:
R  =  200;#  in  ohms
L  =  0.3183;#  in  henry
V  =  240;#  in  volts
f  =  50;#  in  Hz

#calculation:
XL  =  2*math.pi*f*L
Z  =  (R**2  +  XL**2)**0.5
I  =  V/Z
VL  =  I*XL
VR  =  I*R
phid  =  math.atan(XL/R)*180/math.pi

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Inductive  reactance,  XL  =  ",round(XL,2),"  ohms"
print  "\n  (b)Impedance,  Z  =  ",round(Z,2),"  ohms"
print  "\n  (c)current,  I  =  ",round(I,2),"  A"
print  "\n  (d)p.d.  across  Inductor,  VL  =  ",round(VL,2),"  V  and  p.d.  across  resistance,  VR  =  ",round(VR,2),"  V"
print  "\n  (e)circuit  phase  angle  is  ",round(phid,2)," deg lagging\n"


  Result  



  (a)Inductive  reactance,  XL  =   100.0   ohms

  (b)Impedance,  Z  =   223.61   ohms

  (c)current,  I  =   1.07   A

  (d)p.d.  across  Inductor,  VL  =   107.33   V  and  p.d.  across  resistance,  VR  =   214.66   V

  (e)circuit  phase  angle  is   26.56  deg lagging

Example 10, page no. 218

In [2]:
from __future__ import division
import math
#initializing  the  variables:
R  =  100;#  in  ohms
L  =  0.2;#  in  henry
Vmax  =  200;#  in  volts
w  =  500;#  in  rad/sec

#calculation:
Vrms  =  0.707*Vmax
f  =  w/(2*math.pi)
XL  =  2*math.pi*f*L
Z  =  (R**2  +  XL**2)**0.5
I  =  Vrms/Z
VL  =  I*XL
VR  =  I*R
phid  =  math.atan(XL/R)*180/math.pi

\
#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Impedance,  Z  =  ",round(Z,2),"  ohms"
print  "\n  (b)current,  I  =  ",round(I,2),"  A"
print  "\n  (c)p.d.  across  resistance,  VR  =  ",round(VR,2),"  V"
print  "\n  (d)p.d.  across  Inductor,  VL  =  ",round(VL,2),"  V"
print  "\n  (e)circuit  phase  angle  is  ",phid,"deg\n"


  Result  



  (a)Impedance,  Z  =   141.42   ohms

  (b)current,  I  =   1.0   A

  (c)p.d.  across  resistance,  VR  =   99.98   V

  (d)p.d.  across  Inductor,  VL  =   99.98   V

  (e)circuit  phase  angle  is   45.0 deg

Example 11, page no. 218

In [11]:
from __future__ import division
import math
#initializing  the  variables:
R  =  30;#  in  ohms
L  =  1.2273E-3;#  in  henry
f  =  5000;#  in  Hz
VR  =  6;#  in  volts

#calculation:
I  =VR/R
XL  =  2*math.pi*f*L
Z  =  (R**2  +  XL**2)**0.5
V  =  I*Z
VL  =  I*XL

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)supply  voltage  =  ",round(V,2),"  Volts"
print  "\n  (b)p.d.  across  Inductor,  VL  =  ",round(VL,2),"  V"


  Result  



  (a)supply  voltage  =   9.77   Volts

  (b)p.d.  across  Inductor,  VL  =   7.71   V

Example 12, page no. 219

In [12]:
from __future__ import division
import math
#initializing  the  variables:
R  =  60;#  in  ohms
Rc  =  20;#  in  ohms
L  =  159.2E-3;#  in  henry
f  =  50;#  in  Hz
V  =  240;#  in  volts

#calculation:
XL  =  2*math.pi*f*L
Rt  =  R  +  Rc
Z  =  (Rt**2  +  XL**2)**0.5
I  =  V/Z
phid  =  math.atan(XL/Rt)*180/math.pi
VR  =  I*R
Zc  =  (Rc**2  +  XL**2)**0.5
Vc  =  I*Zc
VL  =  I*XL
VRc  =  I*Rc


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Impedance,  Z  =  ",round(Z,2),"  ohms"
print  "\n  (b)current,  I  =  ",round(I,3),"  A"
print  "\n  (c)circuit  phase  angle  is  ",round(phid,0),"deg lagging"
print  "\n  (d)p.d.  across  resistance,  VR  =  ",round(  VR,1),"  V"
print  "\n  (e)p.d.  across  coil,  Vc  =  ",round(Vc,1),"  V"
print  "\n  (f1)p.d.  across  Inductor,  VL  =  ",round(VL,2),"  V"
print  "\n  (f2)p.d.  across  coil  resistance,  VRc  =  ",round(VRc,2),"  V"


  Result  



  (a)Impedance,  Z  =   94.35   ohms

  (b)current,  I  =   2.544   A

  (c)circuit  phase  angle  is   32.0 deg lagging

  (d)p.d.  across  resistance,  VR  =   152.6   V

  (e)p.d.  across  coil,  Vc  =   137.0   V

  (f1)p.d.  across  Inductor,  VL  =   127.23   V

  (f2)p.d.  across  coil  resistance,  VRc  =   50.88   V

Example 13, page no. 220

In [1]:
from __future__ import division
import math
#initializing  the  variables:
R  =  25;#  in  ohms
C  =  45E-6;#  in  Farads
f  =  50;#  in  Hz
V  =  240;#  in  volts

#calculation:
Xc  =  1/(2*math.pi*f*C)
Z  =  (R**2  +  Xc**2)**0.5
I  =  V/Z
phid  =  math.atan(Xc/R)*180/math.pi


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Impedance,  Z  =  ",round(Z,2),"  ohms"
print  "\n  (b)current,  I  =  ",round(I,2),"  A"
print  "\n  (c)phase  angle  between  the  supply  voltage  and  current  is  ",round(phid,2),"deg leading"


  Result  



  (a)Impedance,  Z  =   75.02   ohms

  (b)current,  I  =   3.2   A

  (c)phase  angle  between  the  supply  voltage  and  current  is   70.54 deg leading

Example 14, page no. 221

In [2]:
from __future__ import division
import math
#initializing  the  variables:
R  =  40;#  in  ohms
f  =  60;#  in  Hz
I  =  3;#in  amperes
Z  =  50;#  in  ohms

#calculation:
Xc  =  (Z**2  -  R**2)**0.5
C  =  1/(2*math.pi*f*Xc)
V  =  I*Z
phid  =  math.atan(Xc/R)*180/math.pi
VR  =  I*R
Vc  =  I*Xc


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)capacitance,  C  =  ",round((C/1E-6),2),"  uF"
print  "\n  (b)Voltage,  V  =  ",V,"  Volts"
print  "\n  (c)phase  angle  between  the  supply  voltage  and  current  is  ",round(phid,2),"deg leading"
print  "\n  (d)p.d.  across  resistance,  VR  =  ",  VR,"  V"
print  "\n  (e)p.d.  across  Capacitor,  Vc  =  ",Vc,"  V"


  Result  



  (a)capacitance,  C  =   88.42   uF

  (b)Voltage,  V  =   150   Volts

  (c)phase  angle  between  the  supply  voltage  and  current  is   36.87 deg leading

  (d)p.d.  across  resistance,  VR  =   120   V

  (e)p.d.  across  Capacitor,  Vc  =   90.0   V

Example 15, page no. 222

In [13]:
from __future__ import division
import math
#initializing  the  variables:
R  =  5;#  in  ohms
C  =  100E-6;#  in  Farads
L  =  0.12;#  in  Henry
f  =  50;#  in  Hz
V  =  300;#  in  volts

#calculation:
XL  =  2*math.pi*f*L
Xc  =  1/(2*math.pi*f*C)
X  =  XL  -  Xc
 #Since  XL  is  greater  than  Xc,  the  circuit  is  inductive.
Z  =  (R**2  +  (XL-Xc)**2)**0.5
I  =  V/Z
phid  =  math.atan((XL-Xc)/R)*180/math.pi
Zcl  =  (R**2  +  XL**2)**0.5
Vcl  =  I*Zcl
phidc  =  math.atan(XL/R)*180/math.pi
Vc  =  I*Xc


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Current,I  =  ",round(I,2),"  A"
print  "\n  (b)phase  angle  between  the  supply  voltage  and  current  is  ",round(phid,2),"deg"
print  "\n  (c)Voltage  across  the  coil,  Vcoil  =  ",round(Vcl,0),"  Volts"
print  "\n  (d)p.d.  across  Capacitor,  Vc  =  ",round(Vc,0),"  V"


  Result  



  (a)Current,I  =   38.91   A

  (b)phase  angle  between  the  supply  voltage  and  current  is   49.57 deg

  (c)Voltage  across  the  coil,  Vcoil  =   1480.0   Volts

  (d)p.d.  across  Capacitor,  Vc  =   1239.0   V

Example 16, page no. 224

In [3]:
from __future__ import division
import math
#initializing  the  variables:
R1  =  8;#  in  ohms
C  =  0.25E-6;#  in  Farads
L  =  130E-6;#  in  Henry
Rc  =  5;#  in  ohms
R2  =  10;#  in  ohms
f  =  20000;#  in  Hz
V  =  40;#  in  volts

#calculation:
XL  =  2*math.pi*f*L
Xc  =  1/(2*math.pi*f*C)
X  =  Xc  -  XL
R  =  R1  +  R2  +  Rc
 #Since  Xc  is  greater  than  XL,  the  circuit  is  capacitive.
Z  =  (R**2  +  (Xc-XL)**2)**0.5
I  =  V/Z
phid = math.atan((Xc-XL)/R)*180/math.pi
V1  =  I*R1
V2  =  I*((Rc**2  +  XL**2)**0.5)
V3  =  I*((R2**2  +  Xc**2)**0.5)


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Current,I  =  ",round(I,2),"  A"
print  "\n  (b)circuit  phase  angle  is  ",round(phid,2),"deg leading"
print  "\n  (c1)Voltage  across  the  Resistance  of  8  ohms  =  ",round(V1,2),"  Volts"
print  "\n  (c2)Voltage  across  the  coil,  Vcoil  =  ",round(V2,2),"  Volts"
print  "\n  (c3)p.d.  across  Capacitor  resistance  circuit  =  ",round(V3,2),"  Volts"


  Result  



  (a)Current,I  =   1.44   A

  (b)circuit  phase  angle  is   33.97 deg leading

  (c1)Voltage  across  the  Resistance  of  8  ohms  =   11.54   Volts

  (c2)Voltage  across  the  coil,  Vcoil  =   24.64   Volts

  (c3)p.d.  across  Capacitor  resistance  circuit  =   48.12   Volts

Example 17, page no. 224

In [5]:
from __future__ import division
import math
#initializing  the  variables:
R1  =  4;#  in  ohms
C  =  1.273E-6;#  in  Farads
L  =  0.286E-3;#  in  Henry
R2  =  8;#  in  ohms
f  =  5000;#  in  Hz
I  =  5;#  in  amperes

#calculation:
XL  =  2*math.pi*f*L
phid1  =  math.atan(XL/R1)*180/math.pi
V1  =  I*((R1**2  +  XL**2)**0.5)
Xc  =  1/(2*math.pi*f*C)
V2  =  I*((R2**2  +  Xc**2)**0.5)
phid2  =  math.atan(Xc/R2)*180/math.pi
Z  =  ((R1+R2)**2  +  (Xc-XL)**2)**0.5
V  =  I*Z
phid  =  math.atan((Xc-XL)/(R1+R2))*180/math.pi


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Voltage  supply,  V  =  ",round(V,2),"  V"
print  "\n  (b)circuit  phase  angle  is  ",round(phid,2),"deg leading"


  Result  



  (a)Voltage  supply,  V  =   100.08   V

  (b)circuit  phase  angle  is   53.16 deg leading

Example 18, page no. 226

In [18]:
from __future__ import division
import math
#initializing  the  variables:
R  =  10;#  in  ohms
C  =  60E-6;#  in  Farads
L  =  125E-3;#  in  Henry
V  =  120;#  in  Volts

#calculation:
fr  =  1/(2*math.pi*(L*C)**0.5)
 #At  resonance,  XL  =  Xc  and  impedance  Z  =  R
I  =  V/R


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Resonance  frequency,Fr  =  ",round(fr,2),"  Hz"
print  "\n  (b)Current,  I  =  ",round(I,2)


  Result  



  (a)Resonance  frequency,Fr  =   58.12   Hz

  (b)Current,  I  =   12.0

Example 19, page no. 226

In [19]:
from __future__ import division
import math
#initializing  the  variables:
L  =  0.05E-3;#  in  Henry
fr  =  200000;#  in  Hz
V  =  0.002;#  in  Volts
I  =  0.1E-3;#  in  amperes
#calculation:
#  L-C-R
#At  resonance,  XL  =  Xc  and  impedance  Z  =  R
R  =  V/I
C  =  1/(L*(2*math.pi*fr)**2)


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Resistance,  R  =  ",round(R,2),"  ohms"
print  "\n  (b)Capacitance,  C  =  ",round((C/1E-9),2),"nF"


  Result  



  (a)Resistance,  R  =   20.0   ohms

  (b)Capacitance,  C  =   12.67 nF

Example 20, page no. 227

In [20]:
from __future__ import division
import math
#initializing  the  variables:
L  =  80E-3;#  in  Henry
C  =  0.25E-6;#  in  Farads
R  =  12.5;#  in  ohms
V  =  100;#  in  Volts

#calculation:
fr  =  1/(2*math.pi*((L*C)**0.5))
 #At  resonance,  XL  =  Xc  and  impedance  Z  =  R
I  =  V/R
VL  =  I*(2*math.pi*fr*L)
Vc  =  I/(2*math.pi*fr*C)
Vm  =  VL/V


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  resonant  frequency  =  ",round(fr,2),"  Hz"
print  "\n  (b)Current,  I  =  ",round(I,2),""
print  "\n  (b)Voltage  magnification  at  resonance  =  ",round(Vm,2),"  V"


  Result  



  (a)the  resonant  frequency  =   1125.4   Hz

  (b)Current,  I  =   8.0 

  (b)Voltage  magnification  at  resonance  =   45.25   V

Example 21, page no. 228

In [21]:
from __future__ import division
import math
#initializing  the  variables:
L  =  60E-3;#  in  Henry
C  =  30E-6;#  in  Farads
R  =  2;#  in  ohms

#calculation:
Q  =  ((L/C)**0.5)/R

#Results
print  "\n\n  Result  \n\n"
print  "\n  At  resonance,  Q-factor  =  ",round(Q,2)


  Result  



  At  resonance,  Q-factor  =   22.36

Example 22, page no. 228

In [22]:
from __future__ import division
import math
#initializing  the  variables:
L  =  100E-3;#  in  Henry
C  =  2E-6;#  in  Farads
R  =  10;#  in  ohms
V  =  50;#  in  Volts

#calculation:
fr  =  1/(2*math.pi*((L*C)**0.5))
 #At  resonance,  XL  =  Xc  and  impedance  Z  =  R
I  =  V/R
VL  =  I*(2*math.pi*fr*L)
Vc  =  I/(2*math.pi*fr*C)
Q  =  VL/V


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)the  resonant  frequency  =  ",round(fr,2),"  Hz"
print  "\n  (b)Current,  I  =  ",round(I,2),""
print  "\n  (c)Voltage  across  coil  at  resonance  is  ",round(VL,2),"V  "
print   "and  Voltage  across  capacitance  at  resonance  is  ",round(  Vc,2),"V"
print  "\n  (d)At  resonance,  Q-factor  =  ",round(Q,2)


  Result  



  (a)the  resonant  frequency  =   355.88   Hz

  (b)Current,  I  =   5.0 

  (c)Voltage  across  coil  at  resonance  is   1118.03 V  and  Voltage  across  capacitance  at  resonance  is   1118.03 V

  (d)At  resonance,  Q-factor  =   22.36

Example 23, page no. 230

In [23]:
from __future__ import division
import math
#initializing  the  variables:
L  =  20E-3;#  in  Henry
R  =  10;#  in  ohms
fr  =  5000;#  in  Hz

#calculation:
Qr  =  (2*math.pi*fr)*L/R
bw  =  fr/Qr


#Results
print  "\n\n  Result  \n\n"
print  "\n  Bandwidth,  (f2-f1)  =  ",round(bw,2),"  Hz"


  Result  



  Bandwidth,  (f2-f1)  =   79.58   Hz

Example 24, page no. 231

In [24]:
from __future__ import division
import math
#initializing  the  variables:
R  =  5000;#  in  ohms
Imax  =  0.250;#  in  Amperes

#calculation:
Irms  =  0.707*Imax
P  =  Irms*Irms*R


#Results
print  "\n\n  Result  \n\n"
print  "\n  Power,  P  =  ",round(P,2),"  Watts"


  Result  



  Power,  P  =   156.2   Watts

Example 25, page no. 231

In [25]:
from __future__ import division
import math
#initializing  the  variables:
R  =  60;#  in  ohms
L  =  75E-3;#  in  Henry
V  =  110;#  in  Volts
f  =  60;#  in  Hz

#calculation:
XL  =  2*math.pi*f*L
Z  =  (R**2  +  XL**2)**0.5
I  =  V/Z
P  =  I*I*R


#Results
print  "\n\n  Result  \n\n"
print  "\n  Power,  P  =  ",round(P,2),"  Watts"


  Result  



  Power,  P  =   165.02   Watts

Example 26, page no. 232

In [26]:
from __future__ import division
import math
#initializing  the  variables:
VI  =  300;#  in  VA
V  =  150;#  in  Volts
f  =  50;#  in  Hz

#calculation:
I  =  VI/V
XL  =  V/I
L  =  XL/(2*math.pi*f)


#Results
print  "\n\n  Result  \n\n"
print  "\n  Inductance  =  ",round(L,2),"  H"


  Result  



  Inductance  =   0.24   H

Example 27, page no. 232

In [27]:
from __future__ import division
import math
#initializing  the  variables:
VI  =  200000;#  in  VA
pf  =  0.8;#  power  factor

#calculation:
P  =  VI*pf
Q  =  VI*math.sin(math.acos(pf))

#Results
print  "\n\n  Result  \n\n"
print  "\n  rated  power  output  is  ",round(P/1000,2),"KW  and  the  corresponding  reactive  power  is  ",round(Q/1000,2),"kvar"


  Result  



  rated  power  output  is   160.0 KW  and  the  corresponding  reactive  power  is   120.0 kvar

Example 28, page no. 233

In [15]:
from __future__ import division
import math
#initializing  the  variables:
V  =  120;#  in  Volts
f  =  50;#  in  Hz
P  =  400;#  in  Watt
I  =  8;#  in  Amperes

#calculation:
R  =  P/(I*I)
Z  =  V/I
XL  =  (Z**2  -  R**2)**0.5
pf  =  P/(V*I)
phi  =  math.acos(pf)*180/math.pi


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)resistance  =  ",round(R,2),"  ohm  "
print  "\n  (b)Impedance  Z  =  ",round(Z,2),"  Ohm  "
print  "\n  (c)reactance  =  ",round(XL,2),"  ohm  "
print  "\n  (d)Power  factor  =  ",round(pf,2),""
print  "\n  (e)phase  angle  =  ",round(phi,2),"deg lagging"


  Result  



  (a)resistance  =   6.25   ohm  

  (b)Impedance  Z  =   15.0   Ohm  

  (c)reactance  =   13.64   ohm  

  (d)Power  factor  =   0.42 

  (e)phase  angle  =   65.38 deg lagging

Example 29, page no. 233

In [6]:
from __future__ import division
import math
#initializing  the  variables:
V  =  100;#  in  Volts
f  =  60;#  in  Hz
P  =  100;#  in  Watt
pf  =  0.5;#  power  factor

#calculation:
I  =  P/(pf*V)
phi  =  math.acos(pf)*180/math.pi
R  =  P/(I*I)
Z  =  V/I
Xc  =  (Z**2  -  R**2)**0.5
C  =  1/(2*math.pi*f*Xc)


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Current  I  =  ",round(I,2),"  A  "
print  "\n  (b)phase  angle  =  ",round(phi,2),"deg leading"
print  "\n  (c)resistance  =  ",round(R,2),"  ohm  "
print  "\n  (d)Impedance  Z  =  ",round(Z,2),"  Ohm  "
print  "\n  (e)capacitance  =  ",round((C/1E-6),2),"uF  "


  Result  



  (a)Current  I  =   2.0   A  

  (b)phase  angle  =   60.0 deg leading

  (c)resistance  =   25.0   ohm  

  (d)Impedance  Z  =   50.0   Ohm  

  (e)capacitance  =   61.26 uF