Chapter 39: Dielectrics and dielectric loss

Example 1, page no. 717

In [1]:
from __future__ import division
import math
#initializing  the  variables:
Rs  =  1.5;#  in  ohms
Cs  =  400E-12;#  in  Farads
f  =  8E6;#  in  Hz

#calculation:  
 #for  a  series  equivalent  circuit,
 #tan(del)  =  Rs*w*Cs
 #loss  angle,
de  =  math.atan(Rs*Cs*(2*math.pi*f))
 #power  factor
pf  =  math.cos(de)
 #the  Q-factor
Q  =  1/math.tan(de)
 #dissipation  factor,
D  =  1/Q


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)loss  angle  ",round(de,2),"  rad."
print  "\n  (b)power  factor  ",round(de,2),"  rad."
print  "\n  (c)Q-factor  is  ",round(Q,2)
print  "\n  (d)dissipation  factor  ",round(D,2),"  rad."


  Result  



  (a)loss  angle   0.03   rad.

  (b)power  factor   0.03   rad.

  (c)Q-factor  is   33.16

  (d)dissipation  factor   0.03   rad.

Example 2, page no. 718

In [2]:
from __future__ import division
import math
#initializing  the  variables:
de  =  0.025;#  in  rad.
V  =  5000;#  in  Volts
PL  =  20;#  power  loss
f  =  50;#  in  Hz

#calculation:  
 #power  loss  =  w*C*V**2*tan(del)
Cp  =  PL/(2*math.pi*f*V*V*math.tan(de))
 #for  a  parallel  equivalent  circuit,
 #tan(del)  =  1/(Rp*w*Cp)
Rp  =  1/(2*math.pi*f*Cp*math.tan(de))


#Results
print  "\n\n  Result  \n\n"
print  "\n  capacitance  C  ",round(Cp*1E6,2),"uF  and  parallel  resistance  ",round(Rp,2),"ohm."


  Result  



  capacitance  C   0.1 uF  and  parallel  resistance   1250000.0 ohm.

Example 3, page no. 718

In [1]:
from __future__ import division
import math
#initializing  the  variables:
P  =  500E-6;#  in  Watt
C  =  2000E-12;#  in  Farads
V  =  20;#  in  Volts
f  =  10000;#  in  Hz

 #calculation:  
 #power  loss  =  w*C*V**2*tan(del)
 #loss  angle
de =  math.atan(P/(2*math.pi*f*V*V*C))
 #for  an  equivalent  series  circuit,
 #tan(del)  =  (Rs*w*Cs)
Cs  =  C
Rs  =  (math.tan(de))/(2*math.pi*f*Cs)
 #for  an  equivalent  parallel  circuit
 #tan(del)  =  1/(Rp*w*Cp)
Cp  =  C
Rp  =  1/(2*math.pi*f*Cp*math.tan(de))


#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)loss  angle  ",round(de*180/math.pi,2),"deg"
print  "\n  (b)series  resistance  ",round(Rs,2),"  ohm."
print  "\n  (c)parallel  resistance  ",round(Rp/1000,2),"Kohm."


  Result  



  (a)loss  angle   0.57 deg

  (b)series  resistance   79.16   ohm.

  (c)parallel  resistance   800.0 Kohm.