6: Dielectric Materials

Example number 6.1, Page number 6.34

In [40]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=5*10**16;   #resistivity(ohm m)
l=5*10**-2;    #thickness(m)
b=8*10**-2;    #length(m)
w=3*10**-2;    #width(m)

#Calculation
A=b*w;    #area(m**2)
Rv=rho*l/A;    
X=l+b;      #length(m)
Y=w;      #perpendicular(m)
Rs=Rv*X/Y;    
Ri=Rs*Rv/(Rs+Rv);       #insulation resistance(ohm)

#Result
print "insulation resistance is",round(Ri/10**18,2),"*10**18 ohm"
print "answer varies due to rounding off errors"

insulation resistance is 0.85 *10**18 ohm
answer varies due to rounding off errors

Example number 6.2, Page number 6.34

In [41]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=10**10;   #resistivity(ohm m)
d=10**-3;    #thickness(m)
A=10**4*10**-6;    #area(m**2)
V=10**3;    #voltage(V)
f=50;     #power frequency(Hz)
epsilonr=8;
epsilon0=8.84*10**-12;
tan_delta=0.1;

#Calculation
Rv=rho*d/A; 
dl_DC=V**2/Rv;      #DC dielectric loss(watt)
C=A*epsilon0*epsilonr/d;
dl_AC=V**2*2*math.pi*f*C*tan_delta;     #AC dielectric loss(watt)

#Result
print "DC dielectric loss is",int(dl_DC*10**3),"*10**-3 watt"
print "AC dielectric loss is",round(dl_AC*10**3,2),"*10**-3 watt"

DC dielectric loss is 1 *10**-3 watt
AC dielectric loss is 22.22 *10**-3 watt

Example number 6.3, Page number 6.35

In [42]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilon0=8.84*10**-12;
R=0.55*10**-10;    #radius(m)
N=2.7*10**25;      #number of atoms

#Calculation
alpha_e=4*math.pi*epsilon0*R**3;    #polarisability of He(farad m**2)
epsilonr=1+(N*alpha_e/epsilon0);      #relative permittivity

#Result
print "polarisability of He is",round(alpha_e*10**40,3),"*10**-40 farad m**2"
print "relative permittivity is",round(epsilonr,6)
print "answer varies due to rounding off errors"

polarisability of He is 0.185 *10**-40 farad m**2
relative permittivity is 1.000056
answer varies due to rounding off errors

Example number 6.4, Page number 6.35

In [43]:
#importing modules
import math
from __future__ import division

#Variable declaration
A=360*10**-4;    #area(m**2)
V=15;    #voltage(V)
C=6*10**-6;     #capacitance(farad)
epsilonr=8;
epsilon0=8.84*10**-12;

#Calculation
E=V*C/(epsilon0*epsilonr*A);     #field strength(V/m)
dm=epsilon0*(epsilonr-1)*V*A;    #total dipole moment(Cm)

#Result
print "field strength is",round(E/10**7,3),"*10**7 V/m"
print "total dipole moment is",round(dm*10**12,1),"*10**-12 Cm"

field strength is 3.535 *10**7 V/m
total dipole moment is 33.4 *10**-12 Cm

Example number 6.5, Page number 6.36

In [44]:
#importing modules
import math
from __future__ import division

#Variable declaration
d=0.08*10**-3;    #thickness(m)
A=8*10**-4;    #area(m**2)
epsilonr=2.56;
epsilon0=8.84*10**-12;
tan_delta=0.7*10**-4;
new=10**6;    #frequency(Hz)

#Calculation
C=A*epsilon0*epsilonr/d;     #capacitance(farad)
epsilonrdash=tan_delta*epsilonr;
omega=2*math.pi*new;
R=d/(epsilon0*epsilonrdash*omega*A);     #parallel loss resistance(ohm)

#Result
print "capacitance is",round(C*10**12,1),"*10**-12 farad"
print "parallel loss resistance is",int(R/10**6),"mega ohm"

capacitance is 226.3 *10**-12 farad
parallel loss resistance is 10 mega ohm

Example number 6.6, Page number 6.36

In [45]:
#importing modules
import math
from __future__ import division

#Variable declaration
epsilonr=4.36;      #dielectric constant
t=2.8*10**-2;       #loss tangent(t)
N=4*10**28;         #number of electrons
epsilon0=8.84*10**-12;      

#Calculation
epsilon_r = epsilonr*t;
epsilonstar = (complex(epsilonr,-epsilon_r));
alphastar = (epsilonstar-1)/(epsilonstar+2);
alpha_star = 3*epsilon0*alphastar/N;             #complex polarizability(Fm**2)

#Result
print "the complex polarizability is",alpha_star*10**40,"*10**-40 F-m**2"
print "answer cant be rouned off to 2 decimals as given in the textbook. Since it is a complex number and complex cant be converted to float"

the complex polarizability is (3.50379335033-0.0600074383321j) *10**-40 F-m**2
answer cant be rouned off to 2 decimals as given in the textbook. Since it is a complex number and complex cant be converted to float