5: Conducting Materials

Example number 5.1, Page number 5.34

In [1]:
#importing modules
import math
from __future__ import division

#Variable declaration
Na=6.023*10**26;    #avagadro number
e=1.602*10**-19;
d=8960;     #density
N=1;       #number of free electrons
w=63.54;    #atomic weight
i=10;      #current(ampere)
m=9.1*10**-31;    
rho=2*10**-8;   #resistivity(ohm m)
r=0.08*10**-2;    #radius(m)
c=1.6*10**6;   #mean thermal velocity(m/s)

#Calculation
A=math.pi*r**2;    #area(m**2)
n=Na*d*N/w;
vd=i/(A*n*e);     #drift speed(m/s)
tow_c=m/(n*e**2*rho);
lamda=tow_c*c;      #mean free path(m)

#Result
print "drift speed is",round(vd*10**5,1),"*10**-5 m/s"
print "mean free path is",round(lamda*10**8,2),"*10**-8 m"
print "answer given in the book is wrong"

drift speed is 36.6 *10**-5 m/s
mean free path is 3.34 *10**-8 m
answer given in the book is wrong

Example number 5.2, Page number 5.35

In [3]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.602*10**-19;
m=9.1*10**-31;  #mass(kg)
tow=2*10**-14;    #time(s)
n=8.5*10**28;    

#Calculation
sigma=n*e**2*tow/m;    #electrical conductivity(ohm-1 m-1)

#Result
print "electrical conductivity is",round(sigma/10**7,1),"*10**7 ohm-1 m-1"

electrical conductivity is 4.8 *10**7 ohm-1 m-1

Example number 5.3, Page number 5.35

In [4]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;
m=9.1*10**-31;  #mass(kg)
n=5.8*10**28;  
rho=1.54*10**-8;    #resistivity(ohm m)
E=1*10**2;

#Calculation
tow=m/(rho*n*e**2);      #relaxation time(s)
mew_e=1/(rho*e*n);       #mobility of electrons(m**2/Vs)
vd=mew_e*E;       #drift velocity(m/s)

#Result
print "relaxation time is",round(tow*10**14),"*10**-14 s"
print "mobility of electrons is",round(mew_e*10**3),"*10**-3 m**2/Vs"
print "drift velocity is",round(vd,1),"m/s"

relaxation time is 4.0 *10**-14 s
mobility of electrons is 7.0 *10**-3 m**2/Vs
drift velocity is 0.7 m/s

Example number 5.4, Page number 5.35

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho=1.7*10**-8;    #resistivity(ohm m)
T=300;     #temperature(K)
T1=973;    #temperature(K)

#Calculation
a=rho/T;    
rho_973=a*T1;    #resistivity(ohm m)

#Result
print "resistivity is",round(rho_973*10**8,2),"*10**-8 ohm m"

resistivity is 5.51 *10**-8 ohm m

Example number 5.5, Page number 5.36

In [8]:
#importing modules
import math
from __future__ import division

#Variable declaration
rho1=1.2*10**-8;    #resistivity(ohm m)
rho2=0.12*10**-8;    #resistivity(ohm m)
p1=0.4;    #atomic percent
p2=0.5;    #atomic percent
rho=1.5*10**-8;    #resistivity(ohm m)

#Calculation
rho_i=(rho1*p1)+(rho2*p2);     #increase of resistivity(ohm m)
Tr=rho+rho_i;       #total resistivity of copper alloy(ohm m)

#Result
print "increase of resistivity is",round(rho_i*10**8,2),"*10**-8 ohm m"

increase of resistivity is 0.54 *10**-8 ohm m

Example number 5.6, Page number 5.36

In [16]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;
m=9.1*10**-31;  #mass(kg)
n=6*10**28;     #density(per m**3)
tow=10**-14;    #relaxation time(s)
T=300;    #temperature(K)
k=1.38*10**-23;   #boltzmann constant

#Calculation
sigma=n*e**2*tow/m;    #electrical conductivity(ohm-1 m-1)
K=n*math.pi**2*k**2*T*tow/(3*m);    #thermal conductivity(W/m/K)
L=K/(sigma*T);    #lorentz number(watt ohm K-2)

#Result
print "electrical conductivity is",round(sigma/10**7,3),"*10**7 ohm-1 m-1"
print "thermal conductivity is",round(K,2),"W/m/K"
print "lorentz number is",round(L*10**8,3),"*10**-8 watt ohm K-2"

electrical conductivity is 1.688 *10**7 ohm-1 m-1
thermal conductivity is 123.93 W/m/K
lorentz number is 2.447 *10**-8 watt ohm K-2