# Given
sigma = 5.9*10**5 # in ohm**-1*cm**-1
e = 1.6*10**-19 # Coulombs
d = 8.93 # g/cm**3
Mat = 63.5 # g/mol
NA = 6.02*10**23 # mol**-1
# Calculations and Results
n = d*NA/Mat
u_d = sigma/(e*n) # electron drift mobility
print("Drift mobility of electrons in copper at room temperature in cm2/V/s is {0:.4f}".format(u_d))
# Given
u_d = 3.2*10**-3 # in m**2/V/s
u = 1.2*10**6 # m/s
v_dx = 0.1*u
# Calculations and Results
# drift velocity of conduction electrons is v_dx=u_d*E
E = v_dx/u_d
print("Applied electric field in V/m is {0:.4g}".format(E))
# Given
T_summer = 20.0 # in degree celsius
T_summer += 273.0 # in kelvin
T_winter = -30.0 # in degree celsius
T_winter += 273.0 # in kelvin
# Calculations and Results
# we have R is proportional to A*T
# Hence
R = (T_summer-T_winter)/T_summer
R *= 100
print(" Percentage change in the resistance of a pure metal wire from Saskatchewans summer "
"too winter in % is {0:.4f}".format(R))
import math
# Given
d = 8.96*10**3 # in Kg/m3
NA = 6.02*10**23 # mol**-1
Mat = 63.56*10**-3 # Kg/mol
k = 1.38*10**-23 # J/K
T = 300.0 # kelvin
e = 1.6*10**-19 # in coulombs
m_e = 9.1*10**-31 # in Kg
u = 1.25*10**6 # m/s
f = 4*10**12 # frequency in s**-1
# Calculations and Results
Ns = d*NA/Mat # atomic concentration in m**-3
M = Mat/NA
w = 2*math.pi*f # angular frequency of the vibration
# by virtue of Equipartition of energy theorem
a = math.sqrt((2*k*T)/(M*w**2))
S = math.pi*a**2 # cross sectional area
t = 1.0/(S*u*Ns) # mean free time
u_d = e*t/m_e # drift velocity
u_d *= 10**4 # change in units
Ns /= 10**6 # in cm**-3
sigma = e*Ns*u_d # conductivity
print("drift velocity of electrons in m2/V/s is {0:.4f}".format(u_d))
print("conductivity of copper in ohm**-1/cm is {0:.4g}".format(sigma))
# slight change in the answer is due to the computation method, otherwise answer is matching with textbook
# Given
n = 1.2
To = 293.0 # in kelvin
# Calculations and Results
alpha_o = n/To
print("Theoretical value of TCR at 293K is {0:.4f} which is in "
"well agreement with experimental value".format(alpha_o))
alpha_o = 0.00393 # experimental value
n = alpha_o*To
print("Theoretical value of n at 293K (n = {0:.4f}) is in well agreement with experimental value".format(n))
import math
# Given
P = 40.0 # in Watt
V = 120.0 # in Volts
D = 33*10**-6 # in meter
L = 0.381 # in meter
To = 293.0 # in kelvin
P_radiated = 40.0 # in watt
epsilon = 0.35
sigma_s = 5.6*10**-8 # in W/m2/K4
# Calculations and Results
I = P/V
A = math.pi*D**2/4.0
R = V/I # resistance of the filament
p_t = R*A/L # resistivity of tungsten
p_o = 5.51*10**-8 # resistivity at room temperature in ohm*m
# p_t=p_o*(T/To)**1.2
T = To*(p_t/p_o)**(1.0/1.2)
print("Temperature of the bulb when it is operated at the rated voltage in Kelvin is {0:.4f}".format(T))
A = L*math.pi*D
# Stefans Law
T = (P_radiated/(epsilon*sigma_s*A))**(1.0/4.0)
print("Temperature of the filament in kelvin is {0:.4f}".format(T))
# Given
M_Au = 197.0
w = 0.1
M_Cu = 63.55
p_exp = 108.0 # n*ohm*m
# Calculations and Results
X = M_Au*w/((1-w)*M_Cu+(w*M_Au))
C = 450.0 # n*ohm*m
p_Au = 22.8 # resistivity in n*ohm*m
p = p_Au+C*X*(1-X) # Nordheim rule
x = ((p-p_exp)/p)*100
print("resistivity of the alloy in n*ohm*m is {0:.4f}".format(p))
print("The difference in the value from experimental value in % is {0:.4f}".format(x))
# Given
u = 1.58*10**6 # in m/s
N = 8.5*10**28 # m**-3
e = 1.6*10**-19 # in coulombs
me = 9.1*10**-31 # in Kg
N_I = 0.01*N
# Calculations and Results
l_I = N_I**(-1/3)
t_I = l_I/u
p = me/(e**2*N*t_I)
print(" worst case resistivity in ohm*m {0:.4g}".format(p))
# slight change in answer due to computational method
# Given
Xd = 0.15
p_c = 1*10**-7 # ohm*m
# Calculations and Results
p_eff = p_c*((1+0.5*Xd)/(1-Xd))
print("Effective resistivity in ohm m is {0:.4g}".format(p_eff))
# slight change in the answer due to printing the answer
# Given
Xd = 0.15
p_c = 4*10**-8 # ohm*m
# Calculations and Results
p_eff = p_c*((1+0.5*Xd)/(1-Xd))
print("Effective resistivity in ohm m is {0:.4g}".format(p_eff))
# change in the answer due to coding
import math
# Given
# at f=10MHz
a = 10**-3 # in m
f = 10*10**6 # in Hz
w = 2*math.pi*f
sigma_dc = 5.9*10**7 # in m**-1
u = 1.257*10**-6 # in Wb/A/m
# Calculations and Results
delta = 1.0/math.sqrt(0.5*w*sigma_dc*u)
# let r=r_ac/r_dc=a/(2*delta)
r = a/(2*delta)
print("Change in dc resistance of a copper wire at 10MHz is {0:.4f}".format(r))
# part(b)
f = 1*10**9 # in Hz
w = 2*math.pi*f
delta = 1.0/math.sqrt(0.5*w*sigma_dc*u)
# let r=r_ac/r_dc=a/(2*delta)
r = a/(2*delta)
print("Change in dc resistance of a copper wire at 1GHz is {0:.4f}".format(r))
# Given
sigma = 5.9*10**7 # ohm**-1*m**-2
RH = -0.55*10**-10 # m**3/A/s
# Calculations and Results
u_d = -RH*sigma
print("drift mobility of electrons in copper in m2/V/s is {0:.4g}".format(u_d))
# Given
no = 8.5*10**28 # in m3
e = 1.6*10**-19 # in coulombs
u_d = 3.2*10**-3 # m2/V/s
sigma = 5.9*10**7 # in ohm**-1*m**-1
# Calculations and Results
n = sigma/(e*u_d)
print("concentration of conduction electrons in copper in m**-3 is {0:.4g}".format(n))
A = n/no
print("Average number of electrons contributed per atom is {0:.4f}".format(A))
# Given
sigma = 1*10**7 # ohm**-1*m**-1
T = 300.0 # kelvin
C_WFL = 2.44*10**-8 # W*ohm/K2
X_d = 0.15
# Calculations and Results
K_c = sigma*T*C_WFL
K_eff = K_c*((1-X_d)/(1+0.5*X_d))
print("Thermal Conductivity at room temperature in W/m/K is {0:.4f}".format(K_eff))
import math
# Chapter2
# Ex_21
# Given
sigma = 50*10**-9 # in ohm
T = 300.0 # kelvin
C_WFL = 2.45*10**-8 # in W*ohm/K2
L = 30*10**-3 # in m
d = 20*10**-3 # in m
Q = 10.0 # in W
# Calculations and Results
# Wiedemann-Franz Lorenz Law
k = sigma**-1*T*C_WFL # thermal conductivity
A = math.pi*(d**2)/4.0
theta = L/(k*A) # thermal resistance
delta_T = theta*Q
print("Temperature drop across the disk in degree celsius is {0:.4f}".format(delta_T))