import math
#variable declaration
R75 = 57.2; #resistance at 75 C in Ω
R25 = 55; #resistance at 25 C in Ω
t1 = 25; #temperature in C
t2 = 75 # temperature in C
#formula
#Rt = R0*(1+(alpha*t))
#calculation
alpha = (R25-R75)/float((25*R75)-(75*R25)); #temperature cofficient
#result
print'temperature coefficient =%3.5f'%alpha,'K**-1';
import math
#variable declaration
R1 = 50; #resistance in ohm at temperature 15°C
R2 = 60; # resistance in ohm temperature 15°C
t1 = 15; #temperature in °C
alpha = 0.00425; #temperature coefficient of resistance
#formula
#Rt = R0*(1+(alpha*t))
#Rt1/Rt2 = R0*(1+(alpha*t1))/R0*(1+(alpha*t2))
#calculation
R = R2/float(R1); #resistance in Ω
X = 1+(alpha*t1);
t2 = ((R*X)-1)/float(alpha); #temperature coefficient of resistance in °C
#result
print'temperature coefficient of resistance =%3.2f'%t2,'°C';
import math
#variable declaration
t1 = 20; #temperature in °C
alpha = 5*10**-3; #average temperature coefficient at 20°C
R1 = 8; #resistance in Ω
R2 = 140; #resistaance in Ω
#calculation
t2 = t1+((R2-R1)/float(R1*alpha)); #temperature in °C
#result
print'Hence temperature under normal condition is %3.2f'%t2,'°C';
import math
#variable declaration
l = 100; #length in cm
d = 0.008; #diameter of wire in cm
R = 95.5; #resistance in Ω
d = 0.008; #diameter in cm
#formula
#R=p*l/A
#calculation
A = (math.pi*d*d)/float(4); #cross-sectional area
p = (R*A)/float(l); #resistivity of wire in Ω-cm
#result
print'resistivity=%3.2e'%p,'Ω-m';
import math
#variable declaration
R0 =17.5; #resistance at 0 degree c in Ω
alpha =0.00428; #temperature coefficient of copper in per °C
t =16; #temperature in °C
#calculations
Rt = R0*(1+(alpha*t)); #resistance at 16 °C
P = (R0/float(Rt))*100; #percentage conductivity at 16 °C
#result
print'percentage conductivity=%3.2f'%P,'%';
import math
#variable declaration
l = 60; #length in m
r2 = 38/float(2); #radius of outer cylinder in m
r1 = 18/float(2); #radius of inner cylinder in m
p = 8000; #specific resistance in Ω-m
#calculation
R = (p/float(2*math.pi*l))*math.log(r2/float(r1)); #insulation resistance of liquid resistor in Ω
#result
print'insulation resistance=%3.0f '%R,'Ω';
import math
#variable declaration
d1 = 0.0018; #inner diameter in m
d2 = 0.005; # outer diameter in m
R = 1820*10**6; #insulation resistance in Ω
l = 3000; #length in m
#calculations
r1 = d1/float(2); #inner radius in m
r2 = d2/float(2); #outer radius in m
p = (2*math.pi*l*R)/float(math.log(r2/float(r1))); #resistivity of dielectric in Ω-m
#result
print'resistivity=%3.3e'%p,'Ω-m';
import math
#variable declaration
d1 = 0.05; #inner diametr in m
d2 = 0.07; #outer diameter in m
l = 2000; #length in m
p = 6*10**12; #specific resistance in Ω-m
#calculations
r1 = d1/float(2); #inner radius in m
r2 = d2/float(2); #outer radius in m
R = (p/float(2*math.pi*l))*(math.log(r2/float(r1))); #insulation resistance
#result
print'insulation resistance =%1e'%R,'Ω';
print' Note: calculation mistake in textbook in calculating insulating resistance';
import math
#variable declaration
a = 110*10**-3; #area in m**2
d = 2; #thickness in mm
er = 5; #relative permitivity
E = 12.5*10**3; #electric field strength in V/mm
e0 = 8.854*10**-12; #charge of electron in coulombs
#calculations
A = a*a; #area in m**2
C = e0*((er*A)/float(d*10**-3)) #capacitance in F
V = E*(d);
Q = (C)*(V) #charge on capacitor in C
#result
print'capacitance =%3.2e'%C,'F';
print' charge=%3.3e'%Q,'C';
import math
#variable declaration
I = 15*10**-3; #current in A
t = 5; #time in s
V = 1000; #voltage in volts
d = 10**-3; #thickness in m
a = 120*10**-3;
#calculation
A = a**2 #area in m**2
Q = I*t; #charge on capacitor in C
#since charge and electric field are equal
phi = Q; #electric flux in mc
D = Q/float(A); #electric flux density in c/m**2
E = V/float(d); #electric field strength in dielectric
#result
print'charge=%3.2e'%Q,'C';
print' electric flux=%4.3f'%(phi*10**3),'mc';
print' electric flux density=%3.2f'%D,'c/m**2';
print' electric field strength=%2.3e'%E,'V/m';
import math
#variable declaration
n = 12; #number of plates
er = 4; #relative permitivty
d = 1.0*10**-3; #distance between plates in m
A = 120*150*10**-6; #area in m**2
e0 = 8.854*10**-12; # in F/m
#calculation
c = (n-1)*e0*er*A/float(d); #capacitance in F
#result
print'capacitance=%3.4e'%c,'F';
import math
#variable declaration
e0 = 40000; #dielectric strength in volts/m
d = 33000; #thickness in kV
#calculations
t = d/float(e0); #required thickness of insulation in mm
#result
print'thickness=%3.2f'%t,'mm';
import math
#variable declaration
C = 0.03*10**-6; #capacitance in F
d = 0.001; #thickness in m
er = 2.6; #dielectric constant
e0 = 8.85*10**-12; #dielectric strength
E0 = 1.8*10**7
#formula
#C=e0*er*A/d
#e0=v/d
#calculation
A = (C*d)/float(e0*er); #area of dielectric needed in m**2
Vb = E0*d; #breakdown voltage in m
#result
print'area = %3.2f'%A,'m**2';
print' breakdown voltage=%3.1e'%Vb,'V';
import math
#variable declaration
C = 0.035*10**-6; #capacitance in F
tangent = 5*10**-4; #power factor
f = 25*10**3; #frequency in Hz
I = 250; #current in A
#calculation
V = I/float(2*math.pi*f*C) #voltage across capacitor in volts
P = V*I*tangent; #dielectric loss in watts
#result
print'dielectric loss=%3.1f'%P,'watts';
import math
#variable declaration
Q = 20*10**-6; #charge of electron in coulomb
V = 10*10**3; #potential in V
e0 = 8.854*10**-12; #absolute permitivity
d = 5*10**-4; #separation between plates in m
er = 10; #dielectric constant
#formula
#Q=CV
#C=er*e0*A/d
C = Q/float(V);
A = (C*d)/float(er*e0); #area in m**2
#result
print'area=%1e'%A,'m**2';
import math
#variable declaration
n = 3.0*10**28; #number of electrons per m**3
t = 3*10**-14; #time in s
m = 9.1*10**-31; #mass of electron in kg
L = 2.44*10**-8; #lorentz number in ohm W/K**2
T = 300; #temperature in kelvin
e = 1.6*10**-19; #charge of electron in coulomb
#calculation
sigma = (n*(e**2)*t)/float(m); #electrical conductivity in (ohm-m)**-1
K = sigma*T*L;
#result
print'electrial conductivity=%3.2e'%sigma,'(Ω-m)**-1';
print'lorentz number = %3.2f'%K,'W/mK';