import math
#variable declaration
R =10000; #resistance in Ω
R1 = 3850; #resistance of potentiometer Ω
R2 = 7560; #resistance of potentiometer Ω
l = 50*10**-3; #length of uniform wound wire in m
x = 10;
#calculations
R3 = (R/float(2)); #resistance of potentiometer in .normal position in Ω
r = (R/float(l)); #resistance of potentiometer wire per unit length Ω/mm
dR1 = R3-R1; #change in resistance of potentiometer from its normal position Ω
D1 = (dR1/float(r)); #displacement in mm
dR2 = (R2-R3); #change in resistance of potentiometer from its normal position in Ω
D2 = (dR2/float(r)); #displacement in mm
RE = (x/float(r)); #resolution of potentiometer in mm
#result
print'displacement %3.2f'%(D1*10**3),'mm';
print'displacement %3.3f'%(D2*10**3),'mm';
print'resolution of potentiometer %3.3f'%(RE*10**3),'mm';
import math
#variable declaration
R25 = 100; #resistance of thermistor at 25°C
t2 = 35; #temperature in °C
t1 = 25; #temperature in °C
alpha = 0.05; #temperature coefficient
#calculations
t = t2-t1; #temperaturre difference in °C
x = alpha*t;
R35 = (R25)*(1-x); #resistance in Ω
#result
print'resistance at 35°C is %d'%R35,'Ω';
import math
#variable declaration
l = 1.00; #length in mm
L = 2; #inductance in mH
d = 0.02; #displacement in mm
#calculations
la = l-d; #length of air gap when d=0.02
dl = (2*(1/float(la)))-L; #change in inductance in mH
r = dl/L; #ratio of change in inductance to the original inductance
dd = r/l; #ratio of displacement to original gap length
#result
print'inductance = %3.2f'%dl,'mH';
print'ratio of change in inductance to the original inductance =%3.2f'%r;
print'ratio of change in inductance to the original inductance =%3.2f'%dd;
print'hence dl is directly proportional to displacement';
import math
#variable declaration
d = 1.8; #output voltage at maximum displacement in V
de = 0.0045; #deviation from straight line through the origin
#calculations
a = (de/float(d))*100; #percentage linearity indicating in both -ve and +ve
#result
print'percentage linearity %3.2f'%a,'%';
import math
#variable declaration
Vo = 1.8; #output voltage in mV
Vi = 0.6; #input voltage in mV;
a = 500; #amplification factor
r = 1/float(4); #scale can read
v = 4; #output of voltmetr in V
D = 100; #millivoltmeter readings
#calculation
s = Vo/float(Vi); #sensitivity in mV/mm
sm = a*s; #sensitivity of measurement in mV/mm
s1 = (v/float(D))*10**3; # 1 scale division in mV
Vm = r*s1; #minimum voltage that can be read on voltmeter
R = Vm/float(sm); #resolution in mm
#result
print'sensitivty of LVDT %3.2f'%s,'mV/mm';
print'resolution %3.4f'%R,'mm';
import math
#variable declaration
A = 300*10**-6; #area of plate in m**2
d = 0.2*10**-3; #distance between plates in mm
e0 = 8.85*10**-12; #permittivity in F/m
er2 = 8; #dielectric constant of mica
d1 = 0.18*10**-3; #distance between plates in mm
er1 = 1; #dielectric constant
D1 = 0.19;
D2 = 0.01; #thickness of mica sheet in mm
D3 = 0.17; #displacement in mm
D4 = 0.01;
#calculation
C = ((e0*A)/float(d)); #value of capacitance in pF
dD = d-d1; #change in displacement in mm
dC = ((e0*A)/(float(d1)))-C; #change in capacitance in capacitance
x1 = (dC/float(C)); #per unit change in capacitance
x2 = (dD/float(d)); #per unit change of displacement
d3 = d-d1; #length of air gap between plates in mm
x = x1/float(x2); #ratio of unit change of capacitance to unit change in displacement
D = (D1/(float(er1)))+((D2/float(er2)));
C1 = (e0*A)/float(D*10**-3); #initial capacitance of transducer in mm
d4 = d1-d3; #length of air gap in mm
d1 = (D3/float(er1))+(D4/float(er2));
C2 = (e0*A)/float(d1*10**-3); # capacitance with displacement is applien in pF
dC2 = C2-C1; #change in capacitance in pF
y1 = (dC2/float(C1)); #per unit change in capacitance
y2 = (dD/float(d)); #per unit change of displacement
Y = y1/float(y2); #ratio of unit change of capacitance to unit change in displacement
#result
print'capacitance = %2.3f'%(C*10**12),'pF';
print'change in capacitance %3.3f'%(dC*10**12),'pF';
print'ratio ofper unit change of capacitance to per unit change in displacement = %f'%x;
print'capcitance when mica is inserted = %3.2f'%(C1*10**12),'pF';
print'change in capacitance when mica sheet is inserted = %2.2f'%(dC2*10**12),'pF';
print'ratio ofper unit change of capacitance to per unit change in displacement = %3.3f'%Y;
import math
#variable declaration
t = 2.5*10**-3; #thickness in m
g = 0.055; #voltage intensity in Vm/N
p = 1.4*10**6; #pressure in N/m**2
e = 40.6*10**-12; #permittivity of quartz in F/m
#calculation
E = g*t*p; #output voltage in V
q = e*g; #charge sensitivity in pC/N
#result
print'output voltage = %3.2f'%E,'V';
print'charge sensitivity = %3.3f'%(q*10**12),'pC/N';
import math
#variable declaration
r = 6*10**-3; #radius in m
t = 1.8*10**-3; #thickness in m
g = 0.055; #voltage intensity in Vm/N
E = 120; #voltage developed in V
#calculation
A = r*r; #area in m**2
p = E/(float(g*t)); #pressure in N/m**2
F = p*A; #force in N
#result
print'force = %3.2f'%F,'N';
import math
#variable declaration
r = 6*10**-3; #radius in m
t = 1.5*10**-3; #thickness in m
e = 12.5*10**-9; #permittivity in F/m
F = 6; #force in N
d = 150*10**-12; #charge density in pC/N
E = 12*10**6; #modulus of elasticity in N/m**2
s = 0.167*10**6; #stress
#calculation
A = r*r;
p = F/float(A); #pressure in MN/m**2
p1 = p*10**-6;
e1 = s/float(E); #strain
g = d/float(e); #voltage sensitivity in V*m/N;
E1 = g*t*p; #voltage generated in V
Q = d*F; #charge in C
C = (Q)/float(E1); #capacitance in F
#result
print'strain = %3.5f'%e;
print'charge = %3.1f'%(Q*10**12),'pC';
print'capacitance = %3.3d'%(C*10**12),'pf';
import math
#variable declaration
p = 0.00912; #resistivity in Ωm
B = 0.48; #flux density in Wb/m**2
RH = 3.55*10**-4; #hall coefficient in m**3/C
#calculation
Ex = p; #Ex in terms of Jx in °
Ey = RH*B; #ey interms of Jx in °
x= Ex/float(Ey);
t = math.atan(x);
print'hall angle %3.2f'%t,'°(Equal to 1 minute 4 seconds)';
import math
#variable declaration
p = 0.00912; #resistivity in Ωm
B = 0.48; #flux density in Wb/m**2
RH = 3.55*10**-4; #hall coefficient in m**3/C
I = 0.015; # current in A
l = 15*10**-3; #length in m
b = 10**-3; #breadth in m
#calculation
A = l*b; #area in m**2
Jx = I/float(A); #current density in A/m**2
Ey = RH*B*Jx; #Ey in V/m
V = Ey*I; #voltage between contacts in V
#result
print'voltage between contacts = %5.5f'%V,'V';
import math
#variable declaration
Gf = 4.2; #guage factor of resistance
#calculation
u =(Gf-1)/float(2); #poisson's ratio
#result
print'poissons ratio = %1.1f'%u;
import math
#variable declaration
R = 120; #resistance in Ω
Gf = 2; #guage factor
s = 400*10**6; #elastic limit stress in N/m**2
E = 200*10**9; #modulus of elasticity in N/m**2
alpha = 20*10**-6; #resistance temperature coefficient in /°C
x = 1/float(10); #cahnge in stress
dt = 20; #change in temperature in °C
#calculations
sc = s*x; #change in stress in N/m**2
e = sc/float(E); #strain
dR = Gf*e*R; #change in resistance in mΩ
dR1 = R*alpha*dt; #change in resistance in mΩ
#result
print'change in resistance = %3.2f'%(dR*10**3),'mΩ';
print'Note:printing mistake in textbook';
print'change in resistance = %3.2f'%(dR1*10**3),'mΩ';
import math
#variable declaration
L = 0.12; #length in m
A = 3.8*10**-4; #area in m**2
R = 220; #resistance in Ω
Gf = 2.2; #guage factor
dR = 0.015; #change in resistance in Ω
E = 207*10**9; #elasticity in N/m**2
#calculations
dL = (dR*L)/float(R*Gf); #change in length in m
s = (E*dL)/float(L);
F = s*A; #force in kN
#result
print'change in length = %2.2e'%dL,'m';
print'force = %3.3f'%(F*10**-3),'kN';
import math
#variable declaration
Rg = 100; #resistance in Ω
Rsh = 80000; #resistance in Ω
Gf = 2.1;
#calculations
x = (Rg/float(Rg+Rsh)); #equivalent strain
eeq = x/(float(Gf)); #strain in microstrain
#result
print'strain = %3.1f'%(eeq*10**6),'microstrain';
import math
#variable declaration
n = 4; #four arm bridge
Rg = 200; #resistance in Ω
Rsh = 100*10**3; #resistance in Ω
x = 140; #number of divisions
Gf = 2.0; #guage factor
#calculation
eeff = Rg/float(n*Gf*(Rg+Rsh)); #effective strain
d = eeff/float(x); #1 division scale
s = float(d)*Rg; #strain when loaded
#result
print'strain = %3.2f'%(s*10**6),'microstrain';
print'Note:calculation mistake in text book,Rg value is taken wrong in calculating s';
import math
#variable declaration
ex = 0.00016; #strain values in axial
ey = 0.00064; #strain values in circumferential direction
E = 200*10**9; #modulus of elasticity in N/,**2
u = 0.26; #poisson's ratio
#calculation
sigmax = (E*(ex+(u*ey)))/float(1-(u**2)); #longitudinal stress in N/m**2
sigmay = (E*(ey+(u*ex)))/float(1-(u**2)); #hoop stress in N/m**2
#result
print'longitudinal stress = %3.2f'%(sigmax/10**6),'MN/m**2';
print'longitudinal stress = %3.1f'%(sigmay/10**6),'MN/m**2';
import math
#variable declaration
A = 110*10**-6; #area in m**2
P = 25; #load in kN
ex = 1540; #strain values in axial direction
ey = -420; #strain values in transvers direction
#calculation
sigmax = P/float(A); #axial stress in N/M**2
E = sigmax/float(ex); #modulus of elasticity in N/M**2
u = (-ey*E)/float(sigmax); #poisson's ratio
#result
print'modulus of elasticity = %3.1f'%E,'N/M**2'
print'poissons ratio = %3.4f'%u;
import math
#variable declaration
e1 = 60*10**-6; #strain in microstrains
e2 = 48*10**-6; #strain in microstrain
e3 = -12*10**-6; #strain in microstrain
E = 200*10**9; #modulus of elsticity in N/m**2
u = 0.3;
#calculation
x = (e1+e3)/float(2); #average of strains
a = math.sqrt(((e1-e2)**2)+((e2-e3)**2));
b = 1/math.sqrt(2);
y = a*b;
emax = x+y; #principle strains
emin = x-y; #principle strains
x1 = x/float(1-u);
y1 = y/float(1+u);
sigmamax = E*(x1+y1); #principle stress
sigmamin = E*(x1-y1); #principle stress
tmax = E*y1; #maximum shear stress in MN/m**2
k = ((2*e2)-e1-e3)/float((e1-e3));
theta = (math.atan(k)); #location of principle planes
theta1 =(theta*180)/float(math.pi);
theta2 =theta1+180;
theta11 = (theta1)/float(2);
theta22 = (theta2)/float(2);
print'emax = %2.2e'%(emax);
print'emin = %2.3e'%(emin);
print'sigmamax = %3.3f'%(sigmamax*10**-6),'MN/m**2';
print'sigmamin = %3.3f'%(sigmamin*10**-6),'MN/m**2';
print'maximum shear stress = %3.3f'%(tmax*10**-6),'MN/m**2';
print'location of principle planes = %f'%theta11,'°';
print'location of principle planes = %f'%theta22,'°';
import math
#variable declaration
d = 0.06; #diameter in m
Rg = 120; #nominal resistance of each guage Ω
Gf = 2.0; #guage factor
v = 6; #supply voltage in V
E = 200*10**9; #modulus of elasticity in N/m**2
u = 0.3; #poisson's ratio
P = 1000; #load in N
#calculation
A = (math.pi/float(4))*d*d;
s = P/float(A); #stress in N/m**2
e = s/float(E); #strain
x = Gf*e; #fraction change in resistence i.e dR/R
a = v/float(4);
y = 2*(1+u)*(x)*a; #output volatge in uV
#result
print'sensitivity of load = %3.2f'%(y*10**6),'uV/kN';