Chapter 2 : Static Characteristics of Instruments and Measurement systems

Example 2.1 Page No : 5

In [1]:
# calculating static error and static correction
# Variables
Am  =  127.50;
At  =  127.43;

# Calculations and Results
e = Am-At;
print "Static error(V) = ", e

Sc = -e;
print "Static Correction(V) = ", Sc

Static error(V) =  0.07
Static Correction(V) =  -0.07

Example 2.2 Page No : 7

In [2]:
# calculating true value of the temperature

# Variables
Am  =  95.45;
Sc = -0.08;

# Calculations
At = Am+Sc;

# Results
print "True Temperature(Degree C) = ", At

True Temperature(Degree C) =  95.37

Example 2.3 Page No : 9

In [3]:
# calculating Relative error (expressed as a percentage of f.s.d)

# Variables
Am  =  1.46;
At = 1.50;

# Calculations and Results
e = Am-At;
print "Absolute error(V) = ", e
Sc = -e;
print "Absolute Correction(V) = ", Sc
RE = (e/At)*100;
print "Relative Error in terms of true value(in percentage) = ", RE
REF = (e/2.5)*100;
print "Relative Error in terms of true value(in percentage) = ", REF

Absolute error(V) =  -0.04
Absolute Correction(V) =  0.04
Relative Error in terms of true value(in percentage) =  -2.66666666667
Relative Error in terms of true value(in percentage) =  -1.6

Example 2.4 Page No : 11

In [4]:
# calculating static error and static correction

# Variables
Am  =  0.000161;
At  =  0.159*10**-3;

# Calculations and Results
e = Am-At;
print "Static error(m3/s) = ", e

Sc = -e;
print "Static Correction(m3/s) = ", Sc

Static error(m3/s) =  2e-06
Static Correction(m3/s) =  -2e-06

Example 2.5 Page No : 13

In [5]:
#calculating maximum static error 

# Variables
#Span of the thermometer(degree C)
S = 200.-150;
#Accuracy of the thermometer(in terms of percentage of span)
A = 0.0025;

# Calculations
e =  A*S;

# Results
print "Maximum Static error(degree C) = ", e

Maximum Static error(degree C) =  0.125

Example 2.6 Page No : 15

In [7]:
# calculating the pressure for a dial reading of 100

# Calculations
P = ((27.58-6.895)/150)*100+6.895;

# Results
print "pressure for a dial reading of 100(kN/m2) = ", P

pressure for a dial reading of 100(kN/m2) =  20.685

Example 2.7 Page No : 17

In [8]:
# calculating the noise output voltage of the amplifier

# Variables
Bw = 100.*10**3;
Sn = 7.*10**-21;
R = 50.*10**3;

# Calculations and Results
A = (Sn*R*Bw)**0.5;
En = 2*A;
print "Noise voltage at input(V) = ", En

Ga = 100;
Eno = En*Ga;
print "Noise voltage at output(V) = ", Eno

Noise voltage at input(V) =  1.18321595662e-05
Noise voltage at output(V) =  0.00118321595662

Example 2.8 Page No : 19

In [9]:
# calculating the noise voltage

# Variables
Sn = 20.;
Vs = 3;

# Calculations
Vn = Vs/(Sn)**0.5;

# Results
print "noise Voltage(mV) = ", Vn

noise Voltage(mV) =  0.67082039325

Example 2.9 Page No : 21

In [11]:
import math

# calculating the signal to noise ratio at input
# calculating the signal to noise ratio at output
#calculating the noise factor and noise figure

# Calculations and Results
print "signal to noise ratio at input"
Sni = (3.*10**-6/(1*10**-6))**2;
print "signal to noise ratio at input = ", Sni
print "signal to noise ratio at output"
Sno = (60.*10**-6/(20*10**-6))**2;
print "signal to noise ratio at output = ", Sno
print "New signal to noise ratio at output"
Snno = (60.*10**-6/(25*10**-6))**2;
print "signal to noise ratio at output = ", Snno

F = Sni/Snno;
print "noise Factor = ", F

nf = 10*math.log10(F);
print "noise Figure(dB) = ", nf

signal to noise ratio at input
signal to noise ratio at input =  9.0
signal to noise ratio at output
signal to noise ratio at output =  9.0
New signal to noise ratio at output
signal to noise ratio at output =  5.76
noise Factor =  1.5625
noise Figure(dB) =  1.93820026016

Example 2.10 Page No : 23

In [12]:
# calculating the ratio of output signal to noise signal 

# Variables
Bw = 100.*10**3;
K = 1.38*10**-23;
T = 300.;
R = 120.;

# Calculations and Results
A = (K*T*R*Bw)**0.5;
En = 2*A;
print "Noise voltage (V) = ", En
Eno = 0.12*10**-3;
print "Noise voltage at output(V) = ", Eno
Ra = Eno/En;
print "Ratio of signal votage to Noise voltage  = ", Ra

Noise voltage (V) =  4.45780214904e-07
Noise voltage at output(V) =  0.00012
Ratio of signal votage to Noise voltage  =  269.190951029

Example 2.12 Page No : 25

In [13]:
# Variables
#calculating the average force and range of error
F1 = 10.03;
F2 = 10.10;
F3 = 10.11;
F4 = 10.08;

# Calculations and Results
Fav = (F1+F2+F3+F4)/4;
print "Average Force(N)  = ", Fav
Fmax = F3;
MaxR = Fmax-Fav;
Fmin = F1;
MinR = Fav-Fmin;
AvgR = (MaxR+MinR)/2;
print "Average range of error (N) = ", AvgR

Average Force(N)  =  10.08
Average range of error (N) =  0.04

Example 2.13 Page No : 27

In [14]:
# Variables
#calculating the sum of resistances connected in series with uncertainity of one unit
R1 = 72.3;
R2 = 2.73;
R3 = 0.612;

# Calculations
R = (R1+R2+R3);

# Results
print "sum of resistances(ohm)  = ", R

print "the resultant resistance is 75.6 ohm with 6 as first doutful figure"

sum of resistances(ohm)  =  75.642
the resultant resistance is 75.6 ohm with 6 as first doutful figure

Example 2.14 Page No : 29

In [15]:
#calculating the power with uncertainity of one unit in voltage and current

# Variables
V = 12.16;
I = 1.34;

# Calculations
P = V*I;

# Results
print "Power(W)  = ", P

print "the resultant  is 16.2 W with 2 as first doutful figure"

Power(W)  =  16.2944
the resultant  is 16.2 W with 2 as first doutful figure

Example 2.15 Page No : 31

In [16]:
#calculating the sum of resistances connected in series with appropriate number of significant figure

# Variables
R1 = 28.7;
R2 = 3.624;

# Calculations
R = (R1+R2);

# Results
print "sum of resistances(ohm)  = ", R

print "the resultant resistance is 32.3 ohm as one of the resistance is accurate to three significant figure"

sum of resistances(ohm)  =  32.324
the resultant resistance is 32.3 ohm as one of the resistance is accurate to three significant figure

Example 2.16 Page No : 33

In [17]:
#calculating the voltage drop with appropriate number of significant figure

# Variables
R = 31.27;
I = 4.37;

# Calculations
E = I*R;

# Results
print "voltage drop(V)  = ", E

print "the voltage drop is 137 V as one of the resistance is accurate to three significant figure"

voltage drop(V)  =  136.6499
the voltage drop is 137 V as one of the resistance is accurate to three significant figure

Example 2.17 Page No : 35

In [18]:
#calculating the sensitivity and deflection factor of wheatstone bridge

# Variables
Mo = 3.;
Mi = 7;

# Calculations and Results
Sen = Mo/Mi;
print "sensitivity(mm per ohm)  = ", Sen
Df = Mi/Mo;
print "deflection factor( ohm per mm)  = ", Df

sensitivity(mm per ohm)  =  0.428571428571
deflection factor( ohm per mm)  =  2.33333333333

Example 2.18 Page No : 37

In [19]:
#calculating the volume of the mercury thermometer

# Calculations and Results
Ac = (math.pi/4)*0.25**2;
print "Area of mercury thermometer", Ac
Lc = 13.8*10**3;
Vc = Ac*Lc;
print "Volume of mercury thermometer(mm3)", Vc

Area of mercury thermometer 0.0490873852123
Volume of mercury thermometer(mm3) 677.40591593

Example 2.19 Page No : 39

In [20]:
#calculating the maximum position deviation, resistance deviation 

# Variables
Pl = 0.001;
FSD = 320;
R = 10000;

# Calculations and Results
MDD = (Pl*FSD);
print "Maximum lacement deviation(degree) =",MDD
MRD = Pl*R;
print "Maximum lacement deviation(ohm) = ",MRD

Maximum lacement deviation(degree) = 0.32
Maximum lacement deviation(ohm) =  10.0

Example 2.20 Page No : 41

In [22]:
#calculating the dead zone

# Variables
s = 600;

# Calculations
Dz = 0.00125*s;

# Results
print "Dead zone(degree C) = ", Dz

Dead zone(degree C) =  0.75

Example 2.22 Page No : 43

In [24]:
#calculating the Resolution

# Variables
Fs = 200.;
D = 100.;

# Calculations
SD = Fs/D;
R = SD/10;

# Results
print "resolution (V) = ", R

resolution (V) =  0.2

Example 2.23 Page No : 45

In [25]:
#calculating the Resolution

# Variables
Fs = 9.999;
D = 9999;

# Calculations
SD = Fs/D;
R = SD;

# Results
print "resolution (V) = ", R

resolution (V) =  0.001

Example 2.24 Page No : 47

In [26]:
#calculating the reading of the multimeter and percentage error

# Variables
Zl = 20000.;
Zo = 10000.;
Eo = 6.;

# Calculations and Results
El = Eo/(1+Zo/Zl);
print "Reading of the multimeter (V) = ", El
PE = ((El-Eo)/Eo)*100;
print "Percentage error = ", PE

Reading of the multimeter (V) =  4.0
Percentage error =  -33.3333333333

Example 2.25 Page No : 49

In [27]:
#calculating the reading of the multimeter and percentage error

# Variables
Zl = 20000.;
Zo = 1000.;
Eo = 6;

# Calculations and Results
El = Eo/(1+Zo/Zl);
print "Reading of the multimeter (V) = ", El
PE = ((El-Eo)/Eo)*100;
print "Percentage error = ", PE

Reading of the multimeter (V) =  5.71428571429
Percentage error =  -4.7619047619

Example 2.26 Page No : 51

In [28]:
#calculating the loading error

# Variables
Zl = 1000.;
Zo = 200*200./400;
Eo = 100*200./400;

# Calculations and Results
El = Eo/(1+Zo/Zl);
print "Reading of the multimeter (V) = ", El
PE = ((El-Eo)/Eo)*100;
print "Percentage loading error = ", PE
Ac = 100+PE;
print "Accuracy = ", Ac

Reading of the multimeter (V) =  45.4545454545
Percentage loading error =  -9.09090909091
Accuracy =  90.9090909091

Example 2.27 Page No : 53

In [29]:
import math 
#calculating the voltage across the oscilloscope

# Variables
C = 50*10.**-6;

# Calculations and Results
f = 100000.;
print "frequency = ", f
Xc = 1./(2*math.pi*f*C);
R = 10.**6;
Zl = (R*-1j*Xc)/(R-1j*Xc);
Eo = 1.;
Zo = 10.*10**3;

El = Eo/(1+Zo/Zl);
print "Reading of the multimeter (V) = ", El

frequency =  100000.0
Reading of the multimeter (V) =  (1.02334395478e-11-3.18309886181e-06j)

Example 2.28 Page No : 55

In [31]:
#calculating the actual value of current, measured value of current and percentage error

# Variables
Eo = 10.-((10.*1000)/(1000+1000));
Zo = ((1000.*1000)/(1000+1000))+500;

# Calculations and Results
Io = Eo/Zo;
print "Actual value of current (A) = ", Io
Zl = 100.;
Il = Eo/(Zo+Zl);
print "Measured value of current (A) = ", Il
PE = ((Il-Io)/Io)*100;
print "Percentage loading error = ", PE

Actual value of current (A) =  0.005
Measured value of current (A) =  0.00454545454545
Percentage loading error =  -9.09090909091

Example 2.29 Page No : 57

In [32]:
#calculating the maximum available power

# Variables
Eo = 80.*10**-3;
Il = 5.*10**-9;
Rl = 6.*10**6;

# Calculations
Ro = (Eo/Il)-Rl;
Pmax = (Eo**2)/(4*Ro);

# Results
print "Maximum available Power(W) = ", Pmax

Maximum available Power(W) =  1.6e-10