Chapter 1 Qualities of measurements

Example 1.1 (a) Page no 3

In [14]:
#Given
V=80.0                             #expected value of voltage in Volts
V1=79                            #Volts

#Calculation
E=V-V1
E1=((V-V1)/V)*100
E2=1-((V-V1)/V)
A=100*E2

#Result
print"(i) Absolute error is ",E,"V"
print"(ii) percent error is ", E1,"%"
print"(iii) reletive error is ", E2
print"(iv) percent of accuracy is ", A,"%"

(i) Absolute error is  1.0 V
(ii) percent error is  1.25 %
(iii) reletive error is  0.9875
(iv) percent of accuracy is  98.75 %

Example 1.1 (b) Page no 3

In [13]:
#Given
Yn=20.0                             #mA
Xn=18                             #mA

#Calculation
e=Yn-Xn
E=(e/Yn)*100
A=1-(e/Yn)
a=A*100

#Result
print"(i) Absolute error is ", e,"mA"
print"(ii) Percent error is ",E,"%"
print"(iii) Relative accuracy is ",A
print"(iv) Percent accuracy is ",a,"%"

(i) Absolute error is  2.0 mA
(ii) Percent error is  10.0 %
(iii) Relative accuracy is  0.9
(iv) Percent accuracy is  90.0 %

Example 1.2 Page no 4

In [26]:
#Given
x1=98
x2=101
x3=102
x4=97
x5=101
x6=100
x7=103
x8=98
x9=106
x10=99

#Calculation
X=(x1+x2+x3+x4+x5+x6+x7+x8+x9+x10)/10.0
P=(x6/X)

#Result
print"Precision of the 6th measurment is ",round(P,3)

Precision of the 6th measurment is  0.995

Example 1.3(a) Page no 6

In [14]:
#given
V=80                                  #milliammeter readings
I=10.0                                  #mA
V1=150                                 #Volts
R1=1000                                #ohm/volt

#Calculation
R=V/I
Rv=R1*V1
Rx=(R*V1)/(V1-R)
E=((Rx-R)/Rx)*100

#Result
print"(i) Apparent resistance of the unknown resistance ",R,"K ohm"
print "(ii) Actual resistance of the unknown resistance is ",round(Rx,2),"K ohm"
print "(iii) Error due to the loading effet of the voltmeter ",round(E,1),"%" 

(i) Apparent resistance of the unknown resistance  8.0 K ohm
(ii) Actual resistance of the unknown resistance is  8.45 K ohm
(iii) Error due to the loading effet of the voltmeter  5.3 %

Example 1.3(b) Page no 7

In [113]:
#Given
V=30                             #Volts
V1=150                           #Volts
I=0.6                            #A
R1=1000                          #ohm/volts

#Calculation
R=V/I
Rv=(R1*V1)
Rx=(R*Rv)/(Rv-R)
E=((Rx-R)/Rx)*100

#Result
print"(i) total circuit resistance is ", R,"ohm"
print "(ii) The voltmeter resistance is ",round(Rx,2)
print"(iii) Error due to loading effect of voltmeter ", round(E,3),"%"

(i) total circuit resistance is  50.0 ohm
(ii) The voltmeter resistance is  50.02
(iii) Error due to loading effect of voltmeter  0.033 %

Example 1.4 Page no 12

In [77]:
#Given
x1=49.7
x2=50.1
x3=50.2
x4=49.6
x5=49.7

#Calculation
X=(x1+x2+x3+x4+x5)/5.0
d1=x1-X
d2=x2-X
d3=x3-X
d4=x4-X
d5=x5-X
dtotal=(d1+d2+d3+d4+d5)

#Result
print"(i) Arithmetic mean is ", X
print"(ii) derivations from each value are"
print "d1=",d1,"\nd2=",d2,"\nd3=",d3,"\nd4=",d4,"\nd5=",d5
print"(iii) The algebric sum of derivative is ",round(dtotal,2)

(i) Arithmetic mean is  49.86
(ii) derivations from each value are
d1= -0.16 
d2= 0.24 
d3= 0.34 
d4= -0.26 
d5= -0.16
(iii) The algebric sum of derivative is  0.0

Example 1.5 Page no 13

In [86]:
#Given
x1=49.7
x2=50.1
x3=50.2
x4=49.6
x5=49.7

#Calculation
X=(x1+x2+x3+x4+x5)/5.0
d1=x1-X
d2=x2-X
d3=x3-X
d4=x4-X
d5=x5-X
dtotal=(d1+d2+d3+d4+d5)/5.0

#Result
print"The average deviation is ",round(dtotal*10**14,3)

The average deviation is  0.284

Example 1.6 Page no 13

In [90]:
#Given
d1= -0.16 
d2= 0.24 
d3= 0.34 
d4= -0.26 
d5= -0.16

#Calculation
import math
D=math.sqrt((d1**2+d2**2+d3**2+d4**2+d5**2)/4.0)

#Result
print"The standard deviation is ",round(D,2)

The standard deviation is  0.27

Example 1.7 Page no 14

In [94]:
#Given
V=600                         #Volts
V1=250.0                       #Volts
a=0.02

#Calculation
M=a*V
E=(M/V1)*100

#Result
print"The limited error is ", E,"%"

The limited error is  4.8 %

Example 1.8 (a) Page no 14

In [20]:
#Given
a=0.02
I=500                           #mA
I1=300.0                         #mA

#Calculation
M1=I*a
M2=(M1/I1)*100

#Result
print"Limiting error is ", round(M2,1),"%"

Limiting error is  3.3 %

Example 1.8 (b) Page no 14

In [102]:
#Given
V=70.0                        #Volts
V1=100                      #Volts
I=80.0                        #mA
I1=150                      #mA
a=0.015

#calculation
M=a*V1
E=(M/V)*100
E1=a*I1
E2=(E1/I)*100
E3=E+E2

#Result
print"limiting error is ",round (E3,3),"%"

limiting error is  4.955 %