Chapter3 - Principal of Electrical Measurement & Measuring Instruments

Exa 3.1 page 85

In [13]:
from __future__ import division
from math import asin, pi
print 'For spring controlled Tc is proportional to theta'
theta=90*(3/5)**2 
print "Deflection for spring controlled instrument=%.2f degree"%(theta)
print 'For gravity controlled Tc is proportional to sin(theta)'
theta=asin((3/5)**2)*180/pi 
print "Deflection for gravity controlled instrument=%.2f degree"%(theta)
For spring controlled Tc is proportional to theta
Deflection for spring controlled instrument=32.40 degree
For gravity controlled Tc is proportional to sin(theta)
Deflection for gravity controlled instrument=21.10 degree

Exa 3.2 page 85

In [14]:
I=1000 
Ia=50*10**-3 
Is=I-Ia 
Ra=10 
Va=Ia*Ra 
Rs=10*Va/Is 
print "The shunt resistance=%.2f ohm"%(Rs)
The shunt resistance=0.01 ohm

Exa 3.3 page 85

In [15]:
Is=150*10**-6 
I=50*10**-6 
R=4*10**3 
Rt=R*I/Is 
print "the value of total resistance=%.2f ohm"%(Rt)
the value of total resistance=1333.33 ohm

Exa 3.4 page 86

In [16]:
V=1 
R=2*10**3 
I=(V/R)*1000 
print "Actual current=%.2f mA"%(I)
Rm=1000 
Rt=R+Rm 
I=(V/Rt)*1000 
print "Current when Rm is 1000 ohm =%.2f mA"%(I)
Rm=100 
Rt=R+Rm 
I=(V/Rt)*1000 
print "Current when Rm is 100 ohm =%.2f mA"%(I)
Actual current=0.50 mA
Current when Rm is 1000 ohm =0.33 mA
Current when Rm is 100 ohm =0.48 mA

Exa 3.5 page 86

In [17]:
I=20 
E_expected=2.5*I/100 
print "Expected error=+/-%.2f mA"%(E_expected)
print 'Actual reading for 5mA indication will be 4.5mA to 5.5mA'
print 'Actual reading for 15mA indication will be 14.5mA to 15.5mA'
E_5mA=(0.5/5)*100 
print "Error for 5mA reading=%.2f percent"%(E_5mA)
E_15mA=(0.5/15)*100 
print "Error for 15mA reading=%.2f percent"%(E_15mA)
Expected error=+/-0.50 mA
Actual reading for 5mA indication will be 4.5mA to 5.5mA
Actual reading for 15mA indication will be 14.5mA to 15.5mA
Error for 5mA reading=10.00 percent
Error for 15mA reading=3.33 percent

Exa 3.6 page 87

In [18]:
V=20 
A=20*10**-6 
Ra=25*10**3 
Rx=((V/A)-Ra)*10**-3 
print "The resistance = %.0f Kohm"%(Rx)
E_voltmeter=(2/(100*20))*20*100 
E_current=(2/(100*20))*50*100 
E_total=E_voltmeter+E_current 
print "Maximum possible error=%.1f percent"%(E_total)
The resistance = 975 Kohm
Maximum possible error=7.0 percent

Exa 3.7 page 88

In [19]:
V=20 
A=20*10**-3 
Rv=10*10**3*20 
Rx=(V/(A-(V/Rv)))/1000 
print "The resistance=%.2f Kohm"%(Rx)
E_total=2.5+2.5 
print "Maximum possible error=%.0f percent"%(E_total)
The resistance=1.01 Kohm
Maximum possible error=5 percent

Exa 3.8 page 88

In [20]:
Sp_constant=10.5*10**-6*pi/180 
deflection=83 
Td=Sp_constant*deflection 
I1=10 
K=0.078 
I2=(Td/(K*I1))*10**6 
print "Current in the voltage coil=%.2f uA"%(I2)
Current in the voltage coil=19.50 uA

Exa 3.9 page 89

In [21]:
AH=5*1/2 
print "AH passed in 30 minuties = %.1f percent"%(AH)
V_assumed=0.51*1000/AH 
V_actual=200 
Error=V_actual-V_assumed 
Correction=-Error 
Cor=Correction*100/V_actual 
print "Correction required = %.1f percent"%(Cor)
AH passed in 30 minuties = 2.5 percent
Correction required = 2.0 percent

Exa 3.10 page 89

In [22]:
E_unity_pf=230*6*4*1/1000 
M_constant=2208/E_unity_pf 
print "Meter constant=%.1f rev/kWh"%(M_constant)
E_consumed=1472/M_constant 
pf=(E_consumed/(230*5*4))*1000 
print "power factor=%.2f"%(pf)
Meter constant=400.0 rev/kWh
power factor=0.80

Exa 3.11 page 90

In [23]:
from math import acos
phi=acos(0.8)*180/pi 
alpha_actual=85-phi 
alpha_true=90-phi 
er=(alpha_true-alpha_actual)/(alpha_true)*100 
print "percentage error at full load = %.2f"%(er)
percentage error at full load = 9.41