Chapter3 - Electromechanical Instruments

Example 3.2.1 - page : 3-5

In [1]:
# Torque
#given data :
N=10  # turns
L=1.5*10**-2    # in m
I=1    # in mA
I*=10**-3  #A
B=0.5 #  T
d=1*10**-2    # in m
Td=B*I*L*d*N  # Nm
print "Torque, Td = ", Td,"Nm"

Torque, Td =  7.5e-07 Nm

Example 3.2. - page : 3-5

In [3]:
# number of turns
#given data :
import math
theta=math.pi/2
I=5*10**-3    # in A
B=1.8*10**-3    # in Wb/m2
C=0.14*10**-6    # in Nm/rad
L=15*10**-3    # in m
d=12*10**-3    # in m
N=(C*theta)/(B*I*L*d)
print "Number of turns, N = ", round(N),"turns"

Number of turns, N =  136.0 turns

Example 3.2.3 - page : 3-6

In [4]:
# resistance
#given data :
Tc=240*10**-6    #in Nm
N=100  # Turns
L=40*10**-3  # in m
d=30*10**-3  # in m
B=1    #in Wb/m2
TdBYI=N*B*L*d
I=Tc/TdBYI
#voltage per division=I*(R/100)
R=100/I  # ohm
R*=10**-3  # kohm
print "Resistance, R = ", R,"kohm"
#UNIT IS GIVEN WRONG FOR THE ANSWER IN THE BOOK.

Resistance, R =  50.0 kohm

Example 3.2.4 - page : 3-7

In [6]:
# flux density and diameter
import math
#given data :
p=1.7*10**-8    #in ohm-m
V=100*10**-3    #in V
R=50    # in ohm
theta=120    #in degree
L=30    # in mm
d=25    # in mm
N=100
C=0.375*10**-6    # in Nm/degree
I=V/R  # A
Td_By_B=I*L*10**-3*d*10**-3*N
Tc=C*theta  # N-m
B=Tc/Td_By_B # in Wb/m2
print "The flux density, B = ", B,"Wb/m2"
Rc=0.3*R
Lmt=2*(L+d)
a=(N*p*Lmt*10**-3*10**6)/Rc
D=(4/(math.pi*a))**(1.0/2)
print "Diameter, D = ", round(D,1),"m"

The flux density, B =  0.3 Wb/m2
Diameter, D =  10.1 m

Example 3.4.1 - page : 3-11

In [8]:
# shunt resistor
#given data :
Im=3*10**-3    # in A
Rm=100    # in ohm
I=150*10**-3    #in A
Rsh=(Im*Rm)/(I-Im)
print "Shunt resistor, Rsh = ", round(Rsh,2),"ohm"

Shunt resistor, Rsh =  2.04 ohm

Example 3.4.2 - page : 3-11

In [10]:
# shunt resistormultiplying factor and resistance
#given data :
Rsh=300    #in ohm
Rm=1500    #in ohm
m=1+(Rm/Rsh)
print "Multiplying factor, m = ",m
m1=40.0
Rsh1=Rm/(m1-1)
print "The shunt resistor, Rsh1 = ", round(Rsh1,2),"ohm"

Multiplying factor, m =  6
The shunt resistor, Rsh1 =  38.46 ohm

Example 3.5.1 - page : 3-13

In [13]:
#given data :
Rm=100.0    # in ohm
Im=1.0
#for range 0-20 mA
I1=20.0
m=I1/Im
Rsh1=Rm/(m-1)
print "The shunt resistor, Rsh1 = ", round(Rsh1,2),"ohm"
#for the range of 0-100 mA
I2=100.0
m=I2/Im
Rsh2=Rm/(m-1)
print "The shunt resistor, Rsh2 = ", round(Rsh2,2),"ohm"
#for the range 0-200 mA
I3=200.0
m=I3/Im
Rsh3=Rm/(m-1)
print "The shunt resistor, Rsh3 = ", round(Rsh3,2),"ohm"

The shunt resistor, Rsh1 =  5.26 ohm
The shunt resistor, Rsh2 =  1.01 ohm
The shunt resistor, Rsh3 =  0.5 ohm

Example 3.6.1 - page : 3-15

In [5]:
import numpy
from numpy.linalg import inv
#design
Rm=50.0 #in ohm
Im=2.0 #in mA
Im*=10**-3  # A
I1=2.0 #in A
I2=10.0 #in A
I3=15.0 #in A
#Let Rs=R1+R2+R3
A=numpy.array([[I1,I1,I1],[-Im,I2,I2],[Im,Im,-I3]])
B=numpy.array([[Im*Rm],[Im*Rm],[-Im*Rm]])
Ainv=inv(A)
X=numpy.dot(Ainv,B)
R1=X[0]
R2=X[1]
R3=X[2]
print "Value of shunt resistors are : "
print "R1 is %f ohm, R2 is %.1e ohm & R3 is %.2e ohm" %(round(R1,5), R2, R3)
# Answer is wrong in the textbook.

 Value of shunt resistors are : 
R1 is 0.039990 ohm, R2 is 3.3e-03 ohm & R3 is 6.67e-03 ohm

Example 3.9.1 - page : 3-19

In [14]:
# Multiplier
#Given data :
Vin=20.0 #in volts
I_fsd=50.0*10 **-6 # in Farad
Rm=200.0 # in ohm
Rs=(Vin/I_fsd)-Rm  # in ohm
Rs=Rs/10**3   # kohm
print "The multiplier, Rs = ", Rs, " kohm"

The multiplier, Rs =  399.8  kohm

Example 3.9.2 - page : 3-19

In [15]:
# Full scale deflection current
#given data :
Vin=10.0 # in V
Rs=200.0 #in kohm
Rm=400.0 # in ohm
I_fsd=Vin/((Rs*10 **3)+Rm) # A
I_fsd*=10**6  # micro A
print "Full scale deflection current, I_fsd  = ", round(I_fsd,1), " micro A"

Full scale deflection current, I_fsd  =  49.9  micro A

Example 3.10.1 - page : 3-22

In [33]:
# Multiplier
#given data :
V1=200.0 #in V
V2=100.0 #in V
V3=10.0 # in V
Rm=100.0 #in ohm
I_fsd=50*10 **-3 
#for the range 0-10V   
Rt3=V3/I_fsd 
Rs3=Rt3-Rm # ohm
print "The multiplier, Rs3 = ", Rs3, " ohm."
#for the range 0-100V
Rt2=V2/I_fsd 
Rs2=Rt2-(Rm+Rs3)  # ohm 
print "The multiplier, Rs2 = ", Rs2, " ohm."
Rt1=V1/I_fsd 
Rs1=Rt1-(Rm+Rs3+Rs2) 
print "The multiplier, Rs1 = ", Rs1, " ohm."

The multiplier, Rs3 =  100.0  ohm.
The multiplier, Rs2 =  1800.0  ohm.
The multiplier, Rs1 =  2000.0  ohm.

Example 3.11.1 - page : 3-23

In [9]:
# Multiplier
#given data :
Rm=200.0 #in ohm
I_fsd=150.0*10 **-6 # in A
S=1/I_fsd 
V=50 #in V
Rs=(S*V)-Rm   # ohm 
Rs*=10**-3   # kohm
print "Multiplier, Rs = ", round(Rs,2), " kohm."

Multiplier, Rs =  333.13  kohm.

Example 3.11.2 - page : 3-24

In [11]:
#Accurate voltmeter reading
r1=50.0 # in kohms
r2=50.0 #in kohms
v=100.0 #in V
vr2=(r1/(r1+r2))*v # voltage in V
#case 1
s1=12000.0 #sensivity in ohm/V
rm1=r1*s1*10**-3 # in kohm
req=((rm1*r1)/(rm1+r1)) #equivalent resistance in ohm
v1=((req/(r1+req)))*v # voltmeter reading when sensivity is 12000 ohm/V
#case 2
s2=15000 #sensivity in ohm/V V
rm2=r1*s2*10**-3 # in kohm
req1=((rm2*r1)/(rm2+r1)) #equivalent resistance in ohm
v2=((req1/(r1+req1)))*v # voltmeter reading when sensivity is 15000 ohm/V
print "Voltmeter reading when sensivity is 12000 ohm/V is ", round(v1,2), " V"
print "Voltmeter reading when sensivity is 15000 ohm/V is ", round(v2,2), " V. This voltmeter will measure the correct value."
# Answer in the textbook is not accurate

Voltmeter reading when sensivity is 12000 ohm/V is  48.0  V
Voltmeter reading when sensivity is 15000 ohm/V is  48.39  V. This voltmeter will measure the correct value.

Example 3.15.1 - page : 3-28

In [20]:
#voltage
r1=25.0 # kohms
r2=5.0 #in kohms
v=30.0 #in V
# part(i)
vr2=(r2/(r1+r2))*v # voltage in V across 5 kohms resistance
Vactual=vr2  # V
print "Voltage across 5 kohm Resistance is ", vr2, " V."
#part (ii)
vr2=(r1/(r1+r2))*v # voltage in V across 5 kohm resistance
#case 1
s1=1.0 #sensivity in kohm/V
v1=10.0 # in V
rm1=v1*s1 #in kohm
req=((rm1*r2)/(rm1+r2)) # equivalent resistance in ohm
vrb1=((req/(r1+req)))*v # voltmeter reading when sensivity is 1 kohm/V
print "Voltmeter reading when sensivity is 1 kohm/V is ",round(vrb1,2), " V."
# part(iii)
#case 2
s2=20 #sensivity in kohm/V
v1=10 # in V
rm2=v1*s2 #in kohm
req1=((rm2*r2)/(rm2+r2)) #equivalent resistance in ohm
vrb2=((req1/(r1+req1)))*v # voltmeter reading when sensivity is 1 kohm/V
print "Voltmeter reading when sensivity is 1 kohm/V is ",round(vrb2,2), " V."
#part(iii) #error
er1=(Vactual-vrb1)/Vactual*100 #voltmeter 1 error in %
er2=(Vactual-vrb2)/Vactual*100 #voltmeter 2 error in %
print "Voltmeter 1 error is ",round(er1,2)," %"
print "Voltmeter 2 error is ",round(er2,1)," %"
#Answer is wrong in the textbook

Voltage across 5 kohm Resistance is  5.0  V.
Voltmeter reading when sensivity is 1 kohm/V is  3.53  V.
Voltmeter reading when sensivity is 1 kohm/V is  4.9  V.
Voltmeter 1 error is  29.41  %
Voltmeter 2 error is  2.0  %

Example 3.15.2 - page : 3-29

In [21]:
#Shunt resistance
#Given data :
Im=1.0 # in mA
Rm=100.0 # in ohm
I=100.0 # in mA
Rsh=(Im*10**-3*Rm)/((I-Im)*10**-3) 
print "Shunt resistance, Rsh = ",round(Rsh,3)," ohm."

Shunt resistance, Rsh =  1.01  ohm.

Example 3.15.3 - page : 3-29

In [22]:
#Shunt resistance
#Given data :
Im=1.0 # in mA
P=100.0 # in kW
I=100.0 # in mA
Rm=(P)/(Im)**2 # ohm
Rsh=((Im*10**-3*Rm*10**3)/((I-Im)*10**-3))*10**-3 # ohm
print "Shunt resistance, Rsh = ",round(Rsh,3), " kohm"

Shunt resistance, Rsh =  1.01  kohm

Example 3.15.4 - page : 3-29

In [23]:
# Shunt resistance
#given data :
Rsh=200.0 # in ohm
Rm=100.0 # in ohm
m=50.0 
Rsh=Rm/(m-1) # ohm
print "The shunt resistance, Rsh = ", round(Rsh,2), " ohm." 

The shunt resistance, Rsh =  2.04  ohm.

Example 3.15.5 - page : 3-30

In [24]:
# shunt resistance
#Given data :
Im=1.0 # in mA
Rm=100.0 # in ohm
I=100.0 # in mA
Rsh=(Im*10**-3*Rm)/((I-Im)*10**-3) # ohm
print "Shunt resistance, Rsh = ", round(Rsh,3), " kohm."

Shunt resistance, Rsh =  1.01  kohm.