Chapter4 - Analog Electronic Volt-Ohm Milliammeters

Example 4.2.1 - page : 4-4

In [1]:
#Peak amplitude
#given data :
E_rms=230.0 #in V
Ep=2**(1.0/2)*E_rms 
print "Peak amplitude, Ep = ", round(Ep,2), " V."

Peak amplitude, Ep =  325.27  V.

Example 4.12.1 - page : 4-21

In [2]:
#Resistance
#given data :
import math
Rm=500.0 #in ohm
E_rms=50.0 # in V
E_dc=(2**(1.0/2)*E_rms)/(math.pi/2) 
Im=1*10**-3 #in A
R=E_dc/Im 
Rs=(R-Rm)*10**-3 
print "The resistance, Rs = ", round(Rs,1), " kohm."

The resistance, Rs =  44.5  kohm.

Example 4.14.1 - page : 4-25

In [3]:
#Percentage error
ff1=1.0 #form factor
r=1.11 #sine wave form factor
per=((r-ff1)/ff1)*100 #percentage error
print "Percentage error is ", per, " %"

Percentage error is  11.0  %

Example 4.14.2 - page : 4-26

In [13]:
#part (i)
# form factor
T1=3.0 #
T=range(0,4) 
##Function for integration
def integrate(a,b,f):
    # def function before using this
    # eg. : f=lambda t:200**2*t**2
    #a=lower limit;b=upper limit;f is a function
    import numpy
    N=1000 # points for iteration
    t=numpy.linspace(a,b,N)
    ft=f(t)
    ans=numpy.sum(ft)*(b-a)/N
    return ans
# Calculating Vrms
a=T[0]
b=T[3]
f=lambda t:200**2*t**2
Vrms=(1/T1*integrate(a,b,f))**(1.0/2)  # V
# Calculating Vav
g=lambda t:200*t
Vav=1/T1*integrate(a,b,g)  # V
ff=Vrms/Vav # form factor
print "Form factor is ", round(ff,4)
# part (ii)
ff1=1.11 #form factor of sine wave
per=((ff1/ff)-1)*100 #percentage errpr
print "Percentage error in meter indication is", round(per,3), " %"
# Answer is not accurate in the textbook.

Form factor is  1.155
Percentage error in meter indication is -3.895  %

Example 4.19.1 - page : 4-43

In [4]:
#Current
#Given data :
gm=0.005 #in mho
V1=1.5 #in V
rd=200.0*10**3 # in Ohm
Rd=15.0*10**3 #in ohm
Rm=75.0 #in ohm
I=(gm*V1*((Rd*rd)/(rd+Rd)))/((2*((Rd*rd)/(rd+Rd)))+Rm) # A
I*=10**3  #  mA
print "Current, I = ", round(I,2), " mA"

Current, I =  3.74  mA

Example 4.19.2 - page : 4-44

In [23]:
#Current
#Given data :
gm=0.005 #in mho
V1=[0.2,0.4,0.6,0.8,1.0] #in V
rd=200.0*10**3 # in Ohm
Rd=15.0*10**3 #in ohm
Rm=75.0 #in ohm
Im=[]
for v1 in V1:
    Im.append(gm*(rd*Rd*v1/(rd+Rd))/(2.0*(rd*Rd/(rd+Rd))+Rm)*1000)  # mA
#Im*=1000  # mA
print "Voltage    Current"
i=0
for im in Im:
    print V1[i]," V   ",round(Im[i],3)," A"
    i+=1

Voltage    Current
0.2  V    0.499  A
0.4  V    0.997  A
0.6  V    1.496  A
0.8  V    1.995  A
1.0  V    2.493  A

Example 4.19.3 - page : 4-44

In [26]:
# Design
v1=100.0 # in V
v2=30.0 #in V
v3=103.0 # in V
v4=1.0 #in V
x=9.0 #assume input resistance in Mohm
r4=(v4/v3)*x*10**3 #in kohm
r3=(((v4/v1)*x*10**6)-(r4*10**3))*10**-3 #in kohm
r2=(((v4/v2)*x*10**6)-((r4+r3)*10**3))*10**-3 # in kohm
r1=9*10**6-((r2+r3+r4)*10**3) # in ohm
r1*=10**-6  # Mohm
print "Resistance, R4  is ",round(r4,2)," kohm."
print "Resistance, R3  is ",round(r3,2)," kohm."
print "Resistance, R2  is ",r2," kohm."
print "Resistance, R1  is ",r1," Mohm."

Resistance, R4  is  87.38  kohm.
Resistance, R3  is  2.62  kohm.
Resistance, R2  is  210.0  kohm.
Resistance, R1  is  8.7  Mohm.

Example 4.19.4 - page : 4-51

In [28]:
#Current
#given data :
rd=150.0*10**3 # in ohm
Rm=50.0 # in ohm
Rs=1000.0*10**3 # in ohm
gm=0.0052 #in mho
rd1=rd/((gm*rd)+1) 
V0=gm*((rd1*Rs)/(rd1+Rs))
R0=(2*Rs*rd1)/(Rs+rd1)
I=V0/(R0+Rm) # A
I*=10**3  # mA
print "Curent, I = ", round(I,3)," mA"
# Answer in the textbook is not accurate.

Curent, I =  2.3  mA

Example 4.19.5 - page : 4-52

In [29]:
#Resistance
#given data :
V1=1.0 #in V
I=1.5*10**-3 #in A
rd=200.0*10**3 # in ohm
Rm=50.0 # in ohm
Rs=600.0*10**3 # in ohm
gm=0.005 #in mho
rd1=rd/((gm*rd)+1) 
V0=gm*((rd1*Rs)/(rd1+Rs))*V1
R0=(2*Rs*rd1)/(Rs+rd1)
R_cal=(V0/I)-Rm-R0 
print "Resistance , R_cal = ",round(R_cal,2)," ohm" 
# answer is wrong in book

Resistance , R_cal =  216.31  ohm

Example q.3 - page : 4-73

In [30]:
#Current and voltage
rm=10.0 #in ohm
im=5.0 # in mA
i=1.0 # in A
v=5.0 #in A
ish=i-(im*10**-3) # in A
m=i/(im*10**-3) # ratio
rsh=rm/(m-1) #in ohm
vo=v/i #in V
rsh1=vo/(im) #in kohm
print "Shunt resistance is ",round(rsh,2)," ohm to measure current upto 1 A"
print "Shunt resistance is ", rsh1," kohm to measure voltage upto 5 V"

Shunt resistance is  0.05  ohm to measure current upto 1 A
Shunt resistance is  1.0  kohm to measure voltage upto 5 V