# Chapter 2 - Analog measurement of electrical quantities¶

## Example 1 - pg 130¶

In [1]:
#pg 130
import math,cmath
#given
print "for Ist method"
v=50;#volts
i=20;#amperes
pf=0.8;#power factor
pl=v*i*pf;#true power
vc=(50*pf)+1j*v*math.sqrt(1-pf**2);#complex form
ic=i+1j*0;#
r1=0.01;#ohms
#calculations and results
vpl=vc+(i*r1);#voltage across pressure coil
wrlc1=(vpl.real)*(ic.real);#
er=(wrlc1-pl)/(pl);#
print "percentage error is high (%) = ",er*100
print "for 2nd method"
r2=1000;#ohms
ic1=ic+(vc/r2);#
wrlc2=(vc.real)*(ic1.real)+(vc.imag)*(ic1.imag);#
er1=(wrlc2-pl)/(pl);#
print "percentage error is high (%) = ",er1*100

for Ist method
percentage error is high (%) =  0.5
for 2nd method
percentage error is high (%) =  0.3125


## Example 2 - pg 131¶

In [2]:
#pg 131
#Example 2.2:#self inductance
#calculate the self inductance
#given
c=20.;#pF
rs=10000.;#ohms
#calculations
l=(c*10**-12)*rs**2;#henry
#results
print "self inductance (mH) = ",l*10**3

self inductance (mH) =  2.0


## Example 3 - pg 131¶

In [3]:
#pg 131
#Example 2.3:#percentage error
#calculate the percentage error
#given
import math
v=100;#volts
i=10;#amperes
pf=0.45;#power factor
f=50;#Hz
l=25;#mH
r=4000;#ohms
#calculations
tp=v*i*pf;#true power in watts
e=v*i*math.tan(b)*math.sqrt(1-pf**2);#
per=(e*100)/(tp);#
#results
print "percentage error is (%) = ",round(per,3)

percentage error is (%) =  0.39


## Example 4 - pg 131¶

In [4]:
#pg 131
#Example 2.4:#true power
#calculate the true power
#given
import math
from math import cos
ph=45.;#degree
f=50.;#Hz
l=15.;#mH
r=300.;#ohms
#calculations
k=((cos(ph/57.3))/(cos(b)*cos(42/57.3)));#
nr=20;#nomianl ratio
e=-0.3;#
er=(e*nr)/100;#
ar1=nr-er;#actual ratio
nr1=100;#nomianl ratio
e1=0.9;#
er1=(e1*nr1)/100;#
ar2=nr1-er1;#actual ratio
p=450;#watts
tp=ar1*ar2*k*p;#
#results
print "true power in (kW) = ",round(tp*10**-3,1)
print 'answer is wrong in the textbook'

true power in (kW) =  851.3
answer is wrong in the textbook


## Example 5 - pg 132¶

In [5]:
#pg 132
#Example 2.5:#torque
#calculate the torque required
#given
import math
from math import sin
d=2.5;#diameter in cm
n=500;#turns
b=1.1;#mWb/m**2
v=100;#volts
pf=0.7;#power factor
rp=2000;#ohms
#calculations
x=((math.pi*(d*10**-2)**2*n*b*10**-3*v*pf)/(4*rp));#
ang1=45;#degree
ang2=90;#degree
td1=x*sin(ang1/57.3);#
td2=x*sin(ang2/57.3);#
#results
print "torque in Nm when angle is 45 degree (Nm) = ",round(td1,8)
print "torque in Nm when angle is 90 degree (Nm) = ",round(td2,8)

torque in Nm when angle is 45 degree (Nm) =  6.68e-06
torque in Nm when angle is 90 degree (Nm) =  9.45e-06


## Example 6 - pg 133¶

In [6]:
#pg 133
#Example 2.6:#resistance
#calculate the resistance
#given
import math
la=4.78;#henry
ra=298.;#ohms
lb=3.;#henry
rb=190.;#ohms
v=200.;#volts
#calculations
r=((la*100*lb*100*math.pi**2)-(ra*rb))/(rb+ra);#ohm
#results
print "unknown resistance is (ohm)=",round(r,0)
print 'answer is wrong in the textbook'

unknown resistance is (ohm)= 2784.0
answer is wrong in the textbook


## Example 7 - pg 133¶

In [7]:
#pg 133
#Example 2.7:#resistance
#given
i=20.;#amperes
v=100.;#volts
pf=1;#power factor
rp=5500.;#ohms
th=150.;#angle
wd=20;#watts per degree
#calculations
p=v*i*pf;#watts
kd=((rp*th)/p);#constant
rp1=wd*kd;#in ohms
#results

addition resistance (ohm) =  2750.0


## Example 8 - pg 134¶

In [9]:
#pg 134
#Example 2.8:#resistance,impedance,power,power factor ,voltage and power factor
#calculate the total power factor,supply, impedance and resistance
#given
v=300.;#volts
i2=2.5;#amperes
#calculations and results
r=v/i2;#ohms
print "resistance in (ohm) =",r
i3=4;#amperes
zl=v/i3;#ohms
print "load impedance in (ohm) = ",zl
v=300;#volts
i2=2.5;#amperes
r=v/i2;#ohms
i1=5.6;#amperes
z=v/i1;#ohms
print "impedance of combination in (ohm) = ",round(z,2)
i3=4;#amperes
pl=((i1**2-i2**2-i3**2)*r)/2;#in watts
print "power absorbed by the load in (W) = ",pl
pl=((i1**2-i2**2-i3**2)*r)/2;#in watts
pfl=((i1**2-i2**2-i3**2)/(2*i2*i3));#power factor
print "power factor of the load = ",pfl
pr=i2**2*r;#in watts
tps=pl+pr;#in watts
print "total power supply  is (W) = ",tps
tps=pl+pr;#in watts
tpf=tps/(v*i1);#power factor
print "total power factor = ",round(tpf,3)

resistance in (ohm) = 120.0
load impedance in (ohm) =  75.0
impedance of combination in (ohm) =  53.57
power absorbed by the load in (W) =  546.6
power factor of the load =  0.4555
total power supply  is (W) =  1296.6
total power factor =  0.772


## Example 9 - pg 135¶

In [10]:
#pg 135
#calculate the average power
import math,scipy
from scipy import integrate
v=24.;#volts
r1=6.;#ohms
vm=100;#volts
t0=0.;#
t1=(1./100);#
f=50.;#Hz
#calculations
i=v/r1;#in amperes
z=2*math.pi*f;#
def fun(t):
y=math.sin(z*t)
return y
p=vm*(1/t1)*i*x[0];#
#results
print "average power to be read by wattmeter is (W) = ",round(p,2)

average power to be read by wattmeter is (W) =  127.32


## Example 10 - pg 136¶

In [11]:
#pg 136
#Example 2.10:#load impedance and combination impedance
#calculate the power factor and power, load
#given
v3=80.;#volts
i=4.;#amperes
v1=140;#volts
#calculations and results
zl=v3/i;#ohms
z=v1/i;#ohms
print "load impedance in (ohm) = ",zl
print "impedance of combination in (ohm) = ",z
v2=75.;#volts (it is given 72 in the textbook)
r=v2/i;#
pl=((v1**2-v2**2-v3**2)/(2*r));#watts
pr=i**2*r;#watts
print "power absorbed by the load is,(W) = ",pl
print "power absorbed by the non inductive resistor is,(W) = ",pr
tp=pr+pl;#total power in watts
pfc=tp/(v1*i);#power factor
print "power factor of load is",round(pfl,2)
print "power factor of the whole circuit is",round(pfc,1)

load impedance in (ohm) =  20.0
impedance of combination in (ohm) =  35.0
power absorbed by the load is,(W) =  202.0
power absorbed by the non inductive resistor is,(W) =  300.0
power factor of load is 0.63
power factor of the whole circuit is 0.9


## Example 11 - pg 136¶

In [12]:
#pg 136
import math
from math import sqrt
#given
pf=0.8;#
#calculations
td=(sqrt(1-pf**2))/pf;#
sr=300;#kW
df=(sr/sqrt(3))*td;#
w2=(sr+df)/2;#
w1=sr-w2;#
#results
print "wattmeter (W1) reading in (kW) = ",round(w1)
print "wattmeter (W2) reading in (kW) = ",round(w2)

wattmeter (W1) reading in (kW) =  85.0
wattmeter (W2) reading in (kW) =  215.0


## Example 12 - pg 137¶

In [14]:
#pg 137
#Example 2.12:#power factor and capacitance
#calculate the capacitance and power factor
import math
from math import atan,sqrt,cos
#given
w1=-2000.;#watts
w2=4000.;#watts
v=400.;#volts
pfn=0.5;#power factor
f=50.;#Hz
#calculations
ph=math.atan((sqrt(3.)*(w2-w1))/(w2+w1)) *57.3;#in degree
pf=cos(ph/57.3);#
w=w1+w2;#total power
vp=(v/sqrt(3));#phase voltage
pp=w/3.;#power per phase
pi=(pp)/(vp*pf);#phase current
pim=vp/pi;#phase impedance
rip=pim*pf;#resistance each phase
rep=(sqrt(pim**2-rip**2));#reactance of each phase
pimb=rip/pfn;#impedance per phase
repn=(sqrt(pimb**2-rip**2));#reactance per phase
cp=rep-repn;#capacitive reactance
c=((1/(2*math.pi*f*cp)));#
#results
print "power factor of the system = ",round(pf,3)
print "capacitance (micro-F) = ",round(c*10**6)

power factor of the system =  0.189
capacitance (micro-F) =  322.0


## Example 13 - pg 138¶

In [15]:
#pg 138
#Example 2.13:#power factor and line current
#calculate the line current and power factor
#given
import math
x=1;#
w=50;#kW
v=400.;#volts
#calculations
w2=2*x;#
w1=x;#
ph=math.atan((math.sqrt(3)*(w2-w1))/(w2+w1))*57.3;#in degree
pf=math.cos(ph/57.3);#power factor
il=((w/(math.sqrt(3)*v*pf)))*10**3;#in amperes
#results
print "power factor = ",round(pf,3)
print "line current is (A)=",round(il,1)

power factor =  0.866
line current is (A)= 83.3


## Example 14 - pg 138¶

In [16]:
#pg 138
#Example 2.14:#total power and power factor
#calculate the total power and power factor
#given
import math
print "when both readings are positive"
w2=2300.;#watts
w1=4600.;#watts
#calculations and results
p1=w2+w1;#
ph=57.3*math.atan((math.sqrt(3)*(w2-w1))/(w2+w1));#in degree
pf=math.cos(ph/57.3);#power factor
print "power is (W) = ",p1
print "power factor (leading) = ",round(pf,3)
print "when second readig is negative"
w21=-2300.;#watts
w1=4600.;#watts
p2=w21+w1;#
ph2=57.3*math.atan((math.sqrt(3)*(w21-w1))/(w21+w1));#in degree
pf1=math.cos(ph2/57.3);#power factor
print "power is (W) = ",p2
print "power factor (leading) = ",round(pf1,3)

when both readings are positive
power is (W) =  6900.0
power is (W) =  2300.0


## Example 15 - pg 139¶

In [17]:
#pg 139
#given
import math
from math import atan,cos,sqrt
rp=806.;#watts
#calculations
ph=atan((sqrt(3)*rp)/rw);#in degree
pf=cos(ph/57.3);#power factor
v=440;#volts
i=((rw)/(sqrt(3)*v*pf));#amperes
#results
print "load current in amperes = ",round(i)

load current in amperes =  5.0


## Example 16 - pg 139¶

In [18]:
#pg 139
#Example 2.16:#error
#calculate the error percentage
#given
import math
from math import sin
pf=0.5;#
#calculations
n=(1./4)*sin(d-60/57.3);#
nc=(1./4)*pf*sin(d);#
e=((n-nc)/nc)*100;#error
#results
print "error (slow) in percentage = ",round(-e,1)

error (slow) in percentage =  9.1


## Example 17 - pg 140¶

In [19]:
#pg 140
#Example 2.17:#error
#calculate the error
#given
import math,scipy
from scipy import integrate
i=5;#amperes
t0=0;#
t1=30./60;#
e=0.56;#kWh
v1=220;#volts
#calculations
def function(t):
y=5
return y
v=(e*10**3)/x[0];#volts
ae=v1*i*t1*10**-3;#actual energy
e=((e-ae)/ae)*100;#error
#results
print "error (%)  = ",round(e,2)

error (%)  =  1.82


## Example 18 - pg 140¶

In [20]:
#pg 140
#Example 2.18:#time and error
#calculate the time duration and limits of accuracy
#given
nd=500.;#dvisions
ie=0.05;#inherent error
tea=0.1;#total error allowable
cr1=0.01;#seconds
cr2=0.1;#seconds
nd1=500/10.;#
#calculations
te=re+ie;#total error
per=tea-te;#permissible error
t=per/ter;#seconds
ie1=((ie*nd)/nd1);#new inherent error
ter1=er1+ie1;#
la=ter1+per;#
#results
print "time duration (seconds) = ",round(1./t)
print "limits of accuracy (%) = ",la

time duration (seconds) =  367.0
limits of accuracy (%) =  0.73


## Example 19 - pg 141¶

In [21]:
#pg 141
#Example 2.19:#error
#calculate the error
#given
import math
n=40.;#revolutions
rc=0.12;#registration constant
e2=22000;#volts
e1=110;#volts
i2=500;#amperes
i1=5;#amperes
i=5.25;#amperes
lv=110;#volts
pf=1;#
t=61;#seconds
#calculations
err=n/rc;#energy recorded in kWh is
ae=((math.sqrt(3)*e2*lv*i*i2*pf*t)/(e1*i1*3600))*10**-3;#kWh
e=((err-ae)/ae)*100;#
#results
print "error (slow) is (%)",round(-e,2)

error (slow) is (%) 1.66


## Example 20 - pg 142¶

In [24]:
#pg 142
#Example 2.20:#error and limit of error
#calculate the error and limit of error
#given
mc=1200.;#meter constant in rev/kWh
n=40.;#revolutions
tp=99.8;#seconds
v=240;#volts
i=5;#amperes
#calculations
err=n/mc;#energy recorded in kWh
ae=((v*i*tp*10**-3)/3600);#actual energy in kWh
e=((err-ae)/ae)*100;#error
n=500;#divisions
per=((rn/n)*100);#possible error
ie=0.05;#inherent error
per1=(((rn/10)/tp)*100);#possible error
her=((ie/tp)*100);#human error
tpr=per+per1+her+ie;#total possible error
li1=e-tpr;#
li2=e+tpr;#
#results
print "error (fast) in recording (%) = ",round(e,2)
print "limit of error in the meter is ",round(li1,2),"% or ",round(li2,2),"% "

error (fast) in recording (%) =  0.2
limit of error in the meter is  0.07 % or  0.33 %


## Example 21 - pg 143¶

In [23]:
#pg 143
#Example 2.21:#consumer monthly bill ,power factor and average cost per unit
#calculate the consumer monthly bill ,power factor and average cost per unit
#given
import math
from math import sqrt
kwh=125000.;#
kvarh=100000.;#
kw=180;#
kvar=125;#
d=30.;#days
t=24.;#hours a day
#calculations
kvah=sqrt(kwh**2+kvarh**2);#kVAh
mkva=sqrt(kw**2+kvar**2);#kVA
pkva=15;#rupees
pkvah=0.1;#reupees
tmb=pkva*mkva+pkvah*kvah;#in Rs
pf=kwh/kvah;#power factor
avcp=tmb/kwh;#in paisa
#results
print "total monthly bill in Rs",round(tmb)
print "power factor is",round(pf,2)
print "average cost per unit (kWh) in paisa is",round(avcp*100,1)
print 'total monthly bill and load factor is calculated wrong in the book due to rounding off error'

total monthly bill in Rs 19295.0
power factor is 0.78
average cost per unit (kWh) in paisa is 15.4
total monthly bill and load factor is calculated wrong in the book due to rounding off error


## Example 22 - pg 143¶

In [25]:
#pg 143
#Example 2.22:#full load speed and error
#calculate the full load speed and error
#given
v=220.;#volts
n=30.;#revolutions
i=5.;#in amperes
t=59.5;#seconds
#calculations
wrv=((v*i*10**-3)/(3600.));#kWh
mc=((3600.*10**3)/(v*i));#rev/kWh
ec=((v*i*10**-3)/(3600.));#kWh
sfl=mc*ec;#rps
hler=n*ec;#kWh
hlf=(((i/2.)*v*10**-3*t)/(3600.));#kWh
e=(hler-hlf)/hlf;#
#results
print "number of revolution per kWh is,(revolutions/kWh)=",round(mc)
print "full load speed r.p.s = ",sfl
print "error (fast) in percentage  = ",round(e*100,2)
print 'numberof revolutions is calcultaed wrong in the textbook due to rounding off error'

number of revolution per kWh is,(revolutions/kWh)= 3273.0
full load speed r.p.s =  1.0
error (fast) in percentage  =  0.84
numberof revolutions is calcultaed wrong in the textbook due to rounding off error


## Example 23 - pg 144¶

In [26]:
#pg 144
#Example 2.23:#shunt resistance
#calculate the shunt resistance
#given
ra=1000.;#armature resistance in ohms
i=10.;#mA
ia=500.;#micro amperes
i1=75;#mA
i3=100;#mA
#calculations
rsh1=((ra)/((i/(ia*10**-3))-1));#in ohms
rsh2=((ra)/((i1/(ia*10**-3))-1));#in ohms
ia3=0.4*ia;#micro amperes
rsh3=((ra)/((i3/(ia3*10**-3))-1));#in ohms
#results
print "shunt resistance when current is 10mA (ohm) = ",round(rsh1,2)
print "shunt resistance when current is 75mA (ohm) = ",round(rsh2,2)
print "shunt resistance when current is 100mA (ohm) = ",round(rsh3,3)

shunt resistance when current is 10mA (ohm) =  52.63
shunt resistance when current is 75mA (ohm) =  6.71
shunt resistance when current is 100mA (ohm) =  2.004


## Example 24 - pg 144¶

In [28]:
#pg 144
#Example 2.24:#shunt resistance and series resistance
#calculate the shunt resistance and series resistance
#given
i=125.;#amperes
ia=25.;#armature current in mA
ra=3;#ohms
#calculations
ish=i-(ia*10**-3);#amperes
rsh=((ia*ra)/ish);#milli ohms
pcs=ish**2*rsh*10**-3;#watts
rv=625;#volts
rs=((rv-(ra*ia*10**-3))/(ia*10**-3))*10**-3;#killo ohms
pc=(ia*10**-3)**2*rs*10**3;#watts
#results
print "shunt resistance in milli ohm is",round(rsh,5)
print "power consumption in shunt is,(W)=",round(pcs,2)
print "series resistance in kilo ohm is",rs
print "power consumption in the series resistance is,(W)=",round(pc,3)

shunt resistance in milli ohm is 0.60012
power consumption in shunt is,(W)= 9.37
series resistance in kilo ohm is 24.997
power consumption in the series resistance is,(W)= 15.623


## Example 25 - pg 145¶

In [29]:
#pg 145
#Example 2.25:#mulitplying power
#calculate the mulitplying power in all cases
print "when micro meter resistance is 25 ohm"
#given
ra=25.;#ohms
rsh=5000.;#ohms
r1=1250.;#ohms
r2=2500;#ohms
#calculations and results
n=((ra+rsh)/r1);#
n2=((ra+rsh)/r2);#
print "multiplying power for the shunt for a 1250 ohm is",n
print "multiplying power for the shunt for a 2500 ohm is",n2
print "when micro meter resistance is 2500 ohm"
ra1=2500.;#ohms
rsh=5000.;#ohms
r1=1250.;#ohms
n1=((ra1+rsh)/r1);#
r2=2500.;#ohms
n3=((ra1+rsh)/r2);#
print "multiplying power for the shunt for a 1250 ohm is",n1
print "multiplying power for the shunt for a 2500 ohm is",n3

when micro meter resistance is 25 ohm
multiplying power for the shunt for a 1250 ohm is 4.02
multiplying power for the shunt for a 2500 ohm is 2.01
when micro meter resistance is 2500 ohm
multiplying power for the shunt for a 1250 ohm is 6.0
multiplying power for the shunt for a 2500 ohm is 3.0


## Example 26 - pg 145¶

In [30]:
#pg 145
#Example 2.26:#resistance
#calculate the resistance
r1=185.;#ohm
r2=205.;#ohm
r3=215.;#ohm
R31=195.;#OHM
r4=200.;#ohm
r5=1100.;#ohm
v1=85.;#V
#calculations
R=r1+r2+r3+r4+R31;#ohm
R1=(R-r4)+((r5*r4)/(r5+r4));#
V=(v1*R1)/round(R1-(R-r4));#V
I=round(V)/R;#A
vd4=I*r4;#V
x=0.5;#% allowable
vd41=(vd4)-(vd4*x)/100;#
rv=((vd41*(R-r4)*r4))/((V*r4)-((R*vd41)));#
#results
print "voltage is,(V)=",round(V)
print "resistance is ,(k-ohm)=",round(rv*10**-3)
print 'resistance is calculated wrong in the textbook due to rounding off error'

voltage is,(V)= 487.0
resistance is ,(k-ohm)= 27.0
resistance is calculated wrong in the textbook due to rounding off error


## Example 27 - pg 146¶

In [31]:
#pg 146
#Example 2.27: Sensitivity
#calculate the sensitivity and resistance, relative sensitivity
#given data :
I1=0.1;# in mA
R1=50.;# in ohm
I2=10.;# in mA
I3=10.1;# in mA
I5=10;# in mA
V=2;# in Volt
#calculations
I4=I2-I1;
Rsh=I1*R1/(I3-I1);
Im1=Rsh*I4/(R1+Rsh);
S1=(I1-Im1)/(I3-I4);
R=V/(I5*10**-3);
# formula : Im=((I3-Im)*(R-V))/R1;
Im2=(0.8*I3)-8;
Im3=(0.8*I4)-8
S2=(Im2-Im3)/(I3-I4);
S=S1/S2;
#results
print "(a). The sensitivity of an instrument,S1 = ",round(S1,4)
print "(b). The resistance,R(ohm) = ",R
print "The relative sensitivity,S = ",round(S,3)

(a). The sensitivity of an instrument,S1 =  0.0099
(b). The resistance,R(ohm) =  200.0
The relative sensitivity,S =  0.012


## Example 28 - pg 147¶

In [32]:
#pg 147
#Example 2.28: Error
#calculate the Error, shunt resistance  and inductance
#given data :
import math
from math import sqrt
La=90*10**-6;# in micro-H
Ra=0.09;# in ohm
I=50;# in A
Ia=5;# in A
f=50;# in Hz
#calculations
LsbyRs=La/Ra;
w=2*math.pi*f;
Rs=Ra/9;
Ls=LsbyRs*Rs*10**6;
Ls1=0;# shunt is non-inductive
Ia1=(Rs*I)/sqrt((Ra+Rs)**2+(w**2*La**2));
Error=((Ia-Ia1)/Ia)*100;
#results
print "Shunt resistance,Rs(ohm) = ",Rs
print "Inductance,Ls(micro-H) = ",Ls
print "Current,Ia1(A) = ",round(Ia1,2)
print "Error,(%)(low) = ",round(Error,1)

Shunt resistance,Rs(ohm) =  0.01
Inductance,Ls(micro-H) =  10.0
Current,Ia1(A) =  4.81
Error,(%)(low) =  3.8


## Example 29 - pg 148¶

In [33]:
#pg 148
#Example 2.29 :area and percentage error
#calculate the area and error
#given data
import math
from math import sqrt
v1=18.;#kV
c1=60.;#pF
v2=2.;#
d=2.5;#cm
#calculations
q=v2*10**3*c1*10**-12;#
cs=q/(v1*10**3);#F
eo=8.854*10**-12;#
a=((cs*d*10**-2)/(eo));#
c2=50;#pf
x=c1-c2;#
stf=((v2*10**3)**2*x*10**-12);#
v=sqrt(stf/(x*10**-12*2))/1000;#kV
c3=c2+(x/2);#pf
x1=c3/(cs*10**12);#
V1=(x1+1)*v#
V=10*sqrt(2);#V
er=((V-V1)/V1)*100;#
#results
print "area is (cm^2)=",round(a*10**4)
print "error is (%)=",round(er,2)

area is (cm^2)= 188.0
error is (%)= 8.11


## Example 30 - pg 150¶

In [34]:
#pg 150
#Example 2.30: % Error
#calculate the percentage error
#given data :
Ra=2.;# in ohm
Rsh=0.0004;# constant
alfa=0.004;
t1=288.;# in K
t2=333.;# in K
I=100.;# in A
Rs=50.;# in ohm
#calculations
theta=t2-t1;
Ra1=Ra+(alfa*Ra*theta);
N1=1+(Ra/Rsh);
Ia=I/N1;
N2=1+(Ra1/Rsh);
Ia1=I/N2;
epsilon1=(Ia1-Ia)*100/Ia;
N3=1+((Ra+Rs)/Rsh);
Ia2=I*10**3/N3;
N4=1+((Ra1+Rs)/Rsh);
Ia3=I*10**3/N4;
epsilon2=(Ia3-Ia2)*100/Ia2;
#results
print "The percentage error in case 1 (%) = ",round(epsilon1,2)
print "The percentage error in case 2 (%) = ",round(epsilon2,3)
print 'The answers are a bit different due to rounding off error in textbook'

The percentage error in case 1 (%) =  -15.25
The percentage error in case 2 (%) =  -0.688
The answers are a bit different due to rounding off error in textbook


## Example 31 - pg 151¶

In [35]:
#pg 151
#Example 2.31: Resistance and electromotive force
#calculate the electromotive force and resistance
#given data :
import numpy
from numpy import linalg
i1=20.;# in mA
i2=400.;# in mA
v1=19.5;# in mV
v2=23.4;# in mV
y=100;#mV
#calculations
i3=i1/i2;
K1=i1/i3;
x1=v1/K1;#
k2=y/i3;#
x2=v2/k2;#
A=numpy.matrix([[1, -x1],[1, -x2]]);
B=numpy.matrix([[v1],[v2]]);#
X=numpy.dot(numpy.linalg.inv(A),B);#
#results
print "electromotive force is (mV)=",round(X[0,0],3)
print "resistance is (ohm)=",round(X[1,0],3)

electromotive force is (mV)= 24.632
resistance is (ohm)= 105.263


## Example 32 - pg 151¶

In [36]:
#pg 151
#Example 2.32: error
#calculate the error
#given data :
import math
V=20*10**3;# in V
v1=2*10**3;# in V
R=10*10**3;# in ohm
f=50.;# in Hz
#calculations
r=R*v1/V;
w=2*math.pi*f;
C=0.60*10**-6;# in F
v=V/((R/r)*math.sqrt(1+((w**2*C**2*r**2*(R-r)**2)/R**2)));
Error=((v1-v)/v1)*100;
#results
print "Error (%) = ",round(Error,1)

Error (%) =  1.4


## Example 33 - pg 152¶

In [37]:
#pg 152
#Example 2.33: Flux, actual ratio and phase angle
#calculate the Flux, actual ratio and phase angle
#given data :
import math
from math import sin,cos
I=5.;# in A
r1=4.;# in ohm
r2=0.2;# in ohm
Ts=160;# in turns
F=50;# in Hz
I0=6;# in A
#calculations
Es=I*(r1+r2);
fi=Es*10**3/(4.44*Ts*F);
Ie=I0*cos(theta1);# in A
Im=I0*sin(theta1);# in A
dela=0;
K=Ts+(((Ie*cos(dela))+(Im*sin(dela)))/I);
theta=(180/math.pi)*(((Im*cos(dela))-(Ie*sin(dela)))/(Ts*I));
#results
print "(i). Flux in the core (mWb) = ",round(fi,3)
print "(ii). The actual ratio K = ",round(K,2)
print "(iii). The phase angle (degree)  = ",round(theta,3)

(i). Flux in the core (mWb) =  0.591
(ii). The actual ratio K =  161.04
(iii). The phase angle (degree)  =  0.215


## Example 34 - pg 152¶

In [38]:
#pg 152
#Example 2.34: The ratio errror and phase angle error
#calculate the ratio error and phase angle
#given data :
import math
from math import sin,cos,sqrt
I=5.;# in A
n=1000./5;# normal ratio
sin_alfa=0.4;
Im=1;# in A
dela=0;
#calculations
cos_alfa=sqrt(1-sin_alfa**2);
I0=Im/cos_alfa;
Ie=I0*sin_alfa;
K=n+(((Ie*cos(dela))+(Im*sin(dela)))/I);
er=(n-K)*100/K;
eph=(180/math.pi)*(((Im*cos(dela))-(Ie*sin(dela)))/(n*I));
x=round(eph);#
y=eph-x;#
#results
print "(a). The ratio error (%) = ",round(er,4)
print "(b). phase angle is ",x," degree ",round(y*60,3)," minutes "

(a). The ratio error (%) =  -0.0436
(b). phase angle is  0.0  degree  3.438  minutes


## Example 35 - pg 153¶

In [39]:
#pg 153
#Example 2.35: The ratio errror and phase angle error
#calculate the ratio error and phase angle
#given data :
import math
from math import sin,cos,asin
I=5.;# in A
n=198.;# in turns
L=12.5;#in VA
f=50.;# assume in Hz
Ie=10.;# in A
Im=15.;# in A
l=1.*10**-3;# in H
#calculations
Kn=1000./I;
Zs=L/I**2;
Re=2*math.pi*f*l;# in ohm
dela=asin(Re/Zs)*180/math.pi;
K=n+(((Ie*cos(dela))+(Im*sin(dela)))/I);
Rerror=(Kn-K)*100./K;
eph=(180/math.pi)*(((Im*cos(dela))-(Ie*sin(dela)))/(n*I));
#results
print "The ratio error,(%) = ",round(Rerror,3)
print "The phase angle,(degree) = ",round(eph,3)
print 'The answers are a bit different due to rounding off error in textbook'

The ratio error,(%) =  -0.744
The phase angle,(degree) =  -0.252
The answers are a bit different due to rounding off error in textbook


## Example 36 - pg 154¶

In [40]:
#pg 154
#Example 2.36: phase angle error load in VA
#calculate the phase angle error load
#given data
import math
from math import sqrt
v1=1000.;#V
v2=100.;#V
xp=65.4;#ohm
rp=97.5;#ohm
pf=0.4;#
im=0.02;#A
Xp=110;#ohm
#calculations
r=v1/v2;#
sd=pf;#
csd=sqrt(1-pf**2);#
ie=im*(pf/csd);#A
thd=th*(180/math.pi);#
iss=(r*((im*rp)-(ie*xp)))/(Xp);
va=iss*v2;#VA
#results
print "phase angle is ",round(thd*60,1),"minutes"

phase angle is  -4.7 minutes


## Example 37 - pg 155¶

In [41]:
#pg 155
#Example 2.37: flux and current ratio error
#calculate the flux and ratio error
#given
n1=1000.;#A
n2=5.;#A
r=1.6;#ohm
wt=1.5;#watt
f=50;#Hz
cd1=1;#
sd=0;#
#calculations
kn=n1/n2;#
ts=kn;#
es=n2*r;#v
ph=es/(4.44*f*kn);#m Wb
ep=es/kn;#
ie=wt/ep;#A
K=((kn+(ie/n2)));#
re=((kn-K)/K)*100;#
#results
print "flux is (m-Wb)=",round(ph*10**3,2)
print "ratio error is (%)=",round(re,2)

flux is (m-Wb)= 0.18
ratio error is (%)= -3.61


## Example 38 - pg 155¶

In [42]:
#pg 155
#Example 2.38: RCF ,ratio error and phase angle error
#calculate the ratio error, phase angle error and RCF in all cases
import math
from math import sqrt
#given
vp=2000.;#V
n=20.;#
va1=50.;#
pfl1=0.6;#lagging
va2=25.;#V
ie=0;#
im=0;#
cd1=0.6;#
rs1=0.75;#ohm
rp1=300.;#ohm
xs1=1.5;#ohm
xp1=600.;#ohm
#calculations and results
vs=vp/n;#
iss=va1/vs;#A
iss2=va2/vs;#A
sd1=sqrt(1-cd1**2);#
Rp1=n**2*rs1+rp1;#ohm
Xp1=n**2*xs1+xp1;#ohm
vps1=n+((iss/n)*(Rp1*cd1+Xp1*sd1))/vs;#
RCF1=vps1/n;#
er1=((n-vps1)/vps1)*100;#%
per1=((iss*(Xp1*cd1-Rp1*sd1))/(n**2*vs))*(180/math.pi);#degree
per1a=round(per1);#
x1=per1-per1a;#
print "RCF for case (a) = ",RCF1
print "phase error for case (a) (%)=",round(er1,3)
print "phase angle error for case (a) ",round(x1*60,1)," minutes"
cd11=1;#
sd11=sqrt(1-cd11**2);#
vps2=n+((iss/n)*(Rp1*cd11+Xp1*sd11))/vs;#
RCF2=vps2/n;#
er2=((n-vps2)/vps2)*100;#%
per2=((iss*(Xp1*cd11-Rp1*sd11))/(n**2*vs))*(180/math.pi);#degree
per1a1=round(per2);#
x2=per1-per1a1;#
print "RCF for case (b) =",RCF2
print "phase error for case (b) (%)=",round(er2,3)
print "phase angle error for case (b)is ",round(per2*60,1)," minutes"
cd12=0.6;#
sd12=-0.8;#
vps3=n+((iss/n)*(Rp1*cd12+Xp1*sd12))/vs;#
RCF3=vps3/n;#
er3=((n-vps3)/vps3)*100;#%
per3=((iss*(Xp1*cd12-Rp1*sd12))/(n**2*vs))*(180/math.pi);#degree
per1a1=round(per2);#
x2=per1-per1a1;#
print "RCF for case (c) =",RCF3
print "phase error for case (c) (%)=",round(er3,3)
print "phase angle error for case (c) is ",round(per3*60,1)," minutes"
cd13=0.6;#
sd13=0.8;#
vps4=n+((iss2/n)*(Rp1*cd13+Xp1*sd13))/vs;#
RCF4=vps4/n;#
er4=((n-vps4)/vps4)*100;#%
per4=((iss2*(Xp1*cd13-Rp1*sd13))/(n**2*vs))*(180/math.pi);#degree
per1a1=round(per2);#
x2=per1-per1a1;#
print "RCF for case (d) =",RCF4
print "phase error for case (d) (%)=",round(er4,2)
print "phase angle error for case (d) is ",round(per4*60,3)," minutes"
cd14=1;#
sd14=0;#
vps5=n+((iss2/n)*(Rp1*cd14+Xp1*sd14))/vs;#
RCF5=vps5/n;#
er5=((n-vps5)/vps5)*100;#%
per5=((iss2*(Xp1*cd14-Rp1*sd14))/(n**2*vs))*(180/math.pi);#degree
per1a1=round(per2);#
x2=per1-per1a1;#
print "RCF for case (e) =",RCF5
print "phase error for case (e) (%)=",round(er5,3)
print "phase angle error for case (e) is ",round(per5*60,1)," minutes"
cd15=0.6;#
sd16=-0.8;#
vps6=n+((iss2/n)*(Rp1*cd15+Xp1*sd16))/vs;#
RCF6=vps6/n;#
er6=((n-vps6)/vps6)*100;#%
per6=((iss2*(Xp1*cd15-Rp1*sd16))/(n**2*vs))*(180/math.pi);#degree
per1a1=round(per2);#
x2=per1-per1a1;#
print "RCF for case (f) =",RCF6
print "phase error for case (f) (%)=",round(er6,3)
print "phase angle error for case (f) is ",round(per6*60,1)," minutes"

RCF for case (a) =  1.0165
phase error for case (a) (%)= -1.623
phase angle error for case (a)  10.3  minutes
RCF for case (b) = 1.0075
phase error for case (b) (%)= -0.744
phase angle error for case (b)is  51.6  minutes
RCF for case (c) = 0.9925
phase error for case (c) (%)= 0.756
phase angle error for case (c) is  51.6  minutes
RCF for case (d) = 1.00825
phase error for case (d) (%)= -0.82
phase angle error for case (d) is  5.157  minutes
RCF for case (e) = 1.00375
phase error for case (e) (%)= -0.374
phase angle error for case (e) is  25.8  minutes
RCF for case (f) = 0.99625
phase error for case (f) (%)= 0.376
phase angle error for case (f) is  25.8  minutes


## Example 39 - pg 158¶

In [43]:
#pg 158
#Example 2.39:  ,ratio error and phase angle error
#calculate the ratio error,RCF and phase angle error
#given
import math
from math import cos, sin
vp=1000.;#V
iss=5.;#A
VA=25.;#
wt=0.25;#W
im=15.;#A
xs=1.;#ohm
rs=5.;#ohm
#calculations
n=vp/iss;#
vs=VA/iss;#
vp=iss/n;#V
ie=wt/vp;#A
dl=math.atan(xs/rs)*57.3;#
dlr=dl*(math.pi/180);#
K=n+((ie*cos(dl/57.3)+im*sin(dl/57.3))/iss);#
re=((n-K)/K)*100;#per
RCF=K/n;#
eph=(180/math.pi)*(((im*cos(dl/57.3))-(ie*sin(dl/57.3)))/(n*iss));
#results
print "ratio error (%)=",round(re,2)
print "RCF =",round(RCF,5)
print "phase angle error (degree)=",round(eph,3)

ratio error (%)= -1.26
RCF = 1.01275
phase angle error (degree)= 0.73


## Example 40 - pg 159¶

In [44]:
#pg 159
#Example 2.40: true value of voltage ,current and power
#calculate the true value of voltage ,current and power
#given
import math
from math import acos,cos
vs=102.;#V
iss=4.;#A
ws=375.;#W
rcf=0.995;#
rcf1=1.005;#
a1=2000.;#
a2=100.;#
#calculations
ph=acos(ws/(iss*vs))*57.3;#degree
ph1=round(ph);#
x=ph-ph1;#
y=x*60;#
angd=y+22+10;#
ang=angd/60.;#
ta=ph1+ang;#
nr=a1/a2;#
avr=rcf*nr;#
pv=avr*vs;#
acr=rcf1*(a2/nr);#
pc=acr*iss*iss;#A
psd=pv*pc*cos(ta/57.3)*10**-3;#
#results
print "true value of voltage is,(V)=",round(pv)
print "true value of current is,(A)=",pc
print "true value of power is ,(kW)=",round(psd,1)

true value of voltage is,(V)= 2030.0
true value of current is,(A)= 80.4
true value of power is ,(kW)= 149.4


## Example 41 - pg 160¶

In [46]:
#pg 160
#Example 2.41:primary current ,phase error
#calculate the primary current ,phase error
#given
import math,cmath
from math import cos,sin
zs=0.433+1j*0.25;#ohm
zs1=0.15+1j*0.0;#ohm
nt=2.;#turns
l1=8.;#
l2=4.;#
tnt=198;#turns
iss=5;#A
#calculations
zs2=zs+zs1;#ohm
zsa=math.sqrt((zs2.real)**2+(zs2.imag)**2);#
zsng=math.atan(zs2.imag/zs2.real);#
ie=l2/nt;#
im=l1/nt;#
K=((tnt/2.)+((ie*cos(zsng))+(im*sin(zsng)))/iss);#
ip=K*iss;#A
th=((im*cos(zsng))-(ie*sin(zsng)))/((tnt/2)*iss);#
#results
print "primary current is,(A)=",round(ip,3)

primary current is,(A)= 498.415


## Example 42 - pg 160¶

In [47]:
#pg 158
#Example 2.39:  ,ratio error and phase angle error
#calculate the ratio error,RCF and phase angle error
#given
import math
from math import cos, sin
vp=1000.;#V
iss=5.;#A
VA=25.;#
wt=0.25;#W
im=15.;#A
xs=1.;#ohm
rs=5.;#ohm
#calculations
n=vp/iss;#
vs=VA/iss;#
vp=iss/n;#V
ie=wt/vp;#A
dl=math.atan(xs/rs)*57.3;#
dlr=dl*(math.pi/180);#
K=n+((ie*cos(dl/57.3)+im*sin(dl/57.3))/iss);#
re=((n-K)/K)*100;#per
RCF=K/n;#
eph=(180/math.pi)*(((im*cos(dl/57.3))-(ie*sin(dl/57.3)))/(n*iss));
#results
print "ratio error (%)=",round(re,2)
print "RCF =",round(RCF,5)
print "phase angle error (degree)=",round(eph,3)

ratio error (%)= -1.26
RCF = 1.01275
phase angle error (degree)= 0.73


## Example 43 - pg 161¶

In [48]:
#pg 161
#Example 2.43 :percentage change in current
#calculate the current
#given data
import math,cmath
r=0.5;#kilo ohm
r1=1.;#kilo ohm
f=50.;#Hz
V=1.;#V
#calculations
z1=((1j*r1*r)/(r1+1j*r));#kilo-ohm
z1m=abs(z1);#kilo-ohm
z2=((1j*r1*r)/(r+1j*r1));#kilo-ohm
z2m=abs(z2);#kilo-ohm
tz=z1m+z2m;#kilo-ohm
i=V/tz;#A
v1=i*z1m*10**-3;#V
v2=i*10**-3*z2m;#V
df=f-((f*5)/100);#Hz
rc1=((r*df)/f);#k-ohm
rc2=((r1*df)/f);#k-ohm
z1n=((1j*rc1)/(r1+1j*rc1));#
z1nm=abs(z1n);#k-ohm
z2n=((1j*rc2*r)/(r+1j*rc2));#
z2nm=abs(z2n);#k-ohm
znw=z1nm+z2nm;#k-ohm
inn=V/znw;#
#results
print "current is (mA)=",round(inn,4)
print 'The answer is a bit different due to rounding off error in textbook'

current is (mA)= 1.1474
The answer is a bit different due to rounding off error in textbook


## Example 44 - pg 162¶

In [49]:
#pg 162
#Example 2.44 :Inductance
#calculate the inductance and frequency
#given data
import math,cmath
c=1.;#micro-F
f1=60.;#Hz
f=50.;#Hz
#calculations
l1=((c*10**6)/(f1**2*(2*math.pi)**2));#
r1=100;#ohm
z1=r1+1j*((2*math.pi*f*l1)-(1/(2*math.pi*f*c*10**-6)));#ohm
c2=1.5;#micro-F
l2=((-z1.imag)+(1/(2*math.pi*c2)))/100;#H
f2=(1/(2*math.pi))*math.sqrt(1/(l2*c2*10**-6));#Hz
#results
print "inductance is (H)=",round(l2,2)
print "frequency is (Hz)=",round(f2,1)

inductance is (H)= 9.73
frequency is (Hz)= 41.7


## Example 45 - pg 163¶

In [50]:
#pg 159
#Example 2.40: true value of voltage ,current and power
#calculate the true value of voltage ,current and power
#given
import math
from math import acos,cos
vs=102.;#V
iss=4.;#A
ws=375.;#W
rcf=0.995;#
rcf1=1.005;#
a1=2000.;#
a2=100.;#
#calculations
ph=acos(ws/(iss*vs))*57.3;#degree
ph1=round(ph);#
x=ph-ph1;#
y=x*60;#
angd=y+22+10;#
ang=angd/60.;#
ta=ph1+ang;#
nr=a1/a2;#
avr=rcf*nr;#
pv=avr*vs;#
acr=rcf1*(a2/nr);#
pc=acr*iss*iss;#A
psd=pv*pc*cos(ta/57.3)*10**-3;#
#results
print "true value of voltage is,(V)=",round(pv)
print "true value of current is,(A)=",pc
print "true value of power is ,(kW)=",round(psd,1)

true value of voltage is,(V)= 2030.0
true value of current is,(A)= 80.4
true value of power is ,(kW)= 149.4


## Example 46 - pg 163¶

In [51]:
#pg 160
#Example 2.42: Resistance
#calculate the Series resistance
import math
#given data :
f=50.;#/ in Hz
r=2000.;# in ohm
L=0.5;# in H
V=100.;# in V
#calculations
Zm=math.sqrt(r**2+(2*math.pi*f*L));
im=V/Zm;
Rs=(500.-(im*Zm))/im;
#results
print "Series resistance,Rs(ohm) = ",round(Rs)
print 'answer is wrong in the textbook due to rounding off error'

Series resistance,Rs(ohm) =  8000.0
answer is wrong in the textbook due to rounding off error