Chapter 5 - Magnetic measurement

Example 1 - pg 304

In [1]:
#pg 304
#Example 5.1: Capacity of the capacitor
#calculate the Capacity of the capacitor
#given data :
import math
Ig=0.0001;# in A
T0=3.;# in sec
theta0=200.;
theta=45.;
V=100.;# in V
#calculations
Q=(Ig*T0*theta0)/(theta*2*math.pi);
C=(Q/V)*10**6;
#results
print "Capacity of the capacitor (micro-F) = ",round(C,2)

Capacity of the capacitor (micro-F) =  2.12

Example 2 - pg 304

In [2]:
#pg 304
#Example 5.2: Coulomb sensitivity
#calculate te Coulomb sensitivity
#given data :
C=1.5*10**-6;# in F
V=15;# in V
d1=20;# in cm
#calculations
Q=C*V;
Sb=(d1/Q)*10**-5;
#resutls
print "Coulomb sensitivity (mm/micro-C) = ",round(Sb,2)

Coulomb sensitivity (mm/micro-C) =  8.89

Example 3 - pg 305

In [4]:
#pg 305
#Example 5.3: Logarithmic increment
#calculate the Logarithmic increment and frequency
#given data :
import math
theta1=12.5;
theta2=10.;
#calculations
lamda=math.log(theta1/theta2);
x=lamda**2;#
y=x/(math.pi**2-x);#
y1=math.sqrt(y);#
f=0.125;#Hz
fo=f/(math.sqrt(1-y1**2));#Hz
#results
print "Logarithmic increment = ",round(lamda,4)
print "undamped frequency is (Hz)=",round(fo,4)

Logarithmic increment =  0.2231
undamped frequency is (Hz)= 0.1253

Example 4 - pg 305

In [6]:
#pg 305
#Example 5.4: Flux density
#calculate the flux density
#given data :
I1=5.;# in A
I2=10.;# in A
N1=100.;# number of turns
N2=200.;#number of turns
l=30*10**-2;# in m
R=200.;# in ohm
theta1=45.;# in degree
theta2=30.;# in degree
As=0.3*10**-4;# in m**2
M=100*10**-3;# in H
#calculations
k=(2*M*I1)/(R*theta1);
H=(N1*I2)/l;
fi=(R*k*theta2)/(2*N2);
B=fi/As;
mu=H/B;
#results
print "Flux density B(Wb/m^2) = ",round(B,2)
print "permeability mu(H/m) = ",mu
print 'flux density is calculed wrong in the textbook'

Flux density B(Wb/m^2) =  55.56
permeability mu(H/m) =  60.0
flux density is calculed wrong in the textbook

Example 5 - pg 309

In [8]:
#pg 309
#Example 5.5: Flux density and relative permeability
#calculate the Flux density and relative permeability
#given data :
import math
A=5*10**-4;# in m**2
d=25*10**-2;# in m
N1=150;# turns
N2=300;# turns
k=2*10**-6;# coulomb per division
R=2500;# in ohm
I=10;# in A
theta=75;# in division
#calculations
l=math.pi*d;
mu_0=4*math.pi*10**-7;
B=(k*theta*R)/(2*N2*A);
H=(N1*I)/l;
mu_r=(B/(mu_0*H));
#results
print "Flux density,B(Wb/m^2) = ",B
print "Relative permeability = ",round(mu_r)

Flux density,B(Wb/m^2) =  1.25
Relative permeability =  521.0

Example 6 - pg 308

In [9]:
#pg 308
#Example 5.6 #flux per pole and leakage cofficient
#calculate the flux per pole and leakage cofficient
#given data:
k=0.15;#micro-C
th=120.;#divisions
th1=135.;#divisions
r=4500.;#ohm
n=3.;#turns
#calculations
ft=(k*10**-6*th*r)/n;#Wb
n1=4;#
ft1=(k*10**-6*th1*r)/n1;#Wb
lk=ft/ft1;#
#results
print "In case of total flux is (Wb)=",ft
print "In case of useful flux is (Wb)=",round(ft1,4)
print "leakage coefficient is =",round(lk,3)

In case of total flux is (Wb)= 0.027
In case of useful flux is (Wb)= 0.0228
leakage coefficient is = 1.185

Example 7 - pg 308

In [10]:
#pg 308
#Example 5.7 #relative permeability
#calculate the relative permeability
#given data
import math
n1=320.;#turns
n2=250.;#turns
i=10.;#A
l=32.;#cm
fl=2.5*10**-4;#Wb
sd=100;#
sd1=270;#/
#calculations
N=(n1*i)/(l*10**-2);#AT/m
k=(fl*i)/sd;#
mo=4*math.pi*10**-7;#
A=0.35;#cm**2
ur=((k*sd1)/(2*mo*N*A*10**-4*n2));#
#results
print "relative permeability =",round(ur,1)

relative permeability = 30.7

Example 8 - pg 309

In [11]:
#pg 309
#Example 5.7 # Shunt resistance
#calculate the shunt resistance
#given data :
N=800.;# turns
I=10.;# in A
reluctance=150000;# in AT per Wb
K=.15*10**-3;# in Wb turns/ division
rs=0.025;# in ohm
Ns=1;
theta=120;#divisions
#calculations
fi=(N*I)/reluctance;
S=(K*rs*theta)/((fi*Ns)-(K*theta));
#results
print "The shunt resistance S(ohm) = ",round(S,4)

The shunt resistance S(ohm) =  0.0127

Example 9 - pg 310

In [12]:
#pg 310
#Example 5.9 # Magnetic pole difference
#calculate the Magnetic pole difference
#given data :
N=150.;# turns
I=1.2;# in A
theta=300.;# divisions
t=155.;#change in mmf in division
#calculations
mmf=N*I;
r=2*mmf;# du to reversal
K=360/t;
M=(K*theta);
#results
print "The magnetic potential difference between two points,(AT) = ",round(M)

The magnetic potential difference between two points,(AT) =  697.0

Example 10 - pg 310

In [13]:
#pg 310
#Example 5.10 #relative permeability
#calculate the relative permeability
#given data
import math
n1=600.;#turns
i=3.;#A
d=30.;#cm
ass=6.;#cm^2;#
t1=500.;#turns
r=250.;#ohms
k=3000.;#micro-C
#calculations
H=(n1*i)/(math.pi*d*10**-2);#
mo=4*math.pi*10**-7;#
x=mo*H;#
y=ass*10**-4*x;#
z=t1*y;#
z1=2*z;#
it=z1/r;#
ur=(k*10**-6)/it;#
#results
print "relative permeability =",round(ur)

relative permeability = 521.0

Example 11 - pg 311

In [14]:
#pg 311
#Example 5.11 # Fluxmeter deflection
#calculate the Fluxmeter deflection
#given data :
import math
l=5*10**-2;# in m
N=40;# turns
B=5*10**-3;# in Wb/m**2
b=1.5*10**-2;# in m
cs=2*10**-4;# in  m**2
B1=0.05;# in Wb/m**2
#calculations
fi=B1*cs;
del_fi=2*fi;
theta=(del_fi*10)/(N*B*l*b);
#results
print "Fluxmeter deflection (degree) = ",round((theta*(180/math.pi)),1)

Fluxmeter deflection (degree) =  76.4

Example 12 - pg 311

In [16]:
#pg 311
#Example 5.12 #hysteresis and eddy current components
#calculate the hysteresis and eddy current components
#given data
import numpy
w1=132.;#W
f1=20.;#Hz
w2=425.;#W
f2=50.;#Hz
#calculations
x=w1/f1;#
y=w2/f2;#
A=numpy.matrix([[1, f1],[1, f2]]);#
B=numpy.matrix([[x],[y]]);#
X=numpy.dot(numpy.linalg.inv(A),B);#
Wh=X[0,0]*f2;#W
We=X[1,0]*f2**2;#W
#results
print "Hysteresis current component of the loss (W)=",round(Wh,1)
print "Eddy current component of the loss (W)=",round(We,1)

Hysteresis current component of the loss (W)= 266.7
Eddy current component of the loss (W)= 158.3

Example 13 - pg 312

In [17]:
#pg 312
#Example 5.13 #hysteresis loss
#calculate the hysteresis loss
#given data
Hx=125.;#AT/m
ah=200.;#cm**2
ba=0.15;#Wb/m**2
lo=50;#loos
kg=8.5*10**3;#kg/m**3
#calculations
le=ah*Hx*ba;#J/m**3
po=lo*le;#W/m**3
lkg=po/kg;#watt
#results
print "hysteresis loss is (W)=",round(lkg)

hysteresis loss is (W)= 22.0

Example 14 - pg 312

In [18]:
#pg 312
#Example 5.14 # flux density
#calculate the flux density
#given data :
R=200+50.;# in ohm
k=100*10**-6;# in coulomb
theta=80.;# divisions
A=55*10**-4;# in m**2
N=1500;# turns
#calculations
B=(R*k*theta)/(2*A*N);
#results
print "The flux density B(Wb/m^2) = ",round(B,3)

The flux density B(Wb/m^2) =  0.121

Example 15 - pg 313

In [19]:
#pg 313
#Example 5.15 #loss
#calculate the loss
#given data
f=50.;#Hz
k=2.3*10**-2;#
x=1.7;#
wi=0.6;#W
bm=0.5;#Wb/m**2
f1=20;#Hz
bm1=1;#
#calculations
kd=((wi-(k*bm**x*f))/(bm**2*f**2));#
wi1=((k*bm1**x*f1)+(kd*bm1**2*f1**2));#
#results
print "loss is (W)=",round(wi1,3)

loss is (W)= 0.617

Example 16 - pg 313

In [21]:
#pg 313
#Example 5.16 #MAGNETIC FORCE ,FLUX DENSITY AND RELATIVE PERMEABILITY
#calculate the MAGNETIC FORCE ,FLUX DENSITY AND RELATIVE PERMEABILITY
#given data
import math
k=1;#micro-C
th=100.;#turns
r=5000.;#ohm
n2=350.;#turns
ass=10.;#cm**2
n1=100.;#turns
i=4.;#A
l=100.;#cm
#calculations
b=((k*th*r*10**-6)/(2*n2*ass*10**-4));#Wb/m**2
H=(n1*i)/(l*10**-2);#AT/m**2
mo=4*math.pi*10**-7;#
ur=b/(mo*H);#
#results
print "magnetic flux is (Wb/m^2)=",round(b,3)
print "flux density is (AT/m^2)=",H
print "relative permeability is =",round(ur,2)

magnetic flux is (Wb/m^2)= 0.714
flux density is (AT/m^2)= 400.0
relative permeability is = 1421.03

Example 17 - pg 314

In [20]:
#pg 314
#Example 5.17 # fluxmeter
#calculate the Constant of fluxmeter
#given data :
import math
N1=800.;# turns
I=5;# in A
l=1;# in m
A=5*10**-4;# in m**2
N=500;# turns
theta=25.;# divisions
#calculations
H=(N1*I)/l;
B=(4*math.pi*10**-7*H);
fi=B*A*10**8;
K=((2*N*fi*10**-8)/(theta));
#results
print "Constant is (Wb-turn/scale-div)=",round(K*10**-3,10)

Constant is (Wb-turn/scale-div)= 1.005e-07