# Chapter 8: Magnetic Circuits¶

## Example 1: pg 267¶

In :
#pg 267
#calculate the current
#  Given data
from math import pi
a = 3;#  in cm^2
a = a * 10**-4;#  in m^2
d = 20;#  in cm
N = 500;
phi = 0.5*10**-3;#  in Wb
miu_r = 833.33;
#calculations
miu_o = 4*pi*10**-7;
l = pi*d;#  in cm
l = l * 10**-2;#  in m
S = l/(miu_o*miu_r*a);#  in AT/Wb
# Calculation of the current with the help of flux
# Formula  phi = (m*m*f)/S = (N*I)/S;
I = (phi*S)/N;#  in A
#results
print "The current in A is",round(I)

The current in A is 2.0


## Example 2: pg 268¶

In :
#pg 268
#calculate the reluctance, flux, field strength, coil mmf and permeance
#  Given data
from math import pi
N = 300.;
miu_r = 900.;
l = 40.;#  in cm
a = 5.;#  in cm**2
R = 100.;#  in ohm
V = 250.;#  in V
#calculations
miu_o = 4*pi*10**-7;
I = V/R;#  in A
mmf = N*I;#  in AT
print "The coil mmf in AT is",mmf
H = (N*I)/(l*10**-2);#  in AT/m
print "The field strength in AT/m is",H
B = miu_o*miu_r*H;#  in Wb/m**2
phi = B*a*10**-4;#  in Wb
print "Total flux in Wb is",round(phi,5)
S = mmf/phi;#  in AT/Wb
print "The reluctance of the ring in AT/Wb is",round(S,2)
#  Permeance is recipocal of reluctance
Permeance = 1/S;#  in Wb/AT
print '%s %.1e' %("Permeance of the ring in Wb/AT is",Permeance)

The coil mmf in AT is 750.0
The field strength in AT/m is 1875.0
Total flux in Wb is 0.00106
The reluctance of the ring in AT/Wb is 707355.3
Permeance of the ring in Wb/AT is 1.4e-06


## Example 3: pg 269¶

In :
#pg 269
#calculate the amphere turns
#  Given data
from math import pi
Ig = 4;#  in mm
Ig = Ig * 10**-3;#  in m
B = 1.3;#  in Wb/m**2
miu_r = 1;
#calculations
miu_o = 4*pi*10**-7;
H = B/(miu_o*miu_r);#  in AT/m
Hg = H;#  in AT/m
#  Ampere turn required for air gap
AT = Hg*Ig;#  AT for air gap in AT
#results
print "The amphere turns for the gap in AT is",round(AT)

The amphere turns for the gap in AT is 4138.0


## Example 4: pg 269¶

In :
#pg 269
#calculate the total flux
#  Given data
from math import pi
N = 500.;
R = 4.;#  in ohm
d = 0.25;#  in m
a = 700.;#  in mm^2
a = a*10**-6;#  in m^2
V = 6.;#  in V
miu_r = 550.;
#calculations
miu_o = 4*pi*10**-7;
#  Evaluation of current by ohm's law
I = V/R;#  in A
l = pi*d;#  in m
H = (N*I)/l;#  in A/m
#  Evaluation of flux density
B = miu_o*miu_r*H;#  in T
#  Evaluation of total flux
phi = B*a;#  in Wb
phi= phi*10**3;#  in mWb
#results
print "The total flux in the coil in m/Wb is",phi

The total flux in the coil in m/Wb is 0.462


## Example 5: pg 269¶

In :
#pg 269
#calculate the flux, density, reluctance, mmf
#  Given data
from math import pi
d_r = 8;#  diameter of ring in cm
d_r = d_r*10**-2;#  in m
d_i = 1;#  diameter of iron in cm
d_i = d_i * 10**-2;#  in m
Permeability = 900;
gap = 2;#  in mm
gap = gap * 10**-3;#  in m
N = 400;
I = 3.5;#  in A
#calculations
l_i = (pi*d_r)-gap;#  length of iron in m
a = (pi/4)*(d_i**2);#  in m**2
mmf = N*I;#  in AT
print "The mmf in AT is",mmf
miu_o = 4*pi*10**-7;
miu_r = 900;
Si = l_i/(miu_o*miu_r*a);#  in AT/Wb
miu_r = 1;
Sg = gap/(miu_o*miu_r*a);#  in AT/Wb
S_T = Si+Sg;#  in AT/Wb
print "The total reluctance in AT/Wb is",round(S_T,3)
phi = mmf/S_T;#  in Wb
print '%s %.4e' %("The flux in Wb is",phi)
#  phi = B*a;
B = phi/a;#  in Wb/m**2
print "The flux density of the ring in (Wb/m^2) = ",round(B,4)

The mmf in AT is 1400.0
The total reluctance in AT/Wb is 23071142.12
The flux in Wb is 6.0682e-05
The flux density of the ring in (Wb/m^2) =  0.7726


## Example 6: pg 271¶

In :
#pg 271
#calculate the reluctance and inductance
#  Given data
from math import pi
miu_r = 1400;
l = 70;#  in cm
l = l * 10**-2;#  in m
a = 5;#  in cm**2
a = a * 10**-4;#  in m**2
N = 1000;
#calculations
miu_o = 4*pi*10**-7;
S = l/(miu_o*miu_r*a);#  in AT/Wb
#  Calculation of inductance of the coil
L = (N**2)/S;#  in H
#results
print  '%s %.3e' %("The reluctance of the magnetic circuit in AT/Wb is",S)
print "The inductance of the coil in H is",round(L,3)

print 'Note: In the book the calculated value of L is correct but at last they print its value wrong'

The reluctance of the magnetic circuit in AT/Wb is 7.958e+05
The inductance of the coil in H is 1.257
Note: In the book the calculated value of L is correct but at last they print its value wrong


## Example 7: pg 271¶

In :
#pg 271
#calculate the current
#  Given data
from math import pi
l1 = 25.;#  in cm
l1 = l1 * 10**-2;#  in m
miu_o = 4*pi*10**-7;
miu_r = 750;
a1 = 2.5*2.5*10**-4;#  in m
S1 = l1/(miu_o*miu_r*a1);#  in AT/Wb
l2 = 40;#  in cm
l2 = l2 * 10**-2;#  in m
S2 = l2/(miu_o*miu_r*a1);#  in AT/Wb
phi2 = 2.5*10**-3;#  in Wb
N = 500;
#calculations
# mmf = phi1*S1 = phi2*S2;
phi1 = (phi2*S2)/S1;#  in Wb
phi = phi1+phi2;#  in Wb
#  Sum of mmf required for AEFB
S_AEFB = S2;#  in AT/Wb
mmfforAEFB = S_AEFB*phi;# mmf for AEFB in AT
totalmmf = mmfforAEFB+(phi1*S1);# total mmf in AT
#  N*I = totalmmf;
#  Calculation of current
I = totalmmf/N;#  in A
#results
print "The current in A is",round(I,3)

The current in A is 12.223


## Example 8: pg 272¶

In :
#pg 272
#calculate the current
#  Given data
from math import pi
a = 16*10**-4;#  in m**2
lg = 2*10**-3;#  in m
N = 1000;
phi = 4*10**-3;#  in Wb
miu_r = 2000;
miu_o = 4*pi*10**-7;
l=25.;#  length of magnetic in cm
w= 20.;#  in cm (width)
t= 4.;#  in cm (thickness)
#calculations
li= ((w-t)*t/2+(l-t)*t/2-0.2);#  in cm
li= li*10**-2;#  in m
S_T= 1/(miu_o*a)*(li/miu_r+lg)
#  Calculation of current with the help of flux
# phi = mmf/S_T = N*I/S_T;
I = (phi*S_T)/N;#  in A
#results
print "The current in A is",round(I,3)

The current in A is 4.713


## Example 9: pg 273¶

In :
#pg 273
#calculate the total flux
#  Given data
from math import pi
N = 500.;
R = 4.;#  in ohm
d_mean = 0.25;#  in m
a = 700;#  in mm^2
a = a * 10**-6;#  in m
V = 6;#  in V
miu_r = 550;
miu_o = 4*pi*10**-7;
#calculations
l_i = pi*d_mean;#  in m
S = l_i/(miu_o*miu_r*a);#  in AT/Wb
I = V/R;#  in A
#  Calculation of mmf
mmf = N*I;#  in AT
#  total flux
phi = mmf/S;#  in Wb
phi = phi * 10**6;#  in muWb
#results
print "The total flux in the ring in muWb is",phi

#  Note: In the book the value of flux calculated correct in muWb but at last they print only in Wb, so the answer in the book is wrong.

The total flux in the ring in muWb is 462.0


## Example 10: pg 274¶

In :
#pg 274
#calculate the current and coil inductance
#  Given data
from math import pi
N = 1000.;
a = 5;#  in cm**2
a = a * 10**-4;#  in m**2
l_g = 2;#  in mm
l_g = l_g * 10**-3;#  in m
B = 0.5;#  in T
#calculations
#miu_r= inf;
phi = B*a;#  in Wb
miu_o = 4*pi*10**-7;
S = l_g/(miu_o*a);#  in AT/Wb
#  Calculation of current with the help of flux
# phi = mmf/S = N*I/S;
I = (phi*S)/N;#  in A
#  Evaluation of coil inductance
L = (N**2)/S;#  in H
#results
print "The current required in A is",round(I,4)
print "The coil inductance in H is",round(L,4)

The current required in A is 0.7958
The coil inductance in H is 0.3142


## Example 11: pg 274¶

In :
#pg 274
#calculate the amphere turns
#  Given data
from math import pi
l_g = 4.;#  in mm
l_g = l_g * 10**-3;#  in m
Bg = 1.3;#  in Wb/m**2
#calculations
miu_o = 4*pi*10**-7;
Hg = Bg/miu_o;
#  Ampere turns for the gap
AT = Hg*l_g;#  in AT
#results
print "The amphere turns in AT is",round(AT,2)

The amphere turns in AT is 4138.03


## Example 12: pg 274¶

In :
#pg 274
#calculate the mmf required
#  Given data
from math import pi
phi = 0.015;#  in Wb
l_g = 2.5;#  in mm
l_g = l_g * 10**-3;#  in m
a = 200;#  in cm**2
a = a * 10**-4;#  in m**2
miu_o = 4*pi*10**-7;
#  Calculation of reluctance of air gap
Sg = l_g/(miu_o*a);#  in AT/Wb
mmf = phi*Sg;#  in AT
#results
print "The mmf required in AT is",round(mmf)

The mmf required in AT is 1492.0


## Example 13: pg 275¶

In :
#pg 275
#calculate the reluctance, flux
#  Given data
from math import pi
a = 12;#  in cm**2
a = a * 10**-4;#  in m**2
l_i = 50;#  in cm
l_i = l_i * 10**-2;#  in m
l_g = 0.4;#  in cm
l_g = l_g * 10**-2;#  in m
N = 2*400;
I = 1;#  in A
miu_r = 1300;
#calculations
miu_o = 4*pi*10**-7;
Si = l_i/(miu_o*miu_r*a);#  in AT/Wb
print "The reluctance of magnetic circuit in AT/Wb is",round(Si)
miu_r = 1;
Sg = l_g/(miu_o*miu_r*a);#  in AT/Wb
print "The reluctance of air gap in AT/Wb is",round(Sg)
S_T = Si+Sg;#  in AT/Wb
print "Total reluctance in AT/Wb is",round(S_T)
mmf = N*I;#  in AT
phi_T = mmf/S_T;#  in Wb
phi_T= phi_T*10**3;#  in mWb
print "The total flux in mWb is",round(phi_T,5)
phi_T= phi_T*10**-3;#  in Wb
# phi_T =B*a;
B = (phi_T)/a;#  in Wb/m**2
print "The flux density of air gap in Wb/m^2 is",round(B,4)

The reluctance of magnetic circuit in AT/Wb is 255056.0
The reluctance of air gap in AT/Wb is 2652582.0
Total reluctance in AT/Wb is 2907638.0
The total flux in mWb is 0.27514
The flux density of air gap in Wb/m^2 is 0.2293


## Example 14: pg 276¶

In :
#pg 276
#calculate the current required
#  Given data
from math import pi
l = 30.;#  in cm
d = 2.;#  in cm
N = 500.;
phi = 0.5;#  in mWb
Airgap = 1;#  in mm
miu_r = 4000;
#calculations
miu_o = 4*pi*10**-7;
Ac = (pi/4)*(d**2);#  in cm^2
Ac = Ac * 10**-4;#  in m^2
l_i = (l*10**-2)-(Airgap*10**-3);#  in m
l_g = 1;#  in mm
l_g = l_g * 10**-3;#  in m
Si = l_i/(miu_r*miu_o*Ac);#  in AT/Wb
Sg = l_g/(miu_o*Ac);#  in AT/Wb
S =Si+Sg;#  in AT/Wb
# phi = mmf/S = N*I/S;
I = (phi*10**-3*S)/N;#  in A
#results
print "The current required in A is",round(I,4)

The current required in A is 2.7224


## Example 15: pg 276¶

In :
#pg 276
#calculate the inductance
#  Given data
from math import pi
l = 40;#  in cm
l = l * 10**-2;#  in m
a = 4;#  in cm**2
a = a * 10**-4;#  in m**2
miu_r = 1000;
miu_o = 4*pi*10**-7;
l_g = 1;#  in mm
l_g = l_g * 10**-3;#  in m
N = 1000;
#calculations
l_i = l-l_g;#  in m
Si = l_i/(miu_r*miu_o*a);#  in AT/Wb
Sg = l_g/(miu_o*a);#  in AT/Wb
S = Si+Sg;#  in AT/Wb
#  The inductance of the coil
L = (N**2)/S;#  in H
#results
print "The inductance of the coil in H is",round(L,4)

The inductance of the coil in H is 0.3593