# Chapter 2 : MAGNETIC CIRCUITS¶

## Example 2.1 Page No : 89¶

In :
import math

#INPUT DATA
N = 2000.;			#no of turns
I = 10.;			#current in A
Rm = 25.;			#mean radius in cm
d = 6.;			#diameter of each turn in cm

#CALCULATIONS
MMF = N*I;			#magneto motive force in A
l = 2*math.pi*(Rm/100);			#circumference of coli in m
u = (4*math.pi*10**-7);			#permeability (U = Ur*U0)
a = (math.pi*d*d*10**-4)/4;
reluctance = (l/(a*u));			#reluctance in At/Wb
flux = (MMF)/(reluctance);			#flux in Wb
fluxdensity = (flux/a);			#flux density in Wb/m**2 or tesla

#OUTPUT
print "Thus MMF, flux, flux density  are %d A, %g Wb , %g Wb/m**2 or Tesla respectively "%(MMF,flux,fluxdensity);

Thus MMF, flux, flux density  are 20000 A, 4.52389e-05 Wb , 0.016 Wb/m**2 or Tesla respectively


## Example 2.2 Page No : 90¶

In :
import math
#Chapter-2, Example 2.2, Page 90

#INPUT DATA
phi = 5*10**-2;			#flux in wb
a = 0.2;			#area of cross-section in m**2
lg = 1.2*10**-2;			#length of air gap in m
ur = 1;			#permeability
u = ur*4*math.pi*10**-7;			#permeability

#CALCULATIONS
B = (phi/a);			#flux density in wb/sq.m
H = (B/(4*math.pi*10**-7*ur));			#magnetic flux density in A/m
S = lg/(a*u);			#reluctance of air gap in A/wb
permeance = 1/S;			#permenace in A/wb
mmf_in_airgap = phi*S;			#mmf in A

#OUTPUT
print "Thus B, H,S, permeance, MMF in air gap  are %1.2f Wb/sq.m, %g A/m ,%f A/wb ,\
%g Wb/A %d A  respectively "%(B,H,S,permeance,mmf_in_airgap);

Thus B, H,S, permeance, MMF in air gap  are 0.25 Wb/sq.m, 198944 A/m ,47746.482928 A/wb ,2.0944e-05 Wb/A 2387 A  respectively


## Example 2.3 Page No : 90¶

In :
import math

#INPUT DATA
phi = 0.1*10**-3;			#flux in wb
a = 1.7*10**-4;			#area of cross-section in m**2
lg = 0.5*10**-3;			#length of air gap in m
Rm = 15./2;			#radius of ring in cm
u0 = 4*math.pi*10**-7;			#permeability in free space in henry/m
N = 1500.;			#no of turns of ring

#CALCULATIONS
B = (phi/a);			#flux density in wb/sq.m
H = (B/(4*math.pi*10**-7));			#magnetic flux density in A/m
ampere_turns_provided_fo = H*lg;
total_ampere_turns_provi = N*1;
Available_for_iron_path = N-(H*lg);
length_of_iron_path = (2*Rm*math.pi*10**-2)-(lg);			#length of iron path in m
H_for_iron_path = ((N-(H*lg)))/(length_of_iron_path);
ur = (B/(u0*H_for_iron_path));			#relative permeability of iron

#OUTPUT
print "Thus relative permeability of iron is %d"%(ur);

Thus relative permeability of iron is 174


## Example 2.4 Page No : 91¶

In :
import math

#INPUT DATA
li = 0.5;			#iron path length in m
lg = 10.**-3;			#length of air gap in m
phi = 0.9*10**-3;			#flux in wb
a = 6.66*10**-4;			#area of cross-section of iron in m**2
N = 400.;			#no of turns

#CALCULATIONS
B = (phi/a);			#flux density in wb/sq.m
Hg = (B/(4*math.pi*10**-7));			#magnetic flux density in A/m
AT_required = Hg*lg;			#AT required for air path
Hi = 1000;			#magnetic flux density in A/m
AT_required_for_iron_pat = Hi*li;
total_AT_required = (Hg*lg)+(Hi*li);
I = ((Hg*lg)+(Hi*li))/(N);

#OUTPUT
print "Thus exciting current required is %1.2f A"%(I);

Thus exciting current required is 3.94 A


## Example 2.5 Page No : 92¶

In :
import math
#Chapter-2, Example 2.5, Page 92

#INPUT DATA
r = 0.01;			#radius in m
lg = 10.**-3;			#length of air gap in m
Rm = (30./2)*10**-2;			#mean radius in m
ur = 800.;			#relative permeability of iron
ur2 = 1.;			#relative permeability of air gap
N = 250.;			#no of turns
phi = 20000.*10**-8;			#flux in Wb
u0 = 4*math.pi*10**-7;			#permeability in free space
a = math.pi*(r)**2;			#area of cross-section in m
leakage_factor = 1.1

#CALCULATIONS
reluctance_of_air_gap = (lg/(u0*ur2*a));			#reluctance of air gap in A/wb
li = (math.pi*(2*r)-(lg));			#length of iron path in m
reluctance_of_iron_path = ((math.pi*0.3)-(lg))/(4*math.pi*10**-7*800*a);			#in A/wb
total_reluctance = reluctance_of_air_gap+reluctance_of_iron_path;			#in A/wb
MMF = phi*total_reluctance;			#in Ampere turns
current_required = (MMF)/(N);			#in A

#OUTPUT
print "Thus current required is %1.2f A "%(current_required);
#Including leakage

#CALCULATIONS
MMF_of_airgap = phi*reluctance_of_air_gap;			#in A/wb
Total_flux_in_ironpath = leakage_factor*phi;			#in Wb
MMF_of_ironpath = Total_flux_in_ironpath*reluctance_of_iron_path;			#in A
Total_MMF = MMF_of_ironpath+MMF_of_airgap;			#in A/wb
current_required2 = Total_MMF/(N);			#in A

#OUTPUT
print "Thus current required is %1.3f A"%(current_required2);

Thus current required is 4.41 A
Thus current required is 4.650 A


## Example 2.6 Page No : 93¶

In :
import math

#INPUT DATA
l1 = 0.1;			#length in m
l2 = 0.18;			#length in m
l3 = 0.18;			#length in m
lg = 1.*10**-3;			#airgap length in mm
a1 = 6.25*10**-4;			#area in m**2
a2 = 3.*10**-4;			#area in m**2
ur = 800.;			#relative permeability of iron path
ur2 = 1.;			#relative permeability in free space
u0 = 4*math.pi*10**-7
N = 600.;
phi = 10.**-4;			#airgap flux in Wb

#CALCULATIONS
#for the airgap
Bg = (phi/(a1));			#fluxdensity in Tesla
Hg = (Bg/(u0*ur2));			#magnetimath.sing force in A/m
MMF1 = Hg*lg;			#in A
#for path I1
B1 = 0.16;			# flux density in tesla
H1 = (B1/(ur*u0));			#magnetimath.sing force in A/m
MMF2 = H1*l1;			#in A
#math.since paths l2 and l3 are similar,the total flux divide equally between these two paths.Since these paths are in parallel,consider only one of them
#for path l2
flux = 50*10**-6;			#flux in wb
B2 = (flux/a2);			#fluxdensity in tesla
H2 = (B2/(ur*u0));			#magnetimath.sing force in A/m
MMF3 = H2*l2;			#in A
totalmmf = MMF1+MMF2+MMF3;			#in A
I = (totalmmf/N);			#current required in A

#OUTPUT
print "Thus current required is %1.3f A"%(I);

Thus current required is 0.288 A


## Example 2.7 Page No : 95¶

In :
import math
#Chapter-2, Example 2.7, Page 95

#INPUT DATA
Dm = 0.1			#diameter in m
a = 10.**-3;			#area of cross-section im m**2
N = 150.;			#no of turns
ur = 800.;			#permeability of iron ring
B = 0.1;			#in Wb/m**2
u0 = 4*math.pi*10**-7;			#permeability of free space

#CALCULATIONS
S = (math.pi*Dm)/(a*ur*u0);			#reluctance
I = (B*a*S)/(N);			#current in A

#OUTPUT
print "Thus current is %f A"%(I);

Thus current is 0.208333 A


## Example 2.8 Page No : 95¶

In :
import math

#INPUT DATA
l = 0.3;			#length in m
d = 1.5*10**-2;			#diameter in m
N = 900;			#no of turns
ur = 1;			#relative permeability in free space
u0 = 4*math.pi*10**-7;			#permeability in free space
I = 5;			#current in A

#CALCULATIONS
a = (math.pi*(d)**2/4);			#in m**2
S = (l)/(a*ur*u0);			#reluctance

#OUTPUT
print "Thus reluctance is %f A/wb"%(S);

Thus reluctance is 1350949115.231170 A/wb


## Example 2.9 Page No : 95¶

In :
import math

#INPUT DATA
lg = 10**-3;			#length of air gap in m
B = 0.9;			#flux density in wb/m**2
li = 0.3;			#length of ironpath in m
Hi = 800;			#magnetic flux density in AT/m
u0 = 4*math.pi*10**-7;			#permeabilty in free space

#CALCULATIONS
#for iron path
MMF_required1 = Hi*li;			#magnetic motive force in AT
#for air gap
MMF_required2 = (B/u0)*lg;			#magnetic motive force in AT
Totalmmf = MMF_required1+MMF_required2

#OUTPUT
print "Thus total MMF required is %d AT"%(Totalmmf);

Thus total MMF required is 956 AT


## Example 2.10 Page No : 96¶

In :
import math

#INPUT DATA
li = 0.5;			#length of iron ring mean length in m
N = 220;			#no of turns
I = 1.2;			#current in A
lg = 1.2*10**-3;			#length of airgap in m
ur = 350;			#relative permeability of iron
u0 = 4*math.pi*10**-7;			#permeability in free space

#CALCULATIONS
MMF_produced = N*I;
Si = li/(u0*ur);			#reluctance of iron path
Sg = lg/(u0);			#reluctance of air gap
S = Si+Sg;			#total reluctance
Flux_density = (MMF_produced)/(S);

#OUTPUT
print "Thus fluxdensity is %1.3f Wb/m**2"%(Flux_density);

Thus fluxdensity is 0.126 Wb/m**2