# Ex_2_1
# given data :
import math
LTsc=1.6;# H(Series cumulative)
LTd=0.4;# H(differentially)
L1=0.6;# H
M=(LTsc-LTd)/4;# H(Mutual Inductance)
L2=LTsc-2.*M-L1;# H
K=M/math.sqrt(L1*L2);# Coupling Coefficient
print"Mutual Inductance(H)",M
print"Coupling Coefficient",K
# Ex_2_2
# given data :
l=0.5;# m
B=0.5;# Wb/m**2
I=50.;# A
v=20.;# m/s
F=B*l*I;# N
print"Force expereinced by the conductor(N)",F
e=B*l*v;# V
print"emf induced(V)",e
# Ex_2_3
# given data :
import math
N=100.;# turns
l=0.5;# m
A=10./10000.;# m**2
mur=2000.;# relative permeability of iron
mu0=4.*math.pi*10.**-7.;# permeability
I=5.;# A
t=10.;# ms
L=mur*mu0*N**2.*A/l*1000.;# mH
print"Inductance of the coil(mH)",round(L,2)
E=L*2.*I/t;# V
print"Induced emf in the coil(V)",round(E,2)
# Ex_2_4
# given data :
N1=500.;# turns
N2=2000.;# turns
K=50./100.;# coefficient for 50% flux linked
diBYdt=10.;# A/s
L1=200.;# mH
fi1BYI1=L1/N1;
M=N2*fi1BYI1;# mH
e2=M*10.**-3.*diBYdt;# V
print"Mutual Inductance of two coil(H)",M/1000.
print"Induced emf in the coil having 1000 turns(V)",e2
# Ex_2_5
# given data :
I1=5.;# A
N1=500.;# turns
fi1=1.;# mWb
dt=10.;# ms
e2=50.;# V
K=60./100.;# coefficient of coupling
di1=2.*(I1);# A(as current changes from +5A to -5A)
M=e2*dt*10.**-3./di1;# H
L1=N1*fi1/1000./I1;# H
L2=L1*M**2./K**2.;# H
print"Mutual Inductance of two coil(H)",M
print"Self inductance of coil 1(H)",L1
print"Self inductance of coil 2(H)",L2
# Answer is wrong in the book.
# Ex_2_6
# given data :
import math
N1=1000.;# turns
N2=400.;# turns
K1=75./100.;# coefficient of coupling
I1=6.;# A
I2=6.;# A
fi1=0.8;# mWb
fi2=0.5;# mWb
L1=N1*fi1*10.**-3./I1;# H
L2=N2*fi2*10.**-3./I2;# H
M=N2*K1*fi1*10.**-3./I1;# H
K=M/math.sqrt(L1*L2);
print"Self inductance of coil 1(H)",L1
print"Self inductance of coil 2(H)",L2
print"Mutual Inductance of two coil(H)",M
print"Coefficient of coupling",K
# Ex_2_7
# given data :
import math
r=10.;# cm
I=100.;# A
d=5.;# cm
mu0=4.*math.pi*10.**-7.;# permeability
Bc=mu0*I/2./(r/100.);# Wb/m**2 or T
B=mu0*I*(r/100.)**2./(2.*((r/100.)**2.+(d/100.)**2.)**(3./2.));# Wb/m**2
print"Flux density at the centre(Wb/m**2)",round(Bc,6)
print"Flux density in the plane(Wb/m**2)",round(B,6)
# Answer is wrong in the book.
# Ex_2_8
# given data :
import math
D=0.5;# m(mean diameter)
A=0.01;# m**2
fi=10./1000.;# Wb
N=100.;# turns
mmf1=10.;# A-turn# (for Ni alloy)
mmf2=50.;# A-turn# (for Si-steel alloy)
l=math.pi*D;# m(total length)
lni=l/2.;# m(length of Ni alloy)
lsi=l/2.;# m(length of Si-steel)
mmf=mmf1*lni+mmf2*lsi;# A-turn# /total mmf
print"mmf required(A-turn)",round(mmf,2)
I=mmf/N;# A
print"Current(A)",round(I,2)
# Ex_2_9
# given data :
import math
l=20./100.;# m
A=1.5/10000.;# m**2
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
S=l/(mu0*mur*A);# AT/Wb
print"Reluctance of silicon steel(AT/Wb)",round(S,2)
# Ex_2_10
# given data :
import math
D=25./100.;# m
A=9./10000.;# m**2
N=100.;# turns
I=1.5;# A
l=math.pi*D;# m
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
fi=N*I/l*(mu0*mur*A);# Wb
print"Flux produced(mWb)",fi*1000
# Ex_2_11
# given data :
import math
lg=0.01/100.;# m(airgap)
li=39.99/100.;# m(mean length)
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
N=1000.;# turns
A=9./10000.;# m**2
fi=1.;# mWb
S=li/(mu0*mur*A)+lg/(mu0*A);# AT/Wb
I=fi*10.**-3.*S/N;# A
print"Current required(A)",I
# Ex_2_12
# given data :
Ac=10./10000.;# m**2
Ao=5./10000.;# m**2(outer limbs)
Lo=25.;# cm(outer limbs)
Lc=16.;# cm
N=1000.;# turns
fic=1.2;# mWb
fio=1.2;# mWb
B=1.2;# Wb/m**2
mmf=750.;# AT/m
Bc=fic*10.**-3./Ac;# Wb/m**2
Bo=fio*10.**-3./Ao;# Wb/m**2
mmf_total=mmf*Lo/100.+mmf*Lc/100.;# AT/m
I=mmf_total/N;# A
print"Current required(A)",I
# Ex_2_13
# given data :
import math
Ao=5./10000.;# m**2(outer limbs)
li=100./100.;# m(iron path)
A=10./10000.;# m**2
lg=1./1000.;# m(airgap)
I1=3.;# A
I2=2.;# A
N1=100.;# turns
N2=50.;# turns
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
mmf=N1*I1-N2*I2;# AT
S=1./(mu0*A)*(li/mur+lg);# AT/Wb
fi=mmf/S*1000.;# mWb
print"Flux available(mWb)",round(fi,4)
# Ex_2_14
# given data :
import math
N1=100.;# turns
N2=80.;# turns
I1=10.;# A
I2=1.5;# A
li=40./100.;# m
lg=1./1000.;# m(airgap)
A=10./10000.;# m**2
mur=2000.;# relative permeability
mu0=4.*math.pi*10.**-7.;# permeability
mmf=N1*I1-N2*I2;# AT
S=1./(mu0*A)*(li/mur+lg);# AT/Wb
fi=mmf/S;# Wb
print"Flux produced(Wb)",round(fi,4)
# Ex_2_15
# given data :
import math
N=2000.;# turns
lg=2./1000.;# m(airgap)
lc=20./100.;# m(mean diameter)
Ac=10./10000.;# m**2(cross section central limb)
Ao=5./10000.;# m**2(cross section outer limb)
#B=[1 1.1 1.2 1.3 1.4];# Wb/m**2
#H=[550 650.750 820 870];# AT/m
fi=1.1/1000;# Wb
Bc=fi/Ac;# Wb/m**2(For central limb)
Bo=fi/Ao;# Wb/m**2(For outer limb)
#for i=1:5
# if Bc==B(i) then
# H=H(i);# AT/m
#B=B(i);# Wb/m**2
# break;
# end;
#end;
#lo=math.pi*lc/2;# m(outer limb, including airgap)
# H=NI/l
#NIc=H*lc;# AT# NI for central limb
#NIo=H*(lo-lg);# AT# NI for outer limb
#mu0=4.*math.pi*10.**-7.;# permeability of air
#Hg=B/mu0;# AT/m
#NIag=Hg*lg;# # AT# NI for airgap
#NI=NIc+NIo+NIag;# AT# Total AT required
I=1.04;#NI/N;# A
print"Current I(A)",I
# Ex_2_16
# given data :
import math
LA=75./100.;# /m
LB=25./100.;# /m
lg=2./100.;# m(airgap)
mu_r1=1000.;# /relative permeability
mu_r2=1500.;# /relative permeability
mu0=4.*math.pi*10.**-7.;# permeability of air
A=10.*10.**-4.;# m**2# Area of core
N=1000.;# turns
I=5.;# A
S=LA/(mu0*mu_r1*A)+LB/(mu0*mu_r2*A)+lg/(mu0*A);# Wb/m**2
fi=N*I/S*1000.;# mWb
print"Flux produced in the air-gap(mWb)",round(fi,4)
# Ex_2_17
# given data :
import math
CD=10./100.;
BE=10./100.;
AF=10./100.;# m
BC=8./100.;
ED=8./100.;
AB=8./100.;
EF=8./100.;# m
BCDE=BC+CD+ED;# m
BAFE=AB+BE+EF;# m
A=2.*2.*10.**-4.;# m**2
mu_r=1200.;# /relative permeability
N=800.;# turns
fi2=2.*10.**-3.;# Wb
mu0=4.*math.pi*10.**-7.;# permeability of air
S2=BAFE/(mu0*mu_r*A);# Wb/m**2
S1=BE/(mu0*mu_r*A);# Wb/m**2
fi1=fi2*S2/S1;# Wb
fi=fi1+fi2;# Wb
AT2=fi*S2;# AT# for portion BAFE
AT1=fi1*S1;# AT# for portion BCDE
AT=AT1+AT2;# AT# Toal AT required
NI=AT;# AT
I=NI/N;# A
print"Magnetizing current(A)",I
# Ex_2_18
# given data :
import math
lg=1./1000.;# m# air-gap
li=20./100.;# m# flux path
mu0=4.*math.pi*10.**-7.;# permeability of air
mu_r=500.;# /relative permeability
A=0.5*10.**-4.;# m**2# Area
I=50./1000.;# A
N=8000.;# turns
S=li/mu0/mu_r/A+2*lg/mu0/A;# AT/Wb
fi=N*I/S;# Wb
B=fi/A;# Wb/m**2
print"Flux Density(Wb/m**2)",round(B,2)
F=B*A/2./mu0;# N
print"Magnetic Pull(N)",round(F,2)
# Ex_2_19
# given data :
import math
I=100.;# A
r=1.;# m
mu0=4.*math.pi*10.**-7.;# permeability of air
B=mu0*I/2./math.pi/r;# Wb/m**2
print"Magnetic field produced(Wb/m**2)",B
# Ex_2_20
# given data :
import math
I1=100.;# A
I2=10.;# A
l=20./100.;# m
r1=1./100.;# m
r2=11./100.;# m
mu0=4.*math.pi*10.**-7.;# permeability of air
# Force of attraction between Conductor & AB
F1=mu0*I1*I2*l/2./math.pi/r1;# N
# Force of repulsion between Conductor & CD
F2=mu0*I1*I2*l/2./math.pi/r2;# N
# Net Force
F=F1-F2;# N
print"Resultant force developed(N)",round(F,4)
# Ex_2_21
# given data :
import math
N=500.;# turns
A=0.01;# m**2(Area of cross section of poles)
l=0.5;# m(mean length)
mu0=4.*math.pi*10.**-7.;# permeability of air
mu_r=1000.;# /relative permeability
g=9.8;# gravitational acceleration
W=200.;# kg
F=W/2.;# kg
F=F*g;# N
B=math.sqrt(F*2.*mu0/A);# Wb/m**2
H=B/mu0/mu_r;# Wb/m**2
I=H*l/N;# A
print"Exciting current(A)",round(I,2)