Excercises Electric Machinery Fundamentals

Chapter 1 Problem 1-7



In [1]:

    
%pylab inline
%precision 4
from scipy import constants as c   # we like to use some constants









    



Populating the interactive namespace from numpy and matplotlib

Description

A two-legged core is shown in Figure P1-4 below:

The winding on the left leg of the core ($N_1$) has 600 turns, and the winding on the right ($N_2$) has 200 turns. The coils are wound in the directions shown in the figure.

If the dimensions are as shown, then what flux would be produced by currents $i_1 = 0.5\,A$ and $i_2 = 1.0\,A$?

Assume $\mu_r = 1200$ and constant.



In [2]:

    
N1 = 600
N2 = 200
i1 = 0.5           # A
i2 = 1.0           # A
mu_r = 1200
mu = mu_r * c.mu_0

SOLUTION

The two coils on this core are wound so that their magnetomotive forces are additive, so the total magnetomotive force on this core is $$\mathcal{F}_\text{TOT} = N_1 i_1 + N_2 I_2$$



In [3]:

    
F_tot = N1 * i1 + N2 * i2 
print('F_tot =  {:.1f} At'.format(F_tot))









    



F_tot =  500.0 At

The total reluctance in the core is $\mathcal{R}_\text{TOT} = \frac{l}{\mu_0 \mu_r A}$:



In [4]:

    
l = 4 * (0.075 + 0.5 + 0.075)   # [m] core length on all 4 sides.
A = 0.15**2                     # [m²] 
R_tot = l / (mu * A)
print('R_tot =  {:.1f} kAt/Wb'.format(R_tot/1000))









    



R_tot =  76.6 kAt/Wb

and the flux in the core is $\phi = \frac{\mathcal{F}_\text{TOT}}{\mathcal{R}_\text{TOT}}$:



In [5]:

    
phi = F_tot / R_tot
print('phi =  {:.3f} mWb'.format(phi*1000))









    



phi =  6.525 mWb