Excercises Electric Machinery Fundamentals

Chapter 1 Problem 1-15



In [1]:

    
%pylab inline









    



Populating the interactive namespace from numpy and matplotlib

Description

A transformer core with an effective mean path length of $6 \ in$ has a 200-turn coil wrapped around one leg. Its cross-sectional area is $0.25\ in^2$.



In [2]:

    
c = 0.0254        # transform parameter [m/in]
lc = 6 * c        # [m]
A = 0.25 * c**2   # [m²]
N = 200

And its magnetization curve is shown in Figure 1-10c .

If a current of $0.3\,A$ is flowing in the coil.

What is the total flux in the core?
What is the flux density?



In [3]:

    
i = 0.3    #[A]

SOLUTION

The magnetizing intensity applied to this core is:

$$H = \frac{\mathcal{F}}{l_c} = \frac{Ni}{l_c}$$



In [4]:

    
H = N*i / lc
print('H = {:.0f} At/m'.format(H))
print('============')









    



H = 394 At/m
============

From the magnetization curve, the flux density in the core is:



In [5]:

    
B = 1.35  # [T]

The total flux in the core is:

$$\phi = BA$$



In [6]:

    
phi = B*A
print('ϕ = {:.3f} mWb'.format(phi*1000))
print('=============')









    



ϕ = 0.218 mWb
=============