0195136047.pdf

496 MAGNETIC CIRCUITS AND TRANSFORMERS

11.1.3In plotting a hysteresis loop the following scales
are used: 1 cm=400 At/m and 1 cm=0.3 T. The
area of the loop for a certain magnetic material
is found to be 6.2 cm^2. Calculate the hysteresis
loss in joules per cycle for the specimen tested if
the volume is 400 cm^3.
11.1.4A sample of iron having a volume of 20 cm^3
is subjected to a magnetizing force varying sinu-
soidally at a frequency of 400 Hz. The area of the
hysteresis loop is found to be 80 cm^2 with the flux
density plotted in Wb/m^2 and the magnetizing
force in At/m. The scale factors used are 1 cm=
0.03 T and 1 cm=200 At/m. Find the hysteresis
loss in watts.
11.1.5The flux in a magnetic core is alternating sinu-
soidally at a frequency of 500 Hz. The maximum
flux density is 1 T. The eddy-current loss then
amounts to 15 W. Compute the eddy-current loss
in this core when the frequency is 750 Hz and the
maximum flux density is 0.8 T.
11.1.6The total core loss for a specimen of magnetic
sheet steel is found to be 1800 W at 60 Hz.
When the supply frequency is increased to 90
Hz, while keeping the flux density constant, the
total core loss is found to be 3000 W. Determine
the hysteresis and eddy-current losses separately
at both frequencies.
11.1.7A magnetic circuit is found to have an ac hystere-
sis loss of 10 W when the peak current isIm= 2
A. Assuming the exponent ofBmto be 1.5 in
Equation (11.1.4), estimatePhforIm= 0 .5A
and8A.
11.1.8Ac measurements with constant voltage ampli-
tude reveal that the total core loss of a certain
magnetic circuit is 10 W atf=50 Hz, and 13
Watf=60 Hz. Find the total core loss if the
frequency is increased to 400 Hz.
11.2.1Consider the magnetic circuit of Figure 11.2.1(a).
Let the cross-sectional areaACof the core, be

16 cm^2 , the average length of the magnetic path

in the corelCbe 40 cm, the number of turns

Nof the excitation coil be 100 turns, and the

relative permeabilityμrof the core be 50,000.

For a magnetic flux density of 1.5 T in the core,

determine:

(a) The fluxφ

(b) Total flux linkageλ(=Nφ).

(c) The current required through the coil.

11.2.2Now suppose an air gap 0.1 mm long is cut

in the right leg of the core of Figure 11.2.1(a),

making the magnetic circuit look like that of

Figure 11.2.1(b). Neglect leakage and fringing.

With the new core configuration, repeat Problem

11.2.1 for the same dimensions and values given

in that problem. See what a difference that small

air gap can make!

11.2.3A toroid with a circular cross section is shown in

Figure P11.2.3. It is made from cast steel with a

relative permeability of 2500. The magnetic flux

density in the core is 1.25 T measured at the mean

diameter of the toroid.

(a) Find the current that must be supplied to the

coil.

(b) Calculate the magnetic flux in the core.

(c) Now suppose a 10-mm air gap is cut across

the toroid. Determine the current that must

be supplied to the coil to produce the same

value of magnetic flux density as in part (a).

You may neglect leakage and fringing.

11.2.4For the magnetic circuit shown in Figure P11.2.4,

neglecting leakage and fringing, determine the

mmf of the exciting coil required to produce a

flux density of 1.6 T in the air gap. The material is

M-19. The dimensions arelm 1 =60 cm,Am 1 =

24 cm^2 ,lm 2 =10 cm,Am 2 =16 cm^2 ,lg= 0. 1

cm, andAg=16 cm^2.

8 cm

12 cm

N = 2500

turns

Figure P11.2.3Toroid with circular cross section.

Am 1

Coil

lm 1

lm 2

lm (^2) A
m 2
lg
Figure P11.2.4