11.2 MAGNETIC CIRCUITS 475
(c) Next, suppose that the torus (which was originally laminated for reducing the eddy-
current losses) is redesigned so that it has half the original lamination thickness. Assume
the stacking factor to be unity in both cases. What would be the effect of such a change
in design on the hysteresis loss?
(d) Suppose that the toroidal core of part (a) is to be used on 50-Hz supply. Estimate the
change in hysteresis loss if no other conditions of operation are changed.
Solution
(a) Referring to Figure 11.1.3, the area of each square represents
( 0 .1T)×(25 A/m)= 2. 5
Wb
m^2
×
A
m
= 2. 5
V×s×A
m^3
= 2 .5J/m^3
By counting, the number of squares in the upper half of the loop is found to be 43; the
area of the hysteresis loop is given by
2 × 43 × 2. 5 =215 J/m^3
The toroidal volume is
π× 0. 3 × 0. 052 = 2. 36 × 10 −^3 m^3
The hysteresis loss in the torus is then given by
2. 36 × 10 −^3 × 60 × 215 = 30 .44 W
(b) When all the linear dimensions of the core are doubled, its volume will be eight times
the previous volume. Hence the new core hysteresis loss will be
8 × 30. 44 = 243 .52 W
(c) The lamination thickness has no bearing on the hysteresis loss; it changes only the eddy-
current loss. Hence, the hysteresis loss remains unchanged.
(d) Since the hysteresis loss is directly proportional to the frequency, the loss on the 50 Hz
supply will be
30. 44 ×
50
60
= 25 .37 W
11.2 Magnetic Circuits
A magnetic circuit provides a path for magnetic flux, just as an electric circuit provides a path for
electric current. Magnetic circuits are integral parts of transformers, electric machines, and many
other common devices such as doorbells. Analogous to voltage (electric potential difference) in
the electric circuit, in a magnetic circuit we have themagnetomotive force(mmf), or themagnetic
potential differencewhich produces a magnetic field, and which has units of amperes or ampere-
turns. The two sources of mmf in magnetic circuits are the electric current and the permanent
magnet (which stores energy and is capable of maintaining a magnetic field with no expenditure
