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Electrical machines - Magnetic Circuits and Magnetic Materials

**Solved
problems**

**Eg .No.1**

A
magnetic circuit with a single air gap is shown in Fig. 1.24. The core
dimensions are:

Cross-sectional
area *A*_{c} = 1.8 × 10^{-3}
m^{2}

Mean core
length *l*_{c} = 0.6 m

Gap
length *g* = 2.3 x 10^{-3} m

*N *= 83
turns

Assume
that the core is of infinite permeability ( m -> ¥) and
neglect the effects of fringing fields at the air gap and leakage flux. (a)
Calculate the reluctance of the core

R_{e}
and that of the gap R_{g}. For a current of i = 1.5 A, calculate (b)
the total flux ϕ, (c) the
flux linkages λ of the coil, and (d) the coil inductance L.

**Eg .No.2**

Consider
the magnetic circuit of with the dimensions of Problem 1.1. Assuming infinite
core permeability, calculate (a) the number of turns required to achieve an
inductance of 12 mH and (b) the inductor current which will result in a core
flux density of 1.0 T.

**Eg .No.3**

A square
voltage wave having a fundamental frequency of 60 Hz and equal positive and
negative half cycles of amplitude *E*
is applied to a 1000-turn winding surrounding a closed iron core of 1.25 x 10^{-3}m^{2}
cross section. Neglect both the winding resistance and any effects of leakage
flux.

(a) Sketch the voltage, the winding flux linkage, and the core flux as a function of time.

(b)
Find the maximum permissible value of *E* if the maximum flux density is not to
exceed 1.15 T.

**Eg.No.4**

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