Figure shows an inductor wound on a laminated iron core of rectangular cross section. Assume that the permeability of the iron is infinite. Neglect magnetic leakage and fringing in the two air gaps (total gap length = g). The N-turn winding is insulated copper wire whose resistivity is p ? ? m. Assume that the fraction fw of the winding space is available for copper; the rest of the space is used for insulation.

a. Calculate the cross-sectional area and volume of the copper in the winding space. b. Write an expression for the flux density B in the inductor in terms of the current density Jcu in the copper winding.

c. Write an expression for the copper current density Jcu in terms of the coil current I, the number of turns N, and the coil geometry.

d. Derive an expression for the electric power dissipation in the coil in terms of the current density Jcu.

e. Derive an expression for the magnetic stored energy in the inductor in terms of the applied current density Jcu.

f. From parts (d) and (e) derive an expression for the L/R time constant of the inductor. Note that this expression is independent of the number of turns in the coil and does not change as the inductance and coil resistance are changed by varying the number of turns.

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