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A reluctance motor is made by arranging a material with high permeability, which is free to...

A reluctance motor is made by arranging a material with high permeability, which is free to rotate, in the gap of a magnetic circuit excited by a current i (t).
The inductance of the magnetic circuit varies according to the angle θ of the rotor. The maximum inductance, L_0 + L_1, occurs when θ is null or 180 °, and the minimum inductance, L_0-L_1, for θ = ± 90


(a) What is the magnetic torque of the rotor, T_mag, as a function of angle θ and current i (t)?

(b) For a direct type current i (t), I, a positive and constant mechanical stress T_mech> 0 is applied. What is the maximum value of T_mech = T_max for which the rotor is in its static equilibrium?

(c) If i (t) is a DC type current, I, and a motor moves the rotor angle θ at a constant angular velocity, Ω, such that θ = Ω t, what is the voltage v (t ) on the coil?

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