Inductance (L) has a property called inductive reactance, which for the purposes of this discussion may be thought of as a resistance proportional to frequency and therefore motor speed. According to Ohm’s law, current is equal to voltage divided by resistance. In this case we substitute inductive reactance for resistance in Ohm’s law and conclude motor current is the inverse of motor speed. Since torque is proportional to ampere-turns (current times the number of turns of wire in the winding), and current is the inverse of speed, torque also has to be the inverse of speed. In an ideal step motor, as speed approaches zero, its torque would approach infinity while at infinite speed torque would be zero. Because current is proportional to torque, motor current would be infinite at zero as well.
A step motor is highly resonant because it is a mass-spring system. The “mass” portion is the rotor and load inertia while the “spring” portion is the restoring torque of the magnetic field that drags the rotor along. Because of this, velocity lags torque by 90 degrees.
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