How is the energy of a zero resistance circuit converted to rotational energy?

[Herbert11]

If I have a DC induction motor coil of a zero resistance so that means that to sustain a constant magnetic field I do not need any energy. So in a DC motor how is energy of zero resistance circuit converted to rotational energy of a motor?

 

[Christopher Grayce]

DC motors use a commutator and brushes to reverse the current through the armature every half turn, so the magnetic field does indeed change (grow and shrink) as it does in an AC motor, and of course that requires energy, so even if the *DC* (zero frequency) resistance of the armature is zero, the *AC* resistance (due to the energy required to create the magnetic field) is not.

 

[sophiecentaur]

If I have a DC induction motor coil of a zero resistance so that means that to sustain a constant magnetic field I do not need any energy. So in a DC motor how is energy of zero resistance circuit converted to rotational energy of a motor?

That's a nice 'makes you stop and think' question.
I think the explanation is that, although the coils have no resistance, that's only half of the explanation. During commutation, Energy goes into and out of the magnetic field. If Energy is taken out of the field by the KE gained by the armature, this 'looks like' (to the power supply) a Resistance in series with the coil. Volts and Current will have a non-quadrature phase angle, if you regard the armature current as AC - or you can look at it as a hysteresis effect.
Afaics, it's the same sort of thing as how the power fed to a transformer load appears as a Resistance across the Primary winding, despite the winding impedance being (sufficiently) high.

 

[zanick]

you need current (amper turns in the motor) through the coils , regardless if they are 0 resistance or not. 0 resistance, means there is no heat loss/radiated. Though a DC induction motor (AC induction, where the windings are commutated by through a controller or AC power) the current would be regulated by a controller as well as to maintain rated current values of the motor. energy would always be required for creating the magnetic field strength just as it would be through a motor with windings of 0 resistance. there is also inductance that doesn't change with the resistance...(magnetically induced resistance)

 

[Henryk]

A DC motor is consists of two parts: stator and rotor. Stator is a winding that creates a magnetic field in a certain direction. In small motors, it is replaced by a permanent magnet. Rotor is a series of coils offset at certain angles and connected to the commutator - a series of contacts arranged on a circle and connected to the stator and the coils and two brushes (usually graphite) that supply power to the that rotor coils. The brushes are arranged so that the magnetic field of the rotor is always perpendicular to that of the stator. Therefore, there is a torque acting on the rotor equal (in magnitude) to the stator field times the magnetization of the rotor. The torque converts the electrical energy to the mechanical one.
The field of the rotor is proportional to the current supplied to its windings. Initially, when the rotor is starting, the current is the applied voltage divided by the coil resistance. However, as the rotor starts spinning, There is an induced EMF in the rotor coil opposing the applied voltage. The induced EMF is proportional to the angular velocity of the rotor. Therefore, the current through the rotor coil equals (voltage applied to the stator - induced EMF)/ coil resistance. One of the consequence of this is that every DC motor is a generator. It produces EMF proportional to it's rpm's. Second, when there is no load on the motor, it rotates with angular velocity that makes the induced EMF (almost) equal to the applied voltage.
Now, going back to your original question. if the rotor resistance was zero, the current throught it would go to infinity at any rpms different that that which makes rotor windings' EMF equal to the applied voltage.
In other word, that motor would turn and rpm independent of the applied load.

 

[zanick]

A DC motor is consists of two parts: stator and rotor. Stator is a winding that creates a magnetic field in a certain direction. In small motors, it is replaced by a permanent magnet. Rotor is a series of coils offset at certain angles and connected to the commutator - a series of contacts arranged on a circle and connected to the stator and the coils and two brushes (usually graphite) that supply power to the that rotor coils. The brushes are arranged so that the magnetic field of the rotor is always perpendicular to that of the stator. Therefore, there is a torque acting on the rotor equal (in magnitude) to the stator field times the magnetization of the rotor. The torque converts the electrical energy to the mechanical one.
The field of the rotor is proportional to the current supplied to its windings. Initially, when the rotor is starting, the current is the applied voltage divided by the coil resistance. However, as the rotor starts spinning, There is an induced EMF in the rotor coil opposing the applied voltage. The induced EMF is proportional to the angular velocity of the rotor. Therefore, the current through the rotor coil equals (voltage applied to the stator - induced EMF)/ coil resistance. One of the consequence of this is that every DC motor is a generator. It produces EMF proportional to it's rpm's. Second, when there is no load on the motor, it rotates with angular velocity that makes the induced EMF (almost) equal to the applied voltage.
Now, going back to your original question. if the rotor resistance was zero, the current throught it would go to infinity at any rpms different that that which makes rotor windings' EMF equal to the applied voltage.
In other word, that motor would turn and rpm independent of the applied load.

This is not exactly the case on several levels. first of all, the OP is talking about a DC induction motor, which might not have a permanent magnet, and could be commutated by solid state components. (also called DC servo, AC servo, or DC brushless). you also make a few minor errors. "torque " doesn't convert the electrical energy . Yes, there is an "EMF" that apposes the positive torque , called "BEMF" but it can be varied by construction... laminate rotors vs solid rotors, change the eddy current size and effect, that can kill top speed torque/power. Not every DC motor is a generator. some do not contain magnets, some are purely induction motors. (squirrel cage rotors)
Now, going back to the original question... if winding (not "rotor" as you mentioned) resistance is "0 ", ( say they were liquid nitrogen cooled or something) current would not be controlled by an applied direct DC voltage. it would be controlled by the solid state controller. the current rise would be extremely fast because of the L/R time constant, but current would be limited to the ratings of the coil winding and the other components of the motor. heat losses I^2R would be low. the power would be determined by the amper turns of the motors windings. the resistance is only a factor for the heat dissipated. there would be current induced by other elements of the motor which would generate heat, who's resistance would not be "0".
this is an interesting question, but its important to understand that the windings of a motor are for carrying current and creating an electro magnetic field as well as inducing one into or onto the rotor. semiconductor based switching controllers have the ability to current limit the winding , regardless of their impedance.