What does the back EMF graph of a DC motor look like? Shouldn't it be oscillating like the output voltage of an AC generator? From what I understand, the net emf of a DC motor is made of its supply emf and back emf. The supply emf is constant, whilst the back emf depends on how fast the coil is spinning.
Initially, there is no rotation and hence the coil doesn't experience any change in flux so back emf is zero. As the coil starts rotating, the the coil experiences a faster rate of change of flux and hence induces a larger back emf, thereby resulting in then net emf to decrease. This continues until the net emf approaches zero (in an ideal motor), thereby producing a graph like this:

However, this implies that as the coil reaches a max speed, the back emf is a constant and hence the net emf is zero, but that doesn't make sense to me.
We know from AC generators that when they are rotating at a constant speed, the output emf is sinusoidal, so shouldn't the graph for this DC motor also be sinusoidal at maximum speed? It still experiences a rate of change of flux.
 A: For a simple DC motor described in basic physics texts, the magnetic field is constant in one direction and the back emf for the single rotating coil is a chopped sine wave in time.  For an actual DC motor, the magnetic poles (field shape) and numerous conductors are constructed such that the emf generated by each coil on the rotor rotating at constant speed is essentially constant except for the brief time when the conductor is between the poles (where the emf is zero).  The greater the load, the slower the rotational speed, and the lower the back emf. At no load the back emf exactly counters the supply emf, and no current is drawn from the supply emf.  With increasing load, the back emf decreases and more current is drawn from the source emf.
A: Assume a dc motor with no resistance and no friction.
The speed of the coil which reach a maximum when the applied emf is equal to the back emf and in this condition no current is drawn from the power supply.
This is not unreasonable because the coil is rotating and constant speed ie its rotational kinetic energy is not changing and there are no other dissipative losses (mechanical friction and electrical resistance) so to maintain this condition there needs to be no input of energy from the power supply.
Initially I wrote the following as a comment.
How electrical energy is converted into mechanical energy and the link there in explain what happens when there is resistance..
