The currents induced in the armature conductors of a DC generator are alternating in nature.The commutation process involves The change from a generated alternating current to the direct current applied.these induced currents  flow in one direction  When the conductors of the armature are under the north pole. they are in opposite direction when they are under south pole. As the conductor passes through the influence of the north pole and enters the south pole , the current in them is reversed. the reverse of current takes place along the MNA or brushes axis. whenever a brush spans two commutator segments, the winding element connected to those segments is short circuited. by commutation we means the change that take place in a winding element during the period of short circuit by a brush. these change are show in figure. for simplicity , consider a simple ring winding.

In the position shown in Figure (a), the current I flowing towards the brush from the left-hand side passes round the coil in a clockwise direction.

In the position shown in Figure (b), this coil carries the same current in the same direction, but the coil is short circuited by brush.

In the position shown in Figure (c), the brush make contact bar a and b, thereby short circuiting coil 1. the current is still i from the left hand side and I from the right hand side. It is seen that these two currents can reach the brush without passing through coil 1.

Figure (d) shows that bar b just left the brush and short circuit of coil 1 has ended. it is now necessary for the current I reaching the brush from the right hand side in anticlockwise direction.

From all the above discussion, it is seen that during the period of the short circuit of an armature coil by a brush the current in the coil must be reversed and also brought up to its full value in the reversed direction. The time of the short circuit is called the period of commutation.
The figure shown below shows how the current in the short-circuited coil varies during the brief interval of the short circuit. Curve b shows that the current changes from +I to –I linearly in the commutation period. Such a commutation is called Ideal Commutation or Straight-line Commutation.

If the current through the coil 1 has not reached its full value in the position in the figure (d), then, since the coil 2 carrying full current, the difference between the currents through elements 2 and 1 has to jump from commutator bar to the brush in the form of a spark. Thus, the cause of sparking at the commutator is the failure of the current in the short-circuited elements to reach the full value in the reverse direction by the end of the short circuit.This is known as under commutation or delayed commutation.

The curve of current against time in such a case is shown in the figure E by the curve A. In ideal commutation curve B, the current of the commutating coils changes linearly from +I to –I during the commutation period.Curve C represents overcommutation or accelerated commutation when commutation reaches its final value with zero rate of change at the end of commutation period. Usually this will result in a satisfactory commutation.

In actual practice, the current in the short-circuited coil after commutation period does not reach its full value. This is due to the fact that the short-circuited coil offers self-inductance in addition to the resistance. The rate of change of current is so high that the self-inductance of the coil sets up a back EMF, which opposes the reversal.
Since the current in the coil has to change from +I to –I, the total change is 2I. If tc is the time of short circuit and L is the inductance of the coil (= self-inductance of the short-circuited coil + mutual inductances of the neighboring coils), then the average value of the self-induced voltage is
This is called reactance voltage
The large voltage appearing between commutator segments to which the coil is connected causes sparking at the brushes of the machine. The sparking of the commutator is much harmful, and it will damage both commutator surface and brushes. Its effect is cumulative which may lead to a short circuit of the machine with an arc round the commutator from brush to brush.