“Equalizer connection is needed in lap winding armature but not in wave winding “ why ?

 The equivalent circuit of a four point – pole dynamo with a simplex winding. The voltage induced in each path is assumed to both to be same and should be if the reluctance of each magnetic path is the same, so that the lines of flux cut by each inductor of each path are the same. However wear of the bearings or deflection of the armature shaft may cause the armature to be closer to some poles and farther from others, thus changing the length of the air gap, and therefore the reluctance of the magnetic circuits of the poles is not identical. This factors cause the voltage in the materials making up the magnetic circuit. These factors cause the voltage in each parallel path differ, and the unequal voltages in turn cause flow of a circulating  current through the windings and brushes , undue heating of the armature and waste the power. To reduce the circulating current, points on the winding which should be at the same potentials are brought to the same potentials by connecting them with conductor. These connections called equalizer connections confine the circulating current to the winding, thus reducing the sparking at the brushes. It is found that circulating current flowing through the equalizer connections sets up a magnetic flux of the strong poles. This tends to reduce the higher induced voltage and makes the voltage of each path more nearly equal.

  

 A wave windings requires no equalizer connections. This is true because each path has conductors in series under all poles of the dynamo. Any difference in the lines of the flux from the poles will produce  different voltage in the inductors , but both paths will be equally affected and the total induced voltage of each path will always be the same.