# Back EMF in DC Motor

In a DC Motor, the induced EMF of rotation of the armature is known as Back EMF or Counter EMF. When the current is supplied to the armature conductors placed in the main magnetic field, the torque develops, and the armature of the motor rotates. The armature conductors cut the magnetic flux of the main magnetic field. Therefore, the EMF of rotation Er is induced in the conductors.

The direction of the induced EMF in the armature conductor is determined by Fleming’s Right Hand Rule. It is shown in the figure below.

It can be seen in the figure above that the direction of this induced EMF is opposite to the applied voltage. This is the reason that this induced EMF in the armature, when the machine works as a motor, is called Back EMF (Eb).

Since the back Emf is induced due to the generator action, its magnitude is given by the same expression as that for the generated EMF in a DC generator. It is expressed by the relation shown below.

Where, Eb is the induced emf of the motor known as Back EMF, A is the number of parallel paths through the armature between the brushes of opposite polarity. P is the number of poles, N is the speed, Z is the total number of conductors in the armature and ϕ is the useful flux per pole.

A simple conventional circuit diagram of the machine working as a motor is shown in the diagram below.

In this case the supply voltage is always greater than the induced or back emf i.e. (V > Eb). Therefore, the current is always supplied to the motor from the mains and the relation among the various quantities will be given as Eb = V – IaRa.