# Back EMF and Its Significance in DC Motors

Since the armature of a DC motor rotates in a magnetic field, an emf is induced in the conductors of the armature due to electromagnetic induction (as in a generator). This induced emf acts in the opposite direction to the applied voltage (according to Lenz’s law) and hence is known as back emf or counter emf. It is denoted by Eb and is given by,

$$\mathrm{E_{b}=\frac{NP\varphi Z}{60A}}$$

The magnitude of the back emf is always less than the magnitude of the applied voltage. But under normal operating conditions the difference of these two is small.

## Explanation

Consider a DC shunt motor as shown in the figure. When a DC voltage V is applied across the terminals of the DC motor, a magnetic field is produced and a current starts to flow in the armature conductors. Therefore, a torque acts on the armature which makes it rotating.

As the armature rotates, the back emf Eb is induced in the armature winding and opposes the applied voltage V. Hence, the applied voltage V has to force current through the armature against the back EMF.

The electric energy is expanded in overcoming and causing the current to flow against the back emf and is converted into the mechanical energy in the armature. Therefore, the electromechanical energy conversion in a DC motor is only possible due to the back EMF.

## Significance of Back EMF in DC Motor

The armature current drawn by the DC motor is given by,

$$\mathrm{I_{a}=\frac{V-E_{b}}{R_{a}}}$$

Hence, the back emf makes the DC motor a self-regulating machine i.e. it makes the motor to draw as much armature current as is needed to develop the torque required by the load. Therefore, it automatically changes the armature current to meet the load requirement as follows

• When the motor is running at no-load, a small torque is required to overcome the mechanical losses. Hence, the Ia is small and back emf is nearly equal to the applied voltage.
• Now, if the load is connected to the motor, it causes the armature to slow down and hence, the back emf decreases. The decreased back emf causes the larger current to flow through the armature and the large armature current means increased developed torque by the motor. Hence, the torque is increased when the motor slows down. The motor will stop slowing down when the armature current is sufficient to produce the increased torque required by the load
• When the load on the motor is decreased, then the torque is momentarily more than the requirement so that the armature is accelerated. As the speed of the armature increases, the back emf also increases and causes the armature current is decrease. The motor will stop accelerating when the armature current is sufficient to develop the torque required by the load.