First of all we will see that **what is back emf in dc motor**. As we know that there is a magnetic field which is required for the working of the dc motor. The magnetic field can be either be provided by a permanent magnet or an electromagnet can be used.

Usually the field is present on the stator part of the motor. As we know in a dc motor the armature is the rotating part of the motor. The armature has the windings on it which is supplied by an external power source. The power is supplied to the armature through the carbon brushes and the commutator.

In case an electromagnet is used the DC power supply is given to both of the stator and the armature. Due to these magnetic fields torque is produced and there will be a rotation of the armature of the motor.

Now when there is a rotation in the armature of the motor the electromotive force is induced in the coils of the armature windings. This emf induced is opposite in direction to the applied voltage. This emf is called the **back emf of dc motor**. Note that the back emf is always less than the applied emf.

*Now why the emf is induced in the opposite direction?*

*Now why the emf is induced in the opposite direction?*

This happens in accordance with the lenz laws which says causes opposes the affect. As we know that fleming’s left hand rule gives the motion of conductor in a magnetic field but the direction of the emf induced in the conductor is given by the **fleming’s right hand rule**.

- Thumb gives the motion of the conductor
- The index field points in the direction of the field
- The other finger give us the direction of induced emf

## Back emf Formula:

The following expression gives the magnitude of the emf induced

{ \Epsilon }_{ b }=\frac { \Rho \phi \Zeta \Nu }{ 60A }

- E
_{b}= induced emf of the motor(back emf) - A = number of parallel paths
- P = number of poles
- N = speed of armature
- Z = total number of armature conductors
- ϕ = flux per pole in Wb

## Significance of Back emf:

The back emf plays a very important role in the working of a dc motor. Following are some points which show the significance of back emf in dc motor:

- The back emf actually limits the current through the armature. It increases when the load on the motor decreases and decreases when the load is increased. Hence, as a result creating more torque.

The current in the armature is given by the following expression:

I_{a} = Armature Current

V = Main Supply Voltage

E_{b} = Back Emf

R_{a} = Resistance of Armature

- Whenever there is an increase in the speed of an armature, the
**back emf Eb**also increase and will cause the Ia (armature current) to decline. - When the armature current is sufficient enough to produce the required torque the motor stops any further acceleration. Hence, we can say that the in the dc motor the
- At the low load or no load we know that a dc motor will require only a small torque i.e. for the copper losses etc. So, the motor will draws less armature current and have a high speed but this increase also results in the increase of the back emf and lowers the armature current.
- At the high load, the motor requires a high torque and so its speed become slow. As the motor speed decreases, the value of induced back emf will become low which as a result withdraws high armature current I
_{a}. This high current current is used to overcome the required high torque. The motor will now continue to rotate.