# Back Emf in DC Motors

In this article, we will study about the back emf in dc motors and its importance. In order to understand the concept of back emf more clearly, kindly first read the working principle of dc motor.

How does dc motor works?↗

### Back Emf in DC Motor:

When power is supplied to the armature of dc motor through brushes, current starts to flow in the armature coil. Current carrying armature coil creates magnetic field around it. Armature coil is also under the effect of magnetic field produced by the stator. Due to the Interacting magnetic fields of armature coil and stator, armature coil experiences mechanical force (torque) due to which it starts to rotate. The below diagram helps to understand the above discussion.

When a coil rotates in a stationary magnetic field (relative motion between a magnetic field and conductor occurs), emf will be induced in it according to the faraday law of electromagnetic induction. Emf induced in the armature coil of dc motor is known as back emf. It is denoted by Eb.

Direction of Induced back Emf :

According to Lenz law, direction of the induced emf is such that it opposes the cause which produces it. Since the applied voltage causes the current to flow through the armature coil which results in the production of back emf. Hence the direction of induced back emf is such that it opposes the applied voltage Vs.

Rotation of the armature produces back emf which acts back on the electrical side (i.e. it opposes the supplied voltage V). As it opposes the supplied voltage V, supplied voltage uses more energy to make the current to flow through armature against the back emf.

The total electrical work done for causing the current to flow against the back emf is converted into mechanical energy which is developed in the armature of dc motor. Hence, we can say that energy conversion (from electrical to mechanical) occurs due to the presence of back emf.

Back emf actually represent that part of the supply voltage which is multiplied by the current equal to the mechanical work produced. Some part of the supply voltage is loss as  drop (motor resistance) and produces heat. In simple words, we can say that the mechanical energy produced in dc motor is the product of back emf (Eb)and armature current(Ia). Hence it is always better to have back emf close to the supply voltage as possible. The magnitude of back emf in dc motor is as follows:

…….. eq. (A)

In the above equation, Eb is the induced back emf in dc motor. P is the number of poles, N is the speed of armature in rpm, Z is the total number of armature conductors, ϕ (fi) is the flux per pole in Weber and A is the number of parallel paths for armature current.

Significance of back Emf in DC Motors:

Back emf regulates the flow of armature current according to the need of the motor (i.e. it automatically changes the armature current to meet the load requirement). Back emf adjusts the armature current drawn from the supply by the following relation.

Value of the supply voltage Vs and armature resistance Ra is usually fixed. Hence the value of back emf (Eb) regulates the armature current(Ia). Back emf makes the armature current enough to produce the driving torque required for the load. Back emf regulates the armature current by the following ways:

When there is no load on motor, speed of the motor is high. Due to high speed of motor, back emf also becomes large(since EbN from eq. A ). When back emf is high, motor will draw less armature current due to which produce torque also reduces as TI. Since motor also required only small torque to overcome friction and other losses at no load. Hence produce torque is enough and back emf is nearly equal to the supply voltage in that case.

When motor is loaded, speed of the armature conductors moving through the field is reduced. Decrease in the armature speed will result in less induce back emf .(As back emf is directly proportional to the armature speed (N)). Decrease back emf allows large current to flow through the armature conductors. Since torque is directly proportional to the product of field and armature current (Ia). Hence torque delivered to the motor also increases in order to meet the requirement of the load.

Once the motor delivering torque is just enough for the load torque, the motor stops slowing down and runs at new specific speed. Hence it all settles when motor delivering torque is just equals to the required load torque.

When the load on motor is decreased, driving torque is in excess of the load requirement which accelerates the armature. As the speed of armature increases, back emf also increases which causes the armature current to decrease. This decreasing of armature current automatically decreases the delivering torque of motor till the point required for the load.

Once the motor delivering torque is equal to the load torque, motor will stop accelerating and continue to rotate at newly specific speed. In this way, back emf adjusts the flow of armature current in order to deliver the torque as per load requirement. Thus, motor continue to operate safely in all conditions.

That’s all. Hope this will helps you.

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