## Back EMF in Electric Motors

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### Back EMF in Electric Motors

Q: What is back EMF and how does it affect electric motors?

A: The counter-electromotive force, also known as the back electromotive force (back EMF), is the voltage, or electromotive force, that pushes against the current which induces it. It is the voltage drop in an alternating current (AC) circuit caused by magnetic induction (see Faraday's law of induction, electromagnetic induction, Lenz's Law). For example, the voltage drop across an inductor is due to the induced magnetic field inside the coil, and is equal to the current divided by the impedance of the inductor. The voltage's polarity is the reverse of the input voltage.

The term back-EMF, is most commonly used to refer to the voltage that is generated in electric motors where there is relative motion between the armature of the motor and the magnetic field from the motor's stator magnets, or windings. From Faraday's law, the voltage is proportional to the magnetic field, length of wire in the armature, and the speed of the motor. This effect is not due to the motor's inductance and is a completely separate effect.

In a motor using a rotating armature in the presence of a magnetic flux, the conductors move through the magnetic field lines as they rotate. This produces a voltage in the coil as the motor is acting like a generator (Faraday's law of induction.) at the same time it is a motor. This voltage opposes the original applied voltage; therefore, it is called "back-electromotive force" (by Lenz's law). With a lower overall voltage across the armature, the current flowing into the motor is reduced. One practical application is to use this phenomenon to indirectly measure motor speed and position, since the back-EMF is proportional to the armature rotational speed.

To observe the effect of Back-EMF of a motor, one can perform this simple exercise. With an incandescent light on, cause a large motor such as a drill press, saw, air conditional compressor, or vacuum cleaner to start. The light may dim briefly as the motor starts. When the armature is not turning (called locked rotor) there is no Back-EMF and the motor's current draw is quite high. If the motor's starting current is high enough it will pull the line voltage down enough to notice the dimming of the light.

To understand this, realize that a spinning motor also acts like a generator. A motor has coils turning inside magnetic fields, and a coil turning inside a magnetic field induces an emf. This emf, known as the back emf, acts against the applied voltage that's causing the motor to spin in the first place, and reduces the current flowing through the coils of the motor.

At the motor's operating speed, enough current flows to overcome any losses due to friction and other sources and to provide the necessary energy required for the motor to do work. This is generally much less current than is required to get the motor spinning in the first place.

If the applied voltage is DV, then the initial current flowing through a motor with coils of resistance R is:

I = DV/R

For example, I = 120 V / 6 W = 20 A

A device drawing that much current reduces the voltage and current provided to other electrical equipment in your house, causing lights to dim.

When the motor is spinning and generating a back emf e, the current is reduced to:

I = (DV - e)/R

If the back emf is e = 108 V, we get:

I = (120 - 108)/6 = 12/6 = 2 A

It takes very little time for the motor to reach operating speed and for the current to drop from its high initial value. This is why the lights dim only briefly.

SOURCES:
http://en.wikipedia.org/wiki/Counter-el ... tive_force
http://physics.bu.edu/~duffy/sc545_note ... k_emf.html