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# Counter EMF of a motor

## Description

Counter-electromotive force (abbreviated counter EMF or simply CEMF), also known as back electromotive force (or back EMF), is the electromotive force or “voltage” that opposes the change in current which induced it. CEMF is the EMF caused by magnetic induction (see Faraday’s law of induction, electromagnetic induction, Lenz’s Law).

For example, the voltage appearing across an inductor or “coil” is due to a change in current which causes a change in the magnetic field within the coil, and therefore the self-induced voltage. The polarity of the voltage at every moment opposes that of the change in applied voltage to keep the current constant.

The term back electromotive force is also commonly used to refer to the voltage that occurs in electric motors where there is relative motion between the armature and the magnetic field produced by the motor’s field coils, thus also acting as a generator while running as a motor. This effect is not due to the motor’s inductance but a separate phenomenon.

This voltage is in series with and opposes the original applied voltage and is called “back-electromotive force” (by Lenz’s law). With a lower overall voltage across motor’s internal resistance as the motor turns faster, the current flowing into the motor decreases. One practical application of this phenomenon is to indirectly measure motor speed and position, as the back-EMF is proportional to the rotational speed of the armature.

In motor control and robotics, the term “Back-EMF” often refers most specifically to actually using the voltage generated by a spinning motor to infer the speed of the motor’s rotation for use in better controlling the motor in specific ways.

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 conditioner 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.

By Lenz’s law, a running motor generates a back-EMF proportional to the speed. Once the motor’s rotational velocity is such that the The constant Kv (motor velocity constant, or the back EMF constant) is a value used to describe characteristics of electrical motors.

This formula calculates the back EMF of a motor.

Related formulas

## Variables

 Eb back, induced or counter EMF of a motor (V) Kb back EMF constant (dimensionless) ϕ flux (Wb) π pi n armature frequency - change to rpm (hz)