Electromagnetic Induction, AC Circuits, and Electrical Technologies

51 Back Emf

Learning Objectives

  • Explain what back emf is and how it is produced in an electric motor.

Back Emf

Throughout this chapter, we have seen that electric motors and generators are closely related devices. A generator converts mechanical energy into electrical energy, whereas a motor converts electrical energy into mechanical energy. In fact, the internal construction of many motors and generators is nearly identical. The same coil of wire and magnetic field that allow a motor to produce rotation can also generate an emf whenever the coil rotates.

As a motor operates, its rotating coil continuously experiences a changing magnetic flux. According to Faraday's law of induction, this changing flux induces an emf in the coil. In other words, every running motor also behaves like a generator. The rotation may be produced by an external source, such as a belt drive, or simply by the motor itself as it performs useful work.

Lenz's law tells us that an induced emf always opposes the change that produced it. Therefore, the emf generated by the rotating motor acts in the opposite direction of the applied voltage that powers the motor. This self-generated voltage is called the back emf. Rather than helping the applied voltage, the back emf reduces the net voltage across the motor windings, as illustrated in Figure 51.1.

Circuit model of a DC motor represented by a resistor in series with a variable back emf that opposes the applied voltage.
Figure 51.1: A DC motor can be represented electrically as a resistor together with a variable back emf. The back emf opposes the applied voltage, is zero when the motor is stationary, and increases as the motor spins faster.

Because back emf is generated by the rotation of the motor, it is proportional to the motor's angular speed, [latex]\omega[/latex]. When the motor is first switched on, it is not yet rotating, so the back emf is zero. The full applied voltage therefore appears across the motor windings, causing the motor to draw its maximum current.

As the motor speeds up, the back emf increases. Since it opposes the applied voltage, the effective voltage across the windings decreases, reducing the current drawn from the power source. This automatic regulation explains why motors draw much more current when they first start than they do during normal operation.

Section Summary

  • As a motor rotates, its coil experiences a changing magnetic flux, which induces an emf according to Faraday's law.
  • In a motor, this induced emf is called the back emf because it opposes the applied voltage that powers the motor, as described by Lenz's law.
  • Back emf increases with the motor's rotational speed, reducing the current drawn during normal operation while helping prevent the motor from overheating.

Conceptual Questions

  1. Suppose you find that the belt drive connecting a powerful motor to an air conditioning unit is broken and the motor is running freely. Should you be concerned that the motor is consuming a great deal of electrical energy for no useful purpose? Explain why or why not.

Problems & Exercises

  1. Suppose a motor connected to a 120 V source draws 10.0 A when it first starts.
    1. What is its resistance?
    2. What current does it draw at its normal operating speed when it develops a 100 V back emf?
  2. A motor operating on 240 V electricity has a 180 V back emf at operating speed and draws a 12.0 A current.
    1. What is its resistance?
    2. What current does it draw when it is first started?
  3. What is the back emf of a 120 V motor that draws 8.00 A at its normal operating speed and 20.0 A when first starting?
  4. The motor in a toy car operates on 6.00 V, developing a 4.50 V back emf at normal speed. If it draws 3.00 A at normal speed, what current does it draw when starting?
  5. Integrated Concepts. The motor in a toy car is powered by four batteries connected in series, producing a total emf of 6.00 V. The motor draws 3.00 A and develops a 4.50 V back emf at normal speed. Each battery has a ...

Glossary

back emf
the emf generated by a rotating motor as its coils move through a magnetic field. According to Lenz's law, this induced emf opposes the applied voltage that powers the motor, reducing the current drawn as the motor speeds up.
definition

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Introductory Physics for the Health and Life Sciences II Copyright © 2012 by OSCRiceUniversity is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.