PHYS 2212 Module 9.6

Electric Generators and Back Emf

Recommended Reading

9.6 Electric Generators and Back Emf

Learning Objectives

By the end of this section, you will be able to:

  • Explain how an electric generator works
  • Determine the induced emf in a loop at any time interval, rotating at a constant rate in a magnetic field
  • Show that rotating coils have an induced emf; in motors this is called back emf because it opposes the emf input to the motor

Electric Generators

The electricity you are using right now is being generated at a power plant somewhere many miles away. What we are going to discuss in this module is how that electricity is made and transported to your home. And we’re going to start with Faraday’s law.

What I’ve just described is an electric generator and it is the basis for how all of our electricity is produced. The basic idea is to rotate something – a conducting loop in a B-field or rotate a B-field around a conducting loop. This rotation allows for a periodic change in flux which induces a periodic emf. This periodic emf will drive a current that will also look like a sine function. This type of current is called Alternating Current (AC) and is what you use every time you plug something into a household electrical outlet.

To generate electricity this way, we need to put mechanical energy (kinetic energy of rotation) into the system to convert it to electrical energy. And this is what happens at power plants. They all produce mechanical energy (usually by making something rotate, called a turbine) in some way: 

  • heat water to produce steam, which uses pressure to rotate a turbine (the heating of water can be done with burning coal/oil, or through nuclear reactions)
  • use pressure from a dam or a waterfall to rotate a turbine
  • use wind to turn a windmill, which rotates a turbine 

In the U.S., our systems rotate with a frequency of 60 Hz, or 60 rotations per second. 


Practice 9.6.1
What happens to the amplitude of the induced emf when the rate of rotation of a generator coil is doubled?
Check your answer: B. It becomes two times larger.
Practice 9.6.2
In an AC generator, a coil with N turns of wire spins in a magnetic field. Of the following choices, which does not cause an increase in the emf generated in the coil?
Check your answer: A. replacing the coil wire with one of lower resistance
Practice 9.6.3
At what frequency should a 200-turn, flat coil of cross sectional area of 300 cm2 be rotated in a uniform 30-mT magnetic field to have a maximum value of the induced emf equal to 8.0 V?
Check your answer: B. 7.1 Hz


The coil in an AC generator consists of 8 turns of wire, each of area A = 0.0900 m2, and the total resistance of the wire is 11.5 Ω. The coil rotates in a 0.630 T magnetic field at a constant frequency of 60.0 Hz.

Answer these three questions about this system:

  1. Find the maximum induced emf in the coil. 
  2. What is the maximum induced current in the coil when the output terminals are connected to a low-resistance conductor?
  3. What if at a later time, the maximum induced current was measured to be 6.00 A instead. Assuming the magnetic field is unchanged, at what frequency is the loop spinning?