Motors and generators

An electric motor uses the motor effect: forces on the sides of a current-carrying coil in a magnetic field make it spin. A generator does the reverse: spinning a coil in a field induces an alternating voltage. The same physics runs electric cars, washing machines, wind turbines and power stations.

Key facts

  • Motor: electrical → kinetic energy. Generator: kinetic → electrical energy.
  • A d.c. motor’s split-ring commutator reverses the coil current every half turn, keeping it spinning one way.
  • A motor spins faster with more current, more turns, or a stronger field; reverse the current to reverse it.
  • An alternator uses slip rings and gives a.c.; a dynamo uses a commutator and gives d.c.
  • Spinning a generator faster raises both the peak e.m.f. and the frequency.
  • Peak e.m.f. ε₀ = NBAω, with ω = 2πf. Frequency (Hz) = revolutions per minute ÷ 60.

Worked examples

Example 1

The trace shows two cycles of a generator’s output taking 40 ms, with a peak of 12 V. Find the period and frequency.

  1. One cycle 40 ms ÷ 2 = 20 ms
  2. f = 1 ÷ T f = 1 ÷ 0.020 = 50 Hz

Answer: T = 20 ms, f = 50 Hz

Example 2

A generator gives a peak of 8 V at 25 Hz. What happens if it spins three times as fast?

  1. Faster spinning means the flux changes three times as fast, so the peak e.m.f. × 3 = 24 V.
  2. It also completes three times as many cycles per second: 75 Hz.

Answer: peak 24 V, frequency 75 Hz

Example 3

A 12 V motor draws 2.0 A for 5.0 s while lifting a 4.0 kg mass through 1.5 m. Find its efficiency. (g = 9.8 N/kg)

  1. Energy in E = VIt = 12 × 2.0 × 5.0 = 120 J
  2. Useful energy out E = mgh = 4.0 × 9.8 × 1.5 = 58.8 J
  3. Efficiency 58.8 ÷ 120 × 100 = 49%

Answer: 49%