Describe a simple form of a.c. generator (rotating coil or rotating magnet) and the use of slip rings and brushes where needed

4.5.2 The a.c. generator

Objective

Describe a simple form of an alternating‑current (a.c.) generator (rotating coil or rotating magnet) and explain the role of slip rings and brushes where they are required.

1. Basic principle

An a.c. generator converts mechanical energy into electrical energy by rotating a coil (or a magnet) in a magnetic field. According to Faraday’s law of electromagnetic induction, an emf is induced in a circuit when the magnetic flux through the circuit changes with time:

\$\mathcal{E} = -\frac{d\Phi}{dt}\$

For a coil of N turns, area A, rotating at angular speed \omega in a uniform magnetic field B, the induced emf varies sinusoidally:

\$\mathcal{E}(t)=NAB\omega\sin(\omega t)\$

The sinusoidal variation means the output is alternating current.

2. Simple rotating‑coil generator

In the rotating‑coil (or “armature”) type, the coil is the moving part and the magnetic field is produced by stationary permanent magnets.

• Components

  • Rectangular coil of insulated copper wire (N turns)
  • Two permanent magnets producing a uniform field B
  • Axle and handle to rotate the coil
  • Two slip rings attached to the axle
  • Two carbon brushes in contact with the slip rings

• Operation

  1. The coil is rotated at constant angular speed \omega.
  2. As the coil turns, the magnetic flux through it changes, inducing an emf according to the equation above.
  3. The induced emf is alternating because the flux changes sign every half‑turn.
  4. The slip rings provide a continuous electrical connection to the rotating coil, allowing the alternating voltage to be taken out of the generator.

3. Simple rotating‑magnet generator

In the rotating‑magnet type, the magnetic field rotates while the coil remains stationary.

• Components

  • Stationary rectangular coil (often called the “stator”).
  • Two permanent magnets mounted on a rotating shaft (the “rotor”).
  • Axle and handle to rotate the magnets.
  • Two fixed terminals attached to the coil (no slip rings needed).

• Operation

  1. The magnets are turned, causing the magnetic field through the stationary coil to vary with time.
  2. The varying flux induces an alternating emf in the coil, again given by \$\mathcal{E}=NAB\omega\sin(\omega t)\$.
  3. Because the coil does not move, there is no need for slip rings; the electrical output can be taken directly from the coil terminals.

4. Slip rings and brushes

Slip rings are conductive rings fixed to a rotating shaft. Brushes (usually made of carbon) maintain sliding electrical contact with the rings. Their purpose is to transfer the alternating current from the rotating part of the generator to the external circuit without twisting the wires.

5. Comparison of the two simple generators

6. Key points to remember

• The induced emf in a simple a.c. generator varies sinusoidally with time.
• Rotating the coil or rotating the magnetic field both change the magnetic flux through the coil, producing the same mathematical expression for the emf.
• Slip rings and brushes are essential only when the part that carries the induced emf is rotating.
• In a rotating‑magnet generator the coil is stationary, so the output can be taken directly without slip rings.
• Increasing any of the following increases the peak emf:

  • Number of turns N
  • Coil area A
  • Magnetic field strength B
  • Angular speed \omega

7. Sample exam style question

Question: A rectangular coil of 200 turns, each side 10 cm long, rotates at 300 rev min⁻¹ in a uniform magnetic field of 0.5 T. Calculate the maximum induced emf.

Solution outline:

1. Convert speed to angular velocity: \$\omega = 2\pi \times \frac{300}{60}=10\pi\ \text{rad s}^{-1}\$
2. Area of coil: \$A = (0.10\ \text{m})^2 = 0.01\ \text{m}^2\$
3. Peak emf: \$\mathcal{E}_{\max}=NAB\omega = 200 \times 0.01 \times 0.5 \times 10\pi = 10\pi\ \text{V} \approx 31.4\ \text{V}\$