Dynamos, Motors & Transformers

Three machines built on induction and magnetic force: the DC dynamo, the DC motor and the transformer, which together make it possible to generate, use and ship electrical power across a country.

The DC dynamo#

Same magnet and armature as an AC dynamo, but the slip rings are replaced by a split ring: a cylinder cut into two halves C₁ and C₂, one joined to each end of the coil, with carbon brushes B₁ and B₂ pressing on them. Every half turn the gaps pass under the brushes and the connections to the outside swap. Arranged so that the swap happens just when the emf is zero, the external current always flows the same way.

This split ring with its brushes is the commutator. The output is one-way but pulsing; a second coil at right angles (its emf peaks when the first’s is zero) smooths it, and more coils smooth it further.

The DC motor#

A DC motor is built just like a DC dynamo, but run in reverse: a battery sends current through the armature via the brushes, the field exerts a torque on the coil (largest when the coil’s plane lies along the field, zero when it faces it), and the commutator reverses the current every half turn so the torque keeps the same sense. The shaft turns the load.

As the coil turns it also acts as a generator, producing a back emf e that opposes the applied emf ℰ:

The transformer#

Two coils, a primary (N₁ turns, connected to the AC source) and a secondary (N₂ turns, feeding the load), wound on one laminated soft-iron core. The core’s magnetization dominates the field, so the same flux Φ passes through every turn of both coils.

Neglecting the primary’s resistance, ℰ₁ = N₁ dΦ/dt; the secondary has ℰ₂ = −N₂ dΦ/dt. Dividing:

Power transfer

With the secondary open, the primary is a pure inductor: a small current i_s flows, 90° out of phase with ℰ₁, and no power is drawn. Connect a load and a secondary current i₂ flows. It would change the core’s flux, so an extra primary current i₁ appears that exactly cancels its effect; i₁ is in phase with ℰ₁, and the source now delivers power ℰ₁i₁. With no losses this all reaches the load:

• Step-up (N₂ > N₁): higher voltage, lower current out; the primary is wound from thick wire.
• Step-down (N₂ < N₁): lower voltage, higher current out; the secondary needs thick wire.
• Efficiency η = output power/input power is lowered by coil resistance, hysteresis and eddy currents in the core, but 99 % is achievable.

Long-distance transmission

A power station supplies a fixed power P = Vi. Sent through lines of resistance R, it loses i²R as heat. At high voltage the current, and so the loss, is small. So voltages are stepped up at the station, sent across country, and stepped down near the users.