Transformers and the National Grid

Transformer — a device that changes the size of an alternating voltage. It consists of two coils wound on a soft iron core: the primary (input) and the secondary (output).

How it works:

1. An alternating current in the primary produces a changing magnetic field.
2. The soft iron core carries that changing field to the secondary coil.
3. The changing field through the secondary induces an alternating e.m.f. in it.

A transformer only works with a.c. With d.c. the field would be steady, and a steady field induces nothing. This is the single most important thing to be able to say about transformers, and it follows directly from induction needing change.

The transformer equation:

Vₚ / Vₛ = nₚ / nₛ

where V is voltage and n the number of turns, with subscripts p for primary and s for secondary. The voltage ratio equals the turns ratio.

• Step-up transformer — more turns on the secondary, so the voltage is increased.
• Step-down transformer — fewer turns on the secondary, so the voltage is decreased.

Power is not created. For an ideal transformer:

Vₚ Iₚ = Vₛ Iₛ

so stepping the voltage up steps the current down in the same proportion. A transformer trades voltage for current; it does not manufacture energy.

The National Grid carries electricity from power stations to consumers, and it does so at very high voltage — up to 400 000 V.

Why. The power wasted heating the transmission cables is P = I²R. Because it depends on the square of the current, reducing the current is enormously effective: cut the current to a tenth and the wasted power falls to a hundredth. Since P = VI, transmitting the same power at ten times the voltage needs only a tenth of the current.

So a step-up transformer at the power station raises the voltage and lowers the current for transmission, and step-down transformers near homes reduce it to the safe 230 V used in houses.

Say "reduces the current" and then "because power loss depends on I²". Answers that say only "high voltage wastes less energy" miss the mechanism and usually the marks with it.

Example: 10 MW sent at 10 000 V needs 1000 A; through cables of 0.50 Ω that wastes I²R = 500 kW, or 5% of the power. Sent at 400 000 V it needs only 25 A, wasting 0.31 kW — around 1600 times less.