Transformers

Construction — two coils wound on a common soft iron core. An alternating current in the primary produces a changing magnetic flux; the core carries that flux to the secondary, where the changing flux linkage induces an alternating e.m.f.

The turns ratio

V_s / V_p = N_s / N_p

A step-up transformer has more turns on the secondary and raises the voltage. A step-down transformer has fewer and lowers it.

Transformers only work on AC — a steady direct current produces a constant flux, and constant flux induces nothing. This is not a design limitation but a direct consequence of Faraday's law, and it is the main reason mains electricity is distributed as AC.

For an ideal transformer, power in equals power out:

V_p I_p = V_s I_s

so stepping the voltage up steps the current down in the same proportion. Nothing is gained; voltage is traded for current.

Example: this is what makes the national grid possible. Power lost as heat in transmission lines is I²R, so it depends on the square of the current. Transmitting at 400 kV instead of 400 V cuts the current by a factor of 1000 and the losses by a factor of a million. The energy still has to be paid for at the power station; it simply no longer disappears into warming the countryside.

Why the core is laminated — the changing flux also induces currents in the iron core itself, called eddy currents, which waste energy as heat. Building the core from thin insulated sheets breaks the paths those currents would take, greatly reducing the loss. The sheets lie parallel to the flux so they do not obstruct it.

Other losses, and how they are reduced

Resistance of the windings — thick copper wire lowers it.

Flux leakage, where some flux misses the secondary — a well-designed closed core keeps the flux contained.

Hysteresis, energy spent repeatedly remagnetising the core — soft iron, which magnetises and demagnetises easily, minimises it.

Efficiency — large grid transformers reach well over 99%, which is why the assumption of an ideal transformer in calculations is usually a good one.