A transformer uses magnetic coupling between two windings to transfer alternating electrical power from one circuit to another without a direct electrical connection.

An ideal transformer assumes perfect magnetic coupling, zero winding resistance and no magnetic-core loss.

Turns ratio

If the primary and secondary have $N_1$ and $N_2$ turns and share the same changing core flux, Faraday's law gives the voltage-magnitude ratio

$$\frac{V_2}{V_1}=\frac{N_2}{N_1}.$$

A secondary with more turns has a larger voltage; fewer turns gives a smaller voltage.

Current ratio

For corresponding ideal current magnitudes,

$$\frac{I_2}{I_1}=\frac{N_1}{N_2}.$$

Stepping voltage up therefore steps current down by the reciprocal ratio.

The inverse current ratio is what allows an ideal transformer to transfer power between voltage levels without creating energy.

Why changing flux is necessary

Transformer action depends on electromagnetic induction. A steady DC voltage does not maintain a continually induced secondary voltage once transients have disappeared.

Electrical isolation

Energy crosses from one winding to the other through the shared electromagnetic field. The windings can therefore remain galvanically isolated while exchanging AC power.