Result

Ideal transformer

(E11.4.2) E11.4 · Resonance and Transformers →

\frac{V _{2}}{V _{1}} = \frac{N _{2}}{N _{1}}

Statement

The voltage ratio between a transformer's primary and secondary coils, set by their turns ratio.

Symbols and units

$V_{1}, V_{2}$	primary, secondary voltage	V
$N_{1}, N_{2}$	primary, secondary turns	—

When it applies

An ideal transformer — no resistive or flux losses, both coils linked by the identical flux.

Don't use when

Assumes an ideal transformer with no resistive or flux losses and both coils linked by identical flux — a real transformer has some power loss and imperfect coupling.

Derivation

The same changing flux links both coils; by Faraday's law, each coil's induced emf is proportional to its own number of turns:

\frac{V _{2}}{V _{1}} = \frac{N _{2}}{N _{1}}

Watch out for

An ideal transformer conserves power, not voltage — stepping voltage UP by a turns ratio steps current DOWN by that same ratio.

Connects to

Faraday's law