Transformer Voltage Ratio

A transformer is two coils sharing one magnetic circuit, and the turns ratio follows from Faraday's law applied to each of them. The alternating current in the primary drives an alternating flux around the iron core; that same flux threads the secondary, because the core is there precisely to make sure it does. Each turn of wire, primary or secondary, has the identical $\Delta\Phi/\Delta t$ passing through it, and therefore develops the identical volts per turn. Ten times the turns intercepting the same changing flux means ten times the induced voltage — hence $V_s/V_p = N_s/N_p$. Nothing about the wire gauge, the core size or the load enters into it.

A doorbell transformer stepping 120 V down to 16 V has a turns ratio of 7.5 to 1: a 900-turn primary against a 120-turn secondary. Because an ideal transformer neither creates nor destroys power, $V_p I_p = V_s I_s$, and the current ratio inverts — that 16 V secondary supplying 1 A draws only 0.13 A from the 120 V side. Impedance transforms as the square of the turns ratio, $Z_p/Z_s = (N_p/N_s)^2$, which is the whole reason for the output transformer in a valve amplifier and for matching transformers in radio work.

Michael Faraday wound the first one in 1831 on an iron ring, and the arrangement that carries the modern name was developed by Ottó Bláthy, Miksa Déri and Károly Zipernowsky in Budapest in 1885. It is the reason alternating current won the arguments of the 1890s: no comparably simple device changes DC voltage, and without cheap voltage changing you cannot transmit at high voltage and consume at low. A transformer works only on changing flux. Connect a steady DC supply and the induced secondary voltage is zero, while the primary — with only its winding resistance to limit current — draws whatever the supply will give and burns.

The trap that catches people in the field is that this equation is the ideal, and the ideal is a no-load figure. Measure the secondary of a transformer with nothing connected and you will get close to the turns ratio. Load it and the voltage sags, because the winding resistance and the leakage reactance drop voltage inside the transformer itself — a small unit may deliver 10% less than its nameplate at full load, which is exactly why nameplates quote a rated output at a rated current rather than a bare ratio. This is the transformer's version of a point worth stating plainly: an induced EMF is not the same thing as the terminal voltage you can measure once current flows, any more than a battery's EMF equals its terminal voltage under load. Two further cautions: the turns ratio says nothing about isolation or safety, since an autotransformer shares a winding and offers none; and stepping voltage down steps current up, so a secondary short is a far more violent event than the primary's fuse rating suggests.