Turns ratio
n = N₁/N₂, the ratio of primary to secondary turn counts in a transformer. Sets the voltage step (V₁/V₂ = n), the current step (I₁/I₂ = 1/n), and the impedance step (Z_reflected = n²·Z_load).
Definition
The turns ratio n = N₁/N₂ is the single number that determines everything about an ideal transformer's input-output behaviour. Voltages scale as 1/n viewed from primary to secondary: V₂ = V₁/n. Currents scale as n: I₂ = n·I₁. Both follow from Faraday's law for each winding at the shared core flux, combined with the conservation of power V₁I₁ = V₂I₂.
The impedance transformation is the engineering consequence that matters most. A load Z_L connected across the secondary looks from the primary side like an impedance Z_reflected = n²·Z_L. An 8-ohm loudspeaker connected through a 10:1 step-down transformer looks like an 800-ohm load to the amplifier driving the primary. This is impedance matching, used to couple amplifier output stages (typically designed for high-impedance drive) to low-impedance loudspeakers, antenna feedlines to amplifiers, and high-voltage tube stages to low-impedance following stages.
In power distribution, the turns ratios are chosen to step grid voltage up or down at each stage: 20 kV generator to 400 kV transmission is roughly 1:20; 110 kV distribution to 11 kV local is 10:1; 11 kV to 240 V household is about 46:1. Real transformer design also adds features the ideal turns-ratio picture hides — magnetising current (the small current that flows even with no load, setting up the core flux), leakage inductance (flux that doesn't fully couple between windings), and core losses (hysteresis + eddy currents dissipating in the iron). But the first-order design choice is always the turns ratio, and everything else scales from there.