V₁/V₂ = N₁/N₂, exact, a property of the winding. Power in equals power out for an ideal device, so current runs the other way: I₂/I₁ = N₁/N₂.
N₁I₁ = N₂I₂: the same statement seen from the current side. The magnetomotive force driving the core’s flux must balance.
Core (iron) loss is constant whenever the unit is energised; copper loss goes with the square of load current. Distribution units run 97–99% efficient at full load.
At 40–70% of rated load, where copper loss equals core loss: why distribution transformers are sized a little above their expected load.
Lower voltage at the same power means higher current, and thicker conductors are needed to carry it without excessive resistive heating: exactly the copper-loss mechanism this tool models. It is also why long-distance transmission uses very high voltage: the same power at higher voltage means proportionally lower current, and resistive losses scale with current squared.
Core losses are constant the moment a transformer is energised, load or no load. An oversized unit running well below its rating pays that constant overhead for comparatively little useful output. Real units add leakage inductance, magnetising current and winding resistance, which the core equations do not model; the turns ratio still gets voltage and current exactly right.
A transformer briefly draws far more than its steady-state current the instant it is switched on, because the core’s magnetising flux has not settled into its steady AC cycle and the core saturates first. Transformer circuits use time-delay fuses for it, and a breaker sized on steady-state current alone will nuisance-trip.
Both windings sit in the same changing flux, so their voltages rise and fall together. The flux itself runs a quarter-cycle behind the voltage. The current is set by the load: at a load power factor below 1 the current in both windings lags the voltage by the angle whose cosine is the power factor, and the transformer passes that lag through. Real units add a small extra shift from leakage inductance, which this model leaves out.
Watts at a power factor below one mean more current than the watts suggest: a motor at 0.8 draws 25% more current for the same useful power, and a transformer is rated in kVA rather than kW because the copper carries that current whether or not it does useful work. Drop the power factor and watch the secondary current rise while the watts stay put; drop the rating and watch the load fraction climb past 100% and the page say so.
Off load the secondary is exactly V₁/a. A real transformer sags a few per cent between no load and full load as current passes through the winding resistance and leakage reactance: its regulation, why a supply measured off-load reads higher than one under load. The slider applies it in proportion to load; at 0% the page is the ideal case, and the off-load figure is shown beside the loaded one whenever they differ.
Built from a fixed core loss present whenever the unit is energised and a copper loss rising with the square of load; efficiency peaks where they are equal, which is why the peak sits below full load. The three classes are representative figures, not a specific product. A real winding warms as it works, so its resistance climbs and copper loss with it: there is no temperature in this model at all.
The primary current was computed as load / V₁, the ideal lossless answer, while the panel beside it drew an efficiency curve reading 94%: the two could not both be true. It now divides by the efficiency at the load you have chosen, raising the primary current by up to 12% on a small transformer at light load: the figure you would size a primary fuse from, so worth having right.
Two loss mechanisms eat into it: core (iron) losses from magnetising the core, which are present constantly whenever the transformer is energised regardless of load, and copper losses from winding resistance, which scale with the square of the load current. Distribution transformers typically run 97–99% efficient at full load; large power transformers can exceed 99.5%.
Efficiency is maximised exactly where copper loss equals core loss — since core loss is constant and copper loss grows with current squared, that crossover typically happens around 40–70% of rated load for distribution transformers, which is also why they're deliberately sized a little larger than their average expected load.
A real mains transformer might use hundreds or thousands of turns per winding — this tool draws the turns ratio at a legible scale (the presets pick small whole numbers with the same ratio) so the physics stays identical while the diagram stays readable.
Only for the ideal case. Real transformers also have leakage inductance, magnetising current, and winding resistance that this tool's core equations don't model — turns ratio gets you the voltage and current relationship exactly right, which is most of what matters for a first-pass calculation.
Both windings sit in the same changing magnetic flux at the same instant, so their voltages rise and fall together; there is no mechanism in an ideal transformer to delay one winding behind the other. The flux itself runs a quarter-cycle behind the voltage, because each turn's voltage is set by how fast the flux is changing, not by how much of it there is. The current is a different matter: it is set by the load. At a load power factor below 1 the current in both windings lags the voltage by the angle whose cosine is the power factor, and the transformer passes that lag through rather than creating it. Real transformers add a small extra shift from leakage inductance, which this model leaves out.
Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.