TRANSFORMER
V₁I₁ === V₂I₂ — the invoice, bitwise across the whole plane at 2:1. Volts down, amps up, never free.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
Two coils share one iron core: the primary driven by the source, the secondary feeding a load. The lever traded force for distance. The press traded pressure for area. The tackle traded force for rope pulled. This machine trades volts for amps — the ratio family’s fourth member, and the invoice is the same as ever.
The turns ratio
The core carries one shared flux, and it links every turn of both coils equally — so volts per turn is the conserved currency. The secondary voltage is V-one times N-two over N-one, and when the load draws current, the primary answers with the ratio INVERTED. Ideal transformer disclosed: no leakage, no coil resistance, no core loss. What survives the idealization is the accounting.
The invoice
Machines never cheat, act five: V-one I-one equals V-two I-two. Step the voltage up and the current steps down in exact proportion — at the two-to-one default the ledger is bitwise across the entire slider range. And seen from the source, the load is disguised: Z-in is N-one over N-two squared times R-L, the impedance transform — which is how maximum-power matching gets engineered when era three arrives.
Loading the secondary
The sweep runs the load from two to a hundred ohms, quasi-static, exact at every frame. Lighter load, less current, both invoice bars falling together — pinned equal the whole way down. The transformer passes demand upstream instantly.
Audit
Audited: sixty volts, six amps, three amps at the defaults with the invoice bitwise at three hundred sixty watts — and bitwise across the whole voltage-and-load plane at the dyadic ratio, within two parts in ten to the sixteen off it; the impedance transform exact against V-one over I-one; the step-up case checked with amps rising fourfold upstream; and volts per turn conserved bitwise on both coils.