DIVIDER
A perfect ratio machine — until you connect the thing you built it for.
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 resistors in series make the most-built circuit in electronics: a tap that hands you any fraction of a voltage you like. It works perfectly — right up until you connect the thing you built it for.
One current
Series means one path, so one current — charge conservation leaves it no choice — and the voltage splits in strict proportion to resistance. It is a ratio machine, the electrical cousin of the lever: R₂’s share of the resistance is R₂’s share of the volts.
Solve
The ideal answer takes one line. The gotcha takes the rest: any real device sits in parallel with R₂, shrinking it, shifting the ratio, and sagging the tap — by half a percent for a gentle load, by a third for a greedy one. The 10× rule of thumb exists because of this page.
Connect
The load dials in from open-circuit to full — a rheostat sweep in which every intermediate frame is the exact circuit arithmetic. Watch the node: as the load’s current grows, I₁ grows to feed it, and the ledger I₁ = I₂ + I_L never misses.
Audit
Audited: Kirchhoff’s current law at the node to machine precision — charge conservation, the eleventh law in this site’s index, verified where it lives — and the power ledger closing with nothing missing. Every volume knob and sensor readout is this circuit; now you know why they all droop.