Series shares current; parallel shares voltage

01
The tempting model
Applying the series current rule to parallel branches or the parallel voltage rule to series elements.
02
Why it feels right
Both rules are true somewhere, so the circuit topology gets skipped.
03
Where it breaks · how to catch it
You set branch currents equal in parallel without symmetry, or set series voltage drops equal without equal resistances.
04
The correct model
Elements in series carry the same current. Elements in parallel have the same voltage across them. Current and voltage divide according to resistance.
05
Repair · see it, then test it
worked example A 3 Ω resistor and a 6 Ω resistor are in parallel across a battery. What is the same?
Tempting move
Current through each.
Correct move
Voltage across each; the 3 Ω branch has twice the current.
Test the repair CIR-06 · transfer

A 4 Ω branch and a 12 Ω branch are in parallel. How do their currents compare?
They are equal The 4 Ω branch has three times the current The 12 Ω branch has three times the current Both currents are zero

Make a fresh prediction before referring to the worked example.