Series shares current; parallel shares voltage
The mistake
Applying the series current rule to parallel branches or the parallel voltage rule to series elements.
Why it feels right
Both rules are true somewhere, so the circuit topology gets skipped.
How to catch it
You set branch currents equal in parallel without symmetry, or set series voltage drops equal without equal resistances.
The first principle
Elements in series carry the same current. Elements in parallel have the same voltage across them. Current and voltage divide according to resistance.
A 3 Ω resistor and a 6 Ω resistor are in parallel across a battery. What is the same?
Common wrong move
Current through each.
Correct
Voltage across each; the 3 Ω branch has twice the current.
Make a fresh prediction before referring to the worked example.