FirstPrinciplesa Physoly project
CIR-01circuitstrap · Circuit equivalence error

Series and parallel don't combine by 'adding up'

  1. 01

    The tempting model

    Adding resistances in parallel (or reciprocals in series).

  2. 02

    Why it feels right

    Series and parallel formulas are often recalled without first tracing the circuit topology.

  3. 03

    Where it breaks · how to catch it

    Your parallel resistance came out larger than either resistor.

  4. 04

    The correct model

    Series: R = R₁ + R₂ (adds). Parallel: 1/R = 1/R₁ + 1/R₂ (equivalent is smaller than the smallest branch).

  5. 05

    Repair · see it, then test it

    worked example Two 4 Ω resistors in parallel. Equivalent resistance?

    Tempting move

    8 Ω.

    Correct move

    2 Ω, since 1/R = 1/4 + 1/4.

    Test the repair CIR-01 · transfer
    include Ω

    Make a fresh prediction before referring to the worked example.