Parallel Resistors
Equivalent resistance of two or three resistors in parallel.
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The engineering
Parallel resistance is conductance addition — flip everything, add, flip back. The result is always smaller than the smallest branch, which the second row makes explicit.
Two equal resistors halve; a 10:1 pair lands within 10% of the small one. That instinct catches wiring mistakes faster than the math does.
Where this math comes from
Series and parallel rules crystallized from Ohm's 1827 work and Kirchhoff's 1845 laws, but treating circuits by conductance rather than resistance owes much to Oliver Heaviside, who reformulated circuit analysis in the 1880s with the operational shorthand working engineers actually use.
The 'product over sum' two-resistor shortcut is telegraph-era folklore — the kind of bench arithmetic that predates the pocket calculator by a century.
- 1827Georg Simon OhmResistance defined — the quantity being combined.
- 1845Gustav KirchhoffCurrent law — why parallel conductances add.
- 1885Oliver HeavisideOperational circuit analysis normalizes the conductance view.
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