Fraso / nomograms

Electronics

Resistors in parallel

Two resistors against their combined resistance.

A resistors in parallel nomogram: three vertical scales, R₁ (10 to 1000) on the left, R (5 to 500) in the middle and R₂ (10 to 1000) on the right. A straight line laid across any two scales cuts the third at the value that satisfies 1/R = 1/R₁ + 1/R₂.10111213.5151720253040501002001000R₁Ω10111213.5151720253040501002001000R₂Ω55.5678101215203050100500RΩ

Readings

Ω
Ω
Ω

Drag the red line, or type into any two boxes — the third is solved. The marked box is the one being solved for.

Print at 100% scale, then check the 100 mm bar with a rule before trusting a reading.

Why this one is an instrument

The reciprocal scales bunch their large values into almost nothing, and that crowding is the point rather than a flaw in the drawing: it shows you, geometrically, that a large resistor in parallel with a small one barely matters. You can see the law of diminishing returns as a physical crush of tick marks at one end of the scale.

Equation
1/R = 1/R₁ + 1/R₂
Ranges
R₁ 10–1000 Ω · R₂ 10–1000 Ω
Reading
Any two values fix the third. Outside the printed ranges the instrument stops being valid — that is what the end marks are for.

These are drawn from the stated equation and nothing else. Where an equation is itself an approximation — hyperfocal distance and tap drill sizes both are — the instrument inherits that approximation exactly, no better and no worse.