Resistors in parallel
| Wanted | Pair | Actual | Error |
|---|---|---|---|
| 500 Ω | 1 kΩ ∥ 1 kΩ | 500 Ω | exact |
| 750 Ω | 1 kΩ ∥ 3.3 kΩ | 767 Ω | +2.2% |
| 1.5 kΩ | 2.2 kΩ ∥ 4.7 kΩ | 1.50 kΩ | +0.0% |
| 2 kΩ | 3.3 kΩ ∥ 5.6 kΩ | 2.08 kΩ | +3.8% |
| 5 kΩ | 10 kΩ ∥ 10 kΩ | 5 kΩ | exact |
| 8 kΩ | 10 kΩ ∥ 39 kΩ | 7.96 kΩ | −0.5% |
| 15 kΩ | 22 kΩ ∥ 47 kΩ | 15.0 kΩ | +0.0% |
Two resistors in parallel give R₁R₂ ÷ (R₁ + R₂). Two 10 kΩ resistors make 5 kΩ exactly. Pairing is the standard workshop trick for hitting a value between the E12 steps you actually have in the drawer.
How to pair resistors
Equal resistors halve, which covers the easy cases. The interesting pairs are the ones that land almost exactly on a value between standard steps: 2.2 kΩ with 4.7 kΩ gives 1.499 kΩ, which is closer to 1.5 kΩ than a 5% 1.5 kΩ resistor is guaranteed to be. That is worth knowing when a design needs a value precisely and only the common series is to hand. It is also a reminder that tolerance dominates: two 5% parts in parallel give a result with roughly 5% uncertainty, so a precise pairing on paper still needs 1% parts to mean anything.
Questions
2.2 kΩ in parallel with 4.7 kΩ gives 1.499 kΩ — closer than a 5% 1.5 kΩ part is guaranteed to be.