The formula
Series: R = R₁ + R₂ + … · Parallel: 1/R = 1/R₁ + 1/R₂ + …
What it means
In series the current has no choice but to pass through all of them, so the obstacles add up and the combination resists more than any single one. In parallel you open several routes at once, and the more you open the easier it gets: the combination resists less than the smallest of them. That is the result that surprises people most at the start, which is why it is always compared here with the smallest resistor in the list.
How to work it out by hand
- If they are in series, add all the values and you are done
- If they are in parallel, work out the reciprocal of each one
- Add all those reciprocals together
- Invert the result: that is the equivalent resistance
What is worth knowing
Two equal resistors in parallel give half, and that case is worth memorising because it comes up constantly. In series the largest resistor dominates, and the share in the table is also the share of the voltage: a resistor taking sixty per cent of the ohms takes sixty per cent of the volts. In parallel the share is of the current, and it works the other way round: the smallest resistor takes the biggest share.