Resistors in series

Series resistances add directly. Four 1 kΩ resistors on 9 V total 4 kΩ and pass 2.25 mA, with each resistor dropping 2.25 V. The voltage across any one resistor is its share of the total resistance.

The practical use of a long series chain is a voltage ladder — a string of equal resistors tapped at each junction to produce evenly spaced references, which is exactly how a flash ADC or a simple resistor DAC works. Tolerance behaves better here than intuition suggests: random errors in a long chain partly cancel, so a ten-resistor ladder of 5% parts has a total closer than 5% off, even though any individual tap could still be out by the full amount.