Final answer:
An impedance counter, specifically the Coulter counter, is the instrument used to count particles based on their size by measuring changes in electrical resistance.
Step-by-step explanation:
The instrument that counts particles based on their size is the impedance counter, also known as the Coulter counter. This device counts cells by measuring the change in electrical resistance in an electrolyte solution when a cell passes through a small aperture. The resistance change is detected by an electronic sensor, giving a count of the particles based on their size. This method is important in fields such as materials science, nanotechnology, biomedical research, and laboratory diagnostics.