Final answer:
Resistance in cylindrical conductors is affected by length, viscosity, and significantly by the radius. The radius has a profound impact on resistance because it appears to the fourth power in Poiseuille's law. The correct answer is option 1) radius.
Step-by-step explanation:
The question is concerning the factors on which resistance mostly depends. Resistance in a cylindrical conductor is proportional to its length and inversely proportional to the cross-sectional area, which is determined by its radius. According to Poiseuille's law as applied to resistance, the radius has a significant effect because resistance is inversely proportional to the radius raised to the fourth power.
Changes in viscosity and vessel length affect resistance but these changes happen more slowly. The radius, however, can change quickly through vasoconstriction and vasodilation, dramatically impacting resistance and flow. Therefore, out of the options provided, radius has the most immediate and significant impact on resistance.