Final answer:
Resistance is highly dependent on the radius of a vessel, as it has the most immediate and pronounced effect on resistance due to being raised to the fourth power in the resistance equation. Viscosity and length also play roles in determining resistance, but their changes are not as rapid or substantial as changes in radius.
Step-by-step explanation:
Resistance in a material is influenced by various factors, including the material's resistivity, the object's length, and its cross-sectional area (related to its radius). Viscosity also plays a role when considering fluid resistance in tubes. According to Poiseuille's law, the radius of a tube has a significant impact on resistance, especially since any change in the radius has a pronounced effect due to being raised to the fourth power in the formula.
For instance, doubling the radius would decrease resistance by a factor of 16. Viscosity and length of the vessel also affect resistance but do so more gradually compared to the radius, which can alter significantly and rapidly through mechanisms like vasoconstriction and vasodilation in the body.
Therefore, while viscosity and length are important, the radius is the most critical factor that can rapidly affect resistance. The length and viscosity contribute to resistance but change slowly, allowing for the radius to make the most substantial and immediate impact on resistance within the system.