Final answer:
To have the same effect as a capillary tube with a smaller diameter, a capillary tube with a larger diameter must be longer because capillary action depends on the tube's radius. A smaller-radius tube will have stronger cohesive and adhesive forces, allowing the fluid to rise higher.
Step-by-step explanation:
When a capillary tube has a larger diameter, the length of the capillary tube must be A) Longer to have the same effect as one with a smaller diameter. The principle behind this is the capillary action which depends on the radius of the tube. According to capillary action, the smaller the tube, the greater the height the fluid will rise due to the cohesive and adhesive forces between the liquid and the tube's surface being relatively stronger compared to the gravitational force. Conversely, if the capillary tube has a larger diameter, the cohesive and adhesive forces become comparatively weaker, making the rise of fluid less for the same height. Therefore, to achieve the same effect in a larger-diameter capillary as a smaller one, the tube must be longer to increase the effect of these forces over a greater surface area, thus allowing the fluid to reach an equivalent height.
The concept also relates to the fact that in vessels, such as blood vessels, the length of a vessel is directly proportional to its resistance: the longer the vessel, the greater the resistance and the lower the flow. In this way, the flow of fluid in a capillary tube is analogous to the flow of blood in blood vessels, both being impacted by tube and vessel diameter, length, and the resulting fluid dynamics.