Final answer:
The potential of a larger drop formed by combining twenty-seven identical smaller drops, each charged to 220V, is approximately 73.33V, calculated using the principle of capacitance and the conservation of charge.
Step-by-step explanation:
The potential of a large drop formed by combining twenty-seven smaller identical drops, each charged to 220V, can be calculated using the conservation of charge and the principle of capacitance. The capacitance of a sphere is proportional to its radius, and the charge on the sphere is the product of its potential and capacitance. Since all the smaller drops have the same potential, their combined charge is simply the sum of their individual charges. Assuming the volume of the larger drop is the sum of the volumes of the smaller drops and that they are all formed of the same material, the radius of the larger drop will be three times the radius of each smaller drop (because the volume scales with the cube of the radius), hence the capacitance of the larger drop will be three times that of one of the smaller drops.
When combined, the total charge remains unchanged, but because capacitance is now three times larger, the potential of the larger drop (V) is one-third of the potential of the smaller drops (V/3). Since the potential of each small drop is 220V, the potential of the larger drop would thus be 220V / 3, which is approximately 73.33V.
This is an application of the principles of electrostatics, specifically relating to charge, potential, and capacitance. It provides insight into how the electrical properties of a conductor change with its size, demonstrating an understanding of the conservation of energy and the relationship between charge and potential.