If identical small spherical droplets of mercury, each of radius and capacitance , coalesce to form a single large spherical drop, what is the capacitance of the combined drop?
Answer and explanation
Correct answer: A.
- Step 1: The total volume of mercury is conserved upon coalescence: .
- Step 2: The capacitance of a spherical drop is directly proportional to its radius: .
- Step 3: Therefore, the new capacitance is .
Answer
.
Why not the others: would be true for capacitors in parallel, not geometric coalescence; is the scaling factor for surface energy or potential; inverts the scaling.
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