An ideal air-filled parallel-plate capacitor has round plates and carries a fixed amount of equal but opposite charge on its plates.All the geometric parameters of the capacitor (plate diameter and plate separation)are now DOUBLED.If the original capacitance was C₀,what is the new capacitance? A) 4C₀ B) 2C₀ C) C₀ D) C₀/2 E) C₀/4

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Quizplus · Accepted Answer

The capacitance of a parallel-plate capacitor can be expressed as C = εA/d, where ε is the permittivity of the material between the plates, A is the area of one plate, and d is the distance between the plates. Doubling the diameter of the plates doubles the area (since area is proportional to the square of the diameter), and doubling the separation doubles the distance between the plates. Therefore, the new capacitance is (ε)(2A)/(2d) = (εA/d) = C. In other words, the capacitance remains the same when the geometric parameters are doubled, so the answer is B.

An Ideal Air-Filled Parallel-Plate Capacitor Has Round Plates and Carries