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 is given by C = εA/d, where ε is the permittivity of the medium between the plates, A is the area of the plates, and d is the separation between the plates. When all the geometric parameters are doubled, the area of the plates becomes 4 times larger (π(D/2)^2→π((2D)/2)^2=πD^2), and the separation between the plates is doubled, resulting in halving of the denominator in the formula. Therefore, the new capacitance becomes C' = ε(4A)/(2d) = 2(εA/d) = 2C. Thus, the new capacitance is 2 times larger than the original capacitance, which is option B (2C₀).

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