The capacitance of a capacitor is proportional to which factors?

• A. Distance between plates and inversely proportional to the plate area.
• B. Plate area and is not affected by the distance between the plates.
• C. Plate area and inversely proportional to the distance between the plates.
• D. Distance between the plates and directly proportional to the plate area.

Answer: (C)

Capacitance depends on how much charge the capacitor can hold for a given voltage, which for a parallel-plate arrangement scales with the plate area and with how close the plates are. The relationship is C = ε A / d, where ε is the permittivity of the material between the plates, A is the plate area, and d is the distance between them. Increasing the plate area gives more surface to store charge, so C grows linearly with A. Decreasing the separation distance increases C because the same charge produces a larger voltage drop with a smaller gap, effectively allowing more charge to be stored for the same voltage; that’s why C is inversely proportional to d. So the correct description is that capacitance is proportional to plate area and inversely proportional to the distance between the plates. If a dielectric with higher permittivity is used, capacitance increases in proportion to that permittivity as well.