What happens to the capacitance of a capacitor as the surface area of its plates increases?

The capacitance of a capacitor is directly related to the surface area of its plates. As the surface area increases, the capacitance also increases. This relationship can be mathematically expressed by the formula for capacitance, which is given by:

C = ε(A/d)

where C represents capacitance, ε is the permittivity of the dielectric material between the plates, A is the surface area of the plates, and d is the distance between the plates. According to this formula, if the surface area (A) increases while the distance (d) and the permittivity (ε) remain constant, the overall capacitance (C) will increase. This is because a larger surface area allows for more charge to be stored on the plates.

In contrast, other options do not accurately describe the relationship between plate surface area and capacitance. For example, stating that capacitance decreases or remains the same would not reflect the fundamental principles of how capacitors function in electric circuits. Additionally, describing capacitance as variable does not align with the predictable nature governed by the capacitor's design and materials. Thus, the correct answer clearly illustrates an essential characteristic of capacitors in electronic components.