What does capacitance depend on according to the formula provided?

Capacitance, denoted by the symbol C, is defined by the relationship between the charge stored (Q) on a capacitor and the potential difference (V) across it, expressed as C = Q/V.

The capacitance of a parallel plate capacitor can be specifically expressed with the formula:

[ C = \frac{\varepsilon_0 \cdot A}{d} ]

In this formula, ( \varepsilon_0 ) represents the permittivity of free space, A is the surface area of one of the plates, and d is the distance between the two plates. From this equation, it's clear that capacitance is directly proportional to the area of the plates – larger plates can store more charge – and inversely proportional to the distance between them – as the gap increases, the ability to store charge effectively decreases.

This means that capacitance increases with a larger area of the plates and decreases as the distance between them increases. Thus, the correct understanding of capacitance hinges on these physical characteristics directly defined in the formula, confirming that it depends on both the area of the plates and the distance between the plates.