Question

how is the capacitance related to the distance between the plates of a capacitor

Answer 1

Last choice:  It's inversely proportional.  So if you move the plates farther apart, the capacitance decreases.

Answer 2

Answer:

It is inversely proportional, so the capacitance increases as the distance decreases.

Explanation:

The capacitance of a parallel-plate capacitor is given by:

$C=\epsilon_0 \frac{A}{d}$

where

$\epsilon_0$ is the vacuum permittivity

A is the area of the plate of the capacitor

d is the distance between the plates

In the formula, we see that the distance (d) is at the denominator: this means that as the distance decreases, the capacitance (C) increases. Therefore, it is an inverse proportionality.