Question

What quantity changes among charge stored, voltage involved, and capacitance in the following?

`a)` Doubling the charge
`b)` Tripling the voltage

Answer 1

Capacitance is a characteristic of a capacitor which relates how much charge it stores at a specific voltage. It does not change in either case.

Explanation:

Considering that Capacitance `C` is:

`C = q/V`

a)
If `q->2q`
then `[V = q/C] -> (2q)/C`
`:. color(blue)(V -> 2V)`

b)
If `V->3V`
then `[q=C*V] -> C*3V`
`:. color(blue)(q -> 3q)`

In THIS equation, `C` is a constant. Capacitance is specific to a particular capacitor. Mathematically one might think that a change in `q` would cause a change in `C`. However, adding more charge to a capacitor increases the voltage, `V`.

For a simple parallel plate capacitor, the capacitance (`C`) is proportional to the area (`A`) of the capacitor and inversely proportional to the distance (`d`) between the plates.

`C = epsilon_0*A/d`

Here `epsilon_0` is the permittivity of free space, a fundamental constant of nature. Changing `q` or `V` will not change the size of the capacitor, the distance between the plates, or the universe itself.