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

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

1 Answer
Paul N. · Truong-Son N. · Gió
Sep 24, 2015

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.

Related questions
Impact of this question
1857 views around the world
You can reuse this answer
Creative Commons License