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.

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