In: Physics
If one were to use a different battery, would the capacitance of a capacitor change?
In particular, "while connected to a battery" may imply fixed voltage source. Changing charge on existing plates is in fact what happens in capacitors during charging and discharging cycles. With a fully charged capacitor with applied DC voltage, no more current will flow. This means the charge accumulated in the capacitor is now fixed. To change that you change one of the following: (1) voltage, (2) capacitance via changing physical dimensions or insertion of different dielectric material or varying the dielectric material in the capacitor.

