So, there is something regarding capacitors which is bothering me. It is said that in capacitors connected in parallel, the charge is divided between different capacitors, while potential difference across them remains the same. But we also studied that:
$$V = \frac{kq}{r},$$
which means $V$ is proportional to $q$. So if $q$ across a capacitor changes, then why does potential difference remain the same? And the same logic for capacitors is series.
The equation which you quote is for a point charge whereas the charge stored by a capacitor is spread over the plates of the capacitor.
For a capacitor the charge stored on it is proportional to the voltage across the plates.
For capacitors in parallel the charge stored is redistributed so that the voltage across the each of the capacitors stays the same.
All other things being equal, separation of plates, dielectric etc, a capacitor with four times the area can, for a given voltage, store four times the charge. But now think of the it being five capacitors of equal area all in parallel then perhaps you will understand why a capacitor can store more charge and yet have the same voltage across it.
