Is capacitance dependent or independent of potential? The capacity of a conductor is independent of the charge given or its potential raised.
However, my textbook states:
The principle of a capacitance is based on the fact that capacitance can be increased by reducing potential and keeping the charge constant.
I'm extremely confused as to how capacitance can increased by reducing potential, when it is actually independent of potential. Where am I going wrong?
 A: The capacitance$(C)$ of a capacitor is dependent on only the geometry of the conductor. It is essentially a measure of capacity like how the capacity of a bottle of water is a measure of the volume of water it can store. The capacitance of a conductor is defined as the ratio of magnitude of charge on either conductor to the magnitude of potential difference between its plates $$C = \frac{Q}{\Delta V}$$
You are right in stating that the capacitance is independent of the potential difference between the plates. When you reduce the potential difference between the plates of an isolated capacitor, it is accompanied by a reduction in the charge on each plate such that the ratio $\frac{Q}{\Delta V}$ remains constant. The capacitance is hence unaffected by the reduced potential, which shows that capacitance is independent of the charge and the potential difference.
However in your textbook's statement:

The principle of a capacitance is based on the fact that capacitance can be increased by reducing potential and keeping the charge constant.

Notice the words in bold, The charge on the plates has been forcibly kept constant, while otherwise it would have lost some charge, so quite naturally the capacitor's capacitance is increased.
Hope this helps.
