Capacitance is the ability of a system to store electrical charge. It is measured in units of farads (F) and represents the ratio of the electrical charge stored on a capacitor to the potential difference (voltage) across the capacitor.
A parallel plate condenser consists of two parallel conducting plates separated by a dielectric material. When a potential difference is applied between the plates, an electric field is created and charges accumulate on the plates. The amount of charge that can be stored depends on the capacitance of the condenser, which is determined by the distance between the plates and the dielectric material used.
The formula for capacitance in a parallel plate condenser is C = εA/d, where C is the capacitance in farads, ε is the permittivity of the dielectric material, A is the area of the plates in square meters, and d is the distance between the plates in meters.
Adding a battery to a parallel plate condenser does not affect the capacitance. The battery simply provides a potential difference (voltage) that allows for the accumulation of charges on the plates, increasing the energy stored in the system.
Parallel plate condensers have many practical applications, including as components in electronic circuits, in power storage devices such as capacitors, and in measuring instruments such as oscilloscopes and voltmeters. They are also used in the production of x-rays and in various medical imaging techniques.