A parallel plate capacitor having cross-sectional area 'A' and separated by distance 'd' is filled by copper plate of thickness b. It's capacitance is :

Concept:

The capacitance of a parallel plate capacitor is given by the formula:

C = εA/d

where

C is the capacitance,

ε is the permittivity of the medium between the plates,

A is the area of each plate, and d is the distance between the plates.

Calculation:

When a copper plate of thickness b is placed between the plates of the capacitor, the distance between the plates effectively reduces to d' = d - b, where b is the thickness of the copper plate. The permittivity of copper is very close to that of vacuum, so we can assume that the permittivity between the plates remains the same.

Therefore, the new capacitance of the capacitor is given by:

C' = εA/d'

C' = εA/(d - b)

C' = \(\frac{\varepsilon_0 A}{d-b}\)

The correct answer is option (2)