If the space between capacitor plates is doubled, how will the capacity change?

When the space between the plates of a capacitor is doubled, the capacitance actually decreases. The capacitance (C) of a parallel plate capacitor is given by the formula:

[ C = \frac{{\varepsilon \cdot A}}{d} ]

where ( \varepsilon ) is the permittivity of the dielectric material between the plates, ( A ) is the area of the plates, and ( d ) is the distance between the plates.

In this formula, if the distance ( d ) is increased (doubled), while everything else remains constant, it directly affects the capacitance inversely. Therefore, when ( d ) increases, the capacity ( C ) will decrease proportionally. Specifically, if ( d ) is doubled, the new capacitance becomes:

[ C' = \frac{{\varepsilon \cdot A}}{2d} ]

This illustrates that capacitance decreases since the factor of ( d ) in the denominator increases. Hence, if the distance is doubled, the capacitance decreases to half its original value, which aligns precisely with the concept of capacitance being inversely proportional to the distance between the plates. Thus, the correct answer