Question

The capacitance of a capacitor does not depend on
A. The shape of the plates
B. The size of the plates
C. The charges on the plates
D. The separation between the plates
E. None of the above

Answer 1

Hint:A capacitor is charged by connecting it across a cell or a battery. One plate acquires charge \[ + q\]and the other plate acquires the charge \[ - q\]. The potential difference between the plates is as \[V\]. Then, the capacitance of the capacitor is given by the charge on the plates divided by the potential difference between the plates.

Formula Used:
The capacitance \[C\] is given by: \[C = \dfrac{q}{V}\]
where, \[q\] is the charge=\[V\]is the potential across the capacitor
The capacitance of a parallel plate capacitor is given by: \[C = \dfrac{{k{\varepsilon _0}A}}{d}\]
where, \[A\] is the area of two plates, \[d\] is the distance between two plates and \[{\varepsilon _0}\] is the dielectric constant.

Complete step by step answer:
Capacitor is a device that stores electrical energy. Commonly, it is a form of arrangement of two conductors carrying charges of equal magnitude but opposite signs separated by an insulating medium. The capacitance of the conductor depends on the size and shape of the plates. The ratio of a charge \[q\] and potential \[V\] of a conductor is called capacitance. It is denoted by \[C\].
\[C = \dfrac{q}{V}\]
Therefore, the capacitance also depends on the charges between the plates.
Suppose a parallel plate capacitor consists of two plates of area \[A\], separated by a distance \[d\], having a dielectric slab of same thickness and area. Then, the capacitance of the capacitor is given by
\[C = \dfrac{{k{\varepsilon _0}A}}{d}\]
where, \[{\varepsilon _0}\] is the dielectric constant
Therefore, the capacitance also depends on the separation between the plates.Thus, the capacitance depends upon all the options (A), (B), (C) and (D).

Hence, option E is the correct answer.

Note: Different capacitors have different shapes for the plates. There are parallel plate capacitors, spherical capacitors and cylindrical capacitors. Sometimes, the size of the plates depends on the type of capacitor. For example in parallel plate capacitors, two plates of the same area are separated by a small distance and are parallel to each other. The capacitance of a capacitor also depends upon the medium surrounding it and other conductors in the surrounding.