Q. You have a parallel plate capacitor, a spherical capacitor and a cylindrical capacitor. Each capacitor is charged by and then removed from the same battery. Consider the following situations

(i) the separation between the plates of the parallel plate capacitor is reduced

(ii) the radius of the outer spherical shell of the spherical capacitor is increased

(iii) the radius of the outer cylinder of the cylindrical capacitor is increased

Which of the following is correct?

 1662  193 NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance Report Error

Solution:

Each capacitor is charged and then removed from the battery. Changing the plate separation in a parallel plate capacitor or the radius of any shell or cylinder in the spherical or the cylindrical capacitors will not change the charge on any capacitor. Each capacitor, in the disconnected state, is an isolated system.
In situation (i), since , capacity will increase as is reduced. Therefore, decreases, being the same.
In situation (ii),
and are the radii of the inner and the outer spherical shells, respectively.
As is increased, capacity will reduce and
increases, being the same.
In situation (iii),
is the length of cylinders; and are the radii of inner and outer cylinders, respectively.
As is increased, capacity will decrease and increases, being the same