Physics - Capacitor Question with Solution | TestHub

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$\mathrm{C}=\frac{{\mathrm{\epsilon }}_0\mathrm{A}}{\mathrm{d}}$, capacity will increase as$\mathrm{d}$is reduced. Therefore,$\mathrm{V}=\frac{\mathrm{Q}}{\mathrm{C}}\mathrm{ }$decreases,$\mathrm{Q}$being the same.

In situation (ii),$\mathrm{C}=4\mathrm{\pi }{\mathrm{ϵ}}_0\frac{\mathrm{a}\mathrm{b}}{\mathrm{b}-\mathrm{a}}=4\mathrm{\pi }{\mathrm{ϵ}}_0\frac{\mathrm{a}}{1-\mathrm{a}/\mathrm{b}}$

$\mathrm{a}$and$\mathrm{b}$are the radii of the inner and the outer spherical shells, respectively.

As$\mathrm{b}$is increased, capacity will reduce and

$\mathrm{V}=\frac{\mathrm{Q}}{\mathrm{C}}$increases,$\mathrm{Q}$being the same.

In situation (iii),$\mathrm{C}=2\mathrm{\pi }{\mathrm{\epsilon }}_0\frac{\mathrm{L}}{\ln \left({\displaystyle \frac{\mathrm{b}}{\mathrm{a}}}\right)}$

$\mathrm{L}$is the length of cylinders;$\mathrm{a}$and$\mathrm{b}$are the radii of inner and outer cylinders, respectively.

As$\mathrm{b}$is increased, capacity will decrease and$\mathrm{V}=\frac{\mathrm{Q}}{\mathrm{C}}$increases,$\mathrm{Q}$being the same