Capacitance of an isolated conducting sphere of radius R₁ becomes n times when it is enclosed by a concentric conducting sphere of radius R₂ connected to earth. The ratio of their radii $$\left( {{{{R_2}} \over {{R_1}}}} \right)$$ is :

A condenser of $$2 \,\mu \mathrm{F}$$ capacitance is charged steadily from 0 to $$5 \,\mathrm{C}$$. Which of the following graph represents correctly the variation of potential difference $$(\mathrm{V})$$ across it's plates with respect to the charge $$(Q)$$ on the condenser?

C_o is the capacitance of a parallel plate capacitor with air as a medium between the plates (as shown in Fig. 1). If half space between the plates is filled with a dielectric of relative permittivity $$\varepsilon $$_r (as shown in Fig. 2), the new capacitance of the capacitor will be :

A capacitor is discharging through a resistor R. Consider in time t₁, the energy stored in the capacitor reduces to half of its initial value and in time t₂, the charge stored reduces to one eighth of its initial value. The ratio t₁/t₂ will be