$A$ spherical capacitor has an outer sphere of radius $5 \text{ cm}$ and an inner sphere of radius $2 \text{ cm}$. When the inner sphere is earthed,its capacity is $C_1$,and when the outer sphere is earthed,its capacity is $C_2$. Then $\frac{C_1}{C_2}$ is

The potentials of the two plates of a capacitor are $+10\,V$ and $-10\,V$. The charge on one of the plates is $40\,C$. The capacitance of the capacitor is........$F$.

$A$ spherical capacitor has an inner sphere of radius $12 \;cm$ and an outer sphere of radius $13 \;cm$. The outer sphere is earthed and the inner sphere is given a charge of $2.5 \;\mu C$. The space between the concentric spheres is filled with a liquid of dielectric constant $32$.
$(a)$ Determine the capacitance of the capacitor.
$(b)$ What is the potential of the inner sphere?
$(c)$ Compare the capacitance of this capacitor with that of an isolated sphere of radius $12 \;cm$. Explain why the latter is much smaller.

$A$ solid conducting sphere of radius $R_1$ is surrounded by a hollow conducting sphere of radius $R_2$. The capacitance of this assembly is proportional to ........

$A$ sphere of $4\, cm$ radius is suspended within a hollow sphere of $6\, cm$ radius. The inner sphere is charged to a potential of $3\, e.s.u.$ and the outer sphere is earthed. The charge on the inner sphere is.....$e.s.u.$

The capacitance of a spherical capacitor is $1 \mu F$. If the spacing between the two spheres is $1 \text{ mm}$,the radius of the outer sphere is