If $27$ identical charged conducting spheres each of capacitance $10 \mu F$ combine to form a big sphere,then the capacitance of the big sphere is: (in $\mu F$)

The capacitance $(C)$ of an isolated conducting sphere of radius $(a)$ is given by $4\pi \varepsilon_0 a$. If this sphere is enclosed by an earthed concentric sphere of radius $(b)$,and the ratio of the radii of the spheres is $\frac{b}{a} = n$,then the capacitance of such a system will be increased by a factor of:

$A$ cylindrical capacitor has inner and outer conductors whose radii are in the ratio $10:1$. The inner conductor is replaced by a wire whose radius is half of the original inner conductor. To obtain the same capacitance as the original capacitor,by what ratio should the length of the wire be increased?

The Earth is assumed to be a charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the Earth in free space is ($\epsilon_{0} =$ permittivity of free space).

Four capacitors,each of $25\,\mu F$,are connected as shown in the figure. The $dc$ voltmeter reads $200\,V$. The charge on each plate of the capacitor is

When a $0.75 \mu F$ capacitor is charged to a voltage of $20 \ V$,then the magnitude of charge on each plate is (in $\mu C$)