The potential difference that must be applied across the series and parallel combination of $4$ identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is

$A$ metal sphere of radius $1 \ m$ is charged with $10^{-2} \ C$ in air. Its bulk modulus is $10^{11} / 4 \pi^{2} \ N/m^2$. The volume strain in the sphere is $(\epsilon_{0} = \text{permittivity of free space})$

As shown in the figure,what will be the charge on each capacitor and the potential difference across each,respectively?

In the given figure,three capacitors $C_1, C_2$ and $C_3$ are connected to a battery. With symbols having their usual meanings,the correct conditions are:

Two capacitors of capacitance $C$ and $2C$ are connected in parallel and charged to a potential difference $V$. The battery is then disconnected,and the space between the plates of the capacitors is completely filled with a dielectric material of constant $K$. Determine the new potential difference across the capacitors.

In the circuit shown in the following figure,the potential difference across the $3 \mu F$ capacitor is: (in $V$)