For the given circuit,find the charge on the $4\ \mu F$ capacitor in $\mu C$.

Two metal spheres,one of radius $R$ and the other of radius $2R$,both have the same surface charge density $\sigma$. They are brought in contact and then separated. What will be the new surface charge densities on them?

In the circuit shown,$q_2$ and $q_3$ are respectively (Initially all capacitors are uncharged).

$A$ 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 $(\epsilon_{0} = \text{permittivity of free space})$

The capacitance of a parallel plate capacitor is $C$ when the region between the plates contains air. This region is now filled with a dielectric slab of dielectric constant $k$. The capacitor is connected to a cell of $emf$ $E$,and the slab is then removed. Which of the following statements is correct?

In the circuit shown below, $C_1 = 10 \, \mu F$, $C_2 = C_3 = 20 \, \mu F$, and $C_4 = 40 \, \mu F$. If the charge on $C_1$ is $20 \, \mu C$, then the potential difference between $X$ and $Y$ is ......... $V$.