Two parallel plate capacitors of capacity $C$ and $3C$ are connected in parallel combination and charged to a potential difference $18 \mathrm{V}$. The battery is then disconnected and the space between the plates of the capacitor of capacity $C$ is completely filled with a material of dielectric constant $9$. The final potential difference across the combination of capacitors will be _____ $\mathrm{V}$.

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness ($t_1$ and $t_2$) as shown in figure. The two different dielectric material are separated by a conducting foil $F$. The voltage of the conducting foil is _____ $\mathrm{V}$.

​​​​​​​

A source of potential difference $V$ is connected to the combination of two identical capacitors as shown in the figure. When key $K$ is closed, the total energy stored across the combination is $E_1$. Now key $K$ is opened and dielectric of dielectric constant $5$ is introduced between the plates of the capacitors. The total energy stored across the combination is now $E_2$. The ratio $\frac{E_1}{E_2}$ will be

A $1 \mathrm{m}$ long copper wire carries a current of $1 \mathrm{A}$. If the cross section of the wire is $2.0{ \mathrm{mm}}^2$ and the resistivity of copper is $1.7\times {10}^{-8} \mathrm{\Omega } \mathrm{m}$. The force experienced by moving electron in the wire is _____$\times {10}^{-23} \mathrm{N}$

(Charge of electron$=1.6\times {10}^{-19}\mathrm{C}$ )

A long cylindrical volume contains a uniformly distributed charge of density $\rho \mathrm{C} {\mathrm{m}}^{-3}$. The electric field inside the cylindrical volume at a distance $x=\frac{2{\epsilon }_0}{\rho } \mathrm{m}$ from its axis is _____ $\mathrm{V} {\mathrm{m}}^{-1}$.