An electric field is given by, $E_{\mathrm{x}}=-2x^3 \mathrm{kN} {\mathrm{C}}^{-1}$. The potential of the point $\left(1,-2\right)$, if the potential of the point $\left(2, 4\right)$ is taken as zero is,

A network of resistances, cell and capacitor $C (=2 \mathrm{\mu F})$ is shown in adjoining figure. In steady state condition, the charge on $2 \mathrm{\mu F}$ capacitor is $Q$ while $R$ is unknown resistance. Values of $Q$ and $R$ are, respectively,

Two parallel plate capacitors of capacitances $C$ and $2C$ are connected in parallel and charged to a potential difference $V.$ The battery is then disconnected and the region between the plates of the capacitor $C$ is completely filled with a material of dielectric constant $K\mathit{.}$ The potential difference across the capacitors now becomes -

Find equivalent capacitance between $X$ and $Y$ if each capacitor is $4 \mathrm{\mu F}$.