Two identical charged particles each having a mass $10 \mathrm{g}$ and charge $2.0\times {10}^{-7}\mathrm{C}$ are placed on a horizontal table with a separation of $L$ between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is $0.25$, find the value of $L$. [Use $\mathrm{g}=10{ \mathrm{m} \mathrm{s}}^{-2}$ ]

The equivalent capacitance between points $A$ and $B$ in below shown figure will be _____ $\mu \mathrm{F}$.

The charge on capacitor of capacitance $15\mu \mathrm{F}$ in the figure given below is

A parallel plate capacitor with plate area $A$ and plate separation $d=2 \mathrm{m}$ has a capacitance of $4 \mathrm{\mu F}$. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant $K=3$ (as shown in figure) will be

Two capacitors having capacitance $C_1$ and $C_2$ respectively are connected as shown in figure. Initially, capacitor $C_1$ is charged to a potential difference $V$ volt by a battery. The battery is then removed and the charged capacitor $C_1$ is now connected to uncharged capacitor $C_2$ by closing the switch $S$. The amount of charge on the capacitor $C_2$, after equilibrium, is