In the adjoining figure,four capacitors are shown with their respective capacities and the $P.D.$ applied. The charge and the $P.D.$ across the $4\,\mu F$ capacitor will be

The given circuit shows two capacitors connected to a battery. After the capacitors are completely charged,the battery is removed and the capacitors are connected with plates of opposite polarity together. Then the charge on $2C$ and the energy lost in the process are respectively

Two neutral conducting spheres of diameters $8 \ cm$ and $2 \ cm$ separated with a distance of $15 \ cm$ between their centres are joined by a thin conducting wire. $A$ charge of $100 \ nC$ is given to one of the spheres and the system is allowed to reach electrostatic equilibrium. The electric potential at a point on the line joining the centres of the two spheres where the net electric field becomes zero is . . . . . . $V$. (Neglect the charge acquired by the wire and $\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \ Nm^2 C^{-2}$)

$A$ circuit shown in the figure consists of a battery of $emf$ $10\,V$ and two capacitors $C_1$ and $C_2$ of capacitances $1.0\,\mu F$ and $2.0\,\mu F$ respectively. The potential difference $V_A - V_B$ is $5\,V$. Which of the following statements is correct?

$A$ composite parallel plate capacitor is made up of two different dielectric materials with different thicknesses ($t_{1} = 0.5 \text{ mm}$ and $t_{2} = 1 \text{ mm}$) and dielectric constants ($\epsilon_{r1} = 3$ and $\epsilon_{r2} = 4$) as shown in the figure. The two dielectric materials are separated by a conducting foil $F$. The voltage of the conducting foil is $.....V$.

$1000$ small drops,each of radius $r$ and charge $q$,coalesce to form a single large drop. How many times greater is the potential of the large drop compared to the potential of a small drop?