In the given figure,the charge stored in $6 \ \mu F$ capacitor,when points $A$ and $B$ are joined by a connecting wire is . . . . . . $\mu C$.

$A$ metallic sheet is inserted between the plates of a parallel plate capacitor. The capacitance of the capacitor

Three identical capacitors $C_1, C_2$ and $C_3$ have a capacitance of $1.0 \mu F$ each and they are uncharged initially. They are connected in a circuit as shown in the figure and $C_1$ is then filled completely with a dielectric material of relative permittivity $\varepsilon_r$. The cell electromotive force (emf) $V_0 = 8 \ V$. First,the switch $S_1$ is closed while the switch $S_2$ is kept open. When the capacitor $C_3$ is fully charged,$S_1$ is opened and $S_2$ is closed simultaneously. When all the capacitors reach equilibrium,the charge on $C_3$ is found to be $5 \mu C$. The value of $\varepsilon_r = . . . . $

$A$ spherical shell of radius $6 \ cm$ is placed concentrically with a sphere of radius $4 \ cm$. The outer spherical shell is grounded. If the potential of the inner sphere is $3 \ e.s.u.$,what is the charge on it in $e.s.u.$?

The potential difference between the points $P$ and $Q$ in the adjoining circuit will be :-

Four capacitors of capacitance $10\, \mu F$ and a battery of $200\, V$ are arranged as shown. How much charge will flow through $AB$ after the switch $S$ is closed?