$A$ capacitor of $2\,\mu F$ capacitance is charged steadily from $0$ to $5\,C$. Which of the following graphs correctly represents the variation of potential difference across its plates with respect to the charge on the capacitor?

In the given figure,three capacitors $C_1, C_2$ and $C_3$ are connected to a battery. With symbols having their usual meanings,the correct conditions are:

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

In the given circuit,if the potential difference between $A$ and $B$ is $80 \ V$,then the equivalent capacitance between $A$ and $B$,and the charge on $10 \ \mu F$ capacitor respectively,are

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 = . . . . $

Two conducting shells of radius $a$ and $b$ are connected by a conducting wire as shown in the figure. The larger shell is grounded. The capacitance of the system is: