The resultant capacitance between $A$ and $B$ in the figure is ...... $\mu F$.

$A$ capacitor of $50 \,\mu {F}$ is connected in a circuit as shown in the figure. The charge on the upper plate of the capacitor is $......\,\mu {C} .$

Three uncharged capacitors of capacitance $C_1$,$C_2$ and $C_3$ are connected as shown in the figure to one another and to points $A$,$B$ and $D$ at potentials $V_A$,$V_B$ and $V_D$. Then the potential at point $O$ will be

$A$ conducting sphere $A$ of radius $a$,with charge $Q$,is placed concentrically inside a conducting shell $B$ of radius $b$. $B$ is earthed. $C$ is the common centre of the $A$ and $B$.

Four capacitors with capacitances $C_1 = 1\,\mu F, C_2 = 1.5\,\mu F, C_3 = 2.5\,\mu F$ and $C_4 = 0.5\,\mu F$ are connected as shown and are connected to a $30\,V$ source. The potential difference between points $a$ and $b$ is.....$V$.

The potential difference that must be applied across the series and parallel combination of $4$ identical capacitors is such that the energy stored in them becomes the same. The ratio of potential difference in series to parallel combination is