A resistor circuit is constructed such that $12$ resistors are arranged to form a cube as shown in figure. Each resistor has a resistance of $2\mathrm{\Omega }$. The potential difference of $30\mathrm{}\mathrm{V}$ is applied across two of the opposing points as shown.

The points having the same potential are
(i) $\mathrm{B},\mathrm{D},\mathrm{}\mathrm{E}$ (ii) $\mathrm{C},\mathrm{}\mathrm{F},\mathrm{}\mathrm{H}$ (iii) $\mathrm{C},\mathrm{}\mathrm{E}$

In the given arrangement of resistances, find the equivalent resistance (in $\mathrm{\Omega }$) between points $A$ and $B$ in the figure. Each resistance $R$, in magnitude, is equal to $10 \mathrm{\Omega }$.

In the given network in the figure, find the charge on the capacitor (in $\mathrm{\mu C}$)

If the switches $S_1,S_2$, and $S_3$ in the figure are arranged such that the current through the battery is minimum, find the voltage across points $A$ and $B$ (in $\mathrm{V}$).