The terminals of a battery of emf $3 \mathrm{V}$ and internal resistance $2.5 \mathrm{\Omega }$ are joined to the diagonally opposite corners of a cubical skeleton frame of $12$ wires, each of resistance $3 \mathrm{\Omega }$. Find the current in the battery.

Find the currents $I_1$, $I_2$ and $I_3$ through the three resistors of the circuit shown in Fig. 3.191.

Two cells of emfs ${\xi }_1$ and ${\xi }_2$ are connected together in two ways shown here. The balance points in a

given potentiometer experiment for these two combinations of cells are found to be at $351.0 \mathrm{cm}$ and $70.2 \mathrm{cm}$ respectively. Calculate the ratio of the emfs of the two cells.