Three resistors of resistances $10 \Omega, 20 \Omega$ and $30 \Omega$ are connected as shown in the figure. If the points $A, B$ and $C$ are at potentials $10 \mathrm{~V}, 6 \mathrm{~V}$ and 5 V respectively, then the ratio of the magnitudes of the currents through $10 \Omega$ and $30 \Omega$ resistors is

A potentiometer balances at 44 cm when a cell of internal resistance $1 \Omega$ is in the secondary circuit. To obtains the balancing point at 40 cm , the resistance to be connected parallel to cell is

Two wires made of the same material have lengths in the ratio $2: 3$ and radii in the ratio $8: 9$. If the same potential difference is applied across the ends of the wires, the ratio of the electric currents flowing through them is