When the temperature of a wire is increased from 303 K to 356 K , the resistance of the wire increases by $10 \%$. The temperature coefficient of resistance of the material of the wire is

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 uniform conducting wire $A B$ of length 5 m and resistance $5 \Omega$ is connected as shown in the circuit. If the balancing point is obtained at 3 m from $A$, then the value of $E$ is

In the given circuit, the equivalent resistance between $A$ and $B$ is