$A$ Wheatstone bridge is initially at room temperature and all arms of the bridge have the same value of resistance $(R_1=R_2=R_3=R_4=R)$. When $R_3$ is heated to some temperature,its resistance value increases by $10 \%$. The potential difference $(V_a - V_b)$ (after $R_3$ is heated) is . . . . . . $V$. Given the total voltage is $40 \text{ V}$.

To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor,an electrical arrangement shown in the figure is prepared. The arm $BC$ is made up of the semiconductor. The experiment is being conducted at $25^{\circ} C$ and the resistance of the semiconductor arm $BC$ is $3 \ m\Omega$. Arm $BC$ is cooled at a constant rate of $2^{\circ} C / s$. If the galvanometer $G$ shows no deflection after $10 \ s$,then $\alpha$ is:

The current drawn from the battery in the given network is (Internal resistance of battery is neglected) (in $A$)

Five resistors of given values are connected together as shown in the figure. The current in the arm $BD$ will be

The value of current $I$ in the given current distribution is (in $A$)

In the given circuit,the galvanometer shows zero deflection. What is the value of $R$ in $\Omega$?