Two ideal batteries of emf $V_1$ and $V_2$ and three resistances $R_1, R_2$ and $R_3$ are connected as shown in the figure. The current in resistance $R_2$ would be zero if:
$(A)$ $V_1=V_2$ and $R_1=R_2=R_3$
$(B)$ $V_1=V_2$ and $R_1=2R_2=R_3$
$(C)$ $V_1=2V_2$ and $2R_1=2R_2=R_3$
$(D)$ $2V_1=V_2$ and $2R_1=R_2=R_3$

The figure shows a network of currents. The magnitude of currents is shown in the diagram. The current $i$ will be ................. $A$.

The Wheatstone bridge principle is used to measure the specific resistance $(S_1)$ of a given wire,having length $L$ and radius $r$. If $X$ is the resistance of the wire,then the specific resistance is: $S_1 = X \left( \frac{\pi r^2}{L} \right)$. If the length of the wire is doubled,then the value of the specific resistance will be:

The charge accumulated on the capacitor connected in the following circuit is . . . . . . $\mu C$ (Given $C=150\ \mu F$)

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:

In the circuit shown,what is the potential difference $V_{PQ}$?