The current between $B$ and $D$ in the given figure is .............. $A$.

Two resistances $R_1 = X \Omega$ and $R_2 = 1 \Omega$ are connected to a wire $AB$ of uniform resistivity,as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \text{ mm}$ at $A$ to $1 \text{ mm}$ at $B$. $A$ galvanometer $(G)$ connected to the center of the wire,$50 \text{ cm}$ from each end along its axis,shows zero deflection when $A$ and $B$ are connected to a battery. The value of $X$ is:

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:

Kirchhoff's first law $(\sum i = 0)$ and second law $(\sum iR = \sum E)$,where the symbols have their usual meanings,are respectively based on:

In the circuit diagram shown below,the magnitude and direction of the flow of current respectively would be

In the following electrical network,the value of $I$ is (in $A$)