The resistance of a wire is $10^{-6} \, \Omega$ per meter. It is bent in the form of a circle of diameter $2 \, m$. A wire of the same material is connected across its diameter. The total resistance across its diameter $AB$ will be

Match the List-$I$ with the List-$II$ from the combination shown. In the left side (List-$I$) there are four different conditions and in the right side (List-$II$), there are ratios of heat produced in each resistance for each condition:

List-$I$	List-$II$
$(I)$ Two wires of same resistance are connected in series and same current is passed through them	$(A)$ $1:2$
$(II)$ Two wires of resistance $R$ and $2R$ $\Omega$ are connected in series and same $P.D.$ is applied across them	$(B)$ $4:1$
$(III)$ Two wires of same resistance are connected in parallel and same current is flowing through them	$(C)$ $1:1$
$(IV)$ Two wires of resistances in the ratio $1:2$ are connected in parallel and same $P.D.$ is applied across them	$(D)$ $2:1$

$A$ battery of $emf$ $E$ and internal resistance $r$ is connected across a resistance $R$. Resistance $R$ can be adjusted to any value greater than or equal to zero. $A$ graph is plotted between the current $(i)$ passing through the resistance and potential difference $(V)$ across it. Select the correct alternative$(s)$.

In the circuit shown in the figure,the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition,a current of $1 \,A$ flows through the $1 \,\Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1}=0.36$]
$(A)$ The value of the resistance $R$ is $3 \,\Omega$.
$(B)$ The current through the $3 \,\Omega$ resistor (connected in parallel to the $1 \,\Omega$ and $R$ branches) is $2 \,A$ when $K$ is open.
$(C)$ At $t=t_0+7.2 \,\mu s$,the current in the capacitor branch is $0.6 \,A$.
$(D)$ For $t < \infty$,the charge on the capacitor is $12 \,\mu C$.

The Thomson coefficient of a conductor is $10 \mu V/K$. The two ends of the conductor are kept at $50^{\circ} C$ and $60^{\circ} C$, respectively. The amount of heat absorbed by the conductor when a charge of $10 C$ flows through it is:

In the figure shown below,a resistance of $150.4\ \Omega$ is connected in series to an ammeter $A$ of resistance $240\ \Omega$. $A$ shunt resistance of $10\ \Omega$ is connected in parallel with the ammeter. The reading of the ammeter is $...\ mA$.