When an electric heater is switched on, the current flowing through it $(I)$ is plotted against time $(t)$. Taking into account the variation of resistance with temperature, which of the following best represents the resulting curve?

$A$ cell of emf $E$ is connected to a resistance $R_{1}$ for time $t$ and the amount of heat generated in it is $H$. If the resistance $R_{1}$ is replaced by another resistance $R_{2}$ and is connected to the cell for the same time $t$, the amount of heat generated in $R_{2}$ is $4H$. Then the internal resistance $r$ of the cell is:

Four equal resistances dissipate $5 \, W$ of power together when connected in series to a battery of negligible internal resistance. The total power dissipated in these resistances when connected in parallel across the same battery would be ........... $W$.

Column-$I$ gives certain physical quantities associated with the flow of current through a metallic conductor. Column-$II$ gives some mathematical relations involving electrical quantities. Match Column-$I$ and Column-$II$ with appropriate relations.

$A$. Mobility	$P$. $\frac{m}{ne^2 \rho}$
$B$. Electrical conductivity	$Q$. $neAv_{d}$
$C$. Relaxation period	$R$. $\frac{v_{d}}{E}$
$D$. Current	$S$. $\frac{J}{E}$

The figure shows a network of five resistances and two batteries. The total electrical power consumed by the circuit is ............... $W$.

For what value of the resistor $X$ will the equivalent resistance of the two circuits shown be the same?