You are given several identical resistances each of value $R = 10\,\Omega$ and each capable of carrying a maximum current of $1\,A$. It is required to make a suitable combination of these resistances to produce a resistance of $5\,\Omega$ which can carry a current of $4\,A$. The minimum number of resistances of the type $R$ that will be required for this job is:

For the mixed connection shown in the figure,derive the equation for the equivalent resistance.

$A$ wire is connected to a battery between the points $M$ and $N$ as shown in figure $(1)$. The same wire is bent in the form of a square and then connected to the battery between the points $M$ and $N$ as shown in figure $(2)$. Which of the following quantities increases?

Consider two circuits, $(A)$ and $(B)$, each having two resistors. One of them has a positive temperature coefficient of resistance, $+\alpha$, while the other one has a negative temperature coefficient of resistance, $-\alpha$. The current through these circuits are denoted by $I_A$ and $I_B$. At initial temperature, the resistance of the two resistors is $R_0$. As the temperature is increased, the correct option that describes the variation of current in these circuits is:

$A$ square-shaped wire with a resistance of $3\, \Omega$ for each side is bent to form a complete circle. The resistance between two diametrically opposite points of the circle in units of $\Omega$ will be:

If a resistance ${R_2}$ is connected in parallel with the resistance $R$ in the circuit shown,then the possible value of current through $R$ and the possible value of ${R_2}$ will be: