$10$ resistors,each of resistance $10\,\Omega$,can be connected to obtain maximum and minimum equivalent resistance. The ratio of maximum to minimum equivalent resistance will be $..........$.

$A$ wire is broken into four equal parts. $A$ packet is formed by keeping the four wires together. The resistance of the packet in comparison to the resistance of the original wire will be:

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:

Consider the ladder network shown in the figure. What should be the value of resistance $R$ so that the effective resistance between $A$ and $B$ becomes independent of the number of elements in the combination? ............. $\Omega$

The total current supplied to the circuit by the battery is . . . . . . . (in $A$)

The brightness of a bulb will be reduced,if a resistance is connected in