$A$ wire of resistance $20 \Omega$ is divided into $10$ equal parts. $A$ combination of two parts are connected in parallel and so on. Now,the resulting pairs of parallel combinations are connected in series. The equivalent resistance of the final combination is . . . . . . $\Omega$.

Three resistances of $1\, \Omega$ each are connected in parallel. Such a connection is then connected in series with a $\frac{2}{3}\, \Omega$ resistor. The resultant resistance will be ........... $\Omega$.

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:

$A$ copper wire of resistance $R$ is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance

First,a set of $n$ equal resistors of $R$ each are connected in series to a battery of $emf$ $E$ and internal resistance $R$. $A$ current $I$ is observed to flow. Then,the $n$ resistors are connected in parallel to the same battery. It is observed that the current increases $10$ times. What is $n$?

The voltage across the $10 \, \Omega$ resistor in the given circuit is $x$ volt. The value of $x$ to the nearest integer is..........