$A$ wire of resistance $R$ is divided into $10$ equal parts. These parts are connected in parallel. The equivalent resistance of such a connection will be: (in $, R$)

$A$ wire of resistance $R$ is bent into a circle of radius $r$. What is the equivalent resistance between points $X$ and $Y$?

Let there be $n$ resistors $R_1, \dots, R_n$ with $R_{\max} = \max \{R_1, \dots, R_n\}$ and $R_{\min} = \min \{R_1, \dots, R_n\}$. Show that when they are connected in parallel,the resultant resistance $R_p < R_{\min}$ and when they are connected in series,the resultant resistance $R_s > R_{\max}$. Interpret the result physically.

In the given figure,switches $S_{1}$ and $S_{2}$ are initially open. What is the equivalent resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed? (in $\Omega$)

When two resistances are connected in parallel,the equivalent resistance is $\frac{6}{5} \, \Omega$. When one of the resistances is removed,the effective resistance is $2 \, \Omega$. The resistance of the wire removed will be ................ $\Omega$.

Two conductors have the same resistance at $0\,^{\circ}C$ but their temperature coefficients of resistance are $\alpha_1$ and $\alpha_2$. The respective temperature coefficient of their series combination is