The net resistance between $X$ and $Y$ is ............... $\Omega$.

As shown in the figure,$13$ resistors each of resistance $R$ are connected. The effective resistance between points $A$ and $B$ is:

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.

Twelve wires of equal length and same cross-section are connected in the form of a cube. If the resistance of each of the wires is $R$,then the effective resistance between the two diagonal ends would be

$A$ regular hexagon is formed by six wires each of resistance $r \Omega$ and the corners are joined to the centre by wires of the same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be:

In a series connection of resistors,is the current equal or the voltage? And in a parallel connection of resistors,is the current equal or the voltage?