The equivalent resistance across $AB$ would be ............ $\Omega$

Explain the series connection of resistors. Derive the equation for the equivalent resistance $(R_S)$.

$(a)$ Given $n$ resistors each of resistance $R,$ how will you combine them to get the $(i)$ maximum $(ii)$ minimum effective resistance? What is the ratio of the maximum to minimum resistance?
$(b)$ Given the resistances of $1\; \Omega, 2\; \Omega, 3\; \Omega,$ how will you combine them to get an equivalent resistance of $(i) \;(11 / 3)\; \Omega,$ $(ii)\;(11 / 5)\; \Omega,$ $(iii)\; 6\;\Omega,$ $(iv)\;(6 / 11)\; \Omega ?$
$(c)$ Determine the equivalent resistance of the networks shown in the figure.

In the given circuit, the current in resistance $R_3$ is: (in $\,A$)

$A$ uniform wire of resistance $20 \,\Omega$ having resistance $1 \,\Omega/m$ is bent into a circle as shown in the figure. If the equivalent resistance between $M$ and $N$ is $1.8 \,\Omega$,then the length of the shorter section is ................ $m$.

$A$ wire of resistance $R$ is bent to form a square $ABCD$ as shown in the figure. The effective resistance between $E$ and $C$ is ( $E$ is the mid-point of arm $CD$ ).