In the given network,the equivalent resistance between $A$ and $B$ is .............. $\Omega$.

There are three resistance coils of equal resistance. The maximum number of distinct equivalent resistances you can obtain by connecting them in any manner you choose,being free to use any number of the coils in any way,is

$(a)$ 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.

Consider the following two circuits:
$A$: $20$ bulbs are connected in series to a power supply line.
$B$: $20$ bulbs identical to $A$ are connected in a parallel circuit to an identical power supply line.
Identify which of the following is not true.

In the given circuit,the equivalent resistance between the points $A$ and $B$ is (in $ohm$):

Write the equation for the equivalent resistance of $n$ resistors connected in series and the equation for the equivalent resistance of $n$ resistors connected in parallel.