The equivalent resistance of a series combination of two resistors is $s$. When they are connected in parallel,the equivalent resistance is $p$. If $s = np$,then the minimum value for $n$ is (Round off to the nearest integer).

$(a)$ 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.

Five identical electric filament lamps numbered $1$ to $5$ are joined in parallel across an ideal source as shown in the figure. When all the bulbs are working, the reading in the ammeter is $3 \,A$. When lamp '$1$' is switched off, the reading of the ammeter is (in $\,A$)

An electric kettle has two filaments. The first filament boils a certain amount of water in $10 \text{ minutes}$ and the second filament boils it in $15 \text{ minutes}$. If both filaments are connected in parallel,the water will boil in .............. minutes.

Four wires $AB, BC, CD, DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$,where $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is:

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