What equal length of an iron wire and a copper-nickel alloy wire, each of $2 \; mm$ diameter, connected in parallel, gives an equivalent resistance of $3 \; \Omega$? (Given: resistivities of iron and copper-nickel alloy wire are $12 \; \mu\Omega \cdot cm$ and $51 \; \mu\Omega \cdot cm$ respectively) (in $m$)

$A$ technician has only two resistance coils. By using them singly, in series or in parallel, he is able to obtain the resistances $3, 4, 12$ and $16 \, \Omega$. The resistances of the two coils are ........... $\Omega$.

Three resistors each of $4\,\Omega$ are connected together to form a network. The equivalent resistance of the network cannot be ............ $\Omega$.

$(a)$ 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.

If the power dissipated in the circuit is $150\,W,$ then the value of $R$ is ............... $\Omega$.

In the given circuit,the equivalent resistance between $A$ and $B$ is (in $\Omega$)