The resistance of each wire between any two adjacent dots is $R$. Then the equivalent resistance between $A$ and $B$ as shown in the figure is:

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 $m$)

All resistances in the figure are $1\,\Omega$ each. The value of current '$I$' is $\frac{a}{5}\,A$. The value of $a$ is

In the given circuit,find the value of $V$. (in $V$)

In the given figure,switches $S_{1}$ and $S_{2}$ are initially open. What is the equivalent resistance across $a b$ when the switches $S_{1}$ and $S_{2}$ are closed? (in $\Omega$)

$A$ student has $10$ resistors of resistance $r$. The minimum resistance made by him from given resistors is