The equivalent resistance between $A$ and $B$ is

$A$ uniform ring of conducting wire of radius $r$ has resistance $R$. $A$ and $B$ are two points on the ring which subtend an angle $\theta$ at the centre of the ring. The equivalent resistance between points $A$ and $B$ is:

The resistance across $M$ and $N$ in the given 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 $m$)

You are given a resistance wire of length $50\, cm$ and a battery of negligible resistance. In which of the following cases is the largest amount of heat generated?

$A$ 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 ........... $\Omega$.