$A$ wire of resistance $12 \, \Omega/m$ is bent to form a complete circle of radius $10 \, cm$. The resistance between its two diametrically opposite points, $A$ and $B$, as shown in the figure, is:

In an aluminium $(Al)$ bar of square cross-section,a square hole is drilled and is filled with iron $(Fe)$ as shown in the figure. The electrical resistivities of $Al$ and $Fe$ are $2.7 \times 10^{-8} \ \Omega m$ and $1.0 \times 10^{-7} \ \Omega m$,respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is

$A$ circuit consists of five identical conductors,each of resistance $1 \ \Omega$,as shown in the figure. Two similar conductors are added as indicated by the dotted lines. The ratio of the equivalent resistances before and after the addition is:

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

The resistance of the series combination of two resistances is $S$. When they are joined in parallel,the total resistance is $P$. If $S = nP$,then the minimum possible value of $n$ is

$A$ wire of resistance $R$ is bent to form a circular ring. Find the equivalent resistance between two points $X$ and $Y$ on its circumference. (The angle $XOY = \alpha$ is given.)