The equivalent resistance between the adjacent corners of a regular $n$-sided polygon made of a uniform wire of total resistance $R$ is:

The resistive network shown below is connected to a $D.C.$ source of $16 \, V$. The power consumed by the network is $4 \, W$. The value of $R$ is ............. $\Omega$.

Three conductors draw currents of $1 \,A, 2 \,A$ and $3 \,A$ respectively, when connected in turn across a battery. If they are connected in series and the combination is connected across the same battery, the current drawn will be

$A$ copper wire of radius $r$ and length $\ell$ is coated with a nickel layer until its radius becomes $2r$. If the resistivities of copper and nickel are $\rho_c$ and $\rho_n$ respectively,find the equivalent resistance of the wire.

Two bulbs are connected in parallel. Bulb $A$ is brighter than bulb $B$. If $R_A$ and $R_B$ are their resistances respectively,then:

$A$ wire of resistance $100 \Omega$ is stretched so that its length increases by $20 \%$. The stretched wire is then bent in the form of a rectangle whose length and breadth are in the ratio $3: 2$. The effective resistance between the ends of any diagonal of the rectangle is (in $\Omega$)