$A$ wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\,\Omega$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\,\Omega$?

Two square-shaped metal plates $A$ and $B$ of the same thickness $(t)$ and of the same material are connected as shown in the figure. The side of $B$ is twice that of $A$. If the resistances of $A$ and $B$ are $R_A$ and $R_B$ respectively, then $\frac{R_A}{R_B}$ is:

$A$ rod of a certain metal is $1.0 \, m$ long and $0.6 \, cm$ in diameter. Its resistance is $3.0 \times 10^{-3} \, \Omega$. Another disc made of the same metal is $2.0 \, cm$ in diameter and $1.0 \, mm$ thick. What is the resistance between the round faces of the disc?

$A$ rectangular carbon block has dimensions $1.0 \ cm \times 1.0 \ cm \times 50 \ cm$. The resistance is to be measured first between the two square ends and then between the two rectangular ends. If the resistivity of carbon is $3.5 \times 10^{-5} \ \Omega \cdot m$,find the values of the resistances in both cases respectively.

In the given circuit,the lengths of $AB$ and $BC$ are equal. The radius of $AB$ is three times that of $BC$. What is the ratio of the potential difference across $AB$ to that across $BC$?

The new resistance of a wire of $R \, \Omega$,whose radius is reduced to half,is