$A$ uniform wire of length $l$ and radius $r$ has a resistance of $100\, \Omega$. It is recast into a wire of radius $\frac{r}{2}$. The resistance of the new wire will be ............... $\Omega$.

An aluminium (resistivity $\rho = 2.2 \times 10^{-8} \Omega \cdot m$) wire of diameter $1.4 \text{ mm}$ is used to make a $4 \Omega$ resistor. The length of the wire is: (in $\text{ m}$)

$A$ cylindrical conductor has a uniform cross-section. The resistivity of its material increases linearly from the left end to the right end. If a constant current is flowing through it and at a section at distance $x$ from the left end,the magnitude of the electric field intensity is $E$,which of the following graphs is correct?

Masses of three wires of copper are in the ratio of $1: 3: 5$ and their lengths are in the ratio of $5: 3: 1$. The ratio of their electrical resistances is

The resistance of a conductor is $5\,\Omega$ at $50\,^{\circ}C$ and $6\,\Omega$ at $100\,^{\circ}C$. Its resistance at $0\,^{\circ}C$ is ................ $\Omega$.

Two wires are made of the same material. The length and diameter of the second wire are both double those of the first wire. What will be the resistance of the first wire compared to the second wire?