At what temperature $(^{\circ} C)$ will the resistance of a copper wire become $3$ times its resistance at $0^{\circ} C$? (Given: Temperature coefficient of resistance $\alpha = 4 \times 10^{-3} {}^{\circ} C^{-1}$)

$A$ uniform metal wire carries a current of $2 \, A$ when an ideal cell of $3.4 \, V$ is connected across it. The wire has mass $8.92 \times 10^{-3} \, kg$, density $8.92 \times 10^3 \, kg/m^3$ and resistivity $1.7 \times 10^{-8} \, \Omega m$. Then the length of the wire is (in $m$)

Two conductors are made of the same material and have the same length. Conductor $A$ is a solid wire of diameter $1 \ mm$. Conductor $B$ is a hollow tube of outer diameter $2 \ mm$ and inner diameter $1 \ mm$. Find the ratio of resistance $R_A$ to $R_B$.

Assertion: Bending a wire does not affect electrical resistance.
Reason: Resistance of a wire is proportional to the resistivity of the material.

$A$ 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?

The resistance of a wire is $R \; \Omega$. If it is melted and stretched to $n$ times its original length,its new resistance will be