In a wire of circular cross-section with radius $r$,free electrons travel with a drift velocity $V$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2V$?

The relaxation time $\tau$ is nearly independent of the applied $E$ field,whereas it changes significantly with temperature $T$. The first fact is (in part) responsible for Ohm's law,whereas the second fact leads to the variation of resistivity $\rho$ with temperature. Elaborate why?

Statement $(I)$: Specific resistance depends on the nature of the material and is independent of the temperature of the material.
Statement $(II)$: $A$ wire of resistance $6 \ \Omega$ is drawn out so that its new length is four times its original length. The resistance of the new wire is $48 \ \Omega$.
Statement $(III)$: Drift velocity is the average constant velocity acquired by free electrons inside a metal by the application of an electric field,which results in current.
Which of the following is correct?

Why is current not formed in solid conductors in the absence of an electric field?

For a given electric current,the drift velocity of conduction electrons in a copper wire is $v_d$ and their mobility is $\mu$. When the current is increased at constant temperature,

The current density in a cylindrical wire of radius $4 \; mm$ is $4 \times 10^{6} \; A \cdot m^{-2}$. The current through the outer portion of the wire between radial distance $\frac{R}{2}$ and $R$ is $\dots \; \pi \; A$.