$A$ current flows in a wire of circular cross-section with the free electrons travelling with a mean drift velocity $\vec v$. If an equal current flows in a wire of twice the radius,the new mean drift velocity is:

What is relaxation time?

The electric field $E$,current density $J$ and conductivity $\sigma$ of a conductor are related as

$(a)$ The electron drift speed is estimated to be only a few $mm\; s^{-1}$ for currents in the range of a few amperes. How then is current established almost the instant a circuit is closed?
$(b)$ The electron drift arises due to the force experienced by electrons in the electric field inside the conductor. But force should cause acceleration. Why then do the electrons acquire a steady average drift speed?
$(c)$ If the electron drift speed is so small,and the electron's charge is small,how can we still obtain large amounts of current in a conductor?
$(d)$ When electrons drift in a metal from lower to higher potential,does it mean that all the 'free' electrons of the metal are moving in the same direction?
$(e)$ Are the paths of electrons straight lines between successive collisions (with the positive ions of the metal) in the $(i)$ absence of electric field,$(ii)$ presence of electric field?

Define mobility and write its $SI$ unit.

$A$ current of $2\,A$ flows through a wire of cross-sectional area $25.0\,mm^2$. The number of free electrons per cubic meter is $2.0 \times 10^{28}$. The drift velocity of the electrons is $...............\times 10^{-6}\,ms^{-1}$ (given,charge on electron $= 1.6 \times 10^{-19}\,C$).