Two cylindrical rods of uniform cross-sectional area $A$ and $2A$,having free electrons per unit volume $2n$ and $n$ respectively,are joined in series. $A$ current $I$ flows through them in a steady state. Then the ratio of the drift velocity of free electrons in the left rod to the drift velocity of electrons in the right rod is $\left( \frac{v_L}{v_R} \right)$.

$A$ uniform copper wire carries a current $i$ amperes and has $p$ carriers per meter$^3$. The length of the wire is $\lambda$ meters and its cross-section area is $s$ meter$^2$. If the charge on a carrier is $q$ coulombs,the drift velocity in $ms^{-1}$ is given by

What are called conductors and non-conductors? In which of these are free electrons more abundant: conductors or non-conductors?

$(a)$ 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?

Choose the correct option with respect to the statements $A$ and $B$:
$(A)$: When no electric field is applied across a conductor,the path of free electrons between two successive collisions in it is straight.
$(B)$: When an electric field is applied across a conductor,the drift velocity of electrons is independent of time.

When there is an electric current through a conducting wire along its length,then an electric field must exist