Column - I gives certain physical terms associated with flow of current through a metallic conductor.Column - II gives some mathematical relations involving electrical quantities.

MatchColumn - I and Column - II with appropriate relations.

Column - I	Column - II
(A) Drift  Velocity	(P) m/ne2p
(B) Electrical Resistivity	(Q) nevd
(C) Relaxation Period	(R) (eE/ m)T
(D) Current Density	(S) E/J

The correct matching between the physical terms associated with current flow in Column - I and their mathematical relations in Column - II is (A)-(R), (B)-(S), (C)-(P), (D)-(Q).

Let us derive each relation step-by-step from core physical principles:

(A) Drift Velocity ($v_d$):
When an electric field $E$ is applied across a metallic conductor, each free electron of mass $m$ and charge $e$ experiences an electrostatic force $F=eE$.
This force produces an acceleration:
$a=\frac{eE}{m}$
The average velocity gained by the free electrons between successive collisions is called the drift velocity $v_d$, which is given in terms of the relaxation period (average time between collisions) $T$ as:
$v_d=aT=\left(\frac{eE}{m}\right)T$
Thus, (A) matches with (R).

(B) Electrical Resistivity ($\rho$):
By Ohm's law, the electric field vector $E$ and the current density vector $J$ in a conductor are related by:
$E=\rho J$
Rearranging this formula for electrical resistivity $\rho$ gives:
$\rho =\frac{E}{J}$
Thus, (B) matches with (S).

(C) Relaxation Period ($T$):
Resistivity $\rho$ is micro-scopically related to the electron parameters by:
$\rho =\frac{m}{n{e}^{2}T}$
where $n$ is the number density of free electrons, $e$ is the electron charge, and $m$ is the mass of an electron.
Solving for the relaxation period $T$:
$T=\frac{m}{n{e}^2\rho }$
Thus, (C) matches with (P).

(D) Current Density ($J$):
The electric current $I$ through a conductor is related to the drift velocity $v_d$ by the equation:
$I=neA{v}_d$
where $A$ is the cross-sectional area. Since current density $J$ is defined as the current per unit area ($J=I/A$), we get:
$J=ne{v}_d$
Thus, (D) matches with (Q).