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

Match Column - 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 answer is (A)-(R), (B)-(S), (C)-(P), (D)-(Q).

Let's analyze each physical term associated with the flow of current and find its appropriate mathematical relation:

(A) Drift Velocity:

Drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. The formula for drift velocity is given by:

v_d=\left(\frac{eE}{m}\right)\tau

where e is the elementary charge, E is the applied electric field, m is the mass of an electron, and τ (represented as T in the given column) is the relaxation period. Thus, (A) matches with (R).

(B) Electrical Resistivity:

From the microscopic form of Ohm's law, we know that the electric field (E) is directly proportional to the current density (J). The constant of proportionality is the electrical resistivity, denoted by ρ:

\rho =\frac{E}{J}

Thus, (B) matches with (S).

(C) Relaxation Period:

The relationship between electrical resistivity (ρ), charge carrier density (n), and relaxation time (τ) is given by:

\rho =\frac{m}{n{e}^2\tau }

Rearranging this formula to solve for the relaxation period τ gives:

\tau =\frac{m}{n{e}^2\rho }

In the given options, the resistivity ρ is represented by the letter 'p'. Therefore, the relation becomes m/ne²p. Thus, (C) matches with (P).

(D) Current Density:

Current density (J) is defined as the amount of electric current flowing per unit cross-sectional area. It is related to the drift velocity (v_d) of the charge carriers by the equation:

J=ne{v}_d

where n is the number density of charge carriers and e is the elementary charge. Thus, (D) matches with (Q).

Combining all these correct pairings, we arrive at the final sequence: (A)-(R), (B)-(S), (C)-(P), (D)-(Q).