Question Details

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) $\frac{m}{n e^{2} ρ}$

(B) Electrical Resistivity (Q) neνd

(C) Relaxation Period (R) $\frac{e E}{m} τ$

(D) Current Density (S) $\frac{E}{J}$

Options

(A)-(R), (B)-(P), (C)-(S), (D)-(Q)

(A)-(R), (B)-(Q), (C)-(S), (D)-(P)

(A)-(R), (B)-(S), (C)-(P), (D)-(Q)

(A)-(R), (B)-(S), (C)-(Q), (D)-(P)

Show Answer

Correct Answer :

Option C

(A)-(R), (B)-(S), (C)-(P), (D)-(Q)

Solution :

To match the physical terms associated with the flow of current in Column-I with their appropriate mathematical relations in Column-II, we analyze each term step-by-step:

1. Drift Velocity (A):
When an electric field $E$ is applied across a conductor, the free electrons experience an electric force $F = e E$ , leading to an acceleration $a = \frac{e E}{m}$ , where $e$ is the charge and $m$ is the mass of an electron. The average velocity acquired by these electrons between successive collisions is called the drift velocity ( $v_{d}$ ), given by:
$v_{d} = \frac{e E}{m} τ$
where $τ$ is the relaxation period.
Therefore, (A) matches with (R).

2. Electrical Resistivity (B):
According to Ohm's law in vector form, the relation between the electric field $E$ , current density $J$ , and electrical resistivity $ρ$ is:
$E = ρ J$
Rearranging this formula gives the expression for resistivity:
$ρ = \frac{E}{J}$
Therefore, (B) matches with (S).

3. Relaxation Period (C):
The electrical resistivity $ρ$ is micro-scopically related to the relaxation period $τ$ by the formula:
$ρ = \frac{m}{n e^{2} τ}$
Rearranging this to solve for the relaxation period $τ$ gives:
$τ = \frac{m}{n e^{2} ρ}$
where $n$ is the number density of free electrons.
Therefore, (C) matches with (P).

4. Current Density (D):
Current density $J$ is the electric current per unit cross-sectional area. It is related to the drift velocity $v_{d}$ of the charge carriers by the relation:
$J = n e v_{d}$
Therefore, (D) matches with (Q).

Combining all the individual matches, we get:
(A)-(R), (B)-(S), (C)-(P), (D)-(Q)

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	Column - I		Column - II
(A)	Drift Velocity	(P)	$\frac{m}{n e^{2} ρ}$
(B)	Electrical Resistivity	(Q)	neνd
(C)	Relaxation Period	(R)	$\frac{e E}{m} τ$
(D)	Current Density	(S)	$\frac{E}{J}$