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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)
$n e v_{d}$
C)
Relaxation Period
R)
$\frac{e E}{m} τ$
D)
Current Density
S)
$\frac{E}{J}$

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

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

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

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

answer is B.

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Detailed Solution

The formula of drift velocity is $v_{d} = \frac{e E}{m} τ$

Current density J = $\frac{I}{A} = \frac{n e A v_{d}}{A} = n e v_{d}$

Resistivity is $ρ = \frac{m}{n e^{2} τ} \Rightarrow τ = \frac{m}{n e^{2} ρ}$

Resistance is R = $\frac{V}{l}$

$ρ \frac{l}{A} = \frac{E l}{I} \Rightarrow ρ = \frac{E A}{I} = \frac{E}{J}$

Where, E = electric field, A = area of cross section

e = electronic charge, n = number of density of electrons, $τ$ = relaxation time.

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