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. [20

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Solution

Q.
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. [2021]

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) $\frac{E}{J}$

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

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

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

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

Ans.
(2)

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

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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