Question: 12. 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}{ne^{2}\rho} |
| (B) Electrical Resistivity | (Q) ne v_d |
| (C) Relaxation Period | (R) \frac{eE}{m}\tau |
| (D) Current Density | (S) \frac{E}{J} |
(1) (A)-(R),(B)-(S),(C)-(P),(D)-(Q)
(2) (A)-(R),(B)-(S),(C)-(Q),(D)-(P)
(3) (A)-(R),(B)-(P),(C)-(S),(D)-(Q)
(4) (A)-(R),(B)-(Q),(C)-(S),(D)-(P)
Answer: Option (1)
Explanation:
Drift velocity is defined as the average velocity acquired by charge carriers under the influence of an electric field and is given by v_d=\frac{eE}{m}\tau. Hence, (A) matches with (R).
Electrical resistivity is defined as the ratio of electric field to current density,
so \rho=\frac{E}{J}. Hence, (B) matches with (S).
Relaxation period is the average time between successive collisions of electrons and is given by
\tau=\frac{m}{ne^{2}\rho}. Hence, (C) matches with (P).
Current density is defined as current per unit area and can be written as
J=ne v_d. Hence, (D) matches with (Q).
Therefore, the correct matching corresponds to Option (1)