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Current Electricity

Drift of Electrons and the Origin of Resistivity

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drift velocity, resistivity, relaxation time and current density

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2021 1 question

1 Current Electricity Medium

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.

Pick the matching item from Column II for each row.
Column I
- A. Drift Velocity Match for A
- B. Electrical Resistivity Match for B
- C. Relaxation Period Match for C
- D. Current Density Match for D
Column II
- P. $\frac{m}{ne^2\rho}$
- Q. $nev_d$
- R. $\frac{eE}{m}\tau$
- S. $\frac{E}{J}$
Correct answer: A → R, B → S, C → P, D → Q

Drift velocity: $v_d = \left(\frac{eE}{m}\right)\tau$ Resistivity: $J = \sigma E = \frac{E}{\rho} \Rightarrow \rho = \frac{E}{J}$ Relaxation period: $\rho = \frac{E}{nev_d}$ and $v_d = \frac{eE}{m}\tau$ give $\tau = \frac{m}{ne^2\rho}$ Current density: $i = neAv_d \Rightarrow J = \frac{i}{A} = nev_d$ Correct match: A-R, B-S, C-P, D-Q.