Relation between Current and Drift Velocity: Practice Problem & Solution
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. $$ \begin{array}{ll@{\hspace{2cm}}ll} \textbf{Column-I} & & \textbf{Column-II} & \\[6pt] \text{(A)} & \text{Drift Velocity} & \text{(P)} & \dfrac{m}{ne^2\rho} \\[8pt] \text{(B)} & \text{Electrical Resistivity} & \text{(Q)} & n e v_d \\[8pt] \text{(C)} & \text{Relaxation Period} & \text{(R)} & \dfrac{eE}{m}\tau \\[8pt] \text{(D)} & \text{Current Density} & \text{(S)} & \dfrac{E}{J} \end{array} $$ 2021
Solution Explained:
To solve this problem, we apply the core principles of Relation between Current and Drift Velocity. Understanding the underlying formula is key to arriving at the correct answer below:
Drift velocity $v_d = \frac{eE}{m}\tau$ (A-R). Electrical Resistivity $\rho = \frac{E}{J}$ (B-S). Relaxation Period $\tau = \frac{m}{ne^2\rho}$ (C-P). Current density $J = nev_d$ (D-Q). Hence, the correct matching is (A)-(R), (B)-(S), (C)-(P), (D)-(Q).
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