Question

Column - I gives certain physical terms associated with the 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)	\(nev_d\)
(C)	Relaxation Period	(R)	\(\frac{eE}{m}\tau\)
(D)	Current Density	(S)	\(\frac{E}{J}\)

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

Answer 1

The Correct Option is B

To solve this matching problem, we need to correctly pair the terms from Column - I (physical terms) with the mathematical relations from Column - II. Let's go through each term and match it with the appropriate relation. 

1. Drift Velocity (A): Drift velocity \( v_d \) refers to the average velocity at which electrons move through a conductor when subjected to an electric field. The drift velocity is given by the formula: \(v_d = \frac{eE}{m}\tau\), where:
   • \( e \) is the electron charge.
   • \( E \) is the electric field.
   • \( m \) is the mass of the electron.
   • \( \tau \) is the relaxation time.
2. Electrical Resistivity (B): Electrical resistivity \( \rho \) of a material is the measure of how strongly the material opposes the flow of electric current. It is given by the inverse of conductivity: \(\rho = \frac{E}{J}\), where:
   • \( E \) is the electric field.
   • \( J \) is the current density.
3. Relaxation Period (C): The relaxation period \(\tau\) is the average time between two successive collisions of a charge carrier (electron) in a conductor. From the expression for drift velocity, it can be related to resistivity by: \(\tau = \frac{m}{ne^2\rho}\), where:
   • \( n \) is the number density of electrons.
   • \( e \) is the charge of an electron.
4. Current Density (D): Current density \( J \) is defined as the charge flowing per unit area per unit time in a conductor and is given by: \(J = nev_d\), where:
   • \( n \) is the number of electrons per unit volume.
   • \( e \) is the charge of an electron.
   • \( v_d \) is the drift velocity.

The correct matching is therefore: (A)-(R), (B)-(S), (C)-(P), (D)-(Q).