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 match the terms from Column - I with their corresponding mathematical relations from Column - II, let's analyze each term:

1. Drift Velocity (A): Drift velocity refers to the average velocity that a charged particle, such as an electron, attains due to an electric field. The relation that defines drift velocity involves the electron charge \(e\), electric field \(E\), mass \(m\), and relaxation time \(\tau\):
   • \(v_d = \frac{eE}{m}\tau\)
2. Electrical Resistivity (B): Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. The resistivity \(\rho\) is generally defined by the relation:
   • \(\rho = \frac{E}{J}\) where \(J\) is the current density.
3. Relaxation Period (C): The relaxation period, or relaxation time \(\tau\), is related to resistivity and other parameters by the relation:
   • \(\tau = \frac{m}{ne^2\rho}\) where \(n\) is the number density of electrons.
4. Current Density (D): Current density \(J\) is the current per unit area and is related to drift velocity by:
   • \(J = nev_d\) where \(n\) is the charge density and \(v_d\) is the drift velocity.

Based on the above analysis, the correct matching of Column - I and Column - II is:

• (A)-(R): Drift Velocity - \(\frac{eE}{m}\tau\)
• (B)-(S): Electrical Resistivity - \(\frac{E}{J}\)
• (C)-(P): Relaxation Period - \(\frac{m}{ne^2\rho}\)
• (D)-(Q): Current Density - \(nev_d\)

Thus, the correct answer is: (A)-(R), (B)-(S), (C)-(P), (D)-(Q).