Question

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	\(\frac{ e E }{ m } \tau\)
D	Current Density	S	\(\frac{ E }{ J }\)

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

Answer 1

The Correct Option is A

To match the terms in Column I with their corresponding mathematical relations in Column II, we need to understand the concepts associated with the past and their respective formulas:

1. Drift Velocity (A):

The drift velocity (\( v_d \)) is the average velocity of charged particles in a conductor due to an electric field. It is related to the electric field (\( E \)) and the relaxation time (\( \tau \)) by the formula: \(v_d = \frac{eE}{m} \tau\). Thus, the correct match for Drift Velocity is (R).

1. Electrical Resistivity (B):

Electrical resistivity (\( \rho \)) is a measure of how strongly a material opposes the flow of electric current. The relation which involves electrical resistivity is given by the formula: \(\frac{E}{J} = \rho\), where \( J \) is the current density. Hence, the correct match is (S).

1. Relaxation Period (C):

The relaxation time (\( \tau \)) is related to drift velocity and resistivity by the formula: \(\tau = \frac{m}{ne^2 \rho}\). Therefore, the correct match is (P).

1. Current Density (D):

Current density (\( J \)) is defined as the electric current per unit area of cross-section. It is mathematically expressed as: \(J = ne v_d\). Hence, the correct match for Current Density is (Q).

Thus, the correct matching, based on the understanding of the physical concepts and their expressions, is:

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