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 physical terms associated with the flow of current through a metallic conductor in Column I with the correct mathematical relations in Column II, let's analyze each term:

1. Drift Velocity (A): 

Drift velocity is the average velocity that a charged particle, such as an electron, attains due to an electric field. The formula for drift velocity (\(v_d\)) is given by: \(v_d = \frac{eE\tau}{m}\), where:

• \(e\) is the electron charge,
• \(E\) is the electric field,
• \(\tau\) is the relaxation time,
• \(m\) is the electron mass.

1. Electrical Resistivity (B):

Electrical resistivity (\(\rho\)) is defined as a material's ability to resist the flow of electric current. The relation involving current density (\(J\)) is: \(\rho = \frac{E}{J}\), where \(E\) is the electric field. This matches option (S) in Column II. Thus, (B)-(S).

1. Relaxation Period (C):

In the context of electrical conduction, the relaxation period or time (\(\tau\)) is the average time between subsequent collisions of electrons moving through a metal. It relates to the formula for resistivity: \(\rho = \frac{m}{ne^2\tau}\). Therefore, it matches with option (P) in Column II. Thus, (C)-(P).

1. Current Density (D):

Current density (\(J\)) is the electric current per unit area of cross-section. The formula involving drift velocity is: \(J = nev_d\). This matches with option (Q) in Column II. Thus, (D)-(Q).

Therefore, the correct matching is (A)-(R), (B)-(S), (C)-(P), (D)-(Q), which is consistent with the given correct answer.