Match List-I with List-II
| List-I | List-II | ||
| (A) | Resistivity of a material | (I) | is the magnitude of the drift velocity per unit electric field |
| (B) | Current density | (II) | depends on its length and area of cross-section. |
| (C) | Mobility | (III) | depends on product of free electrons per unit volume and their relaxation time |
| (D) | Resistance of a conductor of a given material | (IV) | the current through unit area normal to the direction of current |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) - (III), (B) - (IV), (C) - (I), (D) - (II)
Each quantity is matched from its defining relation in the drift model of conduction.
(A) Resistivity of a material — this matches (III) depends on product of free electrons per unit volume and their relaxation time. Resistivity is a property of the material, set by n and \( \tau \).
\( \displaystyle \rho = \frac{m}{n e^{2} \tau} \)
(B) Current density — this matches (IV) the current through unit area normal to the direction of current, \( j = I/A \).
(C) Mobility — this matches (I) is the magnitude of the drift velocity per unit electric field, \( \mu = v_d/E \).
(D) Resistance of a conductor of a given material — this matches (II) depends on its length and area of cross-section. For a fixed material, \( R = \rho l/A \), so only the dimensions change it.
NCERT (2026-27):
Temperature Dependence of Resistivity – “… From this equation, resistivity of a material is given by
\( \displaystyle \rho = \frac{1}{\sigma} = \frac{m}{n e^{2} \tau} \qquad (3.27) \)
\( \rho \) thus depends inversely both on the number \( n \) of free electrons per unit volume and on the average time \( \tau \) between collisions.”
Ohm’s Law – “… Current per unit area (taken normal to the current), \( I/A \), is called current density and is denoted by \( \mathbf{j} \).”
Mobility – “… An important quantity is the mobility \( \mu \) defined as the magnitude of the drift velocity per unit electric field:
\( \displaystyle \mu = \frac{|\mathbf{v}_d|}{E} \qquad (3.24) \)”
Ohm’s Law – “… Combining Eqs. (3.5) and (3.7), we have
\( \displaystyle R \propto \frac{l}{A} \qquad (3.8) \)
and hence for a given conductor
\( \displaystyle R = \rho\,\frac{l}{A} \qquad (3.9) \)
where the constant of proportionality \( \rho \) depends on the material of the conductor but not on its dimensions. \( \rho \) is called resistivity.”