Which of the following statements are correct?
(A) The resistance of a conductor and its resistivity both depend on temperature.
(B) For a conductor of \( 1\,\mathrm{m} \) length and of \( 1\,\mathrm{m^2} \) cross-sectional area, the resistance is equal to its resistivity
(C) Resistance and resistivity both depend on cross-sectional area
(D) The resistivity of two wires made of same material but of different dimensions is the same.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A), (B) and (D) only
Resistance \( R = \rho L/A \) depends on the dimensions of the conductor, while resistivity \( \rho \) is a property of the material and its temperature only.
(A) The resistance of a conductor and its resistivity both depend on temperature. — Correct. \( \rho \) changes with temperature, and \( R \) changes with it.
(B) For a conductor of \( 1\,\mathrm{m} \) length and of \( 1\,\mathrm{m^2} \) cross-sectional area, the resistance is equal to its resistivity. — Correct. With \( L = 1\,\mathrm{m} \) and \( A = 1\,\mathrm{m^2} \), \( R = \rho \times 1/1 \), numerically equal to \( \rho \).
(C) Resistance and resistivity both depend on cross-sectional area. — Incorrect. Only the resistance depends on \( A \); resistivity does not depend on the dimensions.
(D) The resistivity of two wires made of same material but of different dimensions is the same. — Correct. Resistivity is fixed by the material (at a given temperature).
NCERT (2026-27):
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 ρ depends on the material of the conductor but not on its dimensions. ρ is called resistivity.”
Temperature Dependence of Resistivity – “The resistivity of a material is found to be dependent on the temperature.”