Question

The resistivity of a wire depends on its

• A. length
• B. area of cross-section
• C. material
• D. all of the above three factors

Answer 1

The correct option is C

material

Explanation for correct option: In the case of option C

1. Resistivity of a substance is an intrinsic property, which is defined by $\rho =\frac{m}{n{e}^2𝜏}$, where $m$ is the mass of electron, $n$is the number of electrons per unit volume, $e$is the charge, and $𝜏$is relaxation time.
2. Different materials will have different values of $n$.

Explanation for incorrect options:

In the case of option A, resistivity is independent of the length as we can see from the above-explained formula.

In the case of option B, resistivity is independent of the area of cross-section as we can see from the above-explained formula.

In the case of option D, since resistivity is independent of both length and area of cross-section, all the above three factors are not the correct choice.

Thus, option C is the correct answer.