The specific resistance of a rod of copper as compared to that of thin wire of copper is.

Question

Accepted Answer

The correct option is (3):

To understand this question, we need to clarify the concept of specific resistance, also known as resistivity ($\rho$). Resistivity is an intrinsic property of a material, meaning it depends only on the nature of the material itself and its temperature, not on its shape, size, length, or cross-sectional area. It's a fundamental characteristic that tells us how strongly a material opposes the flow of electric current. For example, all samples of pure copper at the same temperature will have the same resistivity, whether they are in the form of a thick rod or a thin wire. The formula for resistance ($R$) is $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. While the *resistance* ($R$) of a conductor depends on its dimensions (length and area), the *specific resistance* or *resistivity* ($\rho$) does not. Therefore, a rod of copper and a thin wire of copper, both made of the same material (copper) and at the same temperature, will have the same specific resistance.

The incorrect option is (1) Less:
"Less" is incorrect because specific resistance is an intrinsic property of the material. The thickness or thinness of the copper sample does not alter its fundamental resistivity.

The incorrect option is (2) More:
"More" is incorrect for the same reason as "Less." Resistivity is a material constant; it does not increase or decrease based on the physical dimensions of the conductor.

The incorrect option is (4) Depends upon length:
"Depends upon length" is incorrect because specific resistance (resistivity) is independent of the length of the material. It is the overall resistance ($R$) that depends on length, not the specific resistance ($\rho$).