Question

The specific resistance of a copper as compared to that of a thin wire of copper is:
A. More
B. Less
C. Same
D. Depends upon the length and area of wire

Answer 1

Hint: We know that resistance, $R=\rho \dfrac{L}{A}$ where $\rho$ is a constant and is called the specific resistance. It is a fundamental property of the material. Since both the materials are copper, the resistivity must be the same or depends upon the length and area of wire.

Complete step by step answer:
Resistance is the ability of a substance to oppose the flow of electric current through it. It is given as $R=\rho \dfrac{L}{A}$. Where $\rho$ is a constant and is called the specific resistance. Then, $\rho=R\dfrac{A}{L}$. Thus, specific resistance or resistivity is the resistance of the material with dimensions, \[1m\] length and $1m^{2}$ area of a cross section, when voltage is applied to it.

 Clearly, resistivity is a fundamental property of the material, and is dependent on the nature of the material and temperature. It is independent of the dimensions of the conductor. Whereas, resistance of a material depends on nature, dimensions and temperature of the material.

Here, since both the materials are copper, one is bulk and the other is thin wires. The resistivity cannot be more or less. Thus it must be the same or does not depend upon the length and area of wire. According to above facts, the specific resistance of a copper as compared to that of a thin wire of copper is independent of the dimensions. And hence will remain the same.
Hence, the correct answer is option C.

Note:
Resistivity is a fundamental property of the material and is independent of the dimensions of the conductor. Whereas, resistance of a material depends on both the nature and the dimensions of the material. Also, resistivity is a special case of the resistance.