Question

The specific resistance of a rod of copper as compared to that of 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 is $R = \rho \dfrac{l}{A}$, where ρ is constant and called specific resistance. It is a fundamental property of metal since both the material is copper so resistivity must be the same or depends upon the length and area of wire.

Complete Step By Step Solution
Resistance is the ability of the substance to oppose the flow of the current. It is given that $R = \rho \dfrac{l}{A}$, where ρ is constant and called specific resistance. Then, $\rho = R\dfrac{l}{A}$thus, specific resistance or resistivity is the resistance of the material with dimensions, $1 m$ length and $1 m^2$ area of cross section, when voltage is applied to it.
Clearly, resistivity is the fundamental property of the material, and it's dependent on the nature of the material and temperature. It is independent of the dimension of the conductor. Whereas, resistance of the material depends upon the temperature, nature and dimension of the material.
Hence, since both the materials are copper, one is bulk and other is thin wire. The resistivity cannot be more or less. Thus, it must be the same and does not depend upon the length and area of the wire. According to above facts, the specific resistance of copper as compared to the thin wire of the copper is independent of the dimension. Hence, it will remain the same.
Hence, option (C) is correct.

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