Question

P and Q are the two wires of same length and different cross-sectional areas and made of the same metal. Choose the correct one.
A. Resistance is the same and resistivity is different.
B. Resistance is different and resistivity is the same.
C. Both resistivity and resistance are the same.
D. None of these.

Answer 1

Hint: Resistivity and resistances are two different kinds of property, one is intrinsic and the other one is extrinsic. So, by understanding the given two properties, we can then distinguish which property will vary and which will remain the same.

Complete step by step solution:
We will first understand the given two things that are resistance and resistivity and the difference in their concept.
Resistivity $(\rho)$ is an intrinsic property of every material and is measured as the amount of resistance provided by a material of one-meter length and one square meter cross sectional area and have the unit $\Omega -m$. Thus, it is the same for a metal irrespective of its shape and size or orientation. The resistivity varies enormously with different materials and with the temperature. With increase in temperature, the resistivity of the material will decrease and vice versa.
Resistance is an electric property to obstruct the flow of current. It depends on the resistivity of the material $(\rho)$, its length (L) and area of cross-section (A). Mathematically, it is given by
$R=\rho \dfrac{L}{A}$.
Now, according to the question the material and length of the two wires P and Q are same but the cross sections have been given different, so using the formula of resistance we can say that the resistances will be different and because resistivity is an intrinsic property, it will remain same.
Hence, option b is the correct answer.

Note: Although, both resistance and resistivity are two different kinds of property, but still both depend on the temperature of the material, with increase in temperature, both resistance and resistivity decreases.