Question

The electrical resistivity of a given metallic wire depends upon

• A. its length
• B. its thickness
• C. its shape
• D. nature of the material

Answer 1

The correct option is D

nature of the material

Explanation for Correct Option:

Option (D):

We know that the resistance inside a conductor is directly proportional to the length of the conductor.

$\therefore R\propto l$

We know that the resistance inside a conductor is inversely proportional to the area of the conductor.

$\therefore R\propto \frac{1}{A}$

$$\begin{gathered} \therefore R\propto \frac{l}{A} \\ \Rightarrow R=\rho \frac{l}{A} \end{gathered}$$

where $\rho$ is the constant of the proportionality or resistivity.

Hence, we can see that resistivity is independent of the length or area of the conductor, instead, the resistance is dependent on them.

Resistivity is the unique property of a material, or a particular type of material has the same resistivity present in all various lengths and areas of conductors.

Explanation for Incorrect Options:

Option (A):

From the above expression, we can see that resistance is dependent on length, not resistivity.

Option (B):

From the above expression, we can see that resistance is dependent on area or thickness, not resistivity.

Option (C):

From the above expression, we can see that resistance is dependent on length and area, overall the shape of the wire, but not resistivity.

Hence, the correct answer is option (D).