Question

On what factors does the resistance of a conductor depend?

Answer 1

Hint: Resistance of a conductor is the property by virtue of which it opposes the flow of charge through it. It is equal to the ratio of the potential difference applied across the conductor to the current flowing through it. As it is a physical quantity of a conductor it must depend on the physical as well as structural characteristics of the conductor.

Complete step by step answer:
The materials which conduct electric current or any form of energy fairly well are called conductors. For example all metals.
According to the Definition of Resistance, i.e., The resistance of a conductor is the property by virtue of which it opposes the flow of charge through it. It is equal to the ratio of the potential difference applied across the conductor to the current flowing through it.

Mathematically,
$R = \dfrac{V}{L}$
The SI unit of resistance is the ohm, represented by $\Omega$ .
The resistance of a conductor is said to be one ohm if a current of 1 ampere flows through it on applying a potential difference of 1 volt across its ends.

At constant temperature, the resistance of a conductor depends on the following factors:

1. Length
   The resistance R of a conductor is directly proportional to its length i.e.,
   $R \propto l$

2. Area of cross-section
   The resistance R of a uniform conductor is inversely proportional to its area of cross-section A, i.e.,
   $R \propto \dfrac{1}{A}$

3. Nature of material
   The resistance of a conductor also depends on the nature of the material it is made u of. For example, the resistance of nichrome wire is 60 times that of a copper wire of equal length and area of cross-section.
   Combining all the above expressions, we get:
   $R = \rho \dfrac{l}{A}$
   where $\rho$is the constant of proportionality known as resistivity or specific resistance of the material of the conductor.

Note: The resistivity of a conductor depends only on the above mentioned three factors i.e., length, area of cross-section, and nature of the material of the conductor. Additionally, it also depends upon the physical conditions like temperature and pressure but is independent of its shape and size.