Question

What are the factors on which resistance of a conductor depends?

Answer 1

Hint: The resistance of a conductor increases with increase in the length of the conductor and decreases with the increase in cross-sectional area of the conductor. Higher the resistivity of the conductor, higher is its resistance.

Detailed step by step solution:
According to ohm’s law, the current flowing through a conductor is directly proportional to the potential difference applied across the conductor. It is given as
$
  I \propto V \\
   \Rightarrow I = \dfrac{1}{R} \times V \\
$
where $\dfrac{1}{R}$ is the constant of proportionality and R is called the resistance of the conductor. It is the obstruction offered by a conductor to the flow of current. The reciprocal of resistance is called conductivity of the conductor. It implies how much a conductor allows the current to pass through it.

The resistance of a material is
1. Directly proportional to the length of the conductor
$R \propto l$
This means that resistance increases with increase in length of the conductor.
2. Inversely proportional to the cross-sectional area of the conductor.
$R \propto \dfrac{1}{A}$
This means that resistance decreases with increase in the cross-sectional area of the conductor.
It can written as
$
  R \propto \dfrac{l}{A} \\
  R = \rho \dfrac{l}{A} \\
$
Here $\rho $ is called the resistivity of the conductor which is the resistance offered by a conductor of unit length and unit cross-sectional area.
Hence, we can say that resistance of a conductor depends on the length of the conductor, the cross-sectional area of the conductor and the resistivity of the conductor.

Note: It should be noted that the resistance of a material may change with change in the length and cross-sectional area of the conductor but the resistivity of a conductor is constant and does not change with change in dimensions of the conductor.