Question

Which common factor affects both resistance as well as resistivity and how?

Answer 1

nature of the conductor or material is the main factor which affect both resistance as well as resistivity

Answer 2

The answer to the question is temperature which is the common factor between resistance and resistivity.

EXPLANATION:

The resistance of a wire is directly proportional to the length of the conductor and inversely proportional to the area of cross section of the conductor.

Mathematically it can be written as $R\ \alpha\ l$

                                                     $R\ \alpha\ \frac{1}{A}$

Here, R is the resistance of the conductor.

l is the length of the conductor and A is the area of cross section.

The resistance of the conductor is also dependent on the nature of wire and temperature.

The dependence of resistance on the temperature is given as -

                                  $R_{t} =\ R_{o} (\ 1+\ \alpha t)$

$R_{o}$ is the resistance at zero degree celsius.

$R_{t}$ is the resistance at t degree celsius

$\alpha$ is known as the temperature coefficient of resistance.

Similarly, resistivity of a wire is also dependent on nature of material and temperature.

The temperature dependence of resistivity $(\rho)$ is written as -

                              $\rho_{t} =\ \rho_{0} (1+\alpha t)$

The expression is same like resistance.

But, the resistivity of a wire is independent on length and area of cross section.

Hence, the common factor which is same for resistance and resistivity is temperature.