Question

Technician A says that resistance increases as the diameter of a conductor increases. Technician B says that resistance increases as the temperature of a conductor increases. Which technician is correct?

Answer 1

Explanation:

Resistance is defined as the ability of a substance to resist the flow of current through the substance. Formula to calculate resistance is as follows.

                       R = $\frac{\rho l}{A}$  

As outer surface of a wire is in the shape of sphere. therefore, its area will be as follows.

                     A = $4 \pi r^{2}$

or,                 A = $4 \pi (\frac{d}{2})^{2}$

where,   d = diameter of the sphere

This means that with increase in diameter of a conductor there will occur an increase in area of the wire. As area is inversely proportional to resistance so, increase in area will lead to a decrease in resistance.

On the other hand, relation between resistivity and temperature is as follows.

          $\rho \propto \frac{1}{d} \propto A^{2} \propto T$

where,    $\rho$ = resistivity

                 d = mean free path of electrons

                 A = amplitude of atomic vibrations

                 T = temperature

Also, resistivity is directly proportional to resistance. So, with increase in temperature there will occur an increase in resistance of the conductor.

Thus, we can conclude that only technician B is correct.