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 =
As outer surface of a wire is in the shape of sphere. therefore, its area will be as follows.
A = ![4 \pi r^{2}](https://tex.z-dn.net/?f=4%20%5Cpi%20r%5E%7B2%7D)
or, A = ![4 \pi (\frac{d}{2})^{2}](https://tex.z-dn.net/?f=4%20%5Cpi%20%28%5Cfrac%7Bd%7D%7B2%7D%29%5E%7B2%7D)
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](https://tex.z-dn.net/?f=%5Crho%20%5Cpropto%20%5Cfrac%7B1%7D%7Bd%7D%20%5Cpropto%20A%5E%7B2%7D%20%5Cpropto%20T)
where,
= 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.