Explain why the resistance of a material increases as its temperature increases. (That is, describe why the resistance of material should care about the temperature and whether this makes sense as a physical picture when you think about the motion of the charge carriers on the nanoscale.)
We know that electric resistance apposes the flow of charge/current within the wire/conductor.
In the microscopic level, when the temperature of the material is increased, the collision also increases which obstruct the flow of charge/current even more. Hence the resistance of the wire also increases.
The resistance changes with temperature according to the relation:
R = R0 [ 1 + alpha (T2 - T1)]
where, R is the resistance after the temperature has been increased, alpha is the temperature coefficient of resistance, T2 is the final temo and T1 is the intial temp.
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