Question

why resistance of semiconductors decreases with increase in temperature

Answer 1

As the resistance is directly proportional to the density of the medium in which the current is flowing .And temperature is inversely proportional to the density, i.e if temperature increases the density decreases(mass per unit volume) and vice versa.So if there is an increase in temperature there is decrease in the density and there  is decrease in the density so there is decrease in the resistance nd vice versa i.e if there is an decrease in temperature there  is increase in the density so there is increase in the resistance .
Hence , on increasing the temperature the resistance decreases and we can also conclude that resistance is inversely proportional to the temperature of the medium wether it is a semiconductor or a superconductor.
I hope u got it!