For insulators and semiconductors the resistance decreases with increase in temperature because
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → number density of charge carriers increases
The resistivity of a material depends on the number density \( n \) of free charge carriers and their relaxation time \( \tau \).
\( \displaystyle \rho = \frac{m}{n e^{2} \tau} \)
In insulators and semiconductors very few carriers are free at low temperature. As the temperature rises, more electrons get enough energy to become free, so \( n \) increases rapidly with temperature. This increase outweighs the small fall in \( \tau \), so \( \rho \) and the resistance decrease.
NCERT (2026-27):
Temperature Dependence of Resistivity – “… From this equation, resistivity of a material is given by
\( \displaystyle \rho = \frac{1}{\sigma} = \frac{m}{n e^{2} \tau} \qquad (3.27) \)
\( \rho \) thus depends inversely both on the number n of free electrons per unit volume and on the average time \( \tau \) between collisions.”
Temperature Dependence of Resistivity – “… For insulators and semiconductors, however, n increases with temperature. This increase more than compensates any decrease in \( \tau \) in Eq.(3.23) so that for such materials, \( \rho \) decreases with temperature.”