Concept:Semiconductors possess a negative temperature coefficient of resistance (\( \alpha < 0 \)) because increased thermal energy liberates more valence electrons into the conduction band.
Formula:$$R(T) = R_0 (1 + \alpha \Delta T), \quad \text{where } \alpha < 0$$
Solution:- In semiconductors, thermal excitation rapidly increases carrier concentration (\( n \)), dominating over lattice vibration scattering.
- Consequently, electrical conductivity increases and resistance decreases as temperature rises.
Why other options are incorrect:- Option A: Conductors (metals) have positive temperature coefficients, meaning their resistance increases with temperature.
- Option C: Resistance varies exponentially with temperature in semiconductors.
- Option D: Resistance decreases smoothly; instantaneous drops to zero occur only in superconductors at critical temperatures.
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