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How does the resistivity of a typical semiconductor change as its temperature is increased?
AIt increases linearly with temperature
BIt remains essentially constant
CIt decreases with temperature
DIt first increases then drops to zero
Answer & Solution
Correct answer: C. It decreases with temperature
1. For semiconductors the carrier number density $n$ rises sharply with temperature.
2. This increase outweighs the decrease in collision time $\tau$.
3. Since $\rho = m/(ne^2\tau)$, a large rise in $n$ lowers $\rho$.
4. Hence resistivity decreases (C); the increasing trend (A) applies to metals instead.
_Source: NCERT Class 12 Physics Ch 3 "Current Electricity", p.10_
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